电子学报 ›› 2021, Vol. 49 ›› Issue (6): 1068-1076.DOI: 10.12263/DZXB.20200148

• 学术论文 • 上一篇    下一篇

改进蝴蝶算法求解多维复杂函数优化问题

刘景森1,2, 马义想2, 李煜3   

  1. 1. 河南大学智能网络系统研究所, 河南开封 475004;
    2. 河南大学软件学院, 河南开封 475004;
    3. 河南大学管理科学与工程研究所, 河南开封 475004
  • 收稿日期:2020-02-04 修回日期:2020-05-27 出版日期:2021-06-25 发布日期:2022-06-25
  • 通讯作者: 李煜(通讯作者) 女,1969年生,河南开封人,博士,教授,研究方向:智能算法和电子商务等.E-mail:leey@henu.edu.cn
  • 作者简介:刘景森 男,1968年生,河南开封人,博士,教授,研究方向:智能算法、优化控制和网络安全等.E-mail:ljs@henu.edu.cn;马义想 女,1994年生,河南驻马店人,硕士研究生,研究方向:智能算法.E-mail:myxhenu@163.com
  • 基金资助:
    国家自然科学基金(No.71601071);河南省重点研发与推广专项(No.182102310886);河南大学研究生教育创新与质量提升项目(No.SYL18060145,No.SYL19050104)

Improved Butterfly Algorithm for Multi-dimensional Complex Function Optimization Problem

LIU Jing-sen1,2, MA Yi-xiang2, LI Yu3   

  1. 1. Institute of Intelligent Networks System, Henan University, Kaifeng, Henan 475004, China;
    2. College of Software, Henan University, Kaifeng, Henan 475004, China;
    3. Institute of Management Science and Engineering, Henan University, Kaifeng, Henan 475004, China
  • Received:2020-02-04 Revised:2020-05-27 Online:2021-06-25 Published:2022-06-25

摘要: 针对蝴蝶优化算法存在的问题,提出一种融合差分变异策略并根据进化代数自适应调整权重的蝴蝶优化算法.首先,在全局搜索阶段引入非线性惯性权重改善蝴蝶位置更新公式,自适应调节算法在不同进化时期的搜索范围和粒度,提高算法的收敛速度与寻优精度;然后通过加入F分布全局自适应随机变异对全局公式进一步改进,提升算法的全局探索遍历性,防止出现低精度早熟现象;最后在局部搜索阶段融入具有判定系数和扰动因子的双向差分变异策略,在不减损种群多样性的同时使蝴蝶个体的探索更具方向性,有利于算法摆脱局部极值点,加快收敛速度.理论分析证明了改进算法的时间复杂度与基本蝴蝶优化算法一致,6种代表性对比算法在CEC 2017基准函数上进行的多种维度测试结果表明,改进算法在求解高维复杂函数优化问题时收敛速度和寻优精度明显优于其它对比算法,维度变化对求解性能的影响更小,寻优性能更好更稳定.

关键词: 蝴蝶优化算法, 高维复杂函数, 差分变异, 非线性惯性权重, 扰动因子

Abstract: Aiming at the problem of butterfly optimization algorithm,this paper proposes a butterfly optimization algorithm which fuses the differential mutation strategy and adaptively adjusts the weight according to the evolutionary algebra.The nonlinear inertial weight is introduced in the global search stage to improve the update equation of butterfly position,the search range and granularity of the algorithm in different evolution periods are adjusted adaptively,and the convergence speed and optimization accuracy of the algorithm are improved.The global equation is further improved by adding F distribution global adaptive random mutation to improve the global search ergodicity of the algorithm,and prevent the occurrence of low precision precocious phenomenon.The bidirectional differential mutation strategy with decision coefficient and disturbance factor is integrated in the local search stage,which makes the exploration of butterfly individuals more directional without derogating the diversity of the population,which is beneficial to the algorithm to get rid of the local extremum points and speed up the convergence speed.The theoretical analysis proves that the time complexity of the improved algorithm is consistent with the basic butterfly optimization algorithm.The multi-dimensional test results of six representative contrast algorithms on benchmark functions of CEC 2017 show that the optimization accuracy and convergence speed of the improved algorithm is obviously better than those of other contrast algorithms in solving the optimization problem of high-dimensional complex functions,and the change of dimensions have less impact on the performance of the algorithm,and the optimization performance is better and more stable.

Key words: butterfly optimization algorithm, high-dimensional complex function, difference mutation, non-linearity inertia weight, disturbance factor

中图分类号: