求解高维多模优化问题的自适应差分进化算法

Adaptive differential evolution for high-dimension multimodal optimization problems

在基变量选择方差理论分析的基础上,提出一种自适应差分进化算法(ADE).ADE算法通过设计自适应收敛因子构建自调整的权重质心变异策略,同时在交叉策略中引入发射、收缩两种单纯形操作算子,保证算法全局搜索能力的同时,能有效提高算法后期的局部增强能力.30个优化问题的数值研究结果表明ADE算法具有比DE、DERL以及DERB三种算法更快的收敛速度和可靠性,尤其适合于高维多模优化问题的求解.

Based on the theoretcal analysis of selective variance in mutation operator of original differential evolution （DE） algorithm, we proposed an adaptive differential evolution （ADE） algorithm to tackle the high-dimension multimodal optimization problems. In order to make a good tradeoff between the exploration and exploitation, ADE algorithm adopts an adaptive weighted centroid mutation strategy. Furthermore, modifications in mutation and crossover rule are suggested to the original DE algorithm to intensify the search around the global minima. These modifications intend to exploit the information derived from the previous function evaluations to improve the efficiency of the algorithm in the local search, without deteriorating the behavior of the original DE algorithm in the global search. Numerical experiments indicate that the resulting algorithm is considerably better and more efficient than the DE, DERL and DERB algorithms. Finally, a numerical study is carried out using a set of 30 test problems, many of which are inspired by practical applications.