求矩阵复特征值的双种群改进遗传算法

IMPROVED DOUBLE POPULATIONS GENETIC ALGORITHM FOR SOLVING COMPLEX EIGENVALUE OF MATRIX

针对矩阵复特征值的特点,提出采用双种群改进遗传算法并行求解复特征值的近似值。该算法中双种群采用实数编码,在遗传过程中每个种群都根据适应度自动选择其交叉概率和变异概率,使个体对环境变化具有自适应调节能力。变异中采用了柯西变异,可以使个体很快跳出局部极小。仿真结果表明,此算法可以达到一定的精度,具有一定的通用性,并给求矩阵复特征值提供了一种快速的方法。

In light of the character of complex eigenvalue of matrix, an improved double population genetic algorithm is proposed to use for solving the approximation of complex eigenvalue. In this algorithm the double populations use real-coding, each individual population selects its probability of crossover and mutation automatically according to its fitness, to make each individual owns the ability of self - adaption to the variation of the environment. Cauchy mutation is adopted in mutation,which enables the individual quickly jump out the local minimum. The simulation results show that this algorithm can achieve a certain precision, and has a certain versatility as well as provides a rapid approach to solve the complex eigenvalue of matrix.