Abstract: For the problems that differential evolution algorithm is prone to premature convergence and its local search is slower, a mutation strategy similar to Nelder-Mead method is proposed, which is called reflective mutation strategy. Different from other basic differential strategies, the proposed mutation strategy has a distinct difference direction and has a stronger local convergence speed. In order to avoid the possibility of premature increase due to the greedy of differential orientation, the reflection mutation strategy uses 4 random individuals to complete a mutation operation. An adaptive differential evolution algorithm（RMADE） based on the reflective mutation strategy is developed by combining the generation strategy and the adaptive parameter method based on the reflective mutation strategy. The performance of RMADE is tested by using 12 functions and compared with other algorithms. The results show that RMADE has faster convergence speed and better global detection capability, and reflects the value of reflective mutation strategy.

Key words: differential evolution algorithm, mutation strategy, Nelder-Mead method, global optimization

摘要： 针对差分进化算法易于陷入早熟收敛和局部搜索较慢的问题，提出了一种类似Nelder-Mead方法中的反射操作的变异策略，称为反射变异策略。不同于其他基本的差分策略，提出的变异策略具有明确的差分方向，具有更快的局部收敛速度。为了避免因差分方向的贪婪性而导致算法早熟的可能性增加，反射变异策略使用4个随机的个体完成一次变异操作。将基于反射变异策略的子代生成策略和自适应参数方法组合形成了基于反射变异策略的自适应差分进化算法（RMADE）。使用12个函数测试了RMADE的性能并与其他算法进行比较，结果表明RMADE具有较快的收敛速度和较好的全局探测能力，进而体现了反射变异策略的价值。

关键词: 差分进化算法, 变异策略, Nelder-Mead方法, 全局优化