Estimation of the Pareto front in stochastic simulation through stochastic Kriging

• Published in: Simulation modelling practice and theory 2017-12, Vol.79, p.69-86
• Main Authors: Zhang, Jianxia, Ma, Yizhong, Yang, Taho, Liu, Lijun
• Format: Article
• Language: English
• Subjects: Bootstrapping; Expected hypervolume improvement; Multi-objective simulation optimization; Pareto front; Probability of feasibility; Stochastic Kriging
• ISSN: 1569-190X; 1878-1462
• DOI: 10.1016/j.simpat.2017.09.006

•Solving constrained multi-objective simulation problems under limited costs.•Objective and constraint functions are emulated by stochastic Kriging models.•A sequential sampling strategy is proposed considering improvement and feasibility.•The variability of estimated Pareto front is quantified by nonparameter bootstrapping. Multi-objective optimization of simulated stochastic systems aims at estimating a representative set of Pareto optimal solutions and a common approach is to rely on metamodels to alleviate computational costs of the optimization process. In this article, both the objective and constraint functions are assumed to be smooth, highly non-linear and computationally expensive and are emulated by stochastic Kriging models. Then a novel global optimization algorithm, combing the expected hypervolume improvement of approximated Pareto front and the probability of feasibility of new points, is proposed to identify the Pareto front (set) with a minimal number of expensive simulations. The algorithm is suitable for the situations of having disconnected feasible regions and of having no feasible solution in initial design. Then, we also quantify the variability of estimated Pareto front caused by the intrinsic uncertainty of stochastic simulation using nonparametric bootstrapping method to better support decision making. One test function and an (s, S) inventory system experiment illustrate the potential and efficiency of the proposed sequential optimization algorithm for constrained multi-objective optimization problems in stochastic simulation, which is especially useful in Operations Research and Management Science.