Fourier-Motzkin elimination method in MOLP problems

This paper introduces a method for finding the non‐dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space...

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Veröffentlicht in:Journal of multi-criteria decision analysis Jg. 11; H. 2; S. 55 - 64
Hauptverfasser: Melachrinoudis, Emanuel, Liu, Songan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Chichester, UK John Wiley & Sons, Ltd 01.03.2002
Wiley Periodicals Inc
Schlagworte:
Algorithms
Decision analysis
efficient set
Fourier-Motzkin Elimination (FME)
Linear programming
Methods
multiple objective linear programming (MOLP)
non-dominated set
Problem solving
Students
Variables
vector maximization
ISSN:1057-9214, 1099-1360
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Zusammenfassung:This paper introduces a method for finding the non‐dominated set in criterion space of an MOLP problem based on Fourier–Motzkin Elimination. The method incorporates a procedure that eliminates decision variables from constraints and transforms a feasible region from decision space to criterion space. While avoiding characterization of the efficient set in decision space, it finds the non‐dominated set in criterion space. After the decision maker's most preferred criterion vector has been identified, the corresponding efficient solutions can be found by backward substitution. The method was implemented in MATLAB using a tabular form and computational experiments were conducted. The results indicate that although the method performs well for relatively small problems, it can be computationally intensive for larger problems. Nonetheless, the method is intuitively appealing and it provides useful insights into the geometry and theory of MOLP. As such it makes it a valuable educational tool for students of multi‐criteria decision analysis. Copyright © 2003 John Wiley & Sons, Ltd.
Bibliographie:istex:A11E7B7CDF9A9D20866A35ABE10C0DBB6220B40C
ArticleID:MCDA316
ark:/67375/WNG-8Q1W87WM-S
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1057-9214
1099-1360
DOI:10.1002/mcda.316