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


Doğan I. , Lokman B. , Köksalan M.

European Journal of Operational Research, vol.296, pp.804-818, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 296
  • Publication Date: 2022
  • Doi Number: 10.1016/j.ejor.2021.04.005
  • Title of Journal : European Journal of Operational Research
  • Page Numbers: pp.804-818
  • Keywords: Multi-objective mixed-integer programming, Representative set, Coverage gap, DISCRETE REPRESENTATIONS, SEARCH REGION, EFFICIENT

Abstract

© 2021 Elsevier B.V.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.