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A discussion of scalarization techniques for multiple objective integer programming

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  • Matthias Ehrgott

Abstract

In this paper we consider solution methods for multiobjective integer programming (MOIP) problems based on scalarization. We define the MOIP, discuss some common scalarizations, and provide a general formulation that encompasses most scalarizations that have been applied in the MOIP context as special cases. We show that these methods suffer some drawbacks by either only being able to find supported efficient solutions or introducing constraints that can make the computational effort to solve the scalarization prohibitive. We show that Lagrangian duality applied to the general scalarization does not remedy the situation. We also introduce a new scalarization technique, the method of elastic constraints, which is shown to be able to find all efficient solutions and overcome the computational burden of the scalarizations that use constraints on objective values. Finally, we present some results from an application in airline crew scheduling as evidence. Copyright Springer Science + Business Media, LLC 2006

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  • Matthias Ehrgott, 2006. "A discussion of scalarization techniques for multiple objective integer programming," Annals of Operations Research, Springer, vol. 147(1), pages 343-360, October.
    • Handle: RePEc:spr:annopr:v:147:y:2006:i:1:p:343-360:10.1007/s10479-006-0074-z
    DOI: 10.1007/s10479-006-0074-z
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    1. Gardiner, Lorraine R. & Steuer, Ralph E., 1994. "Unified interactive multiple objective programming," European Journal of Operational Research, Elsevier, vol. 74(3), pages 391-406, May.
    2. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
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