A multiobjective stochastic simulation optimization algorithm

Abstract

The use of kriging metamodels in simulation optimization has become increasingly popular during re- cent years. The majority of the algorithms so far uses the ordinary (deterministic) kriging approach for constructing the metamodel, assuming that solutions have been sampled with infinite precision. This is a major issue when the simulation problem is stochastic: ignoring the noise in the outcomes may not only lead to an inaccurate metamodel, but also to potential errors in identifying the optimal points among those sampled. Moreover, most algorithms so far have focused on single-objective problems. In this ar- ticle, we test the performance of a multiobjective simulation optimization algorithm that contains two crucial elements: the search phase implements stochastic kriging to account for the inherent noise in the outputs when constructing the metamodel, and the accuracy phase uses a well-known multiobjec- tive ranking and selection procedure in view of maximizing the probability of selecting the true Pareto- optimal points by allocating extra replications on competitive designs. We evaluate the impact of these elements on the search and identification effectiveness, for a set of test functions with different Pareto front geometries, and varying levels of heterogeneous noise. Our results show that the use of stochastic kriging is essential in improving the search efficiency; yet, the allocation procedure appears to lose ef- fectiveness in settings with high noise. This emphasizes the need for further research on multiobjective ranking and selection methods.