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Decision Tree: A Step-by-Step Guide with Examples

Today, in our data-driven world, it’s more important than ever to make well-informed decisions. Whether you work with data, analyze business trends, or make important choices in any field, understanding and utilizing decision trees can greatly improve your decision-making process. In this blog post, we will guide you through the basics of decision trees, covering essential concepts and advanced techniques, to give you a comprehensive understanding of this powerful tool.

What is a Decision Tree?

Let’s start with the definition of Decision Tree.

A decision tree is a graphical representation that outlines the various choices available and the potential outcomes of those choices. It begins with a root node, which represents the initial decision or problem. From this root node, branches extend to represent different options or actions that can be taken. Each branch leads to further decision nodes, where additional choices can be made, and these in turn branch out to show the possible consequences of each decision. This continues until the branches reach leaf nodes, which represent the final outcomes or decisions.

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The decision tree structure allows for a clear and organized way to visualize the decision-making process , making it easier to understand how different choices lead to different results. This is particularly useful in complex scenarios where multiple factors and potential outcomes need to be considered. By breaking down the decision process into manageable steps and visually mapping them out, decision trees help decision-makers evaluate the potential risks and benefits of each option, leading to more informed and rational decisions.

Decision trees are useful tools in many fields like business, healthcare, and finance. They help analyze things systematically by providing a simple way to compare different strategies and their likely impacts. This helps organizations and individuals make decisions that are not only based on data but also transparent and justifiable. This ensures that the chosen path aligns with their objectives and constraints.

Decision Tree Symbols

Understanding the symbols used in a decision tree is essential for interpreting and creating decision trees effectively. Here are the main symbols and their meanings:

• Decision node: A point in the decision tree where a choice needs to be made. Represents decisions that split the tree into branches, each representing a possible choice.
• Chance node: A point where an outcome is uncertain. Represents different possible outcomes of an event, often associated with probabilities.
• Terminal (or end) node: The end point of a decision path. Represents the final outcome of a series of decisions and chance events, such as success or failure.
• Branches: Lines that connect nodes to show the flow from one decision or chance node to the next. Represent the different paths that can be taken based on decisions and chance events.
• Arrows: Indicate the direction of flow from one node to another. Show the progression from decisions and chance events to outcomes.

Types of Decision Trees

It’s important to remember the different types of decision trees: classification trees and regression trees. Each type has various algorithms, nodes, and branches that make them unique. It’s crucial to select the type that best fits the purpose of your decision tree.

Classification Trees

Classification trees are used when the target variable is categorical. The tree splits the dataset into subsets based on the values of attributes, aiming to classify instances into classes or categories. For example, determining whether an email is spam or not spam.

Regression Trees

Regression trees are employed when the target variable is continuous. They predict outcomes that are real numbers or continuous values by recursively partitioning the data into smaller subsets. For example, predicting the price of a house based on its features.

How to Make a Decision Tree in 7 Steps

Follow these steps and principles to create a robust decision tree that effectively predicts outcomes and aids in making informed decisions based on data.

1. Define the decision objective

• Identify the goal : Clearly articulate what decision you need to make. This could be a choice between different strategic options, such as launching a product , entering a new market, or investing in new technology.
• Scope : Determine the boundaries of your decision. What factors and constraints are relevant? This helps in focusing the decision-making process and avoiding unnecessary complexity.

2. Gather relevant data

• Collect information : Gather all the necessary information related to your decision. This might include historical data, market research, financial reports, and expert opinions.
• Identify key factors : Determine the critical variables that will influence your decision. These could be costs, potential revenues, risks, resource availability, or market conditions.

3. Identify decision points and outcomes

• Decision points : Identify all the points where a decision needs to be made. Each decision point should represent a clear choice between different actions.
• Possible outcomes : List all potential outcomes or actions for each decision point. Consider both positive and negative outcomes, as well as their probabilities and impacts.

4. Structure the decision tree

• Root node : Start with the main decision or question at the root of your tree. This represents the initial decision point.
• Branches : Draw branches from the root to represent each possible decision or action. Each branch leads to a node, which represents subsequent decisions or outcomes.
• Nodes : At the end of each branch, add nodes that represent the next decision point or the final outcome. Continue branching out until all possible decisions and outcomes are covered.

5. Assign probabilities and values

• Probability of outcomes : Assign probabilities to each outcome based on data or expert judgment. This step is crucial for evaluating the likelihood of different scenarios.
• Impact assessment : Evaluate the impact or value of each outcome. This might involve estimating potential costs, revenues, or other metrics relevant to your decision.

6. Calculate expected values

• Example: For a decision to launch a product, you might have a 60% chance of success with an impact of $500,000, and a 40% chance of failure with an impact of -$200,000.
• Expected value: (0.6 * $500,000) + (0.4 * -$200,000) = $300,000 - $80,000 = $220,000
• Compare paths : Compare the expected values of different decision paths to identify the most favorable option.

7. Optimize and prune the tree

• Prune irrelevant branches : Remove branches that do not significantly impact the decision. This helps in simplifying the decision tree and focusing on the most critical factors.
• Simplify the tree : Aim to make the decision tree as straightforward as possible while retaining all necessary information. A simpler tree is easier to understand and use.

How to Read a Decision Tree

Reading a decision tree involves starting at the root node and following the branches based on conditions until you reach a leaf node, which represents the final outcome. Each node in the tree represents a decision based on an attribute, and the branches represent the possible conditions or outcomes of that decision.

For example, in a project management decision tree, you might start at the root node, which could represent the choice between two project approaches (A and B). From there, you follow the branch for Approach A or Approach B. Each subsequent node represents another decision, such as cost or time, and each branch represents the conditions of that decision (e.g., high cost vs. low/medium cost).

As you continue following the branches, you eventually reach a leaf node, which gives you the final outcome based on the path you took. For instance, if you followed the path for Approach A with high cost, you might reach a leaf node indicating project failure. Conversely, Approach B with a short time might lead you to a leaf node indicating project success.

Decision Tree Best Practices

Follow these best practices to develop and deploy decision trees that are reliable and effective tools for making informed decisions across various domains.

• Define clear objectives : Clearly articulate the decision you need to make and its scope. This helps in focusing the analysis and ensuring the decision tree addresses the right questions.
• Gather quality data : Gather relevant and accurate data that will be used to build and validate the decision tree. Ensure the data is representative and covers all necessary factors influencing the decision.
• Keep it simple : Aim for simplicity in the decision tree structure. Avoid unnecessary complexity that can confuse users or obscure key decision points.
• Understand and involve stakeholders : Involve stakeholders who will be impacted by or involved in the decision-making process. Ensure they understand the decision tree’s construction and can provide input on relevant factors and outcomes.
• Validate and verify : Validate the data used to build the decision tree to ensure its accuracy and reliability. Use techniques such as cross-validation or sensitivity analysis to verify the robustness of the tree.
• Interpretability : Use clear and intuitive visual representations of the decision tree. This aids in understanding how decisions are made and allows stakeholders to follow the logic easily.
• Consider uncertainty and risks : Incorporate probabilities of outcomes and consider uncertainties in data or assumptions. This helps in making informed decisions that account for potential risks and variability.

How Can a Decision Tree Help with Decision Making?

A decision tree simplifies the decision-making process in several key ways:

• Visual clarity : It presents decisions and their possible outcomes in a clear, visual format, making complex choices easier to understand at a glance.
• Structured approach : By breaking down decisions into a step-by-step sequence, it guides you through the decision-making process, ensuring that all factors are considered.
• Risk assessment : It incorporates probabilities and potential impacts of different outcomes, helping you evaluate risks and benefits systematically.
• Comparative analysis : Decision trees allow you to compare different choices side by side, making it easier to see which option offers the best expected value or outcome.
• Informed decisions : By organizing information logically, decision trees help you make decisions based on data and clear reasoning rather than intuition or guesswork.
• Flexibility : They can be easily updated with new information or adjusted to reflect changing circumstances, keeping the decision-making process dynamic and relevant.

Decision Tree Examples

Here are some decision tree examples to help you understand them better and get a head start on creating them. Explore more examples with our page on decision tree templates .

Decision Tree Analysis Example

This template helps make informed decisions by systematically organizing and analyzing complex information, ensuring clarity and consistency in the decision-making process.

Bank decision tree

This Decision Tree helps banks decide if they should launch a new financial product by predicting outcomes based on market demand and customer interest. It guides banks in assessing risks and making informed decisions to meet market needs effectively.

Risk decision tree for software engineering

The tree shows possible outcomes based on the severity and likelihood of each risk, guiding teams to make informed decisions that keep projects on track and within budget.

Simple Decision Tree

Use this simple decision tree to analyze choices systematically and clearly before making a final decision.

Advantages and Disadvantages of a Decision Tree

Understanding these advantages and disadvantages helps in determining when to use decision trees and how to mitigate their limitations for effective machine learning applications.

Using Decision Trees in Data Mining and Machine Learning

Decision tree analysis is a method used in data mining and machine learning to help make decisions based on data. It creates a tree-like model with nodes representing decisions or events, branches showing possible outcomes, and leaves indicating final decisions. This method helps in evaluating options systematically by considering factors like probabilities, costs, and desired outcomes.

The process begins with defining the decision problem and collecting relevant data. Algorithms like ID3 or C4.5 are then used to build the tree, selecting attributes that best split the dataset to maximize information gain. Once constructed, the tree is analyzed to understand relationships between variables and visualize decision paths.

Decision tree analysis is commonly used in;

Business decision making:

• Strategic planning : Evaluating different strategic options and outcomes.
• Operational efficiency : Optimizing workflows and processes.

Healthcare:

• Medical diagnosis : Assisting in diagnosing diseases.
• Treatment plans : Determining the best treatment options.
• Credit scoring : Evaluating creditworthiness of loan applicants.
• Investment decisions : Assessing risks and returns of investments.
• Customer segmentation : Identifying customer groups for targeted marketing.
• Campaign effectiveness : Predicting success of marketing campaigns.

Environmental science:

• Environmental planning : Analyzing impacts of environmental policies.
• Conservation efforts : Identifying critical areas for conservation.

Risk assessment:

• Project risk analysis : Evaluating project risks and their impacts.
• Operational risk management : Identifying and mitigating operational risks.

Diagnostic reasoning:

• Fault diagnosis : Detecting faults in industrial processes.
• System troubleshooting : Guiding troubleshooting in technical systems.

While decision tree analysis offers clarity and flexibility, it can become too specific if not pruned properly and is influenced by variations in input data. Overall, decision tree analysis is valuable for pulling out useful insights from complicated datasets to help with decision-making.

Wrapping up

A decision tree is an invaluable tool for simplifying decision-making processes by visually mapping out choices and potential outcomes in a structured manner. Despite their straightforward approach, decision trees offer robust support for strategic planning across various domains, including project management. While they excel in clarifying decisions and handling different data types effectively, challenges like overfitting and managing complex datasets should be considered. Nevertheless, mastering decision tree analysis empowers organizations to make well-informed decisions by systematically evaluating options and optimizing outcomes based on defined criteria.

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Amanda Athuraliya is the communication specialist/content writer at Creately, online diagramming and collaboration tool. She is an avid reader, a budding writer and a passionate researcher who loves to write about all kinds of topics.

Decision Tree Examples: Problems With Solutions

On this page:

• What is decision tree? Definition.
• 5 solved simple examples of decision tree diagram (for business, financial, personal, and project management needs).
• Steps to creating a decision tree.

Let’s define it.

A decision tree is a diagram representation of possible solutions to a decision. It shows different outcomes from a set of decisions. The diagram is a widely used decision-making tool for analysis and planning.

The diagram starts with a box (or root), which branches off into several solutions. That’s way, it is called decision tree.

Decision trees are helpful for a variety of reasons. Not only they are easy-to-understand diagrams that support you ‘see’ your thoughts, but also because they provide a framework for estimating all possible alternatives.

In addition, decision trees help you manage the brainstorming process so you are able to consider the potential outcomes of a given choice.

Example 1: The Structure of Decision Tree

Let’s explain the decision tree structure with a simple example.

Each decision tree has 3 key parts:

• a root node
• leaf nodes, and

No matter what type is the decision tree, it starts with a specific decision. This decision is depicted with a box – the root node.

Root and leaf nodes hold questions or some criteria you have to answer. Commonly, nodes appear as a squares or circles. Squares depict decisions, while circles represent uncertain outcomes.

As you see in the example above, branches are lines that connect nodes, indicating the flow from question to answer.

Each node normally carries two or more nodes extending from it. If the leaf node results in the solution to the decision, the line is left empty.

How long should the decision trees be?

Now we are going to give more simple decision tree examples.

Example 2: Simple Personal Decision Tree Example

Let’s say you are wondering whether to quit your job or not. You have to consider some important points and questions. Here is an example of a decision tree in this case.

Download  the following decision tree in PDF

Now, let’s deep further and see decision tree examples in business and finance.

Example 3: Project Management Decision Tree Example

Imagine you are an IT project manager and you need to decide whether to start a particular project or not. You need to take into account important possible outcomes and consequences.

The decision tree examples, in this case, might look like the diagram below.

Download  the following decision tree diagram in PDF.

Don’t forget that in each decision tree, there is always a choice to do nothing!

Example 4: Financial Decision Tree Example

When it comes to the finance area, decision trees are a great tool to help you organize your thoughts and to consider different scenarios.

Let’s say you are wondering whether it’s worth to invest in new or old expensive machines. This is a classical financial situation. See the decision tree diagram example below.

Download it.

The above decision tree example representing the financial consequences of investing in old or new machines. It is quite obvious that buying new machines will bring us much more profit than buying old ones.

Need more decision tree diagram examples?

Example 5: Very Simple Desicion Tree Example

As we have the basis, let’ sum the steps for creating decision tree diagrams.

Steps for Creating Decision Trees:

1. Write the main decision.

Begin the decision tree by drawing a box (the root node) on 1 edge of your paper. Write the main decision on the box.

2. Draw the lines 

Draw line leading out from the box for each possible solution or action. Make at least 2, but better no more than 4 lines. Keep the lines as far apart as you can to enlarge the tree later.

3. Illustrate the outcomes of the solution at the end of each line.

A tip: It is a good practice here to draw a circle if the outcome is uncertain and to draw a square if the outcome leads to another problem.

4. Continue adding boxes and lines.

Continue until there are no more problems, and all lines have either uncertain outcome or blank ending.

5. Finish the tree.

The boxes that represent uncertain outcomes remain as they are.

A tip: A very good practice is to assign a score or a percentage chance of an outcome happening. For example, if you know for a certain situation there is 50% chance to happen, place that 50 % on the appropriate branch.

When you finish your decision tree, you’re ready to start analyzing the decisions and problems you face.

How to Create a Decision Tree?

In our IT world, it is a piece of cake to create decision trees. You have a plenty of different options. For example, you can use paid or free graphing software or free mind mapping software solutions such as:

• Silverdecisions

The above tools are popular online chart creators that allow you to build almost all types of graphs and diagrams from scratch.

Of course, you also might want to use Microsoft products such as:

And finally, you can use a piece of paper and a pen or a writing board.

Advantages and Disadvantages of Decision Trees:

Decision trees are powerful tools that can support decision making in different areas such as business, finance, risk management, project management, healthcare and etc. The trees are also widely used as root cause analysis tools and solutions.

As any other thing in this world, the decision tree has some pros and cons you should know.

Advantages:

• It is very easy to understand and interpret.
• The data for decision trees require minimal preparation.
• They force you to find many possible outcomes of a decision.
• Can be easily used with many other decision tools.
• Helps you to make the best decisions and best guesses on the basis of the information you have.
• Helps you to see the difference between controlled and uncontrolled events.
• Helps you estimate the likely results of one decision against another.

Disadvantages:

• Sometimes decision trees can become too complex.
• The outcomes of decisions may be based mainly on your expectations. This can lead to unrealistic decision trees.
• The diagrams can narrow your focus to critical decisions and objectives.

Conclusion:

The above decision tree examples aim to make you understand better the whole idea behind. As you see, the decision tree is a kind of probability tree that helps you to make a personal or business decision.

In addition, they show you a balanced picture of the risks and opportunities related to each possible decision.

If you need more examples, our posts fishbone diagram examples and Venn diagram examples might be of help.

About The Author

Silvia Valcheva

Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI (Artificial Intelligence), IoT (Internet of Things), process automation, etc.

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• What is decision tree analysis? 5 steps ...

What is decision tree analysis? 5 steps to make better decisions

Decision tree analysis involves visually outlining the potential outcomes, costs, and consequences of a complex decision. These trees are particularly helpful for analyzing quantitative data and making a decision based on numbers. In this article, we’ll explain how to use a decision tree to calculate the expected value of each outcome and assess the best course of action. Plus, get an example of what a finished decision tree will look like.

