Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems

In this paper, we focus on multi-objective large-scale nonlinear programming (MOLSNLP) problems with block angular structure. We extend technique for order preference by similarity ideal solution (TOPSIS) approach to solve (MOLSNLP) problems. Compromise (TOPSIS) control minimizes the measure of dist...

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Veröffentlicht in:Applied mathematics and computation Jg. 162; H. 1; S. 243 - 256
Hauptverfasser: Abo-Sinna, Mahmoud A., Amer, Azza H.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Elsevier Inc 04.03.2005
Elsevier
Schlagworte:
Compromise (satisfactory solution)
Exact sciences and technology
Fuzzy set theory
Large-scale systems
Logic and foundations
Mathematical analysis
Mathematical logic, foundations, set theory
Mathematics
Measure and integration
Multi-objective decision making
Negative ideal solution
Numerical analysis
Numerical analysis. Scientific computation
Positive ideal solution
Sciences and techniques of general use
Set theory
Negative ideal solution
Fuzzy set theory
Large-scale systems
Compromise (satisfactory solution)
Positive ideal solution
Multi-objective decision making
Two dimensional space
Decision making
Large system
Nonlinear problems
Non linear programming
Similarity solution
Numerical analysis
Applied mathematics
Positive solution
Set theory
Two-dimensional calculations
Large scale system
ISSN:0096-3003, 1873-5649
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Zusammenfassung:In this paper, we focus on multi-objective large-scale nonlinear programming (MOLSNLP) problems with block angular structure. We extend technique for order preference by similarity ideal solution (TOPSIS) approach to solve (MOLSNLP) problems. Compromise (TOPSIS) control minimizes the measure of distance, providing that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of “closeness” L P -metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure. The concept of membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Also, we get a single objective large-scale nonlinear programming (LSNLP) problem using the max–min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in the paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2003.12.087