BIOBJECTIVE OPTIMIZATION OVER THE EFFICIENT SET OF MULTIOBJECTIVE INTEGER PROGRAMMING PROBLEM

In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decision-makers have to optimize their respective preference functions over many efficient solutions. For this purpose, we develop a branch-and-cut algorithm based on linear programming, for finding efficient solutions in terms of both preference functions and MOILP problem, without explicitly enumerating all efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows us to prune a large number of nodes in the tree to avoid many solutions. An illustrative example and an experimental study are reported.

Automated summary

This article proposes an exact method to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP), and develops a branch-and-cut algorithm based on linear programming to find efficient solutions without explicitly enumerating all solutions. The branch and bound process, strengthened by efficient cuts and tests, allows pruning of a large number of nodes in the tree to avoid many solutions. An illustrative example and experimental study are provided.