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Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization
Gorissen,B.L. den Hertog,D.
Gorissen,B.L.
den Hertog,D.
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.
Description
Subsequently published in Operations Research Letters (2012) Pagination: 14
Date
2012
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Publisher
Operations research
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2012-031.pdf
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Keywords
Pareto set, multiobjective, polynomial inner approximation, robust optimization, polynomial optimization, SOS, C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis
Citation
Gorissen, B L & den Hertog, D 2012 'Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization' CentER Discussion Paper, vol. 2012-031, Operations research, Tilburg.
License
info:eu-repo/semantics/restrictedAccess