TY - JOUR

T1 - Multi-objective optimization using statistical models

AU - Tsionas, M.G.

N1 - 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

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - Bayesian analysis

KW - Decision analysis

KW - Markov chain Monte Carlo

KW - Minimax regret

KW - Multi-objective optimization

KW - Data envelopment analysis

KW - Decision theory

KW - Financial data processing

KW - Linear programming

KW - Markov processes

KW - Monte Carlo methods

KW - Bayesian Analysis

KW - Generalized data envelopment analysis

KW - Markov chain monte carlo simulation

KW - Markov Chain Monte-Carlo

KW - Mean absolute deviations

KW - Multi-objective optimization problem

KW - Portfolio optimization

KW - Multiobjective optimization

U2 - 10.1016/j.ejor.2018.12.042

DO - 10.1016/j.ejor.2018.12.042

M3 - Journal article

VL - 276

SP - 364

EP - 378

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -