A discussion of scalarization techniques for multiple objective integer programming

A discussion of scalarization techniques for multiple objective integer programming

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Article ID: iaor20072088
Country: Germany
Volume: 147
Issue: 1
Start Page Number: 343
End Page Number: 360
Publication Date: Oct 2006
Journal: Annals of Operations Research
Authors:
Keywords: programming: integer, personnel & manpower planning
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.

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