Have you ever made a decision knowing your choice would have major consequences? If you have, you know that it’s especially difficult to determine the best course of action when you aren’t sure what the outcomes will be. 

What is a decision tree?

A decision tree is a flowchart that starts with one main idea and then branches out based on the consequences of your decisions. It’s called a “decision tree” because the model typically looks like a tree with branches. 

These trees are used for decision tree analysis, which involves visually outlining the potential outcomes, costs, and consequences of a complex decision. You can use a decision tree to calculate the expected value of each outcome based on the decisions and consequences that led to it. Then, by comparing the outcomes to one another, you can quickly assess the best course of action. You can also use a decision tree to solve problems, manage costs, and reveal opportunities. 

Decision tree symbols

A decision tree includes the following symbols:

Alternative branches: Alternative branches are two lines that branch out from one decision on your decision tree. These branches show two outcomes or decisions that stem from the initial decision on your tree.

Decision nodes: Decision nodes are squares and represent a decision being made on your tree. Every decision tree starts with a decision node. 

Chance nodes: Chance nodes are circles that show multiple possible outcomes.

End nodes: End nodes are triangles that show a final outcome.

A decision tree analysis combines these symbols with notes explaining your decisions and outcomes, and any relevant values to explain your profits or losses. You can manually draw your decision tree or use a flowchart tool to map out your tree digitally. 

What is decision tree analysis used for?

You can use decision tree analysis to make decisions in many areas including operations, budget planning, and project management . Where possible, include quantitative data and numbers to create an effective tree. The more data you have, the easier it will be for you to determine expected values and analyze solutions based on numbers. 

For example, if you’re trying to determine which project is most cost-effective, you can use a decision tree to analyze the potential outcomes of each project and choose the project that will most likely result in highest earnings. 

How to create a decision tree

Follow these five steps to create a decision tree diagram to analyze uncertain outcomes and reach the most logical solution. 

1. Start with your idea

Begin your diagram with one main idea or decision. You’ll start your tree with a decision node before adding single branches to the various decisions you’re deciding between.

For example, if you want to create an app but can’t decide whether to build a new one or upgrade an existing one, use a decision tree to assess the possible outcomes of each. 

In this case, the initial decision node is: 

Create an app

The three options—or branches—you’re deciding between are: 

Building a new scheduling app

Upgrading an existing scheduling app

Building a team productivity app

2. Add chance and decision nodes

After adding your main idea to the tree, continue adding chance or decision nodes after each decision to expand your tree further. A chance node may need an alternative branch after it because there could be more than one potential outcome for choosing that decision. 

For example, if you decide to build a new scheduling app, there’s a chance that your revenue from the app will be large if it’s successful with customers. There’s also a chance the app will be unsuccessful, which could result in a small revenue. Mapping both potential outcomes in your decision tree is key. 

3. Expand until you reach end points

Keep adding chance and decision nodes to your decision tree until you can’t expand the tree further. At this point, add end nodes to your tree to signify the completion of the tree creation process. 

Once you’ve completed your tree, you can begin analyzing each of the decisions. 

4. Calculate tree values

Ideally, your decision tree will have quantitative data associated with it. The most common data used in decision trees is monetary value. 

For example, it’ll cost your company a specific amount of money to build or upgrade an app. It’ll also cost more or less money to create one app over another. Writing these values in your tree under each decision can help you in the decision-making process . 

You can also try to estimate expected value you’ll create, whether large or small, for each decision. Once you know the cost of each outcome and the probability it will occur, you can calculate the expected value of each outcome using the following formula:

Expected value (EV) = (First possible outcome x Likelihood of outcome) + (Second possible outcome x Likelihood of outcome) - Cost 

Calculate the expected value by multiplying both possible outcomes by the likelihood that each outcome will occur and then adding those values. You’ll also need to subtract any initial costs from your total. 

5. Evaluate outcomes

Once you have your expected outcomes for each decision, determine which decision is best for you based on the amount of risk you’re willing to take. The highest expected value may not always be the one you want to go for. That’s because, even though it could result in a high reward, it also means taking on the highest level of project risk .  

Keep in mind that the expected value in decision tree analysis comes from a probability algorithm. It’s up to you and your team to determine how to best evaluate the outcomes of the tree.

Pros and cons of decision tree analysis

Used properly, decision tree analysis can help you make better decisions, but it also has its drawbacks. As long as you understand the flaws associated with decision trees, you can reap the benefits of this decision-making tool. 

When you’re struggling with a complex decision and juggling a lot of data, decision trees can help you visualize the possible consequences or payoffs associated with each choice. 

Transparent: The best part about decision trees is that they provide a focused approach to decision making for you and your team. When you parse out each decision and calculate their expected value, you’ll have a clear idea about which decision makes the most sense for you to move forward with. 

Efficient: Decision trees are efficient because they require little time and few resources to create. Other decision-making tools like surveys, user testing , or prototypes can take months and a lot of money to complete. A decision tree is a simple and efficient way to decide what to do. 

Flexible: If you come up with a new idea once you’ve created your tree, you can add that decision into the tree with little work. You can also add branches for possible outcomes if you gain information during your analysis. 

There are drawbacks to a decision tree that make it a less-than-perfect decision-making tool. By understanding these drawbacks, you can use your tree as part of a larger forecasting process.

Complex: While decision trees often come to definite end points, they can become complex if you add too many decisions to your tree. If your tree branches off in many directions, you may have a hard time keeping the tree under wraps and calculating your expected values. The best way to use a decision tree is to keep it simple so it doesn’t cause confusion or lose its benefits. This may mean using other decision-making tools to narrow down your options, then using a decision tree once you only have a few options left.

Unstable: It’s important to keep the values within your decision tree stable so that your equations stay accurate. If you change even a small part of the data, the larger data can fall apart.

Risky: Because the decision tree uses a probability algorithm, the expected value you calculate is an estimation, not an accurate prediction of each outcome. This means you must take these estimations with a grain of salt. If you don’t sufficiently weigh the probability and payoffs of your outcomes, you could take on a lot of risk with the decision you choose. 

Decision tree analysis example

In the decision tree analysis example below, you can see how you would map out your tree diagram if you were choosing between building or upgrading a new software app. 

As the tree branches out, your outcomes involve large and small revenues and your project costs are taken out of your expected values.

Decision nodes from this example : 

Build new scheduling app: $50K

Upgrade existing scheduling app: $25K

Build team productivity app: $75K

Chance nodes from this example:

Large and small revenue for decision one: 40 and 55%

Large and small revenue for decision two: 60 and 38%

Large and small revenue for decision three: 55 and 45%

End nodes from this example:

Potential profits for decision one: $200K or $150K

Potential profits for decision two: $100K or $80K

Potential profits for decision three: $250K or $200K

Although building a new team productivity app would cost the most money for the team, the decision tree analysis shows that this project would also result in the most expected value for the company. 

Use a decision tree to find the best outcome

You can draw a decision tree by hand, but using decision tree software to map out possible solutions will make it easier to add various elements to your flowchart, make changes when needed, and calculate tree values. With Asana’s Lucidchart integration, you can build a detailed diagram and share it with your team in a centralized project management tool . 

Decision tree software will make you feel confident in your decision-making skills so you can successfully lead your team and manage projects.

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Blog Graphs and Charts Decision Tree Analysis: Definition, Examples, How to Perform

Decision Tree Analysis: Definition, Examples, How to Perform

Written by: Letícia Fonseca May 05, 2022

The purpose of a decision tree analysis is to show how various alternatives can create different possible solutions to solve problems. A decision tree, in contrast to traditional problem-solving methods, gives a “visual” means of recognizing uncertain outcomes that could result from certain choices or decisions.

For those who have never worked with decision trees before, this article will explain how they function and it will also provide some examples to illustrate the ideas. To save you time, use Venngage’s Decision Tree Maker or browse our gallery of decision tree templates to help you get started.

Click to jump ahead:

What is a decision tree analysis?

What is the importance of decision tree analysis, 4 decision tree analysis examples, 5 steps to create a decision node analysis, when do you use or apply a decision tree analysis, how to create a decision node diagram with venngage, faqs on decision tree analysis.

A decision tree is a diagram that depicts the many options for solving an issue. Given particular criteria, decision trees usually provide the best beneficial option, or a combination of alternatives, for many cases. By employing easy-to-understand axes and graphics, a decision tree makes difficult situations more manageable. An event, action, decision, or attribute linked with the problem under investigation is represented by each box or node.

For risk assessment, asset values, manufacturing costs, marketing strategies, investment plans, failure mode effects analyses (FMEA), and scenario-building, a decision tree is used in business planning. Data from a decision tree can also ‌build predictive models.

There are four basic forms of  decision tree analysis , each with its own set of benefits and scenarios for which it is most useful. These subtypes include decision under certainty, decision under risk, decision-making, and decision under uncertainty. In terms of how they are addressed and applied to diverse situations, each type has its unique impact.

Business owners and other decision-makers can use a decision tree to help them consider their alternatives and the potential repercussions of each one. The examination of a decision tree can be used to:

• Determine the level of risk that each option entails.  Before making a final decision, you can see how changing one component impacts others, so you can identify where more research or information is needed. Data from decision trees can also be utilized to build predictive models or to analyze an expected value.
• Demonstrate how particular acts or occurrences may unfold in the context of other events.  It’s easy to see how different decisions and possible outcomes interact when you’re looking at decision trees.
• Concentrate your efforts.  The most effective ways for reaching the desired and final outcome are shown in decision trees. They can be utilized in a multitude of industries, including goal setting, project management, manufacturing, marketing, and more.

Advantages of using a tree diagram as a decision-making tool

Decision tree analysis can be used to make complex decisions easier. They explain how changing one factor impacts the other and how it affects other factors by simplifying concepts. A summary of data can also be included in a decision tree as a reference or as part of a report. They show which methods are most effective in reaching the outcome, but they don’t say what those strategies should be.

Even if new information arises later that contradicts previous assumptions and hypotheses, decision-makers may find it difficult to change their minds once they have made and implemented an initial choice. Decision-makers can use decision-making tools like tree analysis to experiment with different options before reaching a final decision; this can help them gain expertise in making difficult decisions.

When presented with a well-reasoned argument based on facts rather than simply articulating their own opinion, decision-makers may find it easier to persuade others of their preferred solution. A decision tree is very useful when there is any uncertainty regarding which course of action will be most advantageous or when prior data is inadequate or partial.

Before implementing possible solutions, a decision tree analysis can assist business owners and other decision-makers in considering the potential ramifications of different solutions.

Disadvantages of using a tree diagram as a decision-making tool

Rather than displaying real outcomes, decision trees only show patterns connected with decisions. Because decision trees don’t provide information on aspects like implementation, timeliness, and prices, more research may be needed to figure out if a particular plan is viable.

This type of model does not provide insight into why certain events are likely while others are not, but it can be used to develop prediction models that illustrate the chance of an event occurring in certain situations.

Many businesses employ decision tree analysis to establish an effective business, marketing, and advertising strategies. Based on the probable consequences of each given course of action, decision trees assist marketers to evaluate which of their target audiences may respond most favorably to different sorts of advertisements or campaigns.

A decision tree example is that a marketer might wonder which style of advertising strategy will yield the best results. The decision tree analysis would assist them in determining the best way to create an ad campaign, whether print or online, considering how each option could affect sales in specific markets, and then deciding which option would deliver the best results while staying within their budget.

Another decision tree diagram example is when a corporation that wishes to grow sales might start by determining their course of action, which includes the many marketing methods that they can use to create leads. Before making a decision, they may use a decision tree analysis to explore each alternative and assess the probable repercussions. 

If a company chooses TV ads as their proposed solution, decision tree analysis might help them figure out what aspects of their TV adverts (e.g. tone of voice and visual style) make consumers more inclined to buy, so they can better target new customers or get more out of their advertising dollars.

Related:  15+ Decision Tree Infographics to Visualize Problems and Make Better Decisions

This style of problem-solving helps people make better decisions by allowing them to better comprehend what they’re entering into before they commit too much money or resources. The five-step decision tree analysis procedure is as follows:

1. Determine your options 

Which can help deal with an issue or answer a question. A problem to be addressed, a goal to be achieved, and additional criteria that will influence the outcome are all required for decision tree analysis to be successful, especially when there are multiple options for resolving a problem or a topic.

2. Examine the most effective course of action

Taking into account the potential rewards as well as the risks and expenses that each alternative may entail. If you’re starting a new firm, for example, you’ll need to decide what kind of business model or service to offer, how many employees to hire, where to situate your company, and so on.

3. Determine how a specific course will affect your company’s long-term success.

Depending on the data being studied, several criteria are defined for decision tree analysis. For instance, by comparing the cost of a drug or therapy to the effects of other potential therapies, decision tree analysis can be used to determine how effective a drug or treatment will be. When making decisions, a decision tree analysis can also assist in prioritizing the expected values of various factors.

4. Use each alternative course of action to examine multiple possible outcomes

This way you can decide which decision you believe is the best and what criteria it meets (the “branches” of your decision tree). Concentrate on determining which solutions are most likely to bring you closer to attaining your goal of resolving your problem while still meeting any of the earlier specified important requirements or additional considerations. 

5. To evaluate which choice will be most effective

Compare the potential outcomes of each branch. Implement and track the effects of decision tree analysis to ensure that you appropriately assess the benefits and drawbacks of several options so that you can concentrate on the ones that offer the best return on investment while minimizing the risks and drawbacks.

A decision tree diagram employs symbols to represent the problem’s events, actions, decisions, or qualities. Given particular criteria, decision trees usually provide the best beneficial option, or a combination of alternatives, for many cases. 

By employing easy-to-understand axes and drawings, as well as breaking down the critical components involved with each choice or course of action, decision trees help make difficult situations more manageable. This type of analysis seeks to help you make better decisions about your business operations by identifying potential risks and expected consequences.

In this case, the tree can be seen as a metaphor for problem-solving: it has numerous roots that descend into diverse soil types and reflect one’s varied options or courses of action, while each branch represents the possible and uncertain outcomes. The act of creating a “tree” based on specified criteria or initial possible solutions has to be implemented.

You may start with a query like, “What is the best approach for my company to grow sales?” After that, you’d make a list of feasible actions to take, as well as the probable results of each one. The goal of a decision tree analysis is to help you understand the potential repercussions of your decisions before you make them so that you have the best chance of making a good decision.

Regardless of the level of risk involved, decision tree analysis can be a beneficial tool for both people and groups who want to make educated decisions.

Venngage has built-in templates that are already arranged according to various data kinds, which can assist in swiftly building decision nodes and decision branches. Here’s how to create one with Venngage:

1. Sign up for a free account  here .

2. From  Home  or your dashboard, click on  Templates.

3. There are hundreds of templates to pick from, but Venngage’s built-in  Search  engine makes it simple to find what you’re looking for.

4. Once you have chosen the template that’s best for you, click  Create  to begin editing.

5. Venngage allows you to download your project as a PNG, PNG HD, PDF or PowerPoint with a Business plan . 

Venngage also has a business feature called  My Brand Kit  that enables you to add your company’s logo, color palette, and fonts to all your designs with a single click.

For example, you can make the previous decision tree analysis template reflect your brand design by uploading your brand logo, fonts, and color palette using Venngage’s branding feature.

Not only are Venngage templates free to use and professionally designed, but they are also tailored for various use cases and industries to fit your exact needs and requirements.

A business account also includes the  real-time collaboration feature , so you can invite members of your team to work simultaneously on a project.

Venngage allows you to share your decision tree online as well as download it as a PNG or PDF file. That way, your design will always be presentation-ready.

How important is a decision tree in management?

Project managers can utilize decision tree analysis to produce successful solutions, making it a key element of their success process. They can use a decision tree to think about how each decision will affect the company as a whole and make sure that all factors are taken into account before making a decision.

This decision tree can assist you in making smarter investments as well as identifying any dangers or negative outcomes that may arise as a result of certain choices. You will have more information on what works best if you explore all potential outcomes so that you can make better decisions in the future.

What is a decision tree in system analysis?

For studying several systems that work together, a decision tree is useful. You can use decision tree analysis to see how each portion of a system interacts with the others, which can help you solve any flaws or restrictions in the system.

Create a professional decision tree with Venngage

Simply defined, a decision tree analysis is a visual representation of the alternative solutions and expected outcomes you have while making a decision. It can help you quickly see all your potential outcomes and how each option might play out. 

