基于N阶近邻分析的自适应差分进化算法

针对差分进化算法在求解多模优化问题解可靠性较低的问题,在N阶近邻理论分析及参数整定的基础上,提出一种基于N阶近邻分析的自适应差分进化算法（N--NNADE）.N--NNADE算法在缺少先验知识的情况下,通过分析群体个体间的N阶最短近邻计算种群的全局分布,并利用阶跃信息自适应统计获得种群数量;同时采用K--means算法划分种群,进一步引入不同种群间的交叉变异思想以及父子代同种群则替换最差个体的选择策略实现种群间的协同进化.通过获取更多的全局最优解和部分高质量的局优解来提高算法的可靠性.20个优化问题的数值研究结果表明N--NNADE算法具有比DE（differential evolution）,DERL（differential evolution algorithm withrandom localizations）,ADE（adaptive differential evolution）算法更适合求解复杂的高维多模优化问题.

Adaptive differential evolution algorithm based on Nth-order nearest-neighbor analysis

To improve the reliability of differential evolution(DE) algorithm in dealing with multimodal optimization problem, we propose an adaptive differential evolution(ADE) algorithm based on the Nth-order nearest-neighbor analysis(N--NNADE). Global distribution information of species is obtained by analyzing the Nth-order nearest-neighbor in population, and the number of species is adaptively determined by the step-jumping information in lacking prior knowledge, Furthermore, the K--means algorithm is used for partitioning the population. To realize the co-evolution among species, we introduce the crossover mutation among different species and replace the worst members of current species if parents and children are belonging to the same species. The reliability of the algorithm is continuously improved by acquiring more global optimal solutions and high-quality local suboptimal solutions. The results of 20 benchmark optimization problems show that N--NNADE algorithm is more suitable than DE, DERL(differential evolution algorithm with random localizations) and ADE for solving complex high-dimensional multimodal optimization problems.