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

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.

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.

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.

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.