- 1999 (2) (entfernen)
- On the number of Criteria Needed to Decide Pareto Optimality (1999)
- In this paper we prove a reduction result for the number of criteria in convex multiobjective optimization. This result states that to decide wheter a point x in the decision space is pareto optimal it suffices to consider at most n? criteria at a time, where n is the dimension of the decision space. The main theorem is based on a geometric characterization of pareto, strict pareto and weak pareto solutions
- Geometric Methods to Solve Max-Ordering Location Problems (1999)
- Location problems with Q (in general conflicting) criteria are considered. After reviewing previous results of the authors dealing with lexicographic and Pareto location the main focus of the paper is on max-ordering locations. In these location problems the worst of the single objectives is minimized. After discussing some general results (including reductions to single criterion problems and the relation to lexicographic and Pareto locations) three solution techniques are introduced and exemplified using one location problem class, each: The direct approach, the decision space approach and the objective space approach. In the resulting solution algorithms emphasis is on the representation of the underlying geometric idea without fully exploring the computational complexity issue. A further specialization of max-ordering locations is obtained by introducing lexicographic max-ordering locations, which can be found efficiently. The paper is concluded by some ideas about future research topics related to max-ordering location problems.