A unified robust optimization approach for problems with costly simulation-based objectives and constraints

Abstract

This study proposes a unified robust optimization approach to address min–max problems involving expensive simulation-based objectives and constraints impacted by implementation errors and parameter perturbations. This approach optimizes the worst-case scenarios of stochastic simulation responses across multiple evaluation criteria to achieve robust efficient solutions. It integrates multiple objectives and constraints into a cohesive framework, featuring a novel performance metric designed to rigorously assess solution quality. This metric can simplify the inner constrained multi-objective maximization problem into an unconstrained, stochastic, and single-objective minimization problem, based on which a softened condition is provided to identify robust efficient solutions. Then, these neighborhood exploration and robust local move mechanisms leverage infeasible neighbors’ information to guide the iterative solution process towards a globally robust efficient point. To mitigate computational costs, surrogate models of simulation-based objectives and constraints are utilized to guide the initial exploration of worst-case neighbors. The proposed approach’s effectiveness and superior performance are demonstrated through test results on four synthetic multi-objective robust optimization problems with constraints. Furthermore, the approach is utilized to design robust traffic signal timing plans under cyber-attacks and uncertain traffic volumes, yielding satisfactory results within limited simulation budgets. This approach presents a promising tool for addressing constrained multi-objective simulation-based optimization problems under uncertainty.