Venngage makes the process of creating a decision tree simple and offers a variety of templates to help you. It is the most user-friendly platform for building professional-looking decision trees and other data visualizations. Sign up for a free account and give it a shot right now. You might be amazed at how much easier it is to make judgments when you have all of your options in front of you.

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Hacking the Case Interview

An issue tree is a structured framework used to break down and analyze complex problems or questions into smaller components. It is a visual representation of the various aspects, sub-issues, and potential solutions related to a particular problem.

Issue trees are commonly used in business, consulting, problem-solving, and decision-making processes.

If you’re looking to better understand issue trees and how to use them in consulting case interviews or in business, we have you covered.

In this comprehensive article, we’ll cover:

• What is an issue tree?
• Why are issue trees important?
• How do I create an issue tree?
• How do I use issue trees in consulting case interviews?
• What are examples of issue trees?
• What are tips for making effective issue trees?

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course . These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

What is an Issue Tree?

An issue tree is a visual representation of a complex problem or question broken down into smaller, more manageable components. It consists of a top level issue, visualized as the root question, and sub-issues, visualized as branches and sub-branches.

• Top Level Issue (Root Question) : This is the main problem or question that needs to be addressed. It forms the root of the tree.
• Sub-issues (Branches) : Underneath the top level issue are branches representing the major categories or dimensions of the problem. These are the high-level areas that contribute to the overall problem.
• Further Sub-issues (Sub-branches) : Each branch can be broken down further into more specific sub-issues.

Issue trees generally take on the following structure.

Issue trees get their name because the primary issue that you are solving for can be broken down into smaller issues or branches. These issues can then be further broken down into even smaller issues or branches.

This can be continued until you are left with a long list of small issues that are much simpler and more manageable. No matter how complicated or difficult a problem is, an issue tree can provide a way to structure the problem to make it easier to solve.

As an example, let’s say that we are trying to help a lemonade stand increase their profits. The overall problem is determining how to increase profits.

Since profits is equal to revenue minus costs, we can break this problem down into two smaller problems:

• How can we increase revenues?
• How can we decrease costs?

Since revenue is equal to quantity times price, we can further break this revenue problem down into two even smaller problems:

• How can we increase quantity sold?
• How can we increase price?

Looking at the problem of how to increase quantity sold, we can further break that problem down:

• How can we increase the quantity of lemonade sold?
• How can we increase the quantity of other goods sold?

We can repeat the same procedure for the costs problem since we know that costs equal variable costs plus fixed costs.

• How can we decrease variable costs?
• How can we decrease fixed costs?

Looking at the problem of how to decrease variable costs, we can further break that down by the different variable cost components of lemonade:

• How can we decrease costs of lemons?
• How can we decrease costs of water?
• How can we decrease costs of ice?
• How can we decrease costs of sugar?
• How can we decrease costs of cups?

The overall issue tree for this example would look like the following:

In this example, the issue tree is a special kind of issue tree known as a profit tree.

Why are Issue Trees Important?

Issue trees are helpful because they facilitate systematic analysis, managing complexity, prioritization, generating solutions, identifying root causes, work subdivision, roadmap generation, and effective communication.

Systematic analysis : Issue trees guide a systematic analysis of the problem. By dissecting the problem into its constituent parts, you can thoroughly examine each aspect and understand its implications.

Managing complexity : Complex problems often involve multiple interrelated factors. Issue trees provide a way to manage this complexity by organizing and visualizing the relationships between different components.

Prioritization : Issue trees help in prioritizing actions. By assessing the importance and impact of each sub-issue, you can determine which aspects of the problem require immediate attention.

Generating solutions : Issue trees facilitate the generation of potential solutions or strategies for each component of the problem. This allows for a more comprehensive approach to problem-solving.

Identifying root causes : Issue trees help in identifying the root causes of a problem. By drilling down through the sub-issues, you can uncover the underlying factors contributing to the main issue.

Work subdivision : Issue trees provide you with a list of smaller, distinct problems or areas to explore. This distinction makes it easy for you to divide up work.

Roadmap generation : Issue trees layout exactly all of the different areas or issues that you need to focus on in order to solve the overall problem. This gives you a clear idea of where to focus your attention and work on.

Effective communication : Issue trees are powerful communication tools. Visualizing the problem in a structured format helps in explaining it to others, including team members, stakeholders, or clients.

How Do I Create An Issue Tree?

Creating an issue tree involves several steps. Here's a step-by-step guide to help you through the process:

Step 1: Define the top-level issue

Start by clearly articulating the main problem or question that you want to address. This will form the root of your issue tree.

Step 2: Identify the branches (sub-issues)

Consider the major sub-issues that contribute to the overall problem. These will become the branches of your issue tree. Brainstorm and list them down.

There are four major ways that you can break down the root problem in an issue tree. You can break down the issue by stakeholder, process, segments, or math.

• Stakeholder : Break the problem down by identifying all stakeholders involved. This may include the company, customers, competitors, suppliers, manufacturers, distributors, and retailers. Each stakeholder becomes a branch for the top-level issue.
• Process : Break the problem down by identifying all of the different steps in the process. Each step becomes a branch for the top-level issue.
• Segment : Break the problem down into smaller segments. This may include breaking down the problem by geography, product, customer segment, market segment, distribution channel, or time horizon. Each segment becomes a branch for the top-level issue.
• Math : Break a problem down by quantifying the problem into an equation or formula . Each term in the equation is a branch for the top-level issue.

Step 3: Break down each branch

For each branch, ask yourself if there are further components that contribute to it. If so, break down each branch into more specific components. Continue this process until you've reached a level of detail that allows for meaningful analysis.

Similar to the previous step, you can break down a branch by stakeholder, process, segment, or by math.

Step 4: Review and refine

Take a step back and review your issue tree. Make sure it accurately represents the problem and its components. Look for any missing or redundant branches or sub-issues.

Step 5: Prioritize and evaluate

Consider assigning priorities to different sub-issues or potential solutions. This will help guide your decision-making process.

How Do I Use Issue Trees in Consulting Case Interviews?

Issue trees are used near the beginning of the consulting case interview to break down the business problem into smaller, more manageable components.

After the interviewer provides the case background information, you’ll be expected to quickly summarize the context of the case and verify the case objective. After asking clarifying questions, you’ll ask for a few minutes of silence to create an issue tree.

After you have created an issue tree, here’s how you would use it:

Step 1: Walk your interviewer through the issue tree

Once you’ve created an issue tree, provide a concise summary of how it's structured and how it addresses the problem at hand. Explain the different branches and sub-branches. They may ask a few follow-up questions.

As you are presenting your issue tree, periodically check in with the interviewer to ensure you're on the right track. Your interviewer may provide some input or guidance on improving your issue tree.

Step 2: Identify an area of your issue tree to start investigating

Afterwards, you’ll use the issue tree to help identify a branch to start investigating. There is generally no wrong answer here as long as you have a reason that supports why you want to start with a particular branch.

To determine which branch to start investigating, ask yourself a few questions. What is the most important sub-issue? Consider factors like urgency, impact, or feasibility. What is your best guess for how the business problem can be solved?

Step 3: Gather data and information

Collect relevant facts, data, and information for the sub-issue that you are investigating. This will provide the necessary context and evidence for your analysis.

Step 4 : Record key insights on the issue tree

After diving deeper into each sub-issue or branch on your issue tree, you may find it helpful to write a few bullets on the key takeaways or insights that you’ve gathered through your analysis.

This will help you remember all the work that you have done during the case interview so far. It’ll also help you develop a recommendation at the end of the case interview because you’ll quickly be able to read a summary of all of your analysis.

Step 5: Iterate and adjust as needed

As you work through the problem-solving process, be prepared to adjust and update the issue tree based on new information, insights, or changes in the situation.

Remember, creating an issue tree is not a one-size-fits-all process. It's a dynamic tool that can be adapted to suit the specific needs and complexity of the problem you're addressing.

Step 6: Select the next area of your issue tree to investigate

Once you have finished analyzing a branch or sub-issue on your issue tree and reached a satisfactory insight or conclusion, move onto the next branch or sub-issue.

Again, consider factors like urgency, impact, or feasibility when prioritizing which branch or sub-issue to dive deeper into. Repeat this step until the end of the case interview when you are asked for a final recommendation.

What are Examples of Issue Trees?

Below are five issue tree examples for five common types of business situations and case interviews.

If you want to learn strategies on how to create unique and tailored issue trees for any case interview, check out our comprehensive article on case interview frameworks .

Profitability Issue Tree Example

Profitability cases ask you to identify what is causing a company’s decline in profits and what can be done to address this problem.

A potential issue tree template for this case could explore four major issues:

• What is causing the decline in profitability?
• Is the decline due to changes among customers?
• Is the decline due to changes among competitors?
• Is the decline due to market trends?

Market Entry Issue Tree Example

Market entry cases ask you to determine whether a company should enter a new market.

• Is the market attractive?
• Are competitors strong?
• Does the company have the capabilities to enter?
• Will the company be profitable from entering the market?

Merger and Acquisition Issue Tree Example

Merger and acquisition cases ask you to determine whether a company or private equity firm should acquire a particular company.

• Is the market that the target is in attractive?
• Is the acquisition target an attractive company?
• Are there any acquisition synergies?
• Will the acquisition lead to high returns?

New Product Issue Tree Example

New product cases ask you to determine whether a company should launch a new product or service.

• Will customers like the product?
• Does the company have the capabilities to successfully launch the product?
• Will the company be profitable from launching the product?

Pricing Issue Tree Example

Pricing cases ask you to determine how to price a particular product or service.

A potential issue tree template for this case could explore three major issues:

• How should we price based on the product cost?
• How should we price based on competitors’ products?
• How should we price based on customer value?

What are Tips for Making Effective Issue Trees?

Issue trees are powerful tools to solve complex business problems, but they are much less effective if they don’t follow these important tips.

Issue tree tip #1: Be MECE

MECE stands for mutually exclusive and collectively exhaustive. When breaking down the overall problem in your issue tree, the final list of smaller problems needs to be mutually exclusive and collectively exhaustive.

Mutually exclusive means that none of the smaller problems in your issue tree overlap with each other. This ensures that you are working efficiently since there will be no duplicated or repeated work.

For example, let’s say that two of the issues in your issue tree are:

• Determine how to increase cups of lemonade sold
• Determine how to partner with local organizations to sell lemonade

This is not mutually exclusive because determining how to partner with local organizations would include determining how to increase cups of lemonade sold.

In determining how to increase cups of lemonade sold, you may be duplicating work from determining how to partner with local organizations.

Collectively exhaustive means that the list of smaller problems in your issue tree account for all possible ideas and possibilities. This ensures that your issue tree is not missing any critical areas to explore.

For example, let’s say that you break down the issue of determining how to decrease variable costs into the following issues:

This is not collectively exhaustive because you are missing two key variable costs: sugar and cups. These could be important areas that could increase profitability, which are not captured by your issue tree.

You can read a full explanation of this in our article on the MECE principle .

Issue tree tip #2: Be 80/20

The 80/20 principle states that 80% of the results come from 20% of the effort or time invested.

In other words, it is a much more efficient use of time to spend a day solving 80% of a problem and then moving onto solving the next few problems than to spend five days solving 100% of one problem.

This same principle should be applied to your issue tree. You do not need to solve every single issue that you have identified. Instead, focus on solving the issues that have the greatest impact and require the least amount of work.

Let’s return to our lemonade stand example. If we are focusing on the issue of how to decrease costs, we can consider fixed costs and variable costs.

It may be a better use of time to focus on decreasing variable costs because they are generally easier to lower than fixed costs.

Fixed costs, such as paying for a business permit or purchasing a table and display sign, typically have long purchasing periods, making them more difficult to reduce in the short-term.

Issue tree tip #3: Have three to five branches

Your issue tree needs to be both comprehensive, but also clear and easy to follow. Therefore, your issue tree should have at least three branches to be able to cover enough breadth of the key issue.

Additionally, your issue tree should have no more than five branches. Any more than this will make your issue tree too complicated and difficult to follow. By having more than five branches, you also increase the likelihood that there will be redundancies or overlap among your branches, which is not ideal.

Having three to five branches helps achieve a balance between going deep into specific sub-issues and covering a broad range of aspects. It balances breadth and depth.

Issue tree tip #4: Clearly define the top-level issue

Make sure that you clearly articulate the main problem or question. This sets the foundation for the entire issue tree. If you are addressing the wrong problem or question, your entire issue tree will be useless to you.

Issue tree tip #5: Visualize the issue tree clearly

If you're using a visual representation, make sure it's easy to follow. Use clean lines, appropriate spacing, and clear connections between components.

Keep your issue tree organized and neat. A cluttered or disorganized tree can be confusing and difficult to follow.

Ensure that each branch and sub-issue is labeled clearly and concisely. Use language that is easily understandable to your audience.

Issue tree tip #6: Order your branches logically

Whenever possible, try to organize the branches in your issue tree logically.

For example, if the branches in your issue tree are segmented by time, arrange them as short-term, medium-term, and long-term. This is a logical order that is arranged by length of time.

It does not make sense to order the branches as long-term, short-term, and medium- term. This ordering is confusing and will make the entire issue tree harder to follow.

Issue tree tip #7: Branches should be parallel

The branches on your issue tree should all be on the same logical level.

For example, if you decide to segment the branches on your issue tree by geography, your branches could be: North America, South America, Europe, Asia, Africa, and Australia. This segmentation is logical because each segment is a continent.

It would not make sense to segment the branches on your issue as United States, South America, China, India, Australia, and rest of the world. This segmentation does not follow logical consistency because it mixes continents and countries.

Issue tree tip #8: Practice and get feedback

It takes practice to create comprehensive, clear, and concise issue trees. This is a skill that takes time to develop and refine.

When you initially create your first few issue trees, it may take you a long period of time and you may be missing key sub-issues. However, with enough practice, you’ll be able to create issue trees effortlessly and effectively.

Practice creating issue trees on different problems to improve your skills. Seek feedback from peers or mentors to refine your approach.

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Decision Tree

Decision trees are a popular and powerful tool used in various fields such as machine learning, data mining, and statistics. They provide a clear and intuitive way to make decisions based on data by modeling the relationships between different variables. This article is all about what decision trees are, how they work, their advantages and disadvantages, and their applications.

What is a Decision Tree?

A decision tree is a flowchart-like structure used to make decisions or predictions. It consists of nodes representing decisions or tests on attributes, branches representing the outcome of these decisions, and leaf nodes representing final outcomes or predictions. Each internal node corresponds to a test on an attribute, each branch corresponds to the result of the test, and each leaf node corresponds to a class label or a continuous value.

Structure of a Decision Tree

• Root Node : Represents the entire dataset and the initial decision to be made.
• Internal Nodes : Represent decisions or tests on attributes. Each internal node has one or more branches.
• Branches : Represent the outcome of a decision or test, leading to another node.
• Leaf Nodes : Represent the final decision or prediction. No further splits occur at these nodes.

How Decision Trees Work?

The process of creating a decision tree involves:

• Selecting the Best Attribute : Using a metric like Gini impurity, entropy, or information gain, the best attribute to split the data is selected.
• Splitting the Dataset : The dataset is split into subsets based on the selected attribute.
• Repeating the Process : The process is repeated recursively for each subset, creating a new internal node or leaf node until a stopping criterion is met (e.g., all instances in a node belong to the same class or a predefined depth is reached).

Metrics for Splitting

• [Tex]\text{Gini} = 1 – \sum_{i=1}^{n} (p_i)^2 [/Tex] , where pi ​ is the probability of an instance being classified into a particular class.
• [Tex]\text{Entropy} = -\sum_{i=1}^{n} p_i \log_2 (p_i) [/Tex] , where pi ​ is the probability of an instance being classified into a particular class.
• [Tex]\text{InformationGain} = \text{Entropy}_\text{parent} – \sum_{i=1}^{n} \left( \frac{|D_i|}{|D|} \ast \text{Entropy}(D_i) \right) [/Tex] , where Di ​ is the subset of D after splitting by an attribute.

Advantages of Decision Trees

• Simplicity and Interpretability : Decision trees are easy to understand and interpret. The visual representation closely mirrors human decision-making processes.
• Versatility : Can be used for both classification and regression tasks.
• No Need for Feature Scaling : Decision trees do not require normalization or scaling of the data.
• Handles Non-linear Relationships : Capable of capturing non-linear relationships between features and target variables.

Disadvantages of Decision Trees

• Overfitting : Decision trees can easily overfit the training data, especially if they are deep with many nodes.
• Instability : Small variations in the data can result in a completely different tree being generated.
• Bias towards Features with More Levels : Features with more levels can dominate the tree structure.

