Robust simulation-based optimization for multiobjective problems with constraints

This study proposes a constrained multiobjective robust simulation optimization (CMRSO) method to address black-box problems with multiple objectives and constraints under uncertainties, especially when multiple objectives and constraints are evaluated by costly simulations. Neighborhood exploration is first performed for each iterate to search for its infeasible neighbors and worst-case feasible neighbors with the help of kriging surrogate models of constraints and multiple objectives. Next, a local move direction and a proper step size are determined to obtain an updated iterate that stays away from previous infeasible neighbors and worst-case feasible neighbors. These two steps are repeated until no feasible local move direction exists or the computational budget is exhausted. By evolving iteratively and independently from a set of initial solutions, multiple final solutions will generate a set of robust efficient solutions. Finally, the CMRSO method is applied to a synthetic constrained biobjective optimization problem and a network-wide signal timing simulation optimization (SO) problem under cyber-attacks. Our study shows the effectiveness of CMRSO even with a limited computational budget, indicating that it may be a promising tool for solving simulation-based problems with multiple objectives and constraints under uncertainties.