A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.