陷阱标记联合懒蚂蚁的自适应粒子群优化算法

doi:10.16182/j.issn1004731x.joss.23-0401

摘要/Abstract

摘要：

为解决现有粒子群改进策略无法帮助已陷入局部最优和过早收敛的粒子恢复寻优性能的问题，提出一种陷阱标记联合懒蚂蚁的自适应粒子群优化(adaptive particle swarm optimization based on trap label and lazy ant, TLLA-APSO)算法。陷阱标记策略为粒子群提供动态速度增量，使其摆脱最优解的束缚。利用懒蚂蚁寻优策略多样化粒子速度，提升种群多样性。通过惯性认知策略在速度更新中引入历史位置，增加粒子的路径多样性和提升粒子的探索性能，使粒子更有效地避免陷入新的局部最优。理论证明了引入历史位置的粒子群算法的收敛性。仿真实验结果表明，所提算法不仅能有效解决粒子群已陷入局部最优和过早收敛的问题，且与其他算法相比，具有较快的收敛速度和较高的寻优精度。

关键词: 粒子群优化算法, 懒蚂蚁, 陷阱标记, 局部最优, 过早收敛

Abstract:

Many existing strategies for improving particle swarm optimization (PSO) fall short in assisting particles trapped in local optima and experiencing premature convergence to recover optimization performance. In response, an adaptive particle swarm optimization algorithm based on trap label and lazy ant (TLLA-APSO) is proposed. Firstly, the trap label strategy dynamically adjusts particle velocities, enabling the particle swarm to escape from local optima. Secondly, the lazy ant optimization strategy is employed to diversify particle velocity and enhance population diversity.Finally, the inertia cognition strategy introduces historical position into velocity updates, promoting path diversity and particle exploration while effectively mitigating the risk of falling into new local optimum. The convergence of the particle swarm algorithm with the incorporation of historical positions has been empirically demonstrated. Simulation results validate the efficacy of TLLA-APSO, showcasing its ability to mitigate local optima and premature convergence while achieving faster convergence speed and higher optimization accuracy compared with other algorithms.

Key words: particle swarm optimization algorithm (PSO), lazy ant, trap label, local optima, premature convergence

中图分类号:

TP391.9

张伟,蒋岳峰 . 陷阱标记联合懒蚂蚁的自适应粒子群优化算法[J]. 系统仿真学报, 2024, 36(7): 1631-1642.

Zhang Wei,Jiang Yuefeng . Adaptive Particle Swarm Optimization Algorithm Based on Trap Label and Lazy Ant[J]. Journal of System Simulation, 2024, 36(7): 1631-1642.

图/表 11

图1

图2

图3

表1

表2

参数配置

算法	参数配置
GPSO	w=0.9~0.4, c₁=c₂=2
HPSO-TVAC	c₁=0.5, c₂=0.5~2.5
FIPS	w=0.729 8, $∑ i = 1 3 c i = 4.1$
CLPSO	w=0.729 8, c=1.496 18, m=7, Pc=0.05~0.5
OLPSO	w=0.9~0.4, c=2, G=5
GAPSO	w=0.9~0.4, c₁=c₂=2, P_c =0.5, P_m =0.05, ds=7
GLPSO	w=0.729 8, c=1.496 18, P_m =0.01, sg=7
CAPSO	$w m a x = 0.9, w m i n = 0.4, c m a x = 2.5, c m i n = 0.5, ξ = 0.2$
GEPSO	$c 1 = c 2 = c 3 = c 4 = α 1 = 3, α 2 = α 3 = 2, w 2 = w 3 = w 4 = w 5 = 0.5$
TLLA-APSO	$w = 0.9 ~ 0.4, c 1 = c 2 = 2, t = 10$

