基于自适应交叉概率因子的差分进化算法及其应用

基本差分进化算法的控制参数在进化过程中是保持不变的，但是交叉概率因子的大小影响种群进化的多样性以及种群的收敛速度．本文提出一种根据种群平均适应度方差非线性改变交叉概率因子的方法．在种群多样性降低时增大该因子，使之接受更多变异个体的基因，有利于加强局部搜索和加速收敛速率；多样性增大时减小该因子，避免该个体基因结构遭到过多的破坏，促使该个体的进化，有利于保持种群的多样性和完成全局搜索．并且给出了一种新的变异方式，这种变异方式一方面能提高算法的收敛速度，另一方面能在一定程度上保持较高的种群多样性．最后将其应用到热连轧精轧机组负荷分配优化中，改进后的优化方法在性能上要优于所对比算法．

Differential Evolution Algorithm Based on Adaptive Crossover Probability Factor and Its Application

The parameters of differential evolution algorithm are unchanged during the evolutionary process, however, the diversity and convergence rate of population are affected by the probability of cross-factor. In this paper, a method based on the average of the population fitness variance with crossover factor's nonlinear change is presented. The factor should be increased when the diversity of population reduces, as more genes of variation individual will be accepted, which is beneficial to strengthen the local search and speed up the convergence rate. Relatively, the factor should be decreased when the diversity of population increases, avoiding the excessive damage to the frame of individual gene to promote its evolution, which is conducive to maintaining the diversity and the global search. And a new mutation operation is presented, which could improve the algorithm's convergence rate and maintain a high diversity of the population. Finally, it is applied to the optimum design of scheduling hot strip mills, which is superior in performance to algorithms compared.