Finding highly preferred points for multi-objective integer programs

This article develops exact algorithms to generate all non-dominated points in a specified region of the criteria space in Multi-Objective Integer Programs (MOIPs). Typically, there are too many non-dominated points in large MOIPs and it is not practical to generate them all. Therefore, the problem of generating non-dominated points in the preferred region of the decision-maker is addressed. To define the preferred region, the non-dominated set is approximated using a hyper-surface. A procedure is developed that then finds a preferred hypothetical point on this surface and defines a preferred region around the hypothetical point. Once the preferred region is defined, all non-dominated points in that region are generated. The performance of the proposed approach is tested on multi-objective assignment, multi-objective knapsack, and multi-objective shortest path problems with three and four objectives. Computational results show that a small set of non-dominated points is generated that contains highly preferred points in a reasonable time.