Approximating the Pareto set of multiobjective linear programs via robust optimization

B.L. Gorissen, D. den Hertog

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We consider problems with multiple 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. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.
Original languageEnglish
Pages (from-to)319-324
JournalOperations Research Letters
Volume40
Issue number5
DOIs
Publication statusPublished - 2012

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Pareto Set
Robust Optimization
Linear Program
Piecewise Linear Approximation
Polynomial
Polynomial Approximation
Linear Constraints
Polynomials
Polynomial approximation
Optimise
Optimization Problem
Set theory
Optimization
Pareto
Linear program
Robust optimization
Approximation

Cite this

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title = "Approximating the Pareto set of multiobjective linear programs via robust optimization",
abstract = "We consider problems with multiple 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. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.",
author = "B.L. Gorissen and {den Hertog}, D.",
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Approximating the Pareto set of multiobjective linear programs via robust optimization. / Gorissen, B.L.; den Hertog, D.

In: Operations Research Letters, Vol. 40, No. 5, 2012, p. 319-324.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Approximating the Pareto set of multiobjective linear programs via robust optimization

AU - Gorissen, B.L.

AU - den Hertog, D.

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PY - 2012

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N2 - We consider problems with multiple 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. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.

AB - We consider problems with multiple 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. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.

U2 - 10.1016/j.orl.2012.05.007

DO - 10.1016/j.orl.2012.05.007

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EP - 324

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

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