Approximating the Pareto Set of Multiobjective Linear Programs Via Robust Optimization

CentER Discussion Paper Series No. 2012-031

14 Pages Posted: 13 Apr 2012

See all articles by Bram Gorissen

Bram Gorissen

Tilburg University - Tilburg University School of Economics and Management

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: April 12, 2012

Abstract

The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main difference with existing techniques is that we optimize a single (extended) optimization problem that provides a polynomial approximation whereas existing methods iteratively construct a piecewise linear approximation. The proposed method has several advantages, e.g. it is more useful for visualizing the Pareto set, it can give a local approximation of the Pareto set, and it can be used for determining the shape of the Pareto set.

Keywords: Pareto set, multiobjective, polynomial inner approximation, robust optimization

JEL Classification: C61

Suggested Citation

Gorissen, Bram and den Hertog, Dick, Approximating the Pareto Set of Multiobjective Linear Programs Via Robust Optimization (April 12, 2012). CentER Discussion Paper Series No. 2012-031. Available at SSRN: https://ssrn.com/abstract=2038741 or http://dx.doi.org/10.2139/ssrn.2038741

Bram Gorissen (Contact Author)

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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