一种多样性控制的多目标粒子群算法

doi:10.19665/j.issn1001-2400.2021.03.014

Abstract

Abstract:

For solving the premature in traditional multiobjective particle swarm optimization,a multi-objective particle swarm optimization based on diversity control is proposed.The proposed algorithm utilizes a diversity metric,which is based on weight vectors,to evaluate the population diversity in each generation and control the evolution process of the algorithm adaptively.To maintain population diversity,an adaptive mutation strategy based on Steffensen’s method is adopted to update the repository population.With the purpose of balancing the population diversity and convergence,the global best positions of particles areselected adaptively.This algorithm is compared with several widely used multiobjective evolutionary algorithms on a set of benchmark test problems in the experimental part.Statistical results demonstrate the effectiveness of the proposed algorithm.

Key words: multiobjective optimization, particle swarm optimization, adaptive algorithms, diversity control, Steffensen’s method

CLC Number:

TP301.6

LIU Tianyu,WANG Zhu. Diversity controlled multiobjective particle swarm optimization[J].Journal of Xidian University, 2021, 48(3): 106-114.

Figures/Tables 16

References 17

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算法	参数设置
MOPSO	学习因子w=0.4
dMOPSO	年龄阈值T_a=2;惩罚因子θ=5
NSGA-II	文叉概率p_c=0.9;变异概率p_m=1/N;交叉因子η _c=20;变异因子η_m=20
MOEA/D	对2目标及3目标问题,权值向量数目分别为100和105;邻域规模δ=20
MOPSO-DC	对2目标及3目标问题,权值向量数目分别为10和21;学习因子w=0.4;邻域规模δ=5,控制参数s=0.7

问题	平均IGD值
问题	s=0.1	s=0.3	s=0.5	s=0.7	s=0.9
ZDT 1	4.58e-03	4.89e-03	4.16e-03	4.01e-03	4.25e-03
ZDT 4	1.39e+01	1.60e+01	9.94e+00	1.14e+01	1.64e+01
DTLZ 2	5.55e-02	5.62e-02	5.53e-02	5.48e-02	5.57e-02

问题	算法
问题	MOPSO-DC	MOPSO	dMOPSO	NSGA-II	MOEA/D
ZDT 1	4.01e-03 (1)	2.70e+01 (5)	234e-02 (2)	1.64e-01 (3)	1.76e-01 (4)
ZDT 2	4.18e-03 (1)	4.78e+01 (5)	3.79e-01 (3)	5.21e-01 (4)	3.30e-01 (2)
ZDT 3	3.74e-03 (1)	4.54e+01 (5)	2.32e-02 (2)	1.95e-01 (3)	2.06e-01 (4)
ZDT 4	1.14e+01 (4)	2.32e+01 (5)	5.68e-01 (3)	2.92e-01 (1)	4.38e-01 (2)
ZDT 6	3.40e-03 (1)	4.22e-01 (5)	4.58e-03 (2)	7.27e-02 (3)	9.75e-02 (4)
DTLZ 1	9.07e+00 (4)	1.09e+01 (5)	8.45e+00 (3)	9.16e-02 (2)	4.01e-02 (1)
DTLZ 2	5.48e-02 (1)	1.05e-01 (4)	1.37e-01 (5)	7.14e-02 (3)	6.14e-02 (2)
DTLZ 3	1.90e+02 (4)	2.62e+02 (5)	3.76e+01 (3)	8.31e+00 (1)	1.38e+01 (2)
WFG 1	1.52e+00 (3)	1.96e+00 (5)	1.55e+00 (4)	1.04e+00 (1)	1.16e+00 (2)
WFG 2	2.04e-01 (1)	3.23e-01 (4)	3.71e-01 (5)	2.22e-01 (2)	3.21e-01 (3)
WFG 3	1.56e-01 (2)	3.58e-01 (3)	4.05e-01 (4)	1.18e-01 (1)	4.63e-01 (5)
WFG 4	2.68e-01 (1)	4.15e-01 (5)	3.92e-01 (4)	2.79e-01 (2)	2.95e-01 (3)
WFG 5	2.59e-01 (1)	3.63e-01 (4)	3.95e-01 (5)	2.86e-01 (3)	2.78e-01 (2)
WFG 6	2.64e-01 (1)	4.88e-01 (5)	4.48e-01 (4)	3.27e-01 (3)	3.00e-01 (2)
WFG 7	2.62e-01 (1)	4.43e-01 (4)	4.67e-01 (5)	2.80e-01 (2)	4.35e-01 (3)
WFG 8	3.74e-01 (1)	3.86e-01 (2)	5.99e-01 (5)	3.96e-01 (4)	3.91e-01 (3)
WFG 9	2.53e-01 (1)	3.88e-01 (4)	3.67e-01 (3)	2.64e-01 (2)	4.47e-01 (5)

