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Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization

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  • Gorissen, B.L.
  • Hertog, D. den

    (Tilburg University, Center for Economic Research)

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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.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-031.

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    Date of creation: 2012
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    Handle: RePEc:dgr:kubcen:2012031

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    Web page: http://center.uvt.nl

    Related research

    Keywords: Pareto set; multiobjective; polynomial inner approximation; robust optimization; polynomial optimization; SOS;

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    1. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3736413, Tilburg University.
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