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\iteman{io-port 06091879}
\itemau{Hong, Zhen; Zhang, Guijun; Yu, Li}
\itemti{An adaptive differential evolution algorithm based on $N$th-order nearest-neighbor analysis.}
\itemso{Control Theory Appl. 28, No. 11, 1613-1620 (2011).}
\itemab
Summary: In order 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 $N$th-order nearest-neighbor analysis ($N$-NNADE). Global distribution information of species is obtained by analyzing the $N$th-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 belong 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 the $N$-NNADE algorithm is more suitable than DE, DERL (differential evolution algorithm with random localizations) and ADE for solving complex high-dimensional multimodal optimization problems.
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\itemcc{}
\itemut{multimodal optimization; differential evolution; $N$th-order nearest neighbor; $K$-means clustering}
\itemli{}
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