An interactive algorithm to find the most preferred solution of multi-objective integer programs

Lokman B., Koksalan M., Korhonen P. J., Wallenius J.

ANNALS OF OPERATIONS RESEARCH, vol.245, no.1-2, pp.67-95, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 245 Issue: 1-2
  • Publication Date: 2016
  • Doi Number: 10.1007/s10479-014-1545-2
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.67-95
  • Keywords: Multi-objective optimization, Integer programming, Linear programming, Convex cones, MULTIPLE-CRITERIA PROBLEM, REFERENCE POINT APPROACH, CONVEX CONES, COMBINATORIAL OPTIMIZATION, DECISION-MAKING
  • TED University Affiliated: Yes


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.