Finding the non-dominated Pareto set for multi-objective simulation models

This article considers a multi-objective Ranking and Selection (R+S) problem, where the system designs are evaluated in terms of more than one performance measure. The concept of Pareto optimality is incorporated into the R+S scheme, and attempts are made to find all of the non-dominated designs rather than a single "best" one. In addition to a performance index to measure how non-dominated a design is, two types of errors are defined to measure the probabilities that designs in the true Pareto/non-Pareto sets are dominated/non-dominated based on observed performance. Asymptotic allocation rules are derived for simulation replications based on a Lagrangian relaxation method, under the assumption that an arbitrarily large simulation budget is available. Finally, a simple sequential procedure is proposed to allocate the simulation replications based on the asymptotic allocation rules. Computational results show that the proposed solution framework is efficient when compared to several other algorithms in terms of its capability of identifying the Pareto set.