Abstract: In order to solve the problem of differential evolution algorithm, such as premature convergence, slow convergence speed and low convergence precision, a differential evolution algorithm based on adaptive mutation operator is proposed. In this paper, the definition of individual vector particle and dimensional layer is presented. Based on the different dimension’s selection strategy for weighted dimensional layer, the weighted different dimensional learning is introduced into differential evolution algorithm for the first time, which can effectively improve the diversity of the population. According to the degree of populational aggregation, and an adaptive mutation operator based on degree of populational aggregation is proposed. The operator can adaptively adjust the variation weight of DE/best/1 mutation operator and the different dimensional learning mutation operator according to the degree of populational aggregation currently. It accelerates the convergence speed, improves the convergence precision of the algorithm. 20 typical test functions are tested, the results show that compared with the 7 representative algorithms, the algorithm proposed in this paper has great advantages in solving accuracy and convergence speed, and it shows very good robustness.

Key words: differential evolution, dimensional layer, weighted different dimensional learning, degree of populational aggregation, adaptive mutation operator

摘要： 针对差分演化算法易于早熟、收敛速度慢和收敛精度低等问题，提出一种基于自适应变异算子的差分进化算法。给出个体向量粒子及维度层定义，并提出了基于维度层加权的异维维度选择策略，首次将加权异维学习策略引入差分演化算法中，有效地提高了种群的多样性；根据种群聚集度的思想，提出一种基于种群聚集度自适应的变异算子，该算子能依据种群个体当前的种群聚集度自适应地调整DE/best/1变异算子和加权异维学习变异算子的变异权重，加快算法收敛速度、提高其收敛精度。通过在20个典型的测试函数上进行测试，与7种具有代表性的算法相比，结果表明提出的算法在求解精度和收敛速度上具有很大优势，并显示出了非常好的鲁棒性。

关键词: 差分进化, 维度层, 加权异维学习, 种群聚集度, 自适应变异