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Improved ε-Constraint Method for Multiobjective Programming

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  • M. Ehrgott

    (University of Auckland
    Université de Nantes)

  • S. Ruzika

    (Technische Universität Kaiserslautern)

Abstract

In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the ε-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables. We prove results on (weakly, properly) efficient solutions. The improved ε-constraint method that we propose combines both modifications.

Suggested Citation

  • M. Ehrgott & S. Ruzika, 2008. "Improved ε-Constraint Method for Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 375-396, September.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:3:d:10.1007_s10957-008-9394-2
    DOI: 10.1007/s10957-008-9394-2
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    1. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
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