表2

表3

表4

表5

图4

图5

表6

各算法在9个测试函数上的寻优性能

函数		PSO	HPSO-TVAC	FIPS	CLPSO	OLPSO	GEPSO	GAPSO	GLPSO	CAPSO	TLLA-APSO
f₁	Mean	5.66e+01	2.09e-08	1.66e+01	3.75e-10	2.18e-12	4.16e-01	3.97e-07	8.00e-20	1.98e-02	0
	Best	2.00e+01	5.93e-10	1.40e+01	1.45e-10	9.96e-13	1.87e-02	6.36e-10	1.56e-20	1.50e-03	0
	Std	2.41e+01	2.64e-08	1.87e+01	1.63e-10	8.84e-13	5.17e-01	8.99e-07	4.35e-20	2.33e-02	0
	Rank	10	5	9	4	3	8	6	2	7	1
f₂	Mean	3.35e+03	8.16e-01	4.22e+02	3.41e+02	5.36e-02	3.01e+00	1.70e+00	3.72e-04	6.28e-02	0
	Best	2.01e+03	1.18e-01	2.29e+02	1.83e+02	1.60e-03	7.97e-01	3.23e-01	3.61e-05	1.60e-03	0
	Std	8.20e+02	8.42e-01	1.53e+02	1.21e+02	1.22e-01	2.63e+00	6.21e-01	2.87e-04	6.11e-02	0
	Rank	10	5	9	8	3	7	6	2	4	1
f₃	Mean	1.72e+05	8.78e+01	4.61e+03	5.01e+02	1.56e+01	9.28e+01	4.59e+01	3.11e+02	2.94e+01	9.76e+00
	Best	2.43e+04	1.75e+01	2.79e+03	5.10e+01	1.50e+00	2.02e+01	1.04e+01	2.97e+01	1.65e+01	9.71e-07
	Std	8.86e+04	8.89e+01	1.27e+03	2.89e+02	3.15e+01	4.21e+01	2.24e+01	2.41e+02	2.05e+01	1.30e+01
	Rank	10	5	9	8	2	6	4	7	3	1
f₄	Mean	1.33e+02	3.92e+00	2.00e+02	3.78e+00	7.71e+00	2.40e+01	4.52e-12	2.71e-01	4.81e+01	0
	Best	8.29e+01	5.32e-15	1.73e+02	9.95e-01	2.98e+00	1.99e+01	3.55e-15	0	1.98e+01	0
	Std	2.93e+01	3.13e+00	1.54e+01	1.69e+00	3.59e+00	5.53e+00	1.47e-11	4.53e-01	1.85e+01	0
	Rank	9	5	10	4	6	7	2	3	8	1
f₅	Mean	1.03e+01	2.56e-11	9.15e+00	5.67e-08	4.96e-10	2.54e+00	1.96e-04	6.92e-15	7.73e-04	0
	Best	1.34e+00	1.35e-13	7.96e+00	2.34e-08	1.94e-10	1.65e+00	5.02e-07	3.55e-15	6.52e-06	0
	Std	8.02e+00	5.12e-11	1.04e+00	2.65e-08	2.16e-10	6.01e-01	7.82e-04	7.94e-16	1.10e-03	0
	Rank	10	3	9	5	4	8	6	2	7	1
f₆	Mean	3.73e-02	2.83e-02	4.75e-01	4.58e-02	7.30e-03	7.01e-03	1.54e-12	3.70e-03	2.38e-02	0
	Best	1.69e-07	1.11e-16	3.70e-01	2.51e-05	0	6.21e-04	2.24e-14	0	8.56e-09	0
	Std	4.68e-02	3.60e-02	7.54e-02	2.02e-01	6.90e-03	3.90e-03	3.75e-12	5.60e-03	1.54e-02	0
	Rank	8	7	10	9	5	4	2	3	6	1
f₇	Mean	4.98e+01	2.15e-01	3.39e+01	4.54e-02	2.08e-18	3.23e+00	1.25e-04	1.49e-32	5.16e+00	2.06e-07
	Best	4.22e-01	6.56e-16	1.64e+01	1.33e-08	3.21e-19	1.88e+00	2.14e-15	1.49e-32	2.80e-03	7.83e-09
	Std	4.83e+01	2.69e-01	7.42e+00	1.39e-01	2.00e-18	1.88e+00	4.15e-04	5.60e-48	4.39e+00	1.66e-07
	Rank	10	6	9	5	2	7	4	1	8	3
f₈	Mean	2.21e-01	4.55e-01	7.82e+00	3.94e-01	1.41e+01	1.22e+00	3.25e-01	1.02e-01	5.56e-01	1.77e-01
	Best	1.76e-01	2.03e-01	6.01e+00	3.02e-01	1.20e-01	3.19e-01	1.16e-01	4.11e-02	1.42e-01	1.57e-01
	Std	3.65e-02	1.69e-01	1.90e+00	7.90e-02	3.65e+01	1.22e+00	1.42e-01	4.38e-02	1.85e-01	1.62e-02
	Rank	3	6	9	5	10	8	4	1	7	2
f₉	Mean	1.36e+00	8.39e-01	2.70e+00	5.76e-01	4.55e+00	2.00e+00	1.27e-01	2.78e-01	2.19e+00	1.58e-14
	Best	2.07e-01	1.52e-01	2.34e+00	3.90e-01	4.24e+00	7.02e-01	3.89e-02	9.72e-02	1.73e+00	0
	Std	8.60e-01	5.82e-01	2.11e-01	1.71e-01	1.53e-01	6.41e-01	1.17e-01	3.52e-01	5.64e-01	5.49e-14
	Rank	6	5	9	4	10	7	2	3	8	1

