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  • paper_rev2_November_2018

    Rights statement: This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. 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 European Journal of Operational Research, 276, 1, 2019 DOI: 10.1016/j.ejor.2018.12.042

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Multi-objective optimization using statistical models

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/07/2019
<mark>Journal</mark>European Journal of Operational Research
Issue number1
Volume276
Number of pages15
Pages (from-to)364-378
Publication StatusPublished
Early online date11/01/19
<mark>Original language</mark>English

Abstract

In this paper we consider multi-objective optimization problems (MOOP) from the point of view of Bayesian analysis. MOOP problems can be considered equivalent to certain statistical models associated with the specific objectives and constraints. MOOP that can explore accurately the Pareto frontier are Generalized Data Envelopment Analysis and Goal Programming. In turn, posterior analysis of their associated statistical models can be implemented using Markov Chain Monte Carlo (MCMC) simulation. In addition, we consider the minimax regret problem which provides robust solutions and we develop similar MCMC posterior simulators without the need to define scenarios. The new techniques are shown to work well in four examples involving non-convex and disconnected Pareto problems and to a real world portfolio optimization problem where the purpose is to optimize simultaneously average return, mean absolute deviation, positive and negative skewness of portfolio returns. Globally minimum regret can also be implemented based on post-processing of MCMC draws. © 2019 Elsevier B.V.

Bibliographic note

This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. 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 European Journal of Operational Research, 276, 1, 2019 DOI: 10.1016/j.ejor.2018.12.042