A stochastic-kriging-based multiobjective simulation optimization algorithm

Abstract

We consider the multiobjective simulation optimization problem, where we seek to find the non-dominated set of designs evaluated using noisy simulation evaluations, in the context of numerically expensive simulators. We propose a metamodel-based scalarization approach built upon the famous ParEGO algorithm. Our approach mainly differentiates from ParEGO and similar algorithms in that we use stochastic kriging, which explicitly characterizes both the extrinsic uncertainty of the unknown response surface, and the intrinsic uncertainty inherent in a stochastic simulation. We additionally integrate the Multiobjective Optimal Computing Budget Allocation ranking and selection procedure in view of maximizing the probability of selecting systems with the true best expected performance. We evaluate the performance of the algorithm using standard benchmark test functions for multiobjective optimizers, perturbed by heterogeneous noise. The experimental results show that the proposed method outperforms its deterministic counterpart based on well-known quality indicators and the fraction of the true Pareto set found.