A branch-and-cut technique to solve multiobjective integer quadratic programming problems

This article proposes an exact method to solve the integer programming problem featuring several convex quadratic functions to be minimized (henceforth denoted by MOIQP). The proposed algorithm is a branch and bound based technique suitable for MOIQP problems to generate the set of all efficient solutions. The features of the method are as follows. First, the branch and bound technique allows solving the relaxed problem according to any linear function and progressively generates integer solutions. Then, the efficient cut proposed reduces the search area by truncating domains containing non efficient solutions without having to enumerate them. Finally, at each node of the tree search, three fathoming rules are used to enhance the speed of the procedure. Computational experiments are presented in order to analyze the performance of the algorithm.