To overcome overfitting, pruning techniques are used. Pruning reduces the size of the tree by removing nodes that provide little power in classifying instances. There are two main types of pruning:

• Pre-pruning (Early Stopping) : Stops the tree from growing once it meets certain criteria (e.g., maximum depth, minimum number of samples per leaf).
• Post-pruning : Removes branches from a fully grown tree that do not provide significant power.

Applications of Decision Trees

• Business Decision Making : Used in strategic planning and resource allocation.
• Healthcare : Assists in diagnosing diseases and suggesting treatment plans.
• Finance : Helps in credit scoring and risk assessment.
• Marketing : Used to segment customers and predict customer behavior.

Introduction to Decision Tree

• Decision Tree in Machine Learning
• Pros and Cons of Decision Tree Regression in Machine Learning
• Decision Tree in Software Engineering

Implementation in Specific Programming Languages

• Decision Tree Classifiers in Julia
• Decision Tree in R Programming
• Decision Tree for Regression in R Programming
• Decision Tree Classifiers in R Programming
• Python | Decision Tree Regression using sklearn
• Python | Decision tree implementation
• Text Classification using Decision Trees in Python
• Passing categorical data to Sklearn Decision Tree
• How To Build Decision Tree in MATLAB?

Concepts and Metrics in Decision Trees

• ML | Gini Impurity and Entropy in Decision Tree
• How to Calculate Information Gain in Decision Tree?
• How to Calculate Expected Value in Decision Tree?
• How to Calculate Training Error in Decision Tree?
• How to Calculate Gini Index in Decision Tree?
• How to Calculate Entropy in Decision Tree?
• How to Determine the Best Split in Decision Tree?

Decision Tree Algorithms and Variants

• Decision Tree Algorithms
• C5.0 Algorithm of Decision Tree

Comparative Analysis and Differences

• ML | Logistic Regression v/s Decision Tree Classification
• Difference Between Random Forest and Decision Tree
• KNN vs Decision Tree in Machine Learning
• Decision Trees vs Clustering Algorithms vs Linear Regression
• Difference between Decision Table and Decision Tree
• The Make-Buy Decision or Decision Table
• Heart Disease Prediction | Decision Tree Algorithm | Videos

Optimization and Performance

• Pruning decision trees
• Overfitting in Decision Tree Models
• Handling Missing Data in Decision Tree Models
• How to tune a Decision Tree in Hyperparameter tuning
• Scalability and Decision Tree Induction in Data Mining
• How Decision Tree Depth Impact on the Accuracy

Feature Engineering and Selection

• Feature selection using Decision Tree
• Solving the Multicollinearity Problem with Decision Tree

Visualizations and Interpretability

• How to Visualize a Decision Tree from a Random Forest

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Decision Trees

Choosing by projecting "expected outcomes".

© iStockphoto Nikada

Decision trees help you to evaluate your options.

Decision Trees are excellent tools for helping you to choose between several courses of action.

They provide a highly effective structure within which you can lay out options and investigate the possible outcomes of choosing those options. They also help you to form a balanced picture of the risks and rewards associated with each possible course of action.

Drawing a Decision Tree

You start a Decision Tree with a decision that you need to make. Draw a small square to represent this towards the left of a large piece of paper.

From this box draw out lines towards the right for each possible solution, and write that solution along the line. Keep the lines apart as far as possible so that you can expand your thoughts.

At the end of each line, consider the results. If the result of taking that decision is uncertain, draw a small circle. If the result is another decision that you need to make, draw another square. Squares represent decisions, and circles represent uncertain outcomes. Write the decision or factor above the square or circle. If you have completed the solution at the end of the line, just leave it blank.

Starting from the new decision squares on your diagram, draw out lines representing the options that you could select. From the circles draw lines representing possible outcomes. Again make a brief note on the line saying what it means. Keep on doing this until you have drawn out as many of the possible outcomes and decisions as you can see leading on from the original decisions.

An example of the sort of thing you will end up with is shown in figure 1:

Once you have done this, review your tree diagram. Challenge each square and circle to see if there are any solutions or outcomes you have not considered. If there are, draw them in. If necessary, redraft your tree if parts of it are too congested or untidy. You should now have a good understanding of the range of possible outcomes of your decisions.

Evaluating Your Decision Tree

Now you are ready to evaluate the decision tree. This is where you can work out which option has the greatest worth to you. Start by assigning a cash value or score to each possible outcome. Estimate how much you think it would be worth to you if that outcome came about.

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Next look at each circle (representing an uncertainty point) and estimate the probability of each outcome. If you use percentages, the total must come to 100 percent at each circle. If you use fractions, these must add up to 1. If you have data on past events you may be able to make rigorous estimates of the probabilities. Otherwise write down your best guess.

This will give you a tree like the one shown in figure 2:

Calculating Tree Values

Once you have worked out the value of the outcomes, and have assessed the probability of the outcomes of uncertainty, it is time to start calculating the values that will help you make your decision.

Start on the right hand side of the decision tree, and work back towards the left. As you complete a set of calculations on a node (decision square or uncertainty circle), all you need to do is to record the result. You can ignore all the calculations that lead to that result from then on.

Calculating The Value of Uncertain Outcome Nodes

Where you are calculating the value of uncertain outcomes (circles on the diagram), do this by multiplying the value of the outcomes by their probability. The total for that node of the tree is the total of these values.

In the example in figure 2, the value for "new product, thorough development" is:

Figure 3 shows the calculation of uncertain outcome nodes:

Note that the values calculated for each node are shown in the boxes.

Calculating the Value of Decision Nodes

When you are evaluating a decision node, write down the cost of each option along each decision line. Then subtract the cost from the outcome value that you have already calculated. This will give you a value that represents the benefit of that decision.

Note that amounts already spent do not count for this analysis – these are "sunk costs" and (despite emotional counter-arguments) should not be factored into the decision.

When you have calculated these decision benefits, choose the option that has the largest benefit, and take that as the decision made. This is the value of that decision node.

Figure 4 shows this calculation of decision nodes in our example:

In this example, the benefit we previously calculated for "new product, thorough development" was $420,400. We estimate the future cost of this approach as $150,000. This gives a net benefit of $270,400.

The net benefit of "new product, rapid development" was $31,400. On this branch, we, therefore, choose the most valuable option, "new product, thorough development", and allocate this value to the decision node.

By applying this technique we can see that the best option is to develop a new product. It is worth much more to us to take our time and get the product right, than to rush the product to market. It is better just to improve our existing products than to botch a new product, even though it costs us less.

Decision trees provide an effective method of Decision Making because they:

• Clearly lay out the problem so that all options can be challenged.
• Allow us to analyze fully the possible consequences of a decision.
• Provide a framework to quantify the values of outcomes and the probabilities of achieving them.
• Help us to make the best decisions on the basis of existing information and best guesses.

As with all Decision Making methods, decision tree analysis should be used in conjunction with common sense – decision trees are just one important part of your Decision Making toolkit.

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Comments (31)

• Over a month ago BillT wrote Hi Melissa, As the resource suggests, the value of probability outcomes is an estimate of the likelihood of that outcome occurring. If in your experience sales can increase on average by 10% over 2 years, then the outcome probability of that outcome is the percentage divided by the number of years - 5%. Thanks for your question. BillT Mind Tools Team
• Over a month ago Melissa wrote Great content! As I am very new to the finance topic, I am wondering how is the probability of outcomes calculated/estimated? Melissa
• Over a month ago BillT wrote Hi Sozinho1, Great to hear that. Thank you. BillT Mind Tools Team

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Issue Tree Analysis: Breaking Down Complexities for Simplified Solutions

In an increasingly complex world, businesses and institutions are constantly challenged by complicated problems that require clear and effective solutions. Issue Tree Analysis is a potent visual tool that aids in the dissection of complex issues into manageable parts, promoting a deeper understanding and facilitating effective decision-making. This analytical method is closely aligned with problem solving training and is often integrated into various online certificate programs to impart analytic proficiency. The importance and application of Issue Tree Analysis are vast, extending from corporate strategy sessions to public policy planning, underscoring its versatility as a skeleton key well suited for unlocking intricate dilemmas.

Definition of Issue Tree Analysis

Issue Tree Analysis , also known as Logic Tree or How-Why Analysis, is a hierarchical method for mapping out the elements of a problem and its potential solutions. At its core, it breaks down the main issue into constituent parts, tracing the root causes and outlining pathways to potential remedies. This technique enables users to visualize the relationships between different aspects of a problem systematically.

Importance and Application of Issue Tree Analysis

The value of Issue Tree Analysis cannot be overstated. It sharpens the focus on vital components, prevents oversight of crucial factors, and facilitates a step-by-step approach to address complex situations. From management consultants to policy analysts, this tool has found utility across fields, enabling a structured analysis that enhances critical thinking and enables strategic planning.

Understanding Issue Tree Analysis

To utilize Issue Tree Analysis effectively, one must comprehend its construct and functions. This framework is pivotal for a wide range of applications, from simplifying convoluted scenarios to guiding informed decision-making processes. Its adaptability makes it invaluable for both professionals and those partaking in problem solving training .

Components of an Issue Tree

The First Step in Critical Thinking & Problem Solving

Failure Tree Analysis: Effective Approach for Risk Assessment

Total Productive Maintenance (TPM): A Comprehensive Guide to Improved Efficiency

Plato's Problem Solving: Doing the Right Thing

At the pinnacle of an Issue Tree , there lies the problem statement or key question - a clear articulation of what needs to be addressed. This focal point serves as the guidepost from which all branches extend.

The next tier down consists of causes - significant contributing factors to the central problem. These are the main branches diverging from the trunk, each leading to a different dimension of the issue.

The Sub-Causes

Sub-causes, making up the finer branches, are the more specific elements that feed into the primary causes above. These components allow for granular examination and facilitate an encompassing understanding of the factors at play.

Functions of Issue Tree Analysis

Problem-solving process.

In the problem-solving process, Issue Tree Analysis offers a visual map that aids in systematically identifying and breaking down obstacles. It empowers the solver to delineate the issue and approach the solution methodically.

Decision-making process

In decision-making, the structure of an Issue Tree illuminates various pathways, predicting outcomes and guiding the decision-maker towards the most effective solution through a process of elimination and selection.

Types of Issue Tree Analysis

Issue Tree Analysis can be adapted into three primary forms, each addressing different requirements of investigation and solution framing. If one is pursuing online certificate programs that teach structured thinking, familiarity with these types is fundamental.

Diagnostic Issue Trees

Diagnostic Issue Trees are used to dissect the underlying causes of a problem. They start with an effect and work their way backward to identify all possible causes, akin to a medical diagnosis for the health of an organization or project.

Solution Issue Trees

Solution Issue Trees, conversely, look forward from the issue at hand to map out possible actions and pathways to resolve the identified problem. It is solution-centric and leads to actionable strategies.

Hypothesis-driven Issue Trees

Hypothesis-driven Issue Trees begin with a presumed solution and work to validate its viability through a series of logical deductions. This type is frequently used in time-sensitive situations or when dealing with problems underpinned by numerous assumptions.

Steps in Conducting an Issue Tree Analysis

The process for conducting an Issue Tree Analysis may seem intricate at first. However, by systematically working through each step, one can appreciate its intuitive design and effectiveness in tackling complex situations. This methodology is integral to the frameworks taught in problem solving training modules.

Identifying the Problem or Decision

The initial stage entails a clear identification and articulation of the principal problem or decision to be made. This clarity sets the tone for the rest of the analysis.

Constructing the branches: The Causes

Once the issue is identified, the next stage involves branching out the primary causes. This involves brainstorming and cataloging all relevant factors that impact the central issue.

Breaking down each branch: The Sub-Causes

Each cause is then broken down into its sub-causes, allowing for an in-depth exploration of each contributing element and its respective implications.

Evaluating the tree: Decision-Making and/or Problem Solving

With the tree fully constructed, it can be evaluated to identify the most pertinent issues that require attention for effective decision-making and/or problem solving .

Example of a step-by-step application of Issue Tree Analysis

For instance, a business grappling with declining profits may construct an Issue Tree to pinpoint precise areas of concern - from market trends and customer behavior to operational efficiencies - thus enabling targeted interventions.

Advantages of Issue Tree Analysis

The benefits of employing Issue Tree Analysis are manifold, providing users with tools to cut through the complexity of their challenges. This systematization of thought aids in revealing the structure beneath seemingly chaotic problems.

Clarity and Organization

Issue Tree Analysis imposes order on chaos, offering a clear roadmap from problem statement to potential solutions. This clarity is invaluable in directing collective efforts and communicating issues within a team or organization.

Systematic and Logical Thinking

The method encourages systematic and logical thinking, reducing cognitive load by categorizing information into a coherent structure. This hierarchical organization also supports memory retention and retrieval, an essential aspect of any problem solving training .

Efficient Problem-Solving

By breaking down issues into component parts, Issue Tree Analysis allows for more efficient problem solving . It accelerates the identification of actionable items and minimizes the tendency to tackle problems in an ad-hoc or piecemeal fashion.

Informed Decision Making

Better-quality data and insights gleaned from the analysis empower users to make informed decisions. As part of online certificate programs , learning to utilize this tool can greatly enhance one's leadership and strategic thinking capabilities.

Limitations of Issue Tree Analysis

Despite the many advantages of Issue Tree Analysis , it is not without its limitations. Recognizing these constraints is essential for its effective application and in anticipating potential pitfalls.

Dependency on valid and complete information

The effectiveness of Issue Tree Analysis can be significantly hindered by the availability and accuracy of information. False premises can lead to faulty branches and incorrect conclusions.

Possible oversight of interconnections between issues

The linear nature of Issue Trees can sometimes overlook the complex, web-like interactions between different parts of the problem, potentially leading to an incomplete assessment.

Lack of flexibility for complex and dynamic problems

In cases where problems are excessively dynamic and fluid, the static structure of Issue Tree Analysis might be insufficient to adapt to rapidly changing circumstances.

In essence, Issue Tree Analysis stands out as a robust strategic tool for decomposing and addressing multifaceted issues. Its applications are wide-ranging, from corporate strategy development to the improvement of public policies. Despite its limits, the systematic nature of the Issue Tree encourages thoughtful analysis and fosters clarity in problem solving and decision making.

Recap of the Importance and Application of Issue Tree Analysis

As we have explored, the importance and applications of Issue Tree Analysis touch on multiple facets of contemporary problem-solving and decision-making. It is an integral feature of advanced problem solving training and is frequently highlighted in online certificate programs geared towards producing adept thinkers and leaders.

Final Thoughts on the Use of Issue Tree Analysis in Businesses and Institutions

Businesses and institutions that incorporate Issue Tree Analysis into their problem-solving repertoire stand to gain significantly in precision, clarity, and efficiency. The utilization of this analytical tool can transform overwhelming complexities into approachable and solvable issues.

What is the fundamental principle behind the creation and utilization of issue trees in strategic problem-solving?

Understanding issue trees.

Issue trees play a critical role in strategic problem-solving. They hinge on a basic, yet powerful principle. This principle is dissection. To understand complex issues, one must break them down into smaller, manageable parts.

Breaking Down Complex Problems

Consider any complex question. It likely overwhelms with its scope and intricacies. An issue tree confronts this head-on. It takes the large question and dissects it. The goal is a set of discrete elements. Such elements are easier to tackle individually. This dissection follows a logical and hierarchical structure. Each branch of the tree represents a component of the larger problem.

Visualizing Connections and Hierarchies

Issue trees are not random collections of sub-questions. They reflect the underlying connections within a problem. Think of it as mapping a path through a dense forest. The connections guide the problem solver to the heart of the matter.

Clarity is a central benefit. It stems from visualization. Seeing the problem in tree format illuminates patterns. Paths to solutions become evident. The hierarchy shows which issues are foundational. You see what rests atop them.

Facilitating Communication and Collaboration

Issue trees do more than clarify thought. They serve as a communication aid in teams. Picture discussing a problem without clear structure. The conversation becomes chaotic. The issue tree provides a common framework for discussion.

Team members can reference specific branches. They ensure discussions remain focused. They prevent veering off into unrelated territories. This is critical for cohesive strategic planning. The tree is a shared reference point.

Aligning Focus and Resources

When deploying resources, focus is key. An issue tree helps here. It identifies the problem’s high-impact areas. Teams can then allocate resources where they matter most. The tree's hierarchy signals priority. High-level branches suggest primary concerns. Lower branches might be less urgent.

Enabling Iterative Analysis

Strategic problem-solving is iterative. Solutions rarely emerge at first glance. Issue trees facilitate this iterative process. As one explores a branch, new insights can unfold. These may lead to re-evaluating the tree. The process might add branches. It may prune others. Throughout, the tree adapts and grows. It remains a living document of the problem-solving journey.

