Dynamic Stratification and Post-Stratified Adaptive Sampling for Simulation Optimization

Post-stratification is a variance reduction technique that groups samples in respective strata only after collecting the samples randomly. We incorporate this technique within an adaptive sampling procedure in simulation optimization. We use concomitant variables to increase the accuracy of our proposed post-stratified adaptive sampling. Concomitant variables are auxiliary variables in simulation that approximate the boundaries of the optimal strata at each visited solution during the optimization procedure. A linear relationship between the concomitant variable and the output is desirable but not necessary for the effectiveness of the proposed methodology. In numerical experiments, we observe that performing post-stratified adaptive sampling with dynamically updated strata boundaries robustifies the algorithm in the sense that it reduces the algorithm’s sensitivity to the initial solution and solver input parameters.