Adaptive Particle Swarm Optimization Algorithm Based on Trap Label and Lazy Ant

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

Abstract

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

CLC Number:

TP391.9

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.

Figures/Tables 11

Fig. 1

Fig. 2

Fig. 3

Table 1

Table 2

Optimum configuration

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	$w = 0.9 ~ 0.4, c 1 = c 2 = 2, t = 10$

Table 2

Table 3

Table 4

Fig. 4

Fig. 5

Table 6

Optimization performance of each algorithm on 9 test functions

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

Table 6

References 18

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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

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