- Decompose

- Visualize

- Communicate

- Prioritize

Each word captures a fundamental utility of the issue tree.

Cultivating Critical Thinking

Using issue trees develops critical thinking. It forces problem solvers to seek logical connections. Rarely does an issue stand alone. The tree makes one ask "Why?" and "How?". Such questions are the lifeblood of analysis.

The tree's branches must hold under scrutiny. They must contribute to understanding. Superfluous branches waste time. They distract from vital issues. The discipline of maintaining a clean tree is rigorous. It sharpens the mind.

In conclusion, issue trees are a tool of logic. They give structure to the unstructured. They make the complex manageable. They turn confusion into clarity. Their fundamental principle is simple yet profound. Dissect, then conquer. Address each part with precision. Every branch, a step closer to a solution. That is the beauty of the issue tree.

How does issue tree analysis facilitate the breakdown of complex problems into manageable sub-issues?

What is issue tree analysis.

Issue tree analysis stands as a powerful method. It deconstructs complex issues into smaller, manageable units. This analytical tool promotes clear-thinking. It provides a structured approach. Professionals across fields find it invaluable. It aids in problem-solving and decision-making.

The Breakdown Process

Issue tree analysis begins with a central question. This question represents the core problem. The first step involves identifying the main components of this problem. Each component branches out, resembling a tree's limbs. This visual metaphor aids understanding.

Creating Manageable Sub-issues

Sub-issues emerge from the main components. These sub-issues further break down into more specific elements. Each element becomes a question or a statement. They must be mutually exclusive. They must cover all possibilities. This ensures thorough analysis.

The MECE Principle

MECE stands for mutually exclusive, collectively exhaustive. It is critical in issue tree analysis. It allows for clear categorization. It prevents overlap between branches. It ensures no aspect of the problem gets ignored.

Visual Clarity in Problem-Solving

Often, complex problems overwhelm. An issue tree offers visual clarity. It simplifies the absorption of information. It highlights relationships between sub-issues. It assists in identifying root causes. It helps in developing targeted solutions.

Advantages of Visualization

Visualization has its own merits:

- Enhances comprehension

- Facilitates better communication

- Aids in identifying gaps in reasoning

- Serves as a reference throughout problem-solving

The Benefits of Breakdown

Issue tree analysis offers significant benefits. It promotes systematic thinking. This method fosters depth and breadth in analysis. It makes large problems seem less daunting. As sub-issues become clear, so do pathways to solutions.

Encouraging Focused Effort

Once analysts identify sub-issues, focus sharpens. Teams can address each sub-issue individually. This division of the problem reduces complexity. It streamlines teamwork. It allows for allocation of resources where most needed.

Issue Tree Analysis in Action

In practical scenarios, issue tree analysis guides action. It informs the development of research agendas. It helps in crafting detailed work plans. It shapes the formulation of hypotheses. It directs data collection and analysis efforts.

Facilitating Team Collaboration

Issue trees are collaborative tools. They encourage group participation. They allow all team members to contribute. They ensure a shared understanding of the problem. They align team efforts toward common goals.

Issue tree analysis stands vital in tackling complex problems. It decomposes large questions into smaller, measurable units. Using issue trees allows for greater depth in investigation. It ensures comprehensive exploration of all aspects. It guides teams to effective, efficient solutions.

Can you explain how issue tree analysis contributes to more effective decision-making and problem resolution in the business context?

Issue tree analysis breakdown.

An issue tree frames problems systematically. It promotes thorough, unbiased examination. Visual representations distinguish the technique. It employs a hierarchical, tree-like structure. This structure divides complex problems into manageable components. The first step involves defining the central issue clearly. The tree then branches into contributing factors and sub-problems. Clarity arises from this subdivision.

Decision-making Enhanced by Structure

In the business context, decision-making demands precision. Issue trees provide structure to this process. They aid in identifying various problem aspects. This offers a panoramic view of the situation. Critical analysis becomes simpler. Organized thinking guides decision-making. It steers away from cognitive biases. By doing so, it sharpens focus.

Problem Resolution through Systematic Analysis

Problem-solving benefits from methodical approaches. Issue trees represent reasoning chains. Each branch signifies a potential area for scrutiny. This methodical breakdown highlights cause-and-effect relationships. It facilitates a more granular investigation. With each sub-problem isolated, targeted solutions emerge.

Enhanced Team Collaboration

An issue tree fosters teamwork. It requires collective input. Every team member can see the problem layout. They can add insights to different branches. This collaborative effort consolidates wisdom. As a result, the decision-making process tightens. Solutions reflect the collective expertise.

Prioritization made Simple

Not all issues carry equal weight. An issue tree clarifies priorities. It ranks sub-problems by significance. Critical paths become apparent. Decision-makers can then allocate resources effectively. They devote attention to what impacts the outcome most.

Conclusion: Facilitating Sound Decisions

Through structured analysis, issue tree analysis yields clarity. It divides, conquers, and clarifies problems. Businesses that adopt this technique manage decision-making more adeptly. They resolve problems using systematic approaches. Consequently, firms make informed, effective decisions faster. Issue tree analysis thus stands at the core of strategic thinking within successful organizations.

He is a content producer who specializes in blog content. He has a master's degree in business administration and he lives in the Netherlands.

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A Decision Tree has many analogies in real life and turns out, it has influenced a wide area of M ac hine Learning , covering both C lassification  and Regression . In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making.

So the outline of what I’ll be covering in this blog is as follows.

What is a Decision Tree?

• Advantages and Disadvantages of a Decision Tree

Creating a Decision Tree

A decision tree is a map of the possible outcomes of a series of related choices. It allows an individual or organization to weigh possible actions against one another based on their costs, probabilities, and benefits.

As the name goes, it uses a tree-like model of decisions. They can be used either to drive informal discussion or to map out an algorithm that predicts the best choice mathematically.

A decision tree typically starts with a single node, which branches into possible outcomes. Each of those outcomes leads to additional nodes, which branch off into other possibilities. This gives it a tree-like shape.

There are three different types of nodes: chance nodes, decision nodes, and end nodes. A chance node, represented by a circle, shows the probabilities of certain results. A decision node, represented by a square, shows a decision to be made, and an end node shows the final outcome of a decision path.

Advantages & Disadvantages of Decision Trees

• Decision trees generate understandable rules.
• Decision trees perform classification without requiring much computation.
• Decision trees are capable of handling both continuous and categorical variables.
• Decision trees provide a clear indication of which fields are most important for prediction or classification.

Disadvantages

• Decision trees are less appropriate for estimation tasks where the goal is to predict the value of a continuous attribute.
• Decision trees are prone to errors in classification problems with many class and a relatively small number of training examples.
• Decision trees can be computationally expensive to train. The process of growing a decision tree is computationally expensive. At each node, each candidate splitting field must be sorted before its best split can be found. In some algorithms, combinations of fields are used and a search must be made for optimal combining weights. Pruning algorithms can also be expensive since many candidate sub-trees must be formed and compared.

Let us consider a scenario where a new planet is discovered by a group of astronomers. Now the question is whether it could be ‘the next earth?’ The answer to this question will revolutionize the way people live. Well, literally!

There is n number of deciding factors which need to be thoroughly researched to take an intelligent decision. These factors can be whether water is present on the planet, what is the temperature, whether the surface is prone to continuous storms, flora and fauna survives the climate or not, etc.

Let us create a decision tree to find out whether we have discovered a new habitat.

The habitable temperature falls into the range 0 to 100 Celsius.

Classification Rules:

Classification rules are the cases in which all the scenarios are taken into consideration and a class variable is assigned to each.

Class Variable:

Each leaf node is assigned a class-variable. A class-variable is the final output which leads to our decision.

Let us derive the classification rules from the Decision Tree created:

1. If Temperature is not between 273 to 373K, -> Survival Difficult

2. If Temperature is between 273 to 373K, and  water is not present, -> Survival Difficult

3. If Temperature is between 273 to 373K, water is present, and flora and fauna is not present -> Survival Difficult

4. If Temperature is between 273 to 373K, water is present, flora and fauna is present, and a stormy surface is not present -> Survival Probable

5. If Temperature is between 273 to 373K, water is present, flora and fauna is present, and a stormy surface is present -> Survival Difficult 

Decision Tree 

A decision tree has the following constituents :

• Root Node: The factor of ‘temperature’ is considered as the root in this case.
• Internal Node: The nodes with one incoming edge and 2 or more outgoing edges.
• Leaf Node: This is the terminal node with no out-going edge.

As the decision tree is now constructed, starting from the root-node we check the test condition and assign the control to one of the outgoing edges, and so the condition is again tested and a node is assigned. The decision tree is said to be complete when all the test conditions lead to a leaf node. The leaf node contains the class-labels, which vote in favor or against the decision.

Now, you might think why did we start with the ‘temperature’ attribute at the root? If you choose any other attribute, the decision tree constructed will be different.

Correct. For a particular set of attributes, there can be numerous different trees created. We need to choose the optimal tree which is done by following an algorithmic approach. We will now see ‘the greedy approach’ to create a perfect decision tree.

The Greedy Approach

“Greedy Approach is based on the concept of Heuristic Problem Solving by making an optimal local choice at each node. By making these local optimal choices, we reach the approximate optimal solution globally.”

The algorithm can be summarized as :

1. At each stage (node), pick out the best feature as the test condition.

2. Now split the node into the possible outcomes (internal nodes).

3. Repeat the above steps till all the test conditions have been exhausted into leaf nodes.

When you start to implement the algorithm, the first question is: ‘How to pick the starting test condition?’

The answer to this question lies in the values of ‘Entropy ’ and ‘Information Gain ’. Let us see what are they and how do they impact our decision tree creation.

Entropy:  Entropy in Decision Tree stands for homogeneity. If the data is completely homogenous, the entropy is 0, else if the data is divided (50-50%) entropy is 1.

Information Gain:  Information Gain is the decrease/increase in Entropy value when the node is split.

An attribute should have the highest information gain to be selected for splitting. Based on the computed values of Entropy and Information Gain, we choose the best attribute at any particular step.

Let us consider the following data:

Tree Creation Trial-1 :

Here we take up the attribute ‘Student’ as the initial test condition.

Tree Creation Trial-2 :

 Similarly, why to choose ‘Student’? We can choose ‘Income’ as the test condition.

Creating the Perfect Decision Tree With Greedy Approach 

Let us follow the ‘Greedy Approach’ and construct the optimal decision tree.

Age(<30) ^ student(no) = NO

If a person’s age is less than 30 and he is a student, he will buy the product. Age(<30) ^ student(yes) = YES

If a person’s age is between 31 and 40, he is most likely to buy.

Age(31…40) = YES

If a person’s age is greater than 40 and has an excellent credit rating, he will not buy.

Age(>40) ^ credit_rating(excellent) = NO

If a person’s age is greater than 40, with a fair credit rating, he will probably buy. Age(>40) ^ credit_rating(fair) = Yes

Thus, we achieve the perfect Decision Tree!!

Now that you have gone through our Decision Tree blog, you can check out Edureka’s  Data Science Certification Training.  Got a question for us? Please mention it in the comments section and we will get back to you.

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A DQN based approach for large-scale EVs charging scheduling

• Original Article
• Open access
• Published: 21 August 2024

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• Yingnan Han 1 ,
• Tianyang Li   ORCID: orcid.org/0009-0001-5545-8700 1 &
• Qingzhu Wang 1  

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This paper addresses the challenge of large-scale electric vehicle (EV) charging scheduling during peak demand periods, such as holidays or rush hours. The growing EV industry has highlighted the shortcomings of current scheduling plans, which struggle to manage surge large-scale charging demands effectively, thus posing challenges to the EV charging management system. Deep reinforcement learning, known for its effectiveness in solving complex decision-making problems, holds promise for addressing this issue. To this end, we formulate the problem as a Markov decision process (MDP). We propose a deep Q-learning (DQN) based algorithm to improve EV charging service quality as well as minimizing average queueing times for EVs and average idling times for charging devices (CDs). In our proposed methodology, we design two types of states to encompass global scheduling information, and two types of rewards to reflect scheduling performance. Based on this designing, we developed three modules: a fine-grained feature extraction module for effectively extracting state features, an improved noise-based exploration module for thorough exploration of the solution space, and a dueling block for enhancing Q value evaluation. To assess the effectiveness of our proposal, we conduct three case studies within a complex urban scenario featuring 34 charging stations and 899 scheduled EVs. The results of these experiments demonstrate the advantages of our proposal, showcasing its superiority in effectively locating superior solutions compared to current methods in the literature, as well as its efficiency in generating feasible charging scheduling plans for large-scale EVs. The code and data are available by accessing the hyperlink: https://github.com/paperscodeyouneed/A-Noisy-Dueling-Architecture-for-Large-Scale-EV-ChargingScheduling/tree/main/EV%20Charging%20Scheduling .

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CASA: cost-effective EV charging scheduling based on deep reinforcement learning

Applications of Machine Learning in the Planning of Electric Vehicle Charging Stations and Charging Infrastructure: A Review

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• Artificial Intelligence

Avoid common mistakes on your manuscript.

Introduction

Electric Vehicles (EVs) contribute to numerous benefits such as reduced using cost, environment friendly, and decreased consumption of fossil fuels [ 1 ]. As a result, the amount of EVs has been increasing rapidly [ 2 , 3 ]. However, the lack of convenient charging infrastructure and low effective charging scheduling algorithm for large-scale EVs charging scheduling becomes the key barrier to the EVs penetration [ 4 ]. In some specific scenarios, such as rush hours or extreme weather with low temperatures, there is a noticeable increase in the demand for charging scheduling services [ 4 ]. Uncoordinated charging scheduling strategy could lead to a long queuing time for EVs and traffic congestion [ 5 ]. Therefore, it remains crucial to develop an effective algorithm for managing the large-scale EVs charging schedules while improving the quality of EVs charging service by minimizing the average queuing time of EVs and maximizing charging performance for both EV and charging stations (CSs).

Previous research about EVs charging scheduling has predominantly employed the metaheuristic-based and the Reinforcement Learning (RL)-based methods [ 6 ]. Some of the studies use the metaheuristic-based method to deal with the large-scale real-time scheduling problems. In such scenarios, the genetic algorithm (GA) [ 7 , 8 , 9 ], artificial bee colony (ABC) [ 10 , 11 , 12 ] and particle swarm optimization (PSO) [ 13 , 14 , 15 ] are widely used to search the optimal/suboptimal solution. However, in other studies, the reinforcement learning based algorithms are used to get a better scheduling plan for larger or more complex scenarios. For example, studies in [ 16 , 17 , 19 ] aimed to employ reinforcement learning based algorithm to generate a feasible EV charging scheduling plan to reduce charging costs for users. Similarly, some studies focus on reinforcement learning based algorithms to balance electric load [ 16 , 19 , 20 , 21 ] and increase CSs revenue [ 22 ]. Moreover, some studies proposed the model-based algorithms [ 16 , 23 , 24 ] or multi-agent reinforcement learning (MARL) [ 16 , 21 , 25 ] in different scheduling environments. Generally, metaheuristic-based algorithms can find the optimal/suboptimal solution in real-time, but they need lots of searching time. The aforementioned reinforcement learning based studies primarily generated scheduling plan by using the historical data (such as time series, this needs more steps to update the state/reward information rather get feedback from environment directly) instead of states in real-time. Consequently, these algorithms are difficult to deal with the high real-time EVs charging scheduling problems with high requirement of quick response. To deal with this difficulty, some studies formulated the EVs charging scheduling problem as a sophisticate sequences decision problem or Markov Decision Process (MDP) [ 16 , 21 , 25 ] and the deep reinforcement learning (DRL) is utilized to generate EV charging scheduling plan in the complex situation with multiple of constraints. While, due to the lack of reasonable design of states and exploration mechanism, this type of RL based methods hardly cope with the large state/solution space and cannot find the optimal/suboptimal scheduling solution, which means the large-scale EVs charging scheduling problem may be solved in an inefficient way.

To overcome these gaps, creating an effective deep reinforcement learning-based approach must be undertaken. The states that could represent the global information should be firstly designed and the design of reward should consider the appropriate optimizing target which reflects the service quality of EVs charging scheduling. Furthermore, for obtaining the optimal scheduling plan, DRL-based networks that need to consider the utilization of historical experience of environment interaction and high global search ability should be designed based on the scheduling process. Finally, the training algorithm of the models should pay more attention to scheduling details to avoid being trapped into local optimal solutions.

