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

•An exact algorithm is developed for multi-objective mixed integer programs.•Small representative sets guaranteeing a prespecified precision are found.•Problem-specific information is utilised to select points from dense regions.•The algorithm is efficient based on extensive computational tests. In...

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Bibliographic Details
Published in:European journal of operational research Vol. 296; no. 3; pp. 804 - 818
Main Authors: Doğan, Ilgın, Lokman, Banu, Köksalan, Murat
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2022
Subjects:
Coverage gap
Multi-objective mixed-integer programming
Representative set
Coverage gap
Multi-objective mixed-integer programming
Representative set
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•An exact algorithm is developed for multi-objective mixed integer programs.•Small representative sets guaranteeing a prespecified precision are found.•Problem-specific information is utilised to select points from dense regions.•The algorithm is efficient based on extensive computational tests. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.04.005