A discussion of scalarization techniques for multiple objective integer programming |
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Authors: | Matthias Ehrgott |
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Institution: | (1) Department of Engineering Science, The University of Auckland, Private Bag, 92019 Auckland, New Zealand |
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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.
This research is partially supported by University of Auckland grant 3602178/9275 and by the Deutsche Forschungsgemeinschaft
grant Ka 477/27-1. |
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Keywords: | Multiobjective optimization Integer programming Scalarization Lagrangian duality Elastic constraints Crew scheduling |
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