表6

参考文献 18

1	Hashim Fatma A, Houssein Essam H, Hussain Kashif, et al. Honey Badger Algorithm: New Metaheuristic Algorithm for Solving Optimization Problems[J]. Mathematics and Computers in Simulation, 2022, 192: 84-110.
2	Wang Shengliang, Liu Genyou, Gao Ming, et al. Heterogeneous Comprehensive Learning and Dynamic Multi-swarm Particle Swarm Optimizer with Two Mutation Operators[J]. Information Sciences, 2020, 540: 175-201.
3	Shami T M, El-Saleh Ayman A, Alswaitti M, et al. Particle Swarm Optimization: A Comprehensive Survey[J]. IEEE Access, 2022, 10: 10031-10061.
4	Sengupta S, Basak S, Peters R A II. Particle Swarm Optimization: A Survey of Historical and Recent Developments with Hybridization Perspectives[J]. Machine Learning and Knowledge Extraction, 2019, 1(1): 157-191.
5	Yadav Vikash, Indresh Kumar Gupta. Modified Adaptive Inertia Weight Particle Swarm Optimisation for Data Clustering[J]. International Journal of Innovative Computing and Applications, 2022, 13(1): 34-40.
6	Ratnaweera A, Halgamuge S K, Watson H C. Self-organizing Hierarchical Particle Swarm Optimizer with Time-varying Acceleration Coefficients[J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255.
7	Piotrowski Adam P, Napiorkowski Jaroslaw J, Agnieszka E Piotrowska. Population Size in Particle Swarm Optimization[J]. Swarm and Evolutionary Computation, 2020, 58: 100718.
8	Li Wei, Meng Xiang, Huang Ying, et al. Multipopulation Cooperative Particle Swarm Optimization with a Mixed Mutation Strategy[J]. Information Sciences, 2020, 529: 179-196.
9	Aasam Abdul Karim, Nor Ashidi Mat Isa, Wei Hong Lim. Hovering Swarm Particle Swarm Optimization[J]. IEEE Access, 2021, 9: 115719-115749.
10	Sedighizadeh Davoud, Masehian E, Sedighizadeh Mostafa, et al. GEPSO: A New Generalized Particle Swarm Optimization Algorithm[J]. Mathematics and Computers in Simulation, 2021, 179: 194-212.
11	Liang J J, Qin A K, Suganthan P N, et al. Comprehensive Learning Particle Swarm Optimizer for Global Optimization of Multimodal Functions[J]. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 281-295.
12	Mendes R, Kennedy J, Neves J. The Fully Informed Particle Swarm: Simpler, Maybe Better[J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 204-210.
13	Zhan Zhihui, Zhang Jun, Li Yun, et al. Orthogonal Learning Particle Swarm Optimization[J]. IEEE Transactions on Evolutionary Computation, 2011, 15(6): 832-847.
14	Gong Yuejiao, Li Jingjing, Zhou Yicong, et al. Genetic Learning Particle Swarm Optimization[J]. IEEE Transactions on Cybernetics, 2016, 46(10): 2277-2290.
15	Premalatha K, Natarajan A M. Hybrid PSO and GA for Global Maximization[J]. International Journal of Open Problems in Computer Science and Mathematics, 2009, 2(4): 597-608.
16	Duan Youxiang, Chen Ning, Chang Lunjie, et al. CAPSO: Chaos Adaptive Particle Swarm Optimization Algorithm[J]. IEEE Access, 2022, 10: 29393-29405.
17	Imirzian N, Zhang Yizhe, Kurze C, et al. Automated Tracking and Analysis of Ant Trajectories Shows Variation in Forager Exploration[J]. Scientific Reports, 2019, 9(1): 13246.
18	Tseng H Y, Chu P H, Lu Haochun, et al. Easy Particle Swarm Optimization for Nonlinear Constrained Optimization Problems[J]. IEEE Access, 2021, 9: 124757-124767.

