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General Further Discarding Tests in Geometric Branch‐and‐Bound Methods for Non‐Convex Multicriteria Optimization Problems
Author(s) -
Scholz Daniel
Publication year - 2011
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.474
Subject(s) - pareto principle , mathematical optimization , branch and bound , regular polygon , pareto optimal , multi objective optimization , upper and lower bounds , computer science , mathematics , mathematical analysis , geometry
ABSTRACT 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. Copyright © 2011 John Wiley & Sons, Ltd.