利用改进遗传算法求解方程组

摘要

选择、交叉和变异是遗传算法的几个主要操作算子，它们构成了遗传操作。本文对遗传操作提出了改进方案,即对于交叉操作：如果两个子代的适应度均比父代大就交换，如果子代的适应度1个比父代大而另1个比父代小则保留大的子代而还原小的子代为父代，如果子代的适应度均比父代小则取消此次的交换。变异操作中对每个父代的`多个位置逐个变异,如果子代的适应度比父代大则变异,否则不变异。通过解线性方程组和非线性方程组证明了该方法能够使得遗传始终向着理想的方向，避免了算法陷入死循环，并且收敛速度非常快。
关键词：遗传算法；遗传操作；解方程组；改进遗传算法，最优化

Improvement genetic algorithms for solving equation group

Abstract

 Choice, cross and variation are the main operators of the genetic algorithms, which constitute the so-called genetic operation. The paper give an improvement project of the genetic algorithms. That is :if both of the two children’s flexibility are smaller than their father’s in the choice operation, than cancel the choice; and in the genetic operation, several positions for each father are changed one by one ,if the children’ flexibility is bigger than his father’s, than variating ,otherwise does not happen. This kind of method has been proved that it can make the heredity always go in the perfect direction, the algorithms avoid sinking into dead circulation, and the convergence speed is very quick by using it in solving equations.
Keywords: genetic algorithms; genetic operation; solving equations; improvement genetic algorithms; optimization