Despite the importance of providing an effective DRL-based approach to improve service quality (to get lower average queueing time for EVs and lower average idling time for CSs), current research only focuses on historical experience utilization or inefficient solution space explorations. Moreover, existing DRL-based EVs charging scheduling methods only focus on optimizing EV-side or CS-side targets, without providing a comprehensive approach to optimizing service quality from both perspectives. The lack of effective method precedent raises three questions:

What is the state and reward patterns that cover comprehensive information for both EVs and CSs sides?

How to design deep models for solving MDP of EVs charging scheduling efficiently?

How to train the deep models to effectively obtain the optimal EVs charging scheduling solution while avoiding the local optimal and exploring the action space thoroughly?

To solve these questions, on the basis of our pervious works [ 4 ], we proposed an innovative DQN based approach, including a fined-grained state representation that contains the global information, the reward based on an appropriate optimization target for guiding models to improve service qualities and deep neural networks with novel training algorithms. The deep neural networks, combined with the advantages of dueling net [ 26 ] and noisy layer [ 27 ], is designed to not only make effectively use of historical experience, but also improve the ability of space exploring, which makes the proposed approach have the extraordinary performance. Through a series of experiments, we demonstrate the superiority and effectiveness of our proposal.

The remainder of this paper is organized as follows. “Related Works” review the research related to RL/DRL-based EVs charging scheduling. “Problem Formulation” provides the mathematical background of our proposal. Next, MDP formulation of large-scale EVs charging scheduling is introduced. The “DQN based scheduling network and training algorithm” section details the designing of our proposal. “Experiments and Discussion” shows the efficiency and superiority of our algorithm by a series of experiments and analyzes and discusses the effective mechanism of our proposal from the perspective of capability of solution space exploring”. Finally, the “Conclusion” section summarizes our work, provides an outlook for our research.

Related works

With the rapid penetration of EVs in urban transportation systems, there has been a corresponding increase in related research about EVs charging scheduling [ 6 , 28 , 29 ]. Many studies have focused on utilizing DRL-based methods to address EVs charging scheduling problems from different perspectives. In recent research, more attentions were paid to the design of the optimizing target, state, and deep model.

The design of the optimizing target varies across different studies. A well-designed optimizing target can guide the model effectively achieving the optimal goals. In research [ 30 − 32 ], the authors presented the DRL-based algorithms to reduce the energy costs by managing the scheduling process and predicting the price trends. Similarly, authors in [ 19 , 33 , 34 ] developed the DRL based strategies to maximize the revenue or welfare for charging station in energy distributed system. On another hand, some study focuses on optimizing multiple optimizing targets or the weighted sum (of multiple optimizing targets). For instance, a double-Q learning based algorithm in [ 35 ] was designed to optimize the optimizing targets such as satisfying EV charging demand, minimizing charging operation costs, and reducing transformer overloading at same time. Additionally, studies in [ 36 , 37 ] combined waiting time with energy costs as their optimization targets.

The designing of the state usually depends on the optimizing targets [ 38 ]. For example, studies that aimed to meet EVs charging requirements, such as studies [ 37 , 39 ], used the battery state of charge as a part of state. Parameters like charging or discharging costs were usually included in the state representation to optimize the operational costs [ 40 , 41 ]. Other factors, such as the waiting time [ 42 ]and charging price, were also considered when designing state representations to improve the individual satisfaction, decrease energy consumption levels or the expected charging duration. However, there is still a lack of appropriate state representation that incorporates the global information to determine the EVs scheduling priorities and charging station selection in large-scale EVs scheduling scenarios. Based on carefully designed states, suitable actions for minimizing or maximizing the optimizing goal can be generated by the models. Generally, a model used to map the state to an action-value can take the form of a table that consisting of state-action values or a combination of several neural networks.

For simple problems with low-dimensional action and state spaces, such as the problem in study [ 43 ], a Q-Table was commonly employed as a state-action value function to predict the quality of the charging scheduling. However, this method is not widely applicable to real-world problems due to the complexity and randomness [ 44 ]. For more sophisticated situations, the most commonly used algorithms are DQN, Deep Deterministic Policy Gradient (DDPG) and their variants [ 38 ]. In study [ 40 ], the model combining DDPG and DQN was proposed to predict the action-values based on the features of historical data extracted by a long short-term memory (LSTM) and to obtain feasible solutions. Besides, the MARL was used in some studies, such as [ 45 ] and [ 41 ], where it was used to generate EVs charging scheduling strategies by deeply exploring the state and action spaces. The advantages of the multi-agent over the single agent are that it can easily get the local optimum in a large space and is suitable for more complex scenarios such as high dimensions of features or action spaces [ 6 ]. While, effectively obtaining an optimal scheduling plan remains challenging due to the complexity of surging EVs charging scheduling demands. Existing literature pays little attention to this problem.

In summary, the current studies mainly addressed EVs charging scheduling problems with a small state space or low-dimensional action space from an economic or operational perspective. Some of them focused on getting feasible solutions from historical experience, the others devoted to gain the local optimum. Few studies focus on finding the optimal solution in large-scale state an action spaces, especially for scenarios of EVs charging scheduling with surging demands to improve the quality of charging service. Therefore, an effective scheduling method is needed for managing the surging requests in large-scale EVs charging. To solve this problem, a DRL-based algorithm should be proposed with: (i) well-defined state that can represent the global information of both EVs and CSs sides, and reward that could represent the service quality; (ii) deep networks and training algorithms that can solve MDP of EVs charging scheduling and accurately map the state to action values while incorporating an action space exploration mechanism.

Problem formulation

Entity definition.

The EVs charging scheduling problem typically involves three key entities: EVs, CSs and Charging Devices (CDs). The EV and CD can be represented as a quadruple <  i , elo i , ltd i , ct i  > and a five-tuple <  j , k , ot (k, j) , qn kj  > respectively, while the CS can be described as a triple <  j , clo j , dn j  > .

Without loss of generality, we consider the scheduling of EVs with specific charging requirements. Each EV numbered with i , denoted as EV i , is located at position elo i (represents the current position of EV i ) and requires ct i (represents the charging duration of EV i ) minutes for charging. Each charging station numbered with j , denoted as CS j , is equipped with dn j (the number of charging devices on CS j ) available CDs. The scheduling of EVs charging is to assign a charging station CS j located at position clo j (the position of charging station CS j ) for each EV i with the limitation ltd i (the max left travel distance by remaining battery capacity of EV i ).

We represent the k th CD of CS j as CD kj . Additionally, ot (k, j) denotes the working time of CD kj that occupied by the assigned qn kj (the number of EVs that scheduled at CD kj ) EVs.

In this study, we focus on the scheduling of large-scale EVs charging in a city scenario with a complex traffic situation. Both the EVs and the CSs have the capability to communicate with a Global Aggregator which is a third party that interested in EVs charging scheduling. Our approach may help GA to determine the scheduling sequence of EVs for an appropriate CS with the purpose of high charging efficiency in terms of minimized queueing time of EVs and idling time of CDs.

Mathematical background

In general, an EV will submit a charging request when the battery is low, which mainly includes the expected charging time and the remaining travel distance. Specifically, for any given time, the travel time from EV i to CS j , which is denoted as tt ij , is determined by equation tt ij  =  d (i, j) /(α  ×  v i ) , where the d (i, j) represents the distance between EV i to CS j , the v i represents the average driving speed of EV i and the α  ∈ [0, 1] represents a factor that indicates the level of traffic congestion of route between EV i to CS j . The value of α is determined based on the real-time traffic situation and obtained from the data interface of map Apps (Such as Google map or Baidu map). A lower value of α indicates a higher level of congestion, while a higher value suggests a lower congestion level. If EV i is scheduled at CD kj , which is occupied before EV i arrives, the expected queueing time qt ijk can be calculated by qt ijk  =  (ot (k, j) –tt ij )  ×  I (ot (k, j)  >  tt ij ) . Otherwise, if CD kj is not occupied, its idling time it jk can be updated as it jk  =  (tt ij –ot (k, j) )  ×  I (ot (k, j)  ≤  tt ij ) . I (x) denote the indicator function and can be described as ( 1 ).

Additionally, the occupied time of CD jk can be updated as ( 2 ):

For improving the charging efficiency and quality for both EV and CS sides, the target of charging decision is to minimize the expected queueing time of each EV and the idling time of each CD. To simplify the problem, we transform the EVs charging scheduling problem from a multi-objective optimization to a single-objective optimization. The optimization objective is formulated as ( 3 ), where ω 1 and ω 2 are the hyper-parameters.

Markov decision process of large-scale EVs charging scheduling

The EVs charging scheduling problem can be defined within a discrete MDP considering a discrete time model. Based on the updated state information provided by GA (GA, i.e., global aggregator, is a third party which provides the information of the state for EVs and CSs in real-time; the state of EVs and CSs are denoted as SEV and SCS separately), deep models which include the EV selection model and CS selection model are used as the agent to make decisions regarding which EV should be prioritized for charging and where it should be scheduled. The state, action and reward in our approach are denoted as follows:

STATE : SEV t represents the state used to select which EV is to be scheduled at time step t (the selected EV is denoted as EV s ). It includes the global state information of the CSs and all the not scheduled EVs. Similarly, SCS t refers to the state used to select the optimal CS for EV i at time step t . It includes the information of selected EV and all available CSs.

ACTION : a et represents the action taken at time step t to select an EV that is scheduled. The range of a et is from 0 to N ev , where N ev is the total number of schedulable EVs, indicating the available actions for selecting a schedulable EV. Similarly, a ct represents the action used to select a CS for EV s . The range of a ct is from 0 to N cs , where N cs denotes the total number of available charging stations.

REWARD : In our proposal, we have designed two types of rewards r e and r c . Each reward is based on the weighted values of average queueing time and idling time. The weights are hyperparameters. r e is designed for training the EV selection model. It is a K -steps discounted weighted value with discounted factor γ , where K is a hyper-parameter. This allows to consider the long-term consequences of the selected actions. Additionally, r c is the average queueing time returned from the environment after each step is executed. This reward provides direct feedback on the impact of the chosen charging station for the EVs.

Improved DQN based networks and training algorithms

In the large-scale EV charging scheduling scenario, the high-dimensional action space and state space pose the challenges to find the optima solution effectively when applying the current DRL-based algorithms. To overcome this disadvantage, we carefully designed the state representation and reward setting. Based on this, an improved DQN-based network with feature extracting module is proposed for enhancing EV charging scheduling performance. In addition, for efficiently utilizing the scheduling experience that is obtained from the interaction between the agent and environment, a scheduling-order fine-tunning algorithm is proposed.

Designing of state, action, and reward

Designing of state.

For a schedulable EV, its feature is formed as SE i  = [ dis_to_cs(i), ct i , ltd i , scheduled_flag ], which includes the distance to all available charging stations (denoted as dis_to_cs(i) ), the expected charging time (denoted as ct i ), the remaining travel distance of the EV i (denoted as ltd i ) and the scheduling flag (denoted as scheduled_flag ) used to indicate whether the EV i is scheduled.

In addition, feature of CSs consist of AQT , AIT , CNS and occup_T . Therein, the AQT is a list contains the average queueing time of EVs in each CS, AIT denotes a list contains the average idling time of EVs in each CS and the CNS is a list that contains the number of EVs scheduled at each charging station. Therefore, the state of charging station is collectively denoted as SC  = [ AQT, AIT, CNS, occup_T ].

With above defined features, the state SEV t used to the EV selection model can be represented as SEV  = [ SE 1 , \( \cdot \cdot \cdot \) , SE Nev , SC ] with dimensions = ( N ev  + 4) ×  L , where L represents the dimensions of SE i . For the CS selection that is used to select a charging station for EV s (the selected EV at time step t ), the state SCS is constructed as SCS  = [ SE s , SC ] with dimensions = 5 ×  L .

Designing of action and reward

At each time step t , the models interact with the environment by using the current states SEVt, SCSt to select the optimal EV and CS. The EV selection model operates on schedulable EVs, each output with an associated Q -value representing the expected reward upon selection. Similarly, the CS selection model involves reachable CSs for the chosen EV, each output linked to a Q-value denoting the expected rewards for allocating the CS to EV.

The rewards acquired from the environment rely on both the states and actions taken for optimal EV and CS selection. The reward re for EV selection is a K -step discounted weighted sum of the queueing time about EVi and idling times of the target CDkj , enabling long-term information acquisition. It can be collectively described as \({r}_{et}={\sum }_{m=0}^{K}{\gamma }^{m}\times \left({\omega }_{1}\times {it}_{kj\left(t+m\right)}+{\omega }_{2}\times {qt}_{ikj\left(t+m\right)}\right)\) where itkj ( t  +  m ) represents the idling time of CDkj due to waiting for the arrival of m th EV that scheduled at CDkj from time step t and qtijk ( t  +  m ) represents the queueing time of the m th EV that scheduled at CDkj from time step t . Specifically, the discounted factor γ is set as 0.8 and K is set as 2 (as an experience value) enabling long-term information acquisition.

For CS selection, the reward is the weighted sum of the current average idling and average queueing times of the selected EV and their target CS, providing direct scheduling feedback within a single time-step.

Architecture of Neural networks

In this section, the detail of the overall structure of deep models is introduced, which shown as Fig.  1 . For improving the performance of feature extraction from states of EV selection, a fine-grained feature.

The overall structure of our proposal

extraction module (FFEM) is proposed for EV selection model. Based on the extracted fine-grained features, an improved noisy-based exploring module (INEM) is employed to explore the solution space thoroughly. In the end, a dueling module is used to improve the fitting of performance of Q-value.

Fine-grained feature extracting module (FFEM)

In traditional reinforcement learning/deep reinforcement learning based EV charging scheduling methods, states that acquired from the environment are usually featured with low-dimensional or can be easily transformed into a simpler form [ 6 ]. However, for the large-scale EV charging scheduling scenario, states are high-dimensional and based on the total number of EVs and CSs, which cannot be transformed into a simpler form. Moreover, it is difficult to extract features for interacting with the scheduling environment. Therefore, a more effective feature extraction module is proposed.

For solving this problem, a fine-grained feature extracting module (FFEM) is proposed. The FFEM, which used for helping to extract the feature of the input state SEV, contains two same sub-modules. For each sub-module, as shown in the Fig.  2 , a 3 × 3 convolutional layer is used to extract the key information of the input feature map. Given that fact that the feature of the feature map might be sparse in some scheduling scenarios, a batch normalization is therefore adopted to prevent the disappearance of the gradient. Furthermore, the ReLU (rectifier linear unit) is adopted after each batch normalization layer to improve the ability of nonlinear sub-module feature extracting. In each sub-module, two of sub-structure, i.e., Convolutional-Batch Normlized-ReLU combination, is concatenated linearly and a 1 × 1 convolutional layer is adopted which links the input and the output of the sub-module. It implements the cross-channel integration of input and output features, significantly increasing nonlinearity of the sub-model. Given the reality that the complexity of state space and for extracting more refined features of the input states, the proposed FFEM consists of two linearly concatenated sub-modules.

The overall sub-module structure of FFEM

For each sub-module of FFEM, let X denotes the input state, W 1 , B 1 , W 2 , B 2 denotes the weights and biases of the convolutional layers and W 3 , B 3 denotes the weight and bias of the 1 × 1 convolutional layer. Each sub-module of fine-grained feature extraction module can be collectively summarized as ( 4 ) and ( 5 ):

where σ 1 and σ 2 are the standard deviation of the X and Y , μ 1 and μ 2 are the mean of the X and Y , ε 1 and ε 2 are the hyper-parameters that bigger than 0, β 1 , β 2 , γ 1 , γ 2 are the learnable parameters.

It can be concluded from ( 4 ) and ( 5 ) that the proposed module introduces more weights and biases parameters. By combining with the ReLU function, this structure help improves the ability for the complex non-linearized Q-value function fitting and feature extraction in larger state space. Therein, the ReLU activation function is defined as f ( x ) =  max ( 0, x ), introducing nonlinearity into the model. By allowing only positive values to pass through and setting negative values to zero, ReLU facilitates the learning of complex nonlinear relationships in the data. Furthermore, its sparse activation property promotes feature extraction by selecting relevant features from the input. When integrated into the proposed module, ReLU enhances the model's capability to capture complex patterns in the Q-value function and extract meaningful features, particularly in larger state spaces. The introduction of the proposed module, through the incorporation of additional weights and biases parameters along with the utilization of the ReLU activation function, significantly improves the model's performance in fitting complex nonlinear Q-value functions and extracting features. This approach proves particularly advantageous in scenarios involving larger state spaces, where traditional models may struggle to adequately capture the underlying relationships. Future research could explore further improvements and applications of this framework in various reinforcement learning tasks.

