TY - JOUR

T1 - A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms

AU - Tsionas, Efthymios

N1 - This is the author’s version of a work that was accepted for publication in Omega. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Omega, ??, ??, 2017 DOI: 10.1016/j.omega.2017.05.009

PY - 2017/6/3

Y1 - 2017/6/3

N2 - 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.

AB - 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.

KW - Economics

KW - Multicriteria Decision Making

KW - Sequential Monte Carlo

KW - Global Optimization

KW - Portfolio Analysis

U2 - 10.1016/j.omega.2017.05.009

DO - 10.1016/j.omega.2017.05.009

M3 - Journal article

JO - Omega: The International Journal of Management Science

JF - Omega: The International Journal of Management Science

SN - 0305-0483

ER -