Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization

B.L. Gorissen, D. den Hertog

Research output: Working paperDiscussion paperOther research output

10 Citations (Scopus)
321 Downloads (Pure)

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

Keywords

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

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