Estimation of the Pareto front in stochastic simulation through stochastic Kriging

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.