Polynomial Approximation for Multicriteria Combinatorial Optimization Problems

Eric Angel 1 Evripidis Bampis 2 Laurent Gourvès 3
1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
Abstract : Combinatorial optimization problems serve as models for a great number of real problems, and are studied in order to construct algorithms that are effective in terms of complexity and of the quality of the solutions returned. This chapter begins approximation algorithms with performance guarantees, it refer readers who want information on the other approaches to some publications and the references that they contain. The chapter contains a general presentation of multicriteria problems in combinatorial optimization, and tackles notions of optimality and of complexity. It presents four general approaches to polynomial approximation with performance guarantees. Furthermore, each approach is illustrated with an example from various publications. There are four of these approaches: the criteria weighting approach; the simultaneous approach; the budget approach; the Pareto curve approach. © ISTE Ltd 2014. All rights reserved.
Keywords : Budget approach Criteria weighting/Pareto curve Performance guarantee Polynomial approximation Multicriteria combinatorial
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Submitted on : Tuesday, December 17, 2013 - 9:43:03 AM
Last modification on : Thursday, March 21, 2019 - 12:59:01 PM

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Eric Angel, Evripidis Bampis, Laurent Gourvès. Polynomial Approximation for Multicriteria Combinatorial Optimization Problems. Vangelis Th. Paschos. Paradigms of Combinatorial Optimization: Problems and New Approaches: 2nd Edition, John Wiley & Sons, Inc., pp.511--545, 2014, 978-184821148-3. ⟨10.1002/9781118600207.ch16⟩. ⟨hal-00919601⟩

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