A stochastic-kriging-based multiobjective simulation optimization algorithm

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 SKMOCBA, a metamodel-based approach built upon the famous ParEGO algorithm. Our approach mainly differentiates from 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 (MOCBA) 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 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 members of the true Pareto set found. In addition, we measure the impact of using MOCBA to improve the accuracy of the algorithm during the identification of the observed Pareto front.