问题	算法
问题	MOPSO-DC	MOPSO	dMOPSO	NSGA-II	MOEA/D
ZDT 1	4.54e-03 (1)	2.61e-02 (5)	1.02e-02 (2)	1.32e-02 (3)	2.26e-02 (4)
ZDT 2	4.51e-03 (1)	1.84e-02 (4)	5.40e-03 (2)	4.88e-02 (5)	1.09e-02 (3)
ZDT 3	7.34e-03 (1)	3.18e-02 (4)	2.52e-02 (3)	1.54e-02 (2)	6.46e-02 (5)
ZDT 4	1.04e-01 (3)	1.06e-01 (4)	3.52e-03 (1)	2.22e-01 (5)	1.35e-02 (2)
ZDT 6	2.17e-03 (1)	2.05e-01 (5)	3.37e-03 (2)	1.31e-02 (3)	3.30e-02 (4)
DTLZ 1	2.56e+00 (3)	6.17e+00 (4)	6.25e+00 (5)	2.34e-02 (1)	2.56e-02 (2)
DTLZ 2	5.22e-02 (1)	6.41e-02 (4)	6.55e-02 (5)	5.37e-02 (2)	5.60e-02 (3)
DTLZ 3	2.89e+01 (3)	6.86e+01 (5)	4.87e+01 (4)	4.66e-01 (1)	1.67e+00 (2)
WFG 1	7.18e-02 (1)	4.71e-01 (5)	1.84e-01 (3)	3.58e-01 (4)	1.68e-01 (2)
WFG 2	2.66e-01 (2)	2.88e-01 (4)	2.81e-01 (3)	2.95e-01 (5)	1.19e-01 (1)
WFG 3	1.14e-01 (1)	1.43e-01 (3)	2.13e-01 (4)	1.17e-01 (2)	2.23e-01 (5)
WFG 4	2.26e-01 (3)	2.01e-01 (1)	2.42e-01 (4)	2.25e-01 (2)	2.79e-01 (5)
WFG 5	2.01e-01 (1)	2.04e-01 (2)	3.23e-01 (5)	2.27e-01 (3)	2.42e-01 (4)
WFG 6	2.03e-01 (1)	2.18e-01 (2)	2.51e-01 (4)	2.35e-01 (3)	2.65e-01 (5)
WFG 7	2.15e-01 (3)	1.78e-01 (1)	2.64e-01 (4)	2.04e-01 (2)	3.24e-01 (5)
WFG 8	2.39e-01 (2)	1.99e-01 (1)	2.65e-01 (3)	2.67e-01 (4)	3.00e-01 (5)
WFG 9	2.00e-01 (2)	1.83e-01 (1)	2.88e-01 (4)	2.07e-01 (3)	2.84e-01 (5)

问题	算法
问题	MOPSO-DC	MOPSO	dMOPSO	NSGA-II	MOEA/D
IGD指标	1.71	4.41	3.65	2.35	2.88
SP指标	1.76	3.24	3.41	2.94	3.65

Diversity controlled multiobjective particle swarm optimization

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