Multi-objective optimization using statistical models

Tsionas, M.G. (2019) Multi-objective optimization using statistical models. European Journal of Operational Research, 276 (1). pp. 364-378. ISSN 0377-2217

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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.

Item Type:
Journal Article
Journal or Publication Title:
European Journal of Operational Research
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1802
Subjects:
ID Code:
132183
Deposited By:
Deposited On:
27 Mar 2019 11:20
Refereed?:
Yes
Published?:
Published
Last Modified:
24 Nov 2020 07:19