采用聚类的变异正余弦优化算法研究

Research on varied sine and cosine optimization algorithm using clustering methods

针对传统正余弦优化算法局部搜索收敛不稳定、收敛性差的突出问题,做如下改进:利用拉丁超立方体方法初始化种群,设计了非线性的指数函数对振幅调整因子进行自适应更新的非线性振幅调整因子,采用了柯西混沌变异的扰动机制以增加种群的随机性,增加传统正余弦算法的收敛速度与精度,利用变中心数的KMeans对种群进行聚类以增强局部搜索能力,平衡全局搜索与局部开发能力,避免局部最优,最终形成了采用KMeans聚类的变异正余弦改进算法KVSCA。仿真实验采用了23个基准测试函数和1个实际优化工程问题,分别利用改进后的KVSCA算法、柯西混沌变异改进的正余弦算法、传统的正余弦优化算法对目标问题进行优化,分析优化结果的方差、均值和最小值,KVSCA算法优化结果的稳定性、收敛精度和收敛速度都是最优,验证了KVSCA算法局部收敛的高效性与更强的稳定性。

To address the outstanding problems of unstable local search convergence and poor convergence of traditional sine and cosine optimization algorithms,this paper makes the following improvements:firstly,the population is initialized using the Latin hypercube method.Then,a nonlinear amplitude adjustment factor adaptively updated bya nonlinear exponential function to the adjusted amplitude factors is designed,and the perturbation mechanism of Cauchy chaotic mutation is used to increase the randomness of the population so as to increase the convergence speed and accuracy of the traditional sine and cosine algorithm.The population is clustered with KMeans ofthe variable centernumber to enhance the local search ability,and the global search and the local development capabilities are balanced to avoid local optimum.Finally,an improved algorithm,KMeans variation sine cosine algorithm(KVSCA),is formed,using KMeans clustering.Through an adoption of 23 benchmark test functions and 1 actual optimization engineering problem,the simulation experiment optimizes the target problem by using the improved KVSCA algorithm,the improved sine cosine algorithm of Cauchy chaotic mutation(IWCCSCA),and the traditional sine and cosine optimization algorithm respectively.Through an analysis of the variance,mean,and minimum of the optimization results,the stability,convergence accuracy and convergence speed of the results of the KVSCA algorithm are all optimal,which verifies the efficiency and a stronger stability of the local convergence of the KVSCA algorithm.