基于Lévy飞行的自适应差分进化算法

Adaptive differential evolution algorithm based on Lévy flight

针对目前差分进化算法存在全局搜索与局部寻优的矛盾、搜索停滞、收敛速度慢的问题,提出一种改进算法:基于Lévy飞行的自适应差分进化算法。该算法鉴于Lévy飞行步长符合重尾分布的特点,在变异过程中结合差分进化算法的基本变异和Lévy飞行变异两种模式,并通过引入自适应缩放因子和交叉概率算子,改善种群在交叉与变异过程中的不足。通过理论分析与Benchmark函数的数值验证,并与其他6种算法进行比较。结果表明,所提新算法能够在全局搜索与局部寻优之间进行较好的平衡,而且收敛速度更快,种群多样性得到了很好的保存,一定程度上避免了搜索停滞的出现。

A new improved algorithm:adaptive differential evolution algorithm based on Lévy flight(ADELF)is proposed to improve contradictions between global search and local optimization,search stagnation and slow convergence in current differential evolution algorithm.The algorithm was consistent with the heavy tailed distribution of Lévy flight steps.In consideration of the fact that Lévy flight step size conforms to the characteristics of heavy⁃tailed distribution,this algorithm combines the basic variation of differential evolution algorithm and Lévy flight variation in the variation process.The adaptive scaling factor and crossover probability operator are introduced to improve the shortage of population in the process of cross and mutation.The experiment was performed the theoretical analysis and numerical verification of benchmark function,with which other 6 algorithms are compared.The results show that the new algorithm can make a better balance between the global search and the local optimization,has faster convergence speed,and the population diversity is well preserved,which avoids the appearance of the search stagnation to a certain extent.