TY - INPR
A1 - Ehrgott, Matthias
A1 - Nickel, Stefan
T1 - On the Number of Criteria Needed to Decide Pareto Optimality
N2 - In this paper we address the question of how many objective functions are needed to decide whether a given point is a Pareto optimal solution for a multicriteria optimization problem. We extend earlier results showing that the set of weakly Pareto optimal points is the union of Pareto optimal sets of subproblems and show their limitations. We prove that for strictly quasi-convex problems in two variables Pareto optimality can be decided by consideration of at most three objectives at a time. Our results are based on a geometric characterization of Pareto, strict Pareto and weak Pareto solutions and Helly's Theorem. We also show that a generalization to quasi-convex objectives is not possible, and state a weaker result for this case. Furthermore, we show that a generalization to strictly Pareto optimal solutions is impossible, even in the convex case.
T3 - Report in Wirtschaftsmathematik (WIMA Report) - 61
KW - Multicriteria optimization
KW - Pareto optimality
KW - strictly quasi-convex functions
KW - number of objectives
Y1 - 2000
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1129
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-10682
ER -