Solving multi-objective integer indefinite quadratic fractional programs

Abstract

In this paper, we describe an exact algorithm for solving a multi-objective integer indefinite quadratic fractional maximization problem. The algorithm generates the whole set of efficient solutions of the above mentioned problem. We optimize at first one of the objective functions in the original feasible region; in an iterative way and through the introduction of auxiliary constraints (efficient cut or branching constraint), the same objective function is optimized over progressively restricted or separated parts of the original feasible region, each time we get a candidate solution for non dominated solution, the efficient set is updated, the process ends when there is no unexplored parts of the original domain. The proposed method is based on an efficient cut which allows to reduce the feasible set avoiding non efficient solutions, the simplex like algorithm to solve a mono objective quadratic fractional maximization problem, and the classical branch and bound technique for integer decision variables. We establish theoretical results which prove the effectiveness of this new exact method, for illustration, numerical experiments are reported.