Multi-objective retrospective optimization using stochastic zigzag search

We propose a new retrospective optimization (RO) method for multi-objective simulation optimization (MOSO) problems. RO algorithms generate a sequence of sample-path (SP) problems and solve these SP problems iteratively using a nonlinear optimizer. In this study, a stochastic zigzag search algorithm is chosen in the RO framework to solve SP problems. The key idea of zigzag search is searching around the Pareto front by applying an efficient local-search procedure using the gradients of the objective functions. Many continuous MOSO problems have smooth objective functions and their non-dominated objective function values form a smooth surface in the image space. This fact motivates developing the zigzag search method embedded in RO for such relatively well-posed MOSO problems. A numerical implementation of this method multi-objective retrospective optimization using zigzag search (MOROZS) is presented particularly for continuous bi-objective simulation optimization (BOSO) problems with well-connected Pareto optimal solutions. MOROZS is designed for BOSO problems in which a simulation oracle returns both objective function values and gradients. Due to the local nature of zigzag search, MOROZS- can only guarantee the asymptotic convergence to local Pareto optimality. The efficiency of MOROZS is studied using three BOSO problems with noisy objective functions and is compared to that of Genetic Algorithms based NSGA-II and a recently developed method MO-COMPASS. (C) 2017 Elsevier B.V. All rights reserved.