基于主成分分析的DBSCAN分类差分进化算法改进

Improved differential evolution algorithm based on PCA-DBSCAN classification

差分进化算法(DE)是一类基于种群搜索最优解的全局优化算法,具有收敛速度快、算法简单易懂、参数数量少和稳定性高等特点。但DE算法的性能在很大程度上取决于参数值的设置、个体突变的方向和距离。考虑到不同的种群密度对参数的需求不同,采用主成分分析技术将30或50维的数据降到2维;再采用DBSCAN算法,依据邻域半径和最小邻域数将2维数据分类为簇,通过簇的数量判断种群整体密度和个体之间的差异度,并在不同取值范围内生成合适的变异因子和交叉因子,以此来满足不同种群的进化需求。通过基准函数测试集和多个检验方法验证,证明了所提方法的寻优能力和鲁棒性均优于另外5种先进算法。

Differential evolution(DE)algorithm is a type of global optimization algorithm based on population search for the optimal solution.It has the characteristics of fast convergence speed,simple and easy-to-understand algorithm,few parameters,and high stability.However,the performance of the DE algorithm largely depends on the setting of parameter values and the direction and distance of individual mutations.Considering that different population densities have different requirements for parameters,the principal component analysis(PCA)technique is used to reduce 30 or 50-dimensional data to 2 dimensions.Then,the DBSCAN algorithm is used to classify the 2 dimension data into clusters based on the neighborhood radius and minimum neighborhood number.The number of clusters is used to determine the overall density of the population and the difference between individuals,and appropriate mutation factors and crossover factors are generated within different ranges to meet the evolutionary needs of different populations.The proposed algorithm is verified by means of benchmark function test sets and multiple validation methods,demonstrating its superior optimization ability and robustness comparied with five other advanced algorithms.