An Asymptotically Optimal Set Approach for Simulation Optimization

Abstract

We propose an asymptotically optimal set (AOS) approach for solving stochastic optimization problems with discrete or continuous feasible regions. Our AOS approach is a framework for designing provably convergent algorithms that are adaptive in seeking new points and in resampling or discarding already sampled points. The framework is an improvement over the adaptive search with resampling (ASR) method for stochastic optimization in that it spends less effort on inferior points and uses a more robust estimate of the optimal solution. We present conditions guaranteeing that the AOS approach is globally convergent and will eventually discard suboptimal sampled points with probability one, compare the algorithms, and analyze when (additional) resampling (beyond the minimum) is desirable. Our theoretical results show that AOS has stronger performance guarantees than ASR. Our numerical results suggest that AOS makes substantial improvements over ASR, especially for difficult problems with large numbers of local optima. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0811 .