Methods of Plausible Inference for Multi-Objective Simulation Optimization

We propose a class of output analysis methods for constructing confidence regions for the efficient set and the Pareto front of multi-objective simulation-optimization problems with structure. The methods take simulation runs at a small subset of solutions and leverage known or assumed properties of the objective functions, such as convexity and Lipschitz continuity. Inferring whether a given solution or vector of objectives belongs to the corresponding confidence region entails solving a mathematical program, the size of which scales with the dimension of the solution space, the number of simulated solutions, and the number of objectives. We explore the computational tractability of these optimization problems and approaches to accelerate the construction of the confidence regions or approximations thereof. Inference is accompanied by statistical guarantees, namely uniform confidence and consistency, the latter of which characterizes a confidence region’s ability to screen out dominated solutions or objective vectors as sample sizes increase. Numerical experiments demonstrate the effectiveness of the methods when exploiting different functional properties for an electricity procurement problem and apply them to a realistic supply chain logistics problem.