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

Tsionas, Efthymios (2017) A Bayesian approach to find Pareto optima in multiobjective programming problems using Sequential Monte Carlo algorithms. Omega: The International Journal of Management Science. ISSN 0305-0483

[img]
Preview
PDF (1-s2.0-S0305048317300051-main)
1_s2.0_S0305048317300051_main.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.

Download (707kB)
[img]
Preview
PDF (A Bayesian approach to multicriteria decision making)
A_Bayesian_approach_to_multicriteria_decision_making.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.

Download (398kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Omega: The International Journal of Management Science
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1802
Subjects:
ID Code:
86598
Deposited By:
Deposited On:
05 Jun 2017 09:28
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Sep 2020 03:55