GA矩阵编码方法及其在模糊建模中的应用

在遗传算法(GA)的实际应用中,许多问题都可以采用树结构描述.模糊建模中的结构辨识是指如何划分输入空间,它是一种复杂的非线性优化过程,模糊树模型可将输入空间的划分表示成二叉树结构的形式.本文提出了一种树结构的矩阵编码方法,这种编码方法直观、简单,非常适合遗传算法的各种遗传操作.针对模糊树模型,以树结构为个体,采用矩阵编码方式,利用遗传算法优化输入空间的划分,得到了一个精度较高而复杂度较低的次优模糊树模型.

Matrix Coding in GA and Its Application to Fuzzy Modelling

In the practical applications of genetic algorithm(GA), a lot of problems can be described as tree structures. In fuzzy modelling, the structure identification of a fuzzy model is to partition the input domain, which is in essence a process of complicated nonlinear optimization. The partition of the input domain can be expressed as a binary tree by a fuzzy tree model. A matrix coding approach to representing a binary tree is presented, which is simple and suitable for the genetic operations in GA. The partition of the input domain is optimized by GA with matrix coding for tree structured individuals and the resulting suboptimal fuzzy tree model is obtained, which has higher precision and lower complexity of model. A simulation example is given to validate the proposed method.