Finding Efficient Solutions by Free Disposal Outer Approximation
Résumé
The main purpose of this paper is to present a method for generating a representation of efficient solutions and efficient values for nonconvex multiobjective optimization problems. The method is based on a particular outer approximation of nonconvex sets by so-called free disposal nonconvex polyhedra. The convergence of the method is proven, and a discussion on the rate of convergence is addressed with emphasis on the case of two objectives. Examples of up to four objectives are tested, some of which are taken from the recent literature. The numerical experience shows that the optimal value representation obtained by the algorithm is nicely distributed among the set of efficient values of the problem.