Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization

B.L. Gorissen, D. den Hertog

Research output: Working paperDiscussion paperOther research output

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages14
Volume2012-031
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-031

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Polynomials
Polynomial approximation
Multiobjective optimization
Set theory

Keywords

  • Pareto set
  • multiobjective
  • polynomial inner approximation
  • robust optimization
  • polynomial optimization
  • SOS

Cite this

Gorissen, B. L., & den Hertog, D. (2012). Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization. (CentER Discussion Paper; Vol. 2012-031). Tilburg: Operations research.
Gorissen, B.L. ; den Hertog, D. / Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization. Tilburg : Operations research, 2012. (CentER Discussion Paper).
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author = "B.L. Gorissen and {den Hertog}, D.",
note = "Subsequently published in Operations Research Letters (2012) Pagination: 14",
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Gorissen, BL & den Hertog, D 2012 'Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization' CentER Discussion Paper, vol. 2012-031, Operations research, Tilburg.

Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization. / Gorissen, B.L.; den Hertog, D.

Tilburg : Operations research, 2012. (CentER Discussion Paper; Vol. 2012-031).

Research output: Working paperDiscussion paperOther research output

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N2 - 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.

AB - 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.

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Gorissen BL, den Hertog D. Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization. Tilburg: Operations research. 2012. (CentER Discussion Paper).