Multicriteria discarding tests

Abstract

Under the assumption that the objective functions for a multicriteria optimization problem are differentiable, this chapter presents some general discarding tests that can be used throughout the algorithm presented in the previous chapter. The idea of these discarding tests is to obtain a sharp outer approximation of the set of Pareto optimal solutions. To this end, we recall the well-known Fritz John necessary conditions for Pareto optimality in Section 5.1 before the multicriteria discarding tests are presented in Section 5.2. The theoretical results are again illustrated on two bicriteria location problems introduced in Section 5.3. Some particular instances for these problems are solved in Section 5.4 twice, one time without multicriteria discarding tests and one time using these tests. We show that the second run yields a very sharp outer approximation of the set of all Pareto optimal solutions compared to the first run.