An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition

•A nonlinear optimization problem with a system of fuzzy relational equations as its constraints is studied.•A genetic algorithm is presented, which preserves the feasibility of new generated solutions.•The proposed GA does not need to initially find the minimal solutions.•The obtained results confi...

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Published inApplied soft computing Vol. 69; pp. 475 - 492
Main Authors Ghodousian, Amin, Babalhavaeji, Ali
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2018
Subjects
Fuzzy relational equations
genetic algorithm
Nonlinear optimization
genetic algorithm
Fuzzy relational equations
Nonlinear optimization
Online AccessGet full text
ISSN1568-4946
1872-9681
DOI10.1016/j.asoc.2018.04.029

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Abstract •A nonlinear optimization problem with a system of fuzzy relational equations as its constraints is studied.•A genetic algorithm is presented, which preserves the feasibility of new generated solutions.•The proposed GA does not need to initially find the minimal solutions.•The obtained results confirm the high performance of the proposed method in solving such nonlinear problems. We study a nonlinear optimization problem with a system of fuzzy relational equations as its constraints. We firstly investigate the resolution of the feasible region when it is defined with max-Lukasiewicz composition and present some necessary and sufficient conditions for the feasibility and some procedures for simplifying the problem. Since the feasible solution set of the fuzzy relational equations (FRE) is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional nonlinear programming methods may involve high computational complexity. Based on the theoretical properties of the problem, a genetic algorithm (GA) is presented, which preserves the feasibility of new generated solutions. The proposed GA does not need to initially find the minimal solutions. Also, it does not need to check the feasibility after generating the new solutions. Moreover, we present a method to generate feasible max-Lukasiewicz FREs as test problems for evaluating the performance of our algorithm. The proposed method has been compared with some related works. The obtained results confirm the high performance of the proposed method in solving such nonlinear problems.
AbstractList •A nonlinear optimization problem with a system of fuzzy relational equations as its constraints is studied.•A genetic algorithm is presented, which preserves the feasibility of new generated solutions.•The proposed GA does not need to initially find the minimal solutions.•The obtained results confirm the high performance of the proposed method in solving such nonlinear problems. We study a nonlinear optimization problem with a system of fuzzy relational equations as its constraints. We firstly investigate the resolution of the feasible region when it is defined with max-Lukasiewicz composition and present some necessary and sufficient conditions for the feasibility and some procedures for simplifying the problem. Since the feasible solution set of the fuzzy relational equations (FRE) is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional nonlinear programming methods may involve high computational complexity. Based on the theoretical properties of the problem, a genetic algorithm (GA) is presented, which preserves the feasibility of new generated solutions. The proposed GA does not need to initially find the minimal solutions. Also, it does not need to check the feasibility after generating the new solutions. Moreover, we present a method to generate feasible max-Lukasiewicz FREs as test problems for evaluating the performance of our algorithm. The proposed method has been compared with some related works. The obtained results confirm the high performance of the proposed method in solving such nonlinear problems.
Author Babalhavaeji, Ali
Ghodousian, Amin
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Fuzzy relational equations
Nonlinear optimization
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SubjectTerms Fuzzy relational equations
genetic algorithm
Nonlinear optimization
Title An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition
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