A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms

Abstract

In this paper we consider a new approach to multicriteria decision making problems. Such problems are, usually, cast into a Pareto framework where the objective functions are aggregated into a single one using certain weights. The problem is embedded into a statistical framework by adopting a posterior distribution for both the decision variables and the Pareto weights. This embedding dates back to [25] but in this work we operationalize the concept further. We propose a Metropolis–Hastings and a Sequential Monte Carlo (SMC) to trace out the entire Pareto frontier and/or find the global optimum of the problem. We apply the new techniques to a multicriteria portfolio decision making problem proposed in [37] and to a test problem proposed by [27]. The good performance of new techniques suggests that SMC and other algorithms, like the classical Metropolis–Hastings algorithm, can be used profitably in the context of multicriteria decision making problems to trace out the Pareto frontier and/or find a global optimum. Most importantly SMC can be considered as an off-the-shelf technique to solve arbitrary multicriteria decision making problems routinely and efficiently.