In this article, we develop a new algorithm to solve the problem of optimizing a linear fractional function over the efficient set of multi-objective integer linear programming problem. Indeed, the branch and bound process strengthened by efficient cuts and tests allow us to fathom considerably nodes in the tree. Thus, a large number of feasible and non efficient solutions can be avoided. An experimental study is reported to validate the theoretical results.
Mots clés : Multi-objective optimization, integer programming, fractional programming, Branch and cut