A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

Kuan Lu, Shinji Mizuno, Jianming Shi

Research output: Contribution to journalArticle


This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.

Original languageEnglish
JournalOptimization Letters
Publication statusAccepted/In press - 1 Jan 2020



  • Efficient set
  • Global optimization
  • Linear complementarity conditions
  • Mixed integer programming
  • Multiobjective programming

Cite this