An Integrated Response-Surface-Based Method for Simulation Optimization with Correlated Outputs

Abstract

While nearly all previous algorithms designed to solve simulation optimization problems have treated the outputs of simulation systems at a given design point (input parameter) as being independent of each other, this premise is flawed in that simulated outputs are generally correlated. We propose a decorrelation (DC) procedure that can effectively evaluate and remove the correlation of outputs of a simulation system. The proposed DC procedure is further integrated with STRONG, an improved framework of the well-known Response Surface Methodology (RSM), for tackling the simulation optimization problems with correlated outputs. This integration is particularly synergistic due to the fact that STRONG is a fully automated, response-surface-based procedure possessing appealing convergence properties and DC can take advantage of the concept of trust region as in STRONG to enable the removal of the correlation of outputs at the design points within the same trust region all at once. This is more efficient compared to the traditional approaches where a substantial number of observations are typically required for dealing with correlations. The resulting integrated method, which we call STRONG-DC, requires various adaptations so as to ensure the efficacy and efficiency of the overall framework. STRONG-DC preserves the desirable automation and convergence as STRONG, namely, it does not require human involvements and can be proved to achieve the truly optimal solution(s) with probability one (w.p.1) under reasonable conditions. Moreover, the effectiveness and efficiency of STRONG-DC are evaluated through extensive numerical analyses, along with a case study involving the well-known newsvendor problem.