自适应多样性驱动的粒子群优化算法

张俐

doi:10.12263/DZXB.20250823

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自适应多样性驱动的粒子群优化算法

学术论文 | 更新时间：2026-04-24

- 自适应多样性驱动的粒子群优化算法
- Adaptive Diversity-Driven Particle Swarm Optimization
- 电子学报 2025年53卷第12期页码：4671-4685
- 作者机构：
  
  江苏理工学院计算机工程学院，江苏常州 213001
- 作者简介：
  
  [ "张俐男，1977年11月出生于陕西省汉中市.江苏理工学院计算机工程学院副教授.2019年毕业于北京邮电大学计算机学院（国家示范性软件学院），获工学博士学位.主要研究方向为智能优化算法、强化学习以及特征选择.E-mail: zhangli_3913@163.com" ]
- 基金信息：
  
  符号计算与知识工程教育部重点实验室课题(93K172023K08)
- DOI：10.12263/DZXB.20250823
  中图分类号： TP301.6
- 收稿：2025-09-22，
  
  录用：2025-12-01，
  
  纸质出版：2025-12-25
- 稿件说明：
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张俐. 自适应多样性驱动的粒子群优化算法[J]. 电子学报, 2025, 53(12): 4671-4685.

ZHANG Li. Adaptive Diversity-Driven Particle Swarm Optimization[J]. Acta Electronica Sinica, 2025, 53(12): 4671-4685.
张俐. 自适应多样性驱动的粒子群优化算法[J]. 电子学报, 2025, 53(12): 4671-4685. DOI：10.12263/DZXB.20250823

ZHANG Li. Adaptive Diversity-Driven Particle Swarm Optimization[J]. Acta Electronica Sinica, 2025, 53(12): 4671-4685. DOI：10.12263/DZXB.20250823

摘要

针对粒子群优化算法在处理高维、多峰以及复杂优化问题时存在的种群多样性快速丧失与早熟收敛等固有缺陷，本文提出一种自适应多样性驱动的粒子群优化算法（Adaptive Diversity-Driven Particle Swarm Optimization，ADDPSO）.该算法从初始化策略、多样性量化、参数自适应、信息交互结构与扰动机制五个维度进行系统化重构，以全面提升算法在复杂搜索空间中的全局探索能力、收敛精度与鲁棒性.首先，针对初始种群分布不均问题，设计基于Logistic混沌映射与均匀随机数的加权融合初始化策略，通过7∶3的比例兼顾序列遍历性与随机扰动性，显著提升初始解在高维空间中的覆盖均匀性.随后，引入基于平均欧氏距离的种群多样性量化指标，并定义多样性比率作为演化过程的实时反馈信号，为参数与策略的动态调整提供依据.在此基础上，提出时间递减规则与多样性比率双驱动的参数自适应机制，实现惯性权重与学习因子在探索与开发阶段间的平滑切换.进一步地，为克服传统速度更新对单一全局最优解的过度依赖，构建“个体认知-精英引导-种群分布”三层协同的速度更新架构.其中，精英引导通过维护精英档案并采用基于适应度的概率化选择策略，避免搜索方向趋同；种群分布项则引入基于适应度偏差的全局协同机制，通过均方根归一化与符号保留系数实现差异化引导.此外，算法融合多样性感知的模拟退火机制与多策略自适应变异操作，并引入双阈值接受准则，在维持收敛趋势的同时主动注入多样性，有效抑制早熟收敛.实验基于CEC2017测试集的12个高维复杂函数（包括混合函数F18、F19与复合函数F20~F29）及齿轮系设计问题进行系统验证.结果表明，ADDPSO在绝大多数函数上均取得最优或次优的平均值与标准差，尤其在F18、F20~F24、F27~F29等高度复杂函数上，其求解精度较主流PSO变体提升1~4个数量级，且表现出更优的稳定性.在齿轮系设计问题中，ADDPSO不仅稳定收敛至理论最优解，显著优于对比算法，充分验证其在工程优化中的可靠性与一致性.总之，ADDPSO通过多层次、多机制的协同设计，系统性地解决PSO在高维复杂优化中的多样性衰减与早熟收敛问题，展现出优异的综合性能与实际应用潜力.

Abstract

To address the inherent limitations of particle swarm optimization (PSO) in handling high-dimensional

multi-modal

and complex optimization problems

such as rapid loss of population diversity and premature convergence

an adaptive diversity-driven particle swarm optimization (ADDPSO) algorithm is proposed. This algorithm is systematically reconstructed across five dimensions—initialization strategy

diversity quantification

parameter adaptation

information exchange structure

and perturbation mechanism—to comprehensively enhance its global exploration capability

convergence accuracy

and robustness within complex search spaces. First

to address uneven initial population distribution

a weighted fusion initialization strategy combining Logistic chaotic mapping and uniform random numbers is designed. The ratio at 7:3 balances sequence traversal and random perturbation

significantly improving the uniformity of initial solution coverage in high-dimensional spaces. Second

a population diversity metric based on average Euclidean distance is introduced

with the diversity ratio defined as a real-time feedback signal for evolutionary adjustments

which enables dynamic parameter and strategy tuning. Built upon this

a dual-driven parameter adaptation mechanism combining time-decreasing rules and diversity ratio is proposed

enabling smooth transitions between inertia weight and learning rate during exploration and exploitation phases. Furthermore

to overcome the excessive reliance of traditional velocity updates on a single global optimum

a three-tiered collaborative velocity update architecture “individual cognition-elite guidance-population distribution” is constructed. Elite guidance prevents search direction convergence by maintaining an elite archive and employing probability-based selection strategies based on fitness. While the population distribution component introduces a global coordination mechanism based on fitness deviation

achieving differentiated guidance through root-mean-square normalisation and sign-preserving coefficients. Additionally

the algorithm integrates diversity-aware simulated annealing with multi-strategy adaptive mutation operations and incorporates a dual-threshold acceptance criterion. This approach actively injects diversity while maintaining convergence trends

effectively suppressing premature convergence. Experimental validation was conducted on the CEC2017 test set comprising 12 high-dimensional complex functions (including mixed functions F18~F19 and composite functions F20~F29) and a gear system design problem. Results demonstrate that ADDPSO achieves optimal or near-optimal mean and standard deviation values on most functions. Particularly for highly complex functions such as F18

F20~F24

and F27~F29

their solution accuracy surpasses mainstream PSO variants by 1 to 4 orders of magnitude while exhibiting superior stability. In gear system design problems

ADDPSO not only converged stably to theoretically optimal solutions but also significantly outperformed comparison algorithms

fully validating its reliability and consistency in engineering optimization. In summary

through multi-level

multi-mechanism collaborative design

ADDPSO systematically addresses PSO's diversity decay and premature convergence issues in high-dimensional complex optimization

demonstrating outstanding comprehensive performance and practical application potential.

关键词

Keywords

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