An Adaptive Genetic Algorithm for Solving Ill-Conditioned Linear Equation Group

摘要

Simple genetic algorithm (SGA) may be vibrate at optimum solution because of randomicity of genetic operator in the later stage of evolution, so the algorithm can not converge rapidly and increase numerical solution error. To address the shortcoming brought by this problem, an Adaptive Genetic Algorithm (AGA) is designed. Three genetic operators including selection, crossover and mutation are presented to be improved by joining in several methods in the AGA, for example, penalty function, population migration and elite individuals reservation. Taking several large scale and ill-conditioned linear equations as example, the AGA is verified. The experimental results show that the AGA can promote precision of numerical solution of large scale and ill-conditioned linear equation set effectively.