Optimal computing budget allocation for selecting the optimal subset of multi-objective simulation optimization problems

Abstract

This study aims to develop an efficient budget allocation procedure for the problem of selecting an optimal subset of designs from a finite number of alternative designs in stochastic environments. The optimal subset might contain more alternative designs beyond the Pareto optimal ones. In this study, we adopt the Pareto rank to measure the performance of each design and define the optimal subset. Our objective is to minimize the probability that the optimal subset is falsely selected within a fixed limited simulation budget. We propose an upper bound of the probability of false selection and derive an asymptotically optimal simulation budget allocation rule based on the large deviation theory. We also provide some useful insights into how the simulation budget can be allocated to identify the optimal subset. The proposed budget allocation algorithm is compared with existing methods through numerical experiments, and the results show the efficiency of our proposed algorithm.