Two new algorithms for solving optimization problems with one linear objective function and finitely many constraints of fuzzy relation inequalities

This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solutio...

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Veröffentlicht in:Journal of computational and applied mathematics Jg. 233; H. 8; S. 2090 - 2103
1. Verfasser: Molai, Ali Abbasi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier B.V 15.02.2010
Elsevier
Schlagworte:
Calculus of variations and optimal control
Exact sciences and technology
Fuzzy optimization
Fuzzy relation inequality
Mathematical analysis
Mathematics
Max-Einstein composition
Minimum solution
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Partial solution
Sciences and techniques of general use
Minimum solution
Fuzzy optimization
Max-Einstein composition
Partial solution
Fuzzy relation inequality
Solution uniqueness
Fuzzy system
Optimal algorithm
Decomposition method
Optimization method
Linear model
Numerical analysis
Sufficient condition
Applied mathematics
Optimal solution
Inequality constraint
Problem solving
Variational calculus
Mathematical programming
ISSN:0377-0427, 1879-1778
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.09.042