Improved noisy-based exploring module (INEM)

In our research, the selection of an appropriate exploration strategy within the solution space is crucial for identifying the optimal electric vehicle charging scheduling scheme. Generally, traditional strategies such as ε -greedy and Boltzmann probability-based methods are two primary approaches for exploring the solution space. However, when dealing with large-scale, high-dimensional solution spaces, these methods exhibit inefficiencies in the exploration and the balancing between exploration and exploitation [ 27 ]. To address this issue, we proposed an improved noisy-based exploring module (INEM) that integrates the dropout and noisy linear layer. The aim is to augment the model's exploration capabilities.

The Fig.  3 illustrates the structure of INEM, which comprising three key neural network layers. Initially, the Dropout layer processes the state features extracted by the FFEM module. During training stage, it stochastically deactive a portion of neurons with a probability of p  = 0.5 to inhibit their forward and backward propagation. Following the dropout processing of features, they are fed into two layers of noisy layers designed to incorporate random noise subject to normal distribution, enhancing the model’s generalization capabilities. Each noisy linear layer is adopted the ReLU function for non-linearity, thereby augmenting the module's capacity.

The structure of INEM

Specifically, for the Dropout layer, during each forward propagation, a portion of neurons is randomly deactivated with a probability of p  = 0.5, discarding their original computed results and setting their outputs as 0. Furthermore, concerning these deactivated neurons, their parameter updates are halted during backpropagation. This allows effectively training a sub-model of the original model in each training iteration. This strategy helps reduce reliance between specific neurons, thereby enhancing the model's generalization and mitigating overfitting risks. Mathematically, this layer can be represented as Y  =  X ⨂ m , where ⨂ denotes element-wise multiplication of matrices, and m follows a Bernoulli distribution ( p  = 0.5).

For the noisy linear layers within the module, the generation of parameterized noise adopts the factorized gaussian noise method proposed in [ 27 ]. Based on this method, the representation of the noisy layer can be summarized as Y n  = ( μ ω  +  σ ω ⨂ ε ω ) ×  X n  + ( μ b  +  σ b ⨂ ε b ), where the X n and Y n denotes the input and output of the layer, and the μ ε , μ b , σ ε , σ b are the parameter matrices of the noisy linear layer and each value in the matrices is subjected to normal distribution. The introduction of noisy layers aims to enhance the model's robustness and generalization capabilities. By introducing Gaussian noise at each layer, the model can better adapt to different data distributions and noise conditions, thereby improving its generalization and solution space exploration ability. Additionally, noisy layers help prevent overfitting, thereby enhancing the model’s performance in practical applications.

Combining the dropout skill, the noisy linear layer described in this section, and the Fig.  3 , our proposed module can be mathematically summarized as the form shown in Eq. ( 6 ).

where f in represents the input to the model, \(\mu^{{\omega_{i} }} ,\mu^{{b_{i} }} ,\sigma^{{\omega_{i} }} ,\sigma^{{b_{i} }}\) are the hyper-parameters of the ith noisy linear layer, and \(\varepsilon^{{\omega_{{\text{i}}} }} ,\varepsilon^{{b_{{\text{i}}} }}\) signify the noise introduced by the Noise layer’s weights and biases, respectively.

This module's design yields significant advantages for the model in various aspects. Primarily, it contributes to enhancing the overall training speed, crucial for efficiently handling large-scale tasks. Secondly, the introduction of the Noise layer amplifies the collective adaptability among neural nodes, notably enhancing the model's robustness and performance when dealing with intricate datasets. Additionally, the incorporation of the Noise layer aids in balancing the model's exploration and exploitation, thereby reinforcing its generalization capabilities. These combined factors propel the model towards better adaptation to the challenges posed by large-scale electric vehicle charging scheduling tasks.

Dueling block for a better Q-value fitting

When addressing problems involving large-scale action spaces and high-dimensional state spaces, directly mapping from states to different actions through state-action values (i.e., Q-values) typically demands increased computational resources and struggles to accurately reflect the value information of diverse states. To mitigate this issue, we devised a Q-value estimation module based on Noised Features, employing the structure of a Dueling Network to tackle these challenges.

The Fig.  4 illustrates this module, which takes processed features from the Noisy Linear Layer as input and ultimately produces Q-values for actions. In contrast to other networks (such as the Q-network in DQN), the dueling module employs two parallel sub-network branches that separately estimate the advantage value of state-action pairs and the value of the current state. Here, the advantage value refers to the relative merit of an action concerning the state value, representing the relative value of a particular action in a specific state. To merge the outputs of these two branches into the actual Q-values, an Aggregation Layer is employed to integrate the outputs of these sub-networks.

The dueling module

Let the noised feature as shown in the Fig.  4 be denoted as S noised , the v η and a ψ represent the state value predictor branch and advantage value predictor branch respectively. Therein, η and ψ represents the parameters of the v η and a ψ branches. In this context, a signifies the action chosen in the current state,

while a′ represents the action chosen according to the current action-selection policy in the subsequent state s′ . Hence, the mathematical formalization of this module can be articulated as follows:

where θ  = { η, ψ }.

In the proposed module, the s noised is separately fed into the v η and a ψ branches, thereby decomposing the estimation of Q-values into estimations of the advantage value A and the state value V . Subsequently, the aggregation layer integrating outputs derived from both branches into the Q-value. The design uniquely determines the action advantage values and state values [ 26 ]. This structure aids in optimizing the model's training stage, enhancing both the speed and precision of state value estimation, thus improving the capability for policy evaluation. Simultaneously, this decomposition stabilizes the model's exploration of solution spaces, enhancing its ability to search for the optimal solution to electric vehicle charging scheduling problems within large-scale solution spaces.

Training algorithm

For training the proposed architecture effectively, an assist algorithm which are used to scheduling order fine-tunning is proposed. Based on this algorithm, the models are trained by the sampled experiences.

Charging order fine-tunning

EV charging scheduling models training algorithm

In a large-scale action space, it is difficult to directly identify a scheduling scheme with relatively good performance at the beginning of the training stage. This can lead to a relatively poor quality of experience gathered by the model while interacting with the environment (longer EV queueing times, longer charging equipment idling times). As a result, models trained based on the experience typically perform poorly on EV charging scheduling. To minimize this deficiency, this paper proposes a charging sequence fine-tunning algorithm, which is outlined as Algorithm 1 . In this algorithm, the epat(ev, j) denotes the predicted driving time to the target charging station j of EV ev in current state . And the ct ev denotes the charging time for EV ev .

The main idea of the proposed algorithm is derived from SJF (shortest job first), i.e., to have the shortest process time of the scheduling process is to schedule the not scheduled job/EVs with shortest processing time firstly. However, the situation becomes more complex in the EV charging scheduling process, i.e., both the traveling time and charging time could be the key point for the scheduling result.

To solve this problem, two of skills is introduced. Firstly, calculated the expected occupied time of each EV need to be scheduled at CD (k, j) , which could be described as the sum of the charging time and the expected traveling time (the 1–3 lines of Algorithm 1 ). Based on the calculating results, the optimal EV selection can be simply defined as the EV with minimum summation (i.e., M ev ) (the 4–5 lines of Algorithm 1 ). However, the 6–7 lines of Algorithm 1 shows a special situation. For situations that more than one EVs has the same M ev -value, select the EV that with minimum epat (ev, j) can derive the better plan. This can be simply proved as follows.

Considering the situation where two EVs (denoted as A and B ) need to be scheduled at the charging station CD (j, k) , let C A and C B denote the charging time of A and B , and R A and R B denote the expected travel time to the charging station. If C A  >  C B , R A  <  R B , and C A  +  C B  =  R A  +  R B . If A is firstly selected, then the total finish time of the charging process can be calculated as follows (Eq.  8 ):

otherwise, the total finish time is calculated as ( 9 ):

It can be derived from ( 8 ) and ( 9 ) that,

Based on the assumption, it can be derived that L—F  < 0. Therefore, to select an EV which is closer to the charging station could lead to a better scheduling performance when the M -value of EVs is equal.

The 9–13 lines gives a scheme to update the M -value of EVs, which ensures that the re-arranged scheduling order could lead to a maximum performance on both EV (minimized queueing time) and CS (minimized idling time).

In our model training algorithm, the training process can be divided into two-main part i.e., the pre-training stage and training stage. In this algorithm, two experience storage, i.e., the prioritized replay buffer (PER) [ 35 ], is denoted as ERB and CRB for storing the experience that used to training the EV-selecting model and CS-selecting model respectively. Therein, the PER is used for enhancing the utilization of collected experiences. Based on the experience, the models are pre-trained for PTS time trained for TS times where both the PTS and TS are scalars. The training process is summarized as Algorithm-2.

In Algorithm 2 , it can be divided into two main parts, the pre-training stage and training stage. The advantages of this training setting can be summarized as follows: given the fact that the problem setting has the large-scale and large-dimensional action space and state space, a pre-training process is introduced to accelerating the convergence of models. This could scale the search space back and exclude some solutions with relatively worse performance to alleviate some of the unnecessary exploration in the subsequent training stage.

At the pre-training stage (i.e., the line 1–8), the algorithm collected experiences by Monte Carlo with a sampling process. A sampling mechanism is introduced to re-sampling the original sampled experiences and only 30% of experiences with better scheduling performance is keep. This allows that the pre-training process could lead to a faster performance enhancing in EV charging scheduling task.

The training stage (i.e., the line 9–22) has two main processes, the interacting and training. In interacting process, the models interact with the environment to explore the solution space (i.e., the line 10–16). To prevent introducing the worse experience into replay buffer, the scheduling order fine-tunning is introduced (i.e., the line 17–18). In line 20–21, each trajectory is re-evaluated after fine-tunning. If the re-evaluated experience is better than in the replay buffer, this experience will be added to the experience buffer. This is beneficial for improving the overall quality of the training model. This can be simply explained as follows:

Assuming that N A trajectories are added into the replay buffer with the final weighted reward A , and a new experience is sampled with the final weighted reward r . If the new experiences are added into the replay buffer, the change of A (denoted as B ) follows:

It follows that:

if and only if r  <  A . It shows that, this experience collection method helps to improve the quality of experience used for training models, which is beneficial for accelerating model training.

Experiments and discussion

To demonstrate the superiority of our proposal, we have designed the case studies to showcase its performance. The experiments in each case study were conducted using PyCharm Integrated Development Environment version 2019.1.1 with Python 3.7 on a PC equipped with an 11th Gen Intel(R) Core (TM) i7-11800H processor running at 2.30 GHz, 32 GB of memory, and an Nvidia RTX 3060 graphics card with 6 GB of memory.

Yardstick and dataset

In our experiments, we collected a real-world dataset from an EV charging service company inter-face. The dataset consists of 1000 EVs and 34 charging stations (CSs) of a city. Each CS is equipped with 5 high voltage charging devices. The 1000 EVs are located at different positions and need charging services. During our research, we identified that 101 EVs were unable to be scheduled for charging due to poor battery conditions. These EVs required battery exchanging services. Consequently, only 899 EVs were able to reach at least one charging station with their remaining battery capacity. The details of the dataset can be summarized as Table  1 .

Experiment setting

In our experiment setting, three sets of case studies were conducted to showcase the performance of our model from different perspectives.

In case study I, we investigate the influences of different reward setting, hyperparameters setting on the performance of models in EV charging scheduling. In this part, a group of optimal hyper-parameter setting is identified. The experiments discussed after this section are all conducted based on the optimal parameters shows in this part.

In case study II, we investigated the effectiveness of each proposed module (fine-grained features extraction module, Improved noisy-based exploring module and dueling module) and scheduling order fine-tunning algorithm. A series ablation experiments, and analysis are conducted/proposed based on the results of experiments.

In case study III, some heuristic-based, DRL-based, and dispatching rule-based EV charging scheduling algorithms are compared. The results showcase the advantages of our proposal over other algorithms.

Case study I

In this section, our primary focus lies in presenting and discussing the influence of different reward settings, neural network optimizers and hyperparameters, such as learning rates, on the exploration of the solution space. To investigate this topic comprehensively, we examine various reward combinations (with learning rate = 0.0001and optimizer Adagrad for EV-model, Adam for CS-model), as depicted in Table  2 . Based on these reward settings, a series of controlled experiments are conducted (therein, we sampled experience by Monte Carlo to pre-training the models), and the experiment results are illustrated in Fig.  5 . Furthermore, the effects of different hyper-parameter (mainly about the learning rate) on the performance of the models are then discussed based on the optimal reward setting.

The result of compare experiments

As shown in the Table  2 and Fig.  5 , the result #1—#8 indicates that the bigger weight for the queueing time can lead to a better scheduling performance to some extent. For some extremely situation (i.e., one of the factors (queueing time or idling time) is neglect, such as the #11—#12 version of the control experiment), however, the performance has a downward trend. Therefore, it can be concluded from the Fig.  5 that the performance for EV charging scheduling cannot be improved by simply increasing the weight of the queueing time. Given the fact that the idling time increasing far slower than the queueing time, it can be therefore concluded that it is easier to find the optimal EV charging scheduling solution by considering the target that changes more frequently (such as the queuing time) in this type of problem.

Learning rate and optimizer are of the most important elements in the models training. However, given the complexity of the problem (large solution space) that it is hard to find an appropriate learning rate or an optimizer in large-scale searching space (i.e., solution space in our proposal). Therefore, we conduct a series of experiments to investigate the influence of optimizer selecting and learning rate setting on scheduling results.

In these experiments, we adopt different optimizers and learning rate for training EV-selection model and CS-selection model for comparison. The mainly tested optimizers are Adagrad, Adam, SGD, and the learning rate we adopt are 0.1, 0.01, 0.05, 0.001, 0.005, 0.0001. For simplifying the criterion of scheduling results, we adopt the weighted sum of the average queueing time and weighted idling time (with ω 1  = 0.8, ω 2  = 0.2). The result of experiments is shown as Table  3 .

It can be concluded from the Table  3 that the combination of Adagrad for EV-selecting model training and Adam for CS-selecting model training has the best performance among the scheduling result. It can be inferred that the features of Adagrad (suitable for sparse data and able to automatically adjust the learning rate) is suitable for the solution space of EV charging scheduling with high dimensionality. Therefore, there exists the sparsity in the solution space of EV charging scheduling problem to some extent can be then inferred (i.e., the solution space of EV selecting). This might be contributed to the scheduling constraints that not all the EV could be scheduled in the current state. Given the complexity of solution space, the learning rate adjusts automatically lead to a more convenient paradigm to training the model without introducing the additional hand labor. On the other hand, it could lead to best results by adopt the Adam for CS-model training. This might be since the high-efficient in gradient calculating which lead to a better performance in EV charging scheduling. Therefore, based on the result shown in the Table  3 , all the following comparison experiments are conducted in the following manners:

The optimizers are set as Adam for CS-selecting model with learning rate = 0.0001 and Adagrad for EV-selecting model with learning rate = 0.0001.

The reward for EV selecting is set as the discounted weighted reward with ω 1  = 0.8 , ω 2  = 0.2 and the discounted factor is set as 0.7 (the 0.7 is experienced value).

Case study II

This part, we conducted a series of ablation/compare experiments to investigate the advantages of our proposal. Firstly, we study the feature extract module to show that it is beneficial for enhancing the features extraction for state representing in the large-scale state space. Then, the advantage for noisy block in exploring solution space is analyzed by comparing the results with exploring by Boltzmann probability and ε -greedy. After that, the merits for advantage-value module are further analyzed by the ablation experiments.

For investigating the advantages of the feature extract module, a group of ablation experiments are conducted. In the compared module, the 1 × 1 conv shortcut, batch normalize are erased. As the results shown as the Figs.  6 and 7 , the overall trend from the experimental results suggests that adding a feature extraction module leads to a better large-scale EV scheduling result. On the one hand, the average queuing time corresponding to the overall scheduling result has a decreasing trend compared to the control group as shown in Fig.  7 , which suggests that the enhanced extraction of features helps to improve the ability of the model in generating scheduling plan. On the other hand, it can be concluded from the Fig.  6 that the average idling time corresponding to the scheduling results generated in the model training stage has a greater than its control group in some time steps. This is since the refined feature extraction layer helps to some extent in the exploration of the solution space by other subsequent modules (e.g., the noise module in the EV selecting model) (the oscillations in the idle time indicate that the queuing order is constantly changing during this stage, which suggests that the model is exploring the solution space thoroughly).

The result of average idling time

The result of average queueing time

Based on the features extracted by the proposed feature extraction module, we further investigate the important role played by the noise layer in our proposed network architecture for the exploration of the solution spaces. For clarifying the comparison, we use the weighted sum of the average idling time and the average queueing time with weight ( ω 1  = 0.8 , ω 2  = 0.2) as the indicator to measure the scheduling performance.

