Efficient Sampling When Searching for Robust Solutions
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In the presence of noise on the decision variables, it is often desirable to find robust solutions, i.e., solutions with a good expected fitness over the distribution of possible disturbances. Sampling is commonly used to estimate the expected fitness of a solution; however, this option can be computationally expensive. Researchers have therefore suggested to take into account information from previously evaluated solutions. In this paper, we assume that each solution is evaluated once, and that the information about all previously evaluated solutions is stored in a memory that can be used to estimate a solution’s expected fitness. Then, we propose a new approach that determines which solution should be evaluated to best complement the information from the memory, and assigns weights to estimate the expected fitness of a solution from the memory. The proposed method is based on the Wasserstein distance, a probability distance metric that measures the difference between a sample distribution and a desired target distribution. Finally, an empirical comparison of our proposed method with other sampling methods from the literature is presented to demonstrate the efficacy of our method.
KeywordsFitness Evaluation Robust Solution Latin Hypercube Sampling Final Solution Selection Small Approximation Error
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