Properties of Several Performance Indicators for Global Multi-Objective Simulation Optimization

We discuss the challenges in constructing and analyzing performance indicators for multi-objective simulation optimization (MOSO), and we examine properties of several performance indicators for assessing algorithms designed to solve MOSO problems to global optimality. Our main contribution lies in the definition and analysis of a modified coverage error; the modification to the coverage error enables us to obtain an upper bound that is the sum of deterministic and stochastic error terms. Then, we analyze each error term separately to obtain an overall upper bound on the modified coverage error that is a function of the dispersion of the visited points in the compact feasible set and the sampling error of the objective function values at the visited points. The upper bound provides a foundation for future mathematical analyses that characterize the rate of decay of the modified coverage error.