To investigate the effectiveness of the INEM, the ablation experiment is conducted. In the ablation control experiment, we uniformly sampled 50 samples at equal intervals during both the pre-training and training stages in the control group and our proposed model. The horizontal axis represents sample steps, where 0–50 denotes the pre-training stage, and 51–100 represents the training stage. The vertical axis represents the weighted criterion, i.e., the weighted sum of the average queue time of electric vehicles and the average idle time of CS after each scheduling, with weights set as ω 1  = 0.8 and ω 2  = 0.2. As shown in Fig.  8 , during the pre-training stage (steps 0–50), our proposal and the version without INEM exhibit similar convergence trends. However, our model shows superior performance compared to the control group. This might attribute to the fact that the model with the IENM module has more parameters, a relatively complex structure, i.e., higher model fitting capacity, resulting in a better fit to the pre-training data. Furthermore, in the training stage (steps 51–100), our proposal demonstrates significant fluctuation in the optimal weighted criterion sampled at different time points compared to the control group. This fluctuation stabilizes after a certain period. This phenomenon is attributed to the Noisy Linear Layer embedded in the INEM module, which introduces learnable noise following a normal distribution. In the early stages of model training, these noise in Noise Linear Layer guides the model to explore the solution space thoroughly. By leveraging the scheduling order fine-tuning algorithm, the model can explore strategies with better scheduling results. The trends in the curve from step 70 to step 100 indicate that the model acquires the capability to generate high-quality scheduling strategies. Moreover, the change in the weighted criterion becomes gradually smoother, possibly because the model adapts to the impact of learnable noise and could effectively removing non-critical information from the state features for generating optimal scheduling strategies. These crucial factors contribute to the superiority of INEM over the control group.

The results of the ablation for INEM

We compare the proposed improved noisy-based exploring module with the ε -greedy and Boltzmann probability, where the ε -greedy based algorithm is to select an action with the optimal Q-value by a probability ε , and select the actions randomly by a probability 1– ε . In the Boltzmann probability, the selection probability of each action is proportional to its Q-value, The Boltzmann probability of an action is shown as \(pt(a|st) = e^{Q(st,a)} /\sum\nolimits_{a} {e^{Q(st,a)} }\) where the p t (a |s t ) denotes the selection probability of action a in the state s t and the e denotes the Euler’s number (which equals to 2.71828).

The Fig.  9 shows the results of the comparison for different exploration mechanism ( ε -greedy, Boltzmann probability and our proposal). It can be inferred that the epsilon-greedy based exploration mechanism is less capable of exploring on larger scale action spaces than the other two approaches. This may be because this method only considers a simple trade-off between "utilization" and "exploration", and the actual environmental information is not considered in the exploration stage. As can be seen in the green part of the figure, in a large-scale solution space, the Boltzmann probability-based exploration mechanism tends to explore more solutions in the space (i.e., it is able to search a much larger solution space than the epsilon-greedy-based method). This is reflected in the larger fluctuations in the reward values obtained from the environment during the search stage. However, this property might introduce instability to problems with large solution spaces. Unlike the first two classes of traditional methods, our proposed module has a gentler character in the exploration stage from an overall perspective. Additionally, the final exploration results are better compared to the two types of traditional schemes. This may be since the model directly adds noise to the states during the exploration of the solution space, which on the one hand introduces randomness, and on the other hand the model adapts to the effects brought by the noise as it approaches convergence. This indirectly leads to a strong adaptive ability of the model, which makes the model perform relatively well in solving problems concerning large-scale action space exploration.

The result of weighted reward comparison

Dueling block

For exploring the advantages of the proposed advantage-value module, a group of comparison experiments is conducted. In this experiment, the dueling block is replaced by the fully connected layers.

The structure of the compared model has similarities compare to the original however, the part of value-module is eliminated. Therefore, it can be viewed as a DQN-shaped structure. The experiment result is collectively shown as the Table  4 .

It can be concluded that our proposed structure performs better than the conventional DQN for large-scale EV charging scheduling. This may be due to the decoupling of Q- values by the dueling structure. This makes the advantage value, which really reflects the importance of the action, separated from the original Q-value, as well as the network is used to predict the state value more specialized, which also enhances the ability to fit the actual state value function at same time.

To validate the effect of the Dueling Block on improving the accuracy of Q-value evaluation, we conducted further ablation experiments, with results presented in rows 1 and 3 of Table  5 . The experimental findings indicate that removing the Dueling module resulted in a 16% increase in the weighted reward corresponding to the scheduling policies generated by the model compared to the control group. This suggests that simply using the output of the noise layer as Q -values cannot meet the accuracy requirements for predicting state-action values. On the other hand, experimentally, both the Dueling Block and the CNN module were able to reasonably predict Q-values and maintain their results within appropriate ranges. However, there was variation in prediction accuracy, with a difference of approximately 1.8% observed in the evaluation metrics corresponding to the optimal scheduling strategy for large-scale electric vehicle charging. This indicates that in larger-scale electric vehicle charging scheduling scenarios, our proposed architecture demonstrates a more pronounced advantage, generating strategies more suitable for large-scale electric vehicle charging scheduling.

Case study III

In this case study, we demonstrate the advantages of our proposal over other EV charging scheduling algorithms in our scheduling scenarios and investigate the mechanism of solution space exploration. To achieve this, we surveyed six categories (consisting of fourteen kinds) of algorithms. The aim was to assess their effectiveness in generating feasible EV charging scheduling plans. We conducted rigorous experiments on all these algorithms within our carefully designed EV charging scheduling environment. The summarized results of all comparison experiments can be found in Table  5 .

From Table  5 , it is evident that experiments 1 and 2 yield poorer scheduling performance compared to the others. This suggests that these two algorithms result in a gathering of EVs at the charging station, leading to longer average queuing times. Different from our proposal, solely considering the user or the charging service provider for charging scheduling may overlook global information, resulting in subpar performance of the scheduling strategy generated. Among experiments 3, 4, and 5, there is a notable improvement in EV charging scheduling results compared to experiments 1 and 2. This indicates that the GA-based algorithm effectively addresses the problem. However, searching through the vast solution space with GA may lead to local optima or slow search speeds. The EDA-based algorithm (lines 6 and 7 in Table  5 ) demonstrates better results in solution space exploration. Nevertheless, increasing the number of iterations does not necessarily yield better results for large-scale EV charging scheduling (as observed in experiments 6 and 7, where more iterations led to worse scheduling results). This suggests instability in the EDA-GA based algorithm when tackling such problems. Despite the potential for better solutions with more iterations, the long runtime for solution space exploration is impractical for real-time applications. We further tested the EDA-GA based algorithm with more than 3000 iterations, such as 3500 and 5000. Although some experiments showed improved results, the extended runtime remains a barrier for practical application.

Clearly, the DRL/RL based algorithm proves to be more effective than other algorithms. In the realm of electric vehicle (EV) charging scheduling, deep reinforcement learning (DRL) methods exhibit significant advantages over genetic algorithms (GAs), dispatching rules, and other conventional methods. Firstly, DRL autonomously explores optimal charging strategies through continual trial and error learning, effectively adapting to intricate and ever-changing environments and requirements. In contrast, GAs necessitates evaluating numerous individuals in each generation and rely on randomness to explore solution spaces, potentially resulting in inefficient exploration particularly in high-dimensional and complex problem domains. Dispatching rules, often based on static rules or heuristic methods, lack the flexibility to adjust to real-time changes. Secondly, DRL methods dynamically adjust strategies based on environmental feedback, facilitating adaptation to fluctuating charging demands and grid conditions, thereby enhancing charging efficiency and grid utilization. This dynamic adaptability is lacking in traditional approaches. Consequently, RL offers superior adaptability and efficiency in EV charging scheduling, better aligning with practical application requirements.

For instance, when comparing scheduling outcomes in similar scenarios, such as our observations from experiments 11 and 6, we found that scheduling strategies based on reinforcement learning methods achieve computational speeds approximately 47 times faster than other methods when addressing the large-scale electric vehicle charging scheduling problem. This finding isn't merely reflective of a single experimental result but has been validated through multiple repeated experiments. Moreover, our approach notably outperforms other prominent reinforcement learning-based scheduling algorithms, especially those based on Deep Q-Networks (DQN) and Deep Deterministic Policy Gradients (DDPG). The superiority of our approach can be attributed to several key factors. Firstly, our model incorporates a refined feature extraction module, significantly enhancing the model's capability to extract state features. By fully leveraging this refined state feature extraction module, coupled with pre-training and constrained solution space exploration, our method efficiently explores the solution space while mitigating the issue of excessive randomization. Secondly, we judiciously decompose the actual Q-values, enabling the model to understand the value of each state more accurately, thereby making more effective decisions when exploring the solution space. Such design choices result in our model performing commendably in addressing the large-scale electric vehicle charging scheduling problem. It's worth noting that compared to other reinforcement learning methods, such as Advantage Actor-Critic (A2C) based on policy gradient methods, our proposed approach still holds a slight advantage. This observation underscores the practicality and efficiency of our method over A2C in the field of electric vehicle scheduling. This is because our proposed model architecture bears similarity to the A2C method in predicting Q-values, whereby rational decomposition of Q -values enhances model stability and prediction accuracy. However, in addition, effective exploration mechanisms and a sound understanding of state features within the vast state space are more advantageous for the model to attain optimal solutions compared to traditional Actor-Critic frameworks.

In our study, we conducted experiments comparing the use of Multi-Agent Reinforcement Learning (MARL) and Single-Agent Reinforcement Learning methods for addressing the large-scale electric vehicle (EV) charging scheduling problem. Surprisingly, the experimental results indicated that the MARL-based approach did not exhibit the anticipated superiority in solving this problem and, in fact, performed worse compared to the Single-Agent Reinforcement Learning method. This outcome may stem from the inherent complexity of the problem itself and the associated technical challenges. Firstly, the involvement of numerous electric vehicles in large-scale EV systems led to a proportional increase in the number of agents within the MARL framework. As the number of agents increased, the complexity of interactions within the system grew exponentially. Seeking the optimal scheduling strategy inevitably introduced additional interaction parameters among the agents. However, these supplementary interaction parameters often did not directly correlate with the essence of the problem but rather augmented the computational complexity and uncertainty of the system. Furthermore, the collaboration and competition dynamics inherent in multi-agent systems may have contributed to the performance degradation. When addressing the EV charging scheduling problem, individual agents may engage in competition due to conflicting interests, thereby resulting in instability, and decreased overall system performance. In contrast, our proposal offered a more straightforward approach, enabling more effective exploration of the optimal solution within the solution space and avoiding the complexities of interactions and competition present in multi-agent systems.

Additionally, given the widespread application of Long Short-Term Memory (LSTM) in decision problems involving time series data, we conducted a comparative analysis of our proposal against several LSTM-based decision models (Experiment 12 and Experiment 13). In the control experiments, considering the characteristics of LSTM and the electric vehicle charging scheduling problem, we utilized these models for decision-making regarding the sequence of electric vehicle scheduling, while maintaining the original charging station selection network unchanged. The experimental results, as presented in the "Other" column of Table  5 , indicate that Algorithms 12 and 13 achieved results like our proposal. However, models based on the INEM module exhibited a more thorough exploration of the solution space, particularly in generating optimal strategies for EV charging schedules. This might be attributed to the fact that, in the context of EV charging scheduling problems, the design of states incorporates current global information. On the other hand, LSTM-based models, in the process of addressing sequential decision-making problems, appropriately utilize memory gates to retain information from the previous state. Due to this, the combination of this information with the current state might adversely impact the accuracy of the Q-value prediction module, potentially hindering the overall accuracy of Q-value predictions. From an experimental standpoint, it is observed that algorithm 12 and 13 exhibit slightly longer inference speeds compared to our proposal. Consequently, our proposal demonstrates a superior advantage in exploring the solution space.

Based on the three proposed modules, we further investigate the mechanism of action space exploration. As illustrated in Fig.  10 , the training process of our proposed model can be divided into two parts: the pre-training stage and the training stage with exploration. During the pre-training stage, the EV charging service quality, represented as the weighted sum of the average queueing time of EVs and the average idling time of charging stations, shows a gradual improvement for the solutions (depicted as blue dots). This improvement suggests that the model's performance in electric vehicle scheduling tasks has been enhanced through pre-training. The solutions tend to concentrate within the solution space and gradually extend towards the optimal solution (represented by the blue dot). This observation indicates that training the model using pretraining samples obtained from better-performing trajectories can expedite the model's training progress in the initial stage. However, as depicted in the figure, it can be concluded that solely conducting pre-training may result in a limited exploration of the solution space. During the model's training and exploration stages (represented by yellow dots), the positions of these solutions obtained through our model exhibit relatively more dispersion. This dispersion signifies that sufficient exploration of the solution space has taken place during the model training process. In summary, the pre-training stage contributes to the initial performance improvement of the model in EV scheduling tasks. While pre-training accelerates the training speed and leads to concentrated solutions, further training and exploration stages are essential for achieving a more diverse and comprehensive exploration of the solution space. This two-stage training approach and our proposed architecture/modules ensure thorough exploration of solutions and enhance the algorithm’s capability to find optimal solutions for EV scheduling.

The pattern for exploration

The advantage of our model lies in the appropriate combination of the proposed three modules i.e., the fine-grained features extraction module (FFEM), the Improved noisy-based exploring module (INEM) and the dueling block. The model utilizes the fine-grained features extraction module and the dueling block to efficiently extract state features to fit the empirical data to roughly determine the approximate location of the subspace where the optimal solution is located. Based on this, the model introduces constrained noise through the improved noisy-based exploring module in the training stage to help the model explore the subspace adequately. In this process, our proposed an effective empirical filtering strategy (refer to the line 20–21 in Algorithm 2 ) which ensures that the model can explore the solution space and identifies the location of the optimal solution by iteratively. The reasonable combination of the three main modules in the training process can enable the model to efficiently obtain the global optimal solution in a large-scale solution space (This phenomenon can be well verified in Fig.  10 ). Unlike our proposal, the swarm intelligence algorithm can only continue to explore those subspaces that have already been explored. This model has some drawbacks in the search of global optimal solutions, i.e., the swarm intelligence algorithm can only generate new solutions based on the existing solutions through basic operations (e.g., crossover or mutation operation in genetic algorithms), which is relatively easy to ignore the subspace of the global optimal solutions.

Based on the analysis, our proposed model helps to improve the current large-scale EV charging efficiency and has higher execution efficiency compared to traditional algorithms as well as other reinforcement learning based algorithms. This has an enlightening significance for further research on large-scale electric vehicle charging scheduling methods in more complex scenarios.

The growing significance of large-scale EV charging scheduling challenges across diverse scenarios underscores the urgent need for effective solutions in this domain. In this study, we introduce a novel model architecture tailored specifically to tackle the complexities inherent in large-scale EV charging scheduling. Our approach revolves around the creation of two distinct state representations encapsulating the global scheduling information. Furthermore, we introduce a performance metric aimed at quantifying the quality of EV charging service. To optimize scheduling performance, we employ the Fine-Grained Feature Extraction Module (FFEM), the Improved Noise-Based Exploration Module (INEM), and a dueling block for enhancing feature extraction, solution space exploration ability, and Q-value prediction accuracy, respectively. To ensure effective model training, we propose a two-stage algorithm encompassing model pretraining proficient trajectory sampling, and action space exploration.

The effectiveness of our proposed methodology is rigorously demonstrated through three comprehensive case studies. Our experimental findings clearly indicate that our approach excels in generating optimal EV charging schedules, outperforms existing methodologies in terms of efficiency and effectivity. Overall, our proposal furnishes valuable insights for large-scale EV charging scheduling service providers and furnishes a roadmap for addressing challenges characterized by extensive action spaces using Deep Reinforcement Learning (DRL) techniques.

Our future research endeavors will be geared towards further enhancing the performance of the EV charging algorithm. By focusing on improving computational efficiency and optimizing the scheduling process, we aim to elevate the overall efficiency and effectiveness of EV charging services.

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This work was supported by the Scientific Research Funds of Northeast Electric Power University (No. BSZT07202107) and the science and technology development program of Jilin province (No. 20240101362JC).

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Han, Y., Li, T. & Wang, Q. A DQN based approach for large-scale EVs charging scheduling. Complex Intell. Syst. (2024). https://doi.org/10.1007/s40747-024-01587-w

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Received : 16 December 2023

Accepted : 06 July 2024

Published : 21 August 2024

DOI : https://doi.org/10.1007/s40747-024-01587-w

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