应用自适应混合遗传算法求解病态线性方程组

Adaptive Hybrid Genetic Algorithm and It's Application in Ill-conditioned Linear Equation Groups Solving

简单遗传算法(SGA)在进化的后期由于种群个体的多样性急剧降低,可能会收敛于局部最优解,即出现"早熟"现象。针对简单遗传算法的早熟问题,从选择、交叉和变异三个遗传算子入手,设计了自适应遗传算子。同时为了克服SGA局部搜索能力差的缺点,结合共轭梯度法,实现了一种自适应混合遗传算法(Adaptive GA-conjugate gradient,即AGA-CG)。以核磁共振测井曲线线性化后的大型病态方程组为测试实例,对AGA-CG算法进行了验证。实验结果表明:AGA-CG算法是求解大型病态线性方程组的一种有效算法。

Simple genetic algorithm（SGA）may be converge at local optimum solution because of rapid decrement of population individual＇s diversity in the period of later evolution,namely the occurrence of premature convergence.To point against this phenomenon,a adaptive genetic algorithm is designed from starting with three genetic operators of selection,crossover and mutation.Meanwhile for overcoming the shortcoming of local searchging inability of SGA,a adaptive hybrid genetic algorithm which combine conjugate gradient method（namely AGA-CG） is brought about. Taking the large scale,and ill-conditioned linear equation groups worked out on the logging data of nuclear magnetic resonance as the test case,the AGA-CG is verified.The experimental results show that the AGA-CG algorithm is an efficient way to working out the issue of large scale and ill-condition linear equation groups solving.