An indefinite quadratic optimization over an integer efficient set

In this paper, a new exact method is proposed for solving the maximization problem, say, of an indefinite quadratic utility function over the efficient set of a multi-objective integer linear programming (MOILP) problem. Indeed, we develop a branch and cut algorithm based on a continuous indefinite quadratic optimization, for reaching an integer optimal solution of problem without having to enumerate explicitly all integer efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows 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.