遗传交叉和变异对种群多样性的影响

Effect of genetic crossover and mutation on population diversity

首先,定义了群体的算术交叉扩展子空间、寻优空间和基因位直方图概念,并分析了交叉在解空间的扩展性.然后,证明了在二进制编码中,交叉不能改变基因层次上的多样性;而在实数编码中,在一定条件下,算术交叉可改变基因层次上的多样性,但以扩大寻优空间、产生无用解为代价.随后,证明了交叉可改变个体层次上的多样性,而变异可改变以上两个层次上的多样性.最后,分析了所得结论对遗传算法的改进和应用具有的指导意义,并通过仿真加以验证.

The arithmetic crossover extended subspace of population, the space for searching optimum solution and gene bit bar chart are defined, and the extensibility of crossover in solution space is analyzed. It is proved that crossover can＇t effect the diversity in gene level in binary code, but arithmetic crossover can effect the diversity in gene level in real number code under a certain condition, the cost for which is extending the searching space and producing the void solution. Crossover can effect the diversity in individual level, and mutation can not only effect the diversity in gene level but also in dividual level. Finally, the instruction significance of all study results above to genetic algorithm in improvement and application are analyzed and validated by simulation.