Representing the nondominated set in multi-objective mixed-integer programs

Ilgin Dogan, Banu Lokman*, Murat Koksalan

*Corresponding author for this work

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Abstract

In this paper, we consider generating a representative subset of nondominated points at a prespecified precision in multi-objective mixed-integer programs (MOMIPs). The number of nondominated points grows exponentially with problem size and finding all nondominated points is typically hard in MOMIPs. Representing the nondominated set with a small subset of nondominated points is important for a decision maker to get an understanding of the layout of solutions. The shape and density of the nondominated points over the objective space may be critical in obtaining a set of solutions that represent the nondominated set well. We develop an exact algorithm that generates a representative set guaranteeing a prespecified precision. Our experiments on a variety of problems demonstrate that our algorithm outperforms existing approaches in terms of both the cardinality of the representative set and computation times.
Original languageEnglish
Pages (from-to)804-818
Number of pages15
JournalEuropean Journal of Operational Research
Volume296
Issue number3
Early online date29 Sept 2021
DOIs
Publication statusPublished - 1 Feb 2022

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