函数	含义	搜索范围
f₁	Schwefel	[-10,10]
f₂	Quadric	[-100,100]
f₃	Rosenbrock	[-30,30]
f₄	Rastrigin	[-5.12,5.12]
f₅	Ackley	[-32,32]
f₆	Griewank	[-30,30]
f₇	Levy	[-30,30]
f₈	Happy Cat	[-100,100]
f₉	Expanded Schaffer’s F6	[-100,100]

函数	陷阱值
Schwefel	1.42e-06
Rosenbrock	2.02e+01
Rastrigin	9.65e+01
Quadric	1.38e+00
Levy	8.90e+00
Griewank	3.45e-02
Ackley	1.77e+00

函数	GLPSO			TLLA-APSO
函数	跳出陷阱	迭代次数	最优解	跳出陷阱	迭代次数	最优解
Schwefel	√	183	3.26e-08	√	13	2.32e-08
Rosenbrock	×	—	1.71e+01	√	853	1.87e+00
Rastrigin	√	20	1.89e+01	√	16	4.17e+00
Quadric	√	387	1.32e-01	√	12	5.10e-03
Levy	√	11	3.98e-01	√	51	5.48e-01
Griewank	×	—	3.45e-02	√	15	1.80e-03
Ackley	√	183	1.18e-01	√	12	1.18e-01

函数	CLPSO		OLPSO		GLPSO		TLLA-APSO
函数	多样性	排名	多样性	排名	多样性	排名	多样性	排名
Schwefel	4.71e-52	4	5.04e-47	3	3.72e-14	2	5.49e-12	1
Rosenbrock	2.47e-07	3	4.73e-09	4	1.98e+01	2	2.87e+02	1
Rastrigin	2.20e-19	3	5.02e-19	4	1.96e+00	2	1.81e+01	1
Quadric	1.05e-05	3	2.73e-05	4	4.40e+00	2	2.82e+01	1
Levy	3.75e-17	4	1.18e-16	3	1.15e+01	2	2.73e+03	1
Griewank	2.24e-16	4	1.92e-16	3	3.21e+00	2	2.03e+01	1
Ackley	1.00e-18	3	2.75e-18	4	1.06e+00	2	1.37e+01	1

[1]	张振利, 汪永壮, 秦耀, 杨杰. 基于Levant微分器的磁浮球控制算法研究[J]. 系统仿真学报, 2024, 36(7): 1586-1595.
[2]	龚建兴, 王子沐, 杨奇龙. 基于粒子群算法的训练仿真想定优化生成方法[J]. 系统仿真学报, 2023, 35(9): 1860-1870.
[3]	王闯, 张勇, 李学贵, 董宏丽. 改进粒子群优化算法及其在聚类分析中应用[J]. 系统仿真学报, 2020, 32(8): 1577-1587.
[4]	陈海亮, 陈彬, 袁鹏, 董健, 艾川. 基于观测数据的社交网络推断方法研究[J]. 系统仿真学报, 2019, 31(12): 2712-2720.
[5]	曾艳阳, 张泽浩, 冯云霞. 自适应可调混沌粒子群算法的体绘制视点选择[J]. 系统仿真学报, 2018, 30(12): 4595-4601.
[6]	仇永斌, 张树春, 王元诚, 范文澜, 李德鑫. 最优粒子初值有效估计的线阵列方向图优化算法[J]. 系统仿真学报, 2018, 30(11): 4079-4085.
[7]	黄松, 王艳, 纪志成. 多信息特征粒子群优化算法的动态经济负荷分配[J]. 系统仿真学报, 2017, 29(9): 2159-2167.
[8]	徐小平, 朱秋秋, 王峰. 求解圆排列问题的粒子群蚁群优化算法[J]. 系统仿真学报, 2017, 29(2): 248-254.
[9]	贾盼盼, 曾艳阳, 冯云霞. 粒子群优化算法的三维可视化最佳视点选取[J]. 系统仿真学报, 2017, 29(10): 2384-2390.
[10]	张聚伟, 王宇. 基于PSO的有向传感器网络覆盖增强策略及仿真[J]. 系统仿真学报, 2017, 29(1): 181-189.
[11]	刘俊霞, 熊新荣, 胡兵. 基于PSO和ESNs的马铃薯贮藏库温度预测控制[J]. 系统仿真学报, 2016, 28(7): 1701-1705.
[12]	王兴武, 王兵树, 张照彦, 刘志宾. 基于铭牌数据结合PSO的异步电机参数辨识研究[J]. 系统仿真学报, 2016, 28(6): 1469-1475.
[13]	孙欣欣, 王兴伟, 黄敏. 一种基于自适应和声粒子群搜索的可信QoS路由机制[J]. 系统仿真学报, 2016, 28(3): 741-748.
[14]	张彪, 邢健峰, 纪志成. 基于优化SVM的反渗透脱盐水故障诊断[J]. 系统仿真学报, 2015, 27(5): 1057-1063.