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基于维数学习和二次插值的混沌飞蛾火焰优化算法

王秋萍,郭佳丽,王晓峰   

  1. 西安理工大学理学院, 西安 710054
  • 出版日期:2021-05-25 发布日期:2021-08-11

王秋萍, 郭佳丽, 王晓峰. 基于维数学习和二次插值的混沌飞蛾火焰优化算法[J]. 系统科学与数学, 2021, 41(5): 1233-1244.

WANG Qiuping, GUO Jiali, WANG Xiaofeng. A Chaotic Moth Flame Optimization Algorithm Based on Dimension Learning and Quadratic Interpolation[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(5): 1233-1244.

A Chaotic Moth Flame Optimization Algorithm Based on Dimension Learning and Quadratic Interpolation

WANG Qiuping, GUO Jiali, WANG Xiaofeng   

  1. Faculty of Sciences, Xi’an University of Technology, Xi’an 710054
  • Online:2021-05-25 Published:2021-08-11
针对K-means算法对初始聚类中心敏感和容易陷入局部最优的 问题, 首先提出一种基于维数学习和二次插值的飞蛾火焰优化算法以提高 基本算法的求解精度和收敛速度, 即采用Tent混沌映射产生多样性较好的初始种群, 增 强算法的全局搜索能力; 对火焰位置采用维数学习策略生成更优良的火焰来指导飞蛾寻 优, 以提高算法的搜索效率; 把二次插值引入基本飞蛾火焰算法, 每次迭代利用二次函 数的极值点产生新的飞蛾个体, 增强算法的局部开发能力, 更好地平衡算法的探索与开 发能力, 从而改善了解的精度. 选取CEC 2017测试函数进行数值实验测试所提算法的性 能, 并与5个先进的元启发式算法比较, 结果表明: 所提出的算法具有更高的求解精度 和更强的鲁棒性. 然后, 将改进的飞蛾火焰算法用来优化聚类中心的位置, 5个UCI数 据集的实验结果表明改进的算法适用于求解K-means聚类问题, 且取得了好的聚类效果.
Aiming at the problem that the K-means algorithm suffers from being sensitive to the initial cluster center and being easily trapped into local optimum, this paper first presents a chaotic moth flame optimization algorithm based on dimension learning and quadratic interpolation to improve the quality of solution and convergence rate of the basic algorithm. The Tent chaotic map is used to generate the initial population with better diversity to enhance the global searching ability of the algorithm. Dimension learning strategy for flame location generates better flame to guide the moth finding the optimal solution so that the searching efficiency of the algorithm is improved. The quadratic interpolation is introduced into the basic moth flame algorithm. The algorithm uses extreme point of quadratic function to generate new moth individual in each iteration, which enhances the local exploitation ability of the algorithm, and better balances the exploration and exploitation ability of the algorithm, so as to improve the accuracy of solution. The CEC 2017 test functions are used to verify the proposed algorithm compared with 5 state-of-art meta-heuristic algorithms. The experimental results show that the proposed algorithm has higher accuracy and stronger robustness than the compared algorithms. The better performance of the proposed algorithm is then employed for optimizing the location of cluster centers and is tested using five benchmark datasets available from UCI machine learning laboratory. The experimental results show that the improved algorithm is suitable for solving K-means clustering problem, and good clustering results are obtained.} \EKeywords{Moth flame optimization algorithm, tent chaotic map, dimension learning, quadratic interpolation, K-means clustering.
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