Representing the nondominated set in multi-objective mixed-integer programs - Doğan, Ilgın; Lokman, Banu; Köksalan, Murat (European journal of operational research, 2022)
•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.