An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition
An efficient genetic algorithm for solving nonlinear optimization problems defined with fuzzy relational equations and max-Lukasiewicz composition
复制标题
DOI：
10.1016/j.asoc.2018.04.029
复制
发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
A. Ghodousian;A. Babalhavaeji
中科院分区：
文献类型：
--
作者：
A. Ghodousian;A. Babalhavaeji
我们研究以模糊关系方程组作为约束的非线性优化问题。我们首先研究了用 max-Lukasiewicz 组合定义可行区域时的分辨率，并提出了可行性的一些充要条件和简化问题的一些步骤。由于模糊关系方程（FRE）的可行解集是非凸的，并且寻找所有最小解是一个NP难题，因此传统的非线性规划方法可能涉及较高的计算复杂度。基于问题的理论特性，提出了遗传算法（GA），它保留了新生成的解决方案的可行性。所提出的遗传算法不需要最初找到最小解决方案。而且，生成新解后不需要检查可行性。此外，我们提出了一种生成可行的 max-Lukasiewicz FRE 作为测试问题的方法，用于评估我们算法的性能。所提出的方法已与一些相关工作进行了比较。获得的结果证实了所提出的方法在解决此类非线性问题方面的高性能。
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.