An interactive analytic center trade-off cutting plane algorithm for multi-objective linear programming

This paper proposes the use of an interior point algorithm for Multiobjective Linear Programming problems. At each iteration of the algorithm, the decision maker furnishes his precise trade-offs. From these trade-offs, a cut is formed in the objective space. This cut induces a cut in the decision space that defines a half-space of promising points. We compute the analytic center of the restricted feasible region in the decision space and then we calculate the trade-offs of the decision maker at the image of the analytic center in the objective space. Therefore, we obtain a trajectory of analytic centers that converges to the best compromise solution. Since the proposed algorithm moves through the interior of the feasible region, it avoids the combinatorial difficulties of visiting extreme points and is less sensitive to problem size. We illustrate the method through a numerical example and provide computational experience.