Multiple objective probabilistic branch and bound for Pareto optimal approximation

We present a multiple objective simulation optimization algorithm called multiple objective probabilistic branch and bound (MOPBnB) with the goal of approximating the efficient frontier and the associated Pareto optimal set in the solution space. MOPBnB is developed for both deterministic and noisy problems with mixed continuous and discrete variables. When the algorithm terminates, it provides a set of non-dominated solutions that approximates the Pareto optimal set and the associated objective function estimates that approximate the efficient frontier. The quality of the solutions is statistically analyzed using a measure of distance between solutions to the true efficient frontier. We also present numerical experiments with benchmark functions to visualize the algorithm and its performance.