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Last updated on 2024年6月3日

How do you compare and evaluate different scenario reduction methods in terms of accuracy and efficiency?

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Scenario reduction methods are techniques that reduce the number of possible future outcomes in a stochastic optimization problem, to make it more tractable and computationally efficient. However, different methods may have different impacts on the accuracy and quality of the optimal solution. In this article, you will learn how to compare and evaluate different scenario reduction methods in terms of accuracy and efficiency.

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1 Accuracy measures

One way to measure the accuracy of a scenario reduction method is to compare the optimal objective value and the optimal decision variables obtained from the reduced scenario set with those obtained from the original scenario set. This can be done by calculating the relative error, the absolute error, or the optimality gap. Another way to measure the accuracy is to compare the probability distributions of the objective value and the decision variables under the reduced scenario set with those under the original scenario set. This can be done by using statistical tests, such as the Kolmogorov-Smirnov test, the Chi-square test, or the Wasserstein distance.

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Ali PapiRAD

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Sample average approximation (SAA) can also be viewed as a scenario reduction method. Recently, machine learning-based methods for data-driven scenario generation (e.g., Fuzzy C-Means (FCM) or Support Vector Classification (SVC)) have gained popularity in the context of data-driven distributionally robust optimization, which embeds robust optimization principles into the stochastic programming approach.

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Warren Powell

Professor Emeritus, Princeton University/ Co-Founder, Optimal Dynamics/ Executive-in-Residence Rutgers Business School
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This is the classical way the stochastic programming community approaches this problem, and it is fundamentally flawed. The correct approach is to recognize that a stochastic program is a lookahead policy using a two-stage approximation. This policy has to be tested in a simulator, where the policy is used many times to test how well it makes decisions over time. It is important that the simulator be as realistic as possible, recognizing that the lookahead models in a stochastic program are almost always simplified representations.

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2 Efficiency measures

One way to measure the efficiency of a scenario reduction method is to compare the computational time and the memory requirements needed to solve the optimization problem with the reduced scenario set and with the original scenario set. This can be done by using benchmarks, such as the CPLEX solver, the GAMS software, or the Python libraries. Another way to measure the efficiency is to compare the scalability and the robustness of the scenario reduction method with respect to the size and the complexity of the problem, the number and the type of scenarios, and the level of uncertainty and variability.

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3 Common methods

Scenario reduction methods are used to reduce the number of scenarios for optimization. Forward selection begins with an empty set and adds dissimilar scenarios until a desired size is reached. Backward selection removes least important scenarios based on a sensitivity measure. Clustering groups scenarios into clusters based on similarity, then selects one representative from each cluster. Sampling randomly selects scenarios from the original set, based on a probability measure like uniform distribution or importance sampling.

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4 Comparison criteria

To compare and evaluate different scenario reduction methods, you need to consider criteria such as the objectives and constraints of the optimization problem, the nature and structure of the scenarios, the trade-off between accuracy and efficiency, and the performance and reliability of the methods. The method chosen should take into account whether the problem is linear, nonlinear, convex, or nonconvex; if it has equality or inequality constraints; if it involves discrete, continuous, or mixed scenarios; and if it has correlation, dependence, or hierarchy. Additionally, you should consider which method is more accurate yet efficient for your problem characteristics and scenario features. Furthermore, you should consider which method has better empirical results or theoretical guarantees than others, or is more consistent or stable across different problems and scenarios.

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Warren Powell

Professor Emeritus, Princeton University/ Co-Founder, Optimal Dynamics/ Executive-in-Residence Rutgers Business School
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This paragraph is completely ignoring the fact that a stochastic program is a policy for making decisions in some sequential decision problem. Policies are best evaluated using simulators. The opening sentence of this paragraph is completely misguided. Again, please see chapter 19 of https://tinyurl.com/RLandSO/

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5 Evaluation tools

To compare and evaluate different scenario reduction methods, you can use tools such as simulation, optimization, and visualization. Simulation allows you to compare the outcomes of the optimization problem based on statistics like mean, variance, confidence interval, and risk measure. Optimization helps to compare solutions by looking at objective value, decision variables, feasibility, and optimality. Visualization provides insight into scenario sets and solutions by examining patterns such as distribution, shape, diversity, and similarity.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Rohit Gawli

Product @ DoubleVerify | Co-Founder @Lokal Kitchen | Product Enthusiast | Solving Business Problems through Analytics
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Robustness: A scenario reduction method's robustness can be assessed by how well it operates when used with various data sets or under various circumstances. A technique is deemed more robust if it regularly performs well across a variety of data sets and situations. Interpretability: A method is deemed more interpretable if it generates a condensed set of scenarios that stakeholders can quickly comprehend and interpret. Scalability: A scenario reduction method's capacity to handle big data sets and intricate models is referred to as scalability, a technique that works with big amounts of data sets and complex models without significant performance degradation is considered more scalable.

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How do you compare and evaluate different scenario reduction methods in terms of accuracy and efficiency?

1

2

3

4

5

6

1 Accuracy measures

2 Efficiency measures

3 Common methods

4 Comparison criteria

5 Evaluation tools

6 Here’s what else to consider

Operations Research

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How do you compare and evaluate different scenario reduction methods in terms of accuracy and efficiency?

1

2

3

4

5

6

1 Accuracy measures

2 Efficiency measures

3 Common methods

4 Comparison criteria

5 Evaluation tools

6 Here’s what else to consider

Operations Research

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