General Further Discarding Tests in Geometric Branch-and-Bound Methods for Non-Convex Multicriteria Optimization Problems

Using a geometric branch-and-bound technique, my goal in this paper is to compute a sharp outer approximation of all Pareto-optimal solutions in multicriteria optimization problems. To this end, I propose some general further discarding tests that are based on the Fritz John necessary conditions for Pareto optimality. The branch-and-bound solution method as well as the general further discarding tests leads to a very useful tool especially for multicriteria facility location problems. Therefore, my suggested approach is demonstrated on some multicriteria facility location problems with excellent numerical results.