An exact method for optimizing a quadratic function over the efficient set of multiobjective integer linear fractional program

Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer linear program MOILFP. However, in many real-world problems, the objective functions or the utility function are nonlinear. In this paper, we propose an exact method to optimize a quadratic function over the efficient set of a multiobjective integer linear fractional program MOILFP. The proposed method solves a sequence of quadratic integer problems. Where, at each iteration, the search domain is reduced s6uccessively, by introducing cuts, to eliminate dominated solutions. We conducted a computational experiment, by solving randomly generated instances, to analyze the performance of the proposed method.