Article ID: | iaor20163516 |
Volume: | 245 |
Issue: | 1 |
Start Page Number: | 67 |
End Page Number: | 95 |
Publication Date: | Oct 2016 |
Journal: | Annals of Operations Research |
Authors: | Korhonen Pekka, Kksalan Murat, Wallenius Jyrki, Lokman Banu |
Keywords: | combinatorial optimization, programming: integer, decision theory: multiple criteria, programming: multiple criteria |
In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi‐objective integer programming problems. We assume that the DM’s preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the most preferred solution for integer programs. We test the performance of the algorithm on multi‐objective assignment, knapsack, and shortest path problems and show that it works well.