Optimal sampling laws for bi-objective simulation optimization on finite sets

We consider the bi-objective simulation optimization (SO) problem on finite sets, that is, an optimization problem where for each “system,” the two objective functions are estimated as output from a Monte Carlo simulation. The solution to this bi-objective SO problem is a set of non-dominated systems, also called the Pareto set. In this context, we derive the large deviations rate function for the rate of decay of the probability of a misclassification event as a function of the proportion of sample allocated to each competing system. Notably, we account for the presence of dependence between the estimates of each system's performance on the two objectives. The asymptotically optimal allocation maximizes the rate of decay of the probability of misclassification and is the solution to a concave maximization problem.