Multi-objective simulation optimization on finite sets: Optimal allocation via scalarization

We consider the multi-objective simulation optimization problem on finite sets, where we seek the Pareto set corresponding to systems evaluated on multiple performance measures, using only Monte Carlo simulation observations from each system. We ask how a given simulation budget should be allocated across the systems, and a Pareto surface retrieved, so that the estimated Pareto set minimally deviates from the true Pareto set according to a rigorously defined metric. We show that the optimal simulation budget allocation under such scalarization is the solution to a bi-level optimization problem, for which the outer problem is concave, but some inner problems are non-convex.