Rights statement: 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
Accepted author manuscript, 691 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Rights statement: 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
Accepted author manuscript, 389 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -