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.