Abstract:

Aiming at the problems of premature convergence and search stagnation in the Differential Evolution（DE） Algorithm, a multi-strategy covariance matrix learning differential evolution algorithm is proposed. Firstly, a feature coordinate system is established through the covariance matrix, and mutation and crossover operations are performed in the feature coordinate system to make full use of the distribution information of the current population and the relationship between the variables to ensure that the population can evolve in the direction of the global optimal solution. The method of selecting mutation strategies based on historical evolution information enables individuals to choose the most suitable mutation strategy at present, increasing the probability of finding the optimal solution. Finally, the adaptation of the cross probability also balances the global exploration ability and local exploration of the algorithm to a certain extent ability. In this paper, the convergence of the algorithm is proved, and the algorithm is simulated on the CEC2017 test set, and the experimental results are compared with other excellent differential evolution algorithms. The comparison results show the effectiveness of the algorithm.

Key words: differential evolution, covariance matrix, feature coordinate system, multi-strategy mutation, parameter adaptation

摘要：

针对差分进化算法（DE）存在的早熟收敛和搜索停滞的问题，提出了多策略协方差矩阵学习的差分进化算法。通过协方差矩阵建立特征坐标系，通过在特征坐标系中执行变异和交叉操作，来充分利用当前种群的分布信息以及各变量之间的关系，保证种群能朝着全局最优解的方向进化；根据历史进化信息来选择变异策略的方式使得个体能选择当前最合适的变异策略，提高找到最优解的概率；交叉概率的自适应也一定程度上平衡算法的全局探索能力和局部探索能力。对算法的收敛性进行了证明，同时将算法在CEC2017测试集上进行了仿真实验，并将实验结果跟其他优秀的差分进化算法进行了对比，对比结果表明了该算法的有效性。

关键词: 差分进化, 协方差矩阵, 特征坐标系, 多策略变异, 参数自适应