Vol.5 , No. 2, Publication Date: May 31, 2018, Page: 68-87

[1] | Amin Ghodousian, Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran. |

[2] | Maryam Raeisian Parvari, Department of Algorithms and Computation, University of Tehran, Tehran, Iran. |

[3] | Raziyeh Rabie, Department of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran. |

[4] | Tarane Azarnejad, Department of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran. |

Schweizer-Sklar family of t-norms is a parametric family of continuous t-norms, which covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Schweizer-Sklar t-norm. We firstly investigate the resolution of the feasible region and present some necessary and sufficient conditions for determining the feasibility of the problem. Moreover, two procedures are presented for simplifying the problem. Since the feasible solutions set of FREs is non-convex, conventional nonlinear programming methods may not be directly employed. For this reason, a genetic algorithm is presented to solve the nonlinear non-convex problems. The proposed GA preserves the feasibility of new generated solutions. Additionally, we propose a method to generate feasible max-Schweizer-Sklar 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.

Keywords

Fuzzy Relational Equations, Nonlinear Optimization, Genetic Algorithm

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