Hybrid dragonfly algorithm based on subpopulation and differential evolution

doi:10.11772/j.issn.1001-9081.2022060813

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (9): 2868-2876.DOI: 10.11772/j.issn.1001-9081.2022060813

• Advanced computing • Previous Articles Next Articles

Hybrid dragonfly algorithm based on subpopulation and differential evolution

Bo WANG, Hao WANG, Xiaoxin DU, Xiaodong ZHENG, Wei ZHOU

School of Computer and Control Engineering，Qiqihar University，Qiqihar Heilongjiang 161006，China

Received:2022-06-06 Revised:2022-08-17 Accepted:2022-08-22 Online:2022-09-22 Published:2023-09-10
Contact: Bo WANG
About author:WANG Hao， born in 1996， M. S. candidate. His research interests include intelligent optimization algorithm.
DU Xiaoxin， born in 1983， M. S.， professor. Her research interests include intelligent optimization algorithm， machine learning.
ZHENG Xiaodong， born in 1981， M. S.， lecturer. His research interests include machine learning.
ZHOU Wei， born in 1999， M. S. candidate. Her research interests include intelligent optimization algorithm.
Supported by:
Fundamental Research Funds for Young Innovative Talents in Heilongjiang Provincial Higher Education Institutions(135509210)

基于亚群和差分进化的混合蜻蜓算法

王波, 王浩, 杜晓昕, 郑晓东, 周薇

齐齐哈尔大学计算机与控制工程学院，黑龙江齐齐哈尔 161006

通讯作者: 王波
作者简介:王浩（1996—），男，河南商丘人，硕士研究生，主要研究方向：智能优化算法
杜晓昕（1983—），女，江苏徐州人，教授，硕士，主要研究方向：智能优化算法、机器学习
郑晓东（1981—），男，黑龙江齐齐哈尔人，讲师，硕士，主要研究方向：机器学习
周薇（1999—），女，河北保定人，硕士研究生，主要研究方向：智能优化算法。
基金资助:
黑龙江省省属本科高校基本科研业务费青年创新人才项目(135509210)

Abstract

Abstract:

Aiming at the problems such as weak development ability， low population diversity， and premature convergence to local optimum in Dragonfly Algorithm （DA）， an HDASDE （Hybrid Dragonfly Algorithm based on Subpopulation and Differential Evolution） was proposed. Firstly， the basic dragonfly algorithm was improved： the chaotic factor and purposeful Levy flight were integrated to improve the optimization ability of the dragonfly algorithm， and a chaotic transition mechanism was proposed to enhance the exploration ability of the basic dragonfly algorithm. Secondly， opposition-based learning was introduced on the basis of DE （Differential Evolution） algorithm to strengthen the development ability of DE algorithm. Thirdly， a dynamic double subpopulation strategy was designed to divide the entire population into two dynamically changing subpopulations according to the ability that the subpopulation can improve the algorithm’s ability to jump out of the local optimum. Fourthly， the dynamic subgroup structure was used to fuse the improved dragonfly algorithm and the improved DE algorithm. The fused algorithm had good global exploration ability and strong local development ability. Finally， HDASDE was applied to 13 typical complex function optimization problems and three-bar truss design optimization problem， and was compared with the original DA， DE and other meta-heuristic optimization algorithms. Experimental results show that， HDASDE outperforms DA， DE and ABC （Artificial Bee Colony） algorithms in all 13 test functions， outperforms Particle Swarm Optimization （PSO） algorithm in 12 test functions， and outperforms Grey Wolf Optimizer （GWO） algorithm in 10 test functions. And it performs well in the design optimization problem of three-bar truss.

Key words: dragonfly algorithm, dynamic double subpopulation, swarm intelligence algorithm, opposition-based learning, differential evolution

摘要：

针对蜻蜓算法（DA）存在开发能力弱、种群多样性低、易过早收敛至局部最优等问题，提出一种基于亚群和差分进化的混合蜻蜓算法（HDASDE）。首先，对基本蜻蜓算法进行改进：融入混沌因子和有目的的莱维飞行来提升蜻蜓算法的寻优能力，并提出混沌跃迁机制加强基本蜻蜓算法的勘探能力；其次，在差分进化（DE）算法的基础上引入反向学习加强DE算法的开发能力；再次，利用亚群策略提高算法跳出局部最优的能力，设计了一种动态双亚群策略将整个种群划分为动态变化的两个亚群；然后使用动态亚群结构将改进蜻蜓算法和改进DE算法进行融合，融合后的算法具有较好的全局勘探能力以及较强的局部开发能力。最后，将HDASDE应用于13个典型的复杂函数优化问题和三杆桁架的设计优化问题，并与原始的DA、DE算法以及其他元启发式优化算法进行对比。实验结果表明，HDASDE在所有13个测试函数中优于DA、DE、人工蜂群（ABC）算法；在12个测试函数中优于粒子群优化（PSO）算法；在10个测试函数中优于灰狼优化（GWO）算法。并且，在三杆桁架的设计优化问题中效果较好。

关键词: 蜻蜓算法, 动态双亚群, 群智能算法, 反向学习, 差分进化

CLC Number:

TP301.6

Bo WANG, Hao WANG, Xiaoxin DU, Xiaodong ZHENG, Wei ZHOU. Hybrid dragonfly algorithm based on subpopulation and differential evolution[J]. Journal of Computer Applications, 2023, 43(9): 2868-2876.

王波, 王浩, 杜晓昕, 郑晓东, 周薇. 基于亚群和差分进化的混合蜻蜓算法[J]. 《计算机应用》唯一官方网站, 2023, 43(9): 2868-2876.

Figures/Tables 12

Fig. 1 Schematic diagram of dynamic double subpopulation strategy

Fig.2 Levy flight trajectory

Fig. 3 One-dimensional opposition-based learning

Fig. 4 Flowchart of HDASDE

Tab.1 Test functions

函数表达式	维度d	搜索区域	全局最优
$F 1 (x) = ∑ i = 1 n x i 2$	30	［-100，100］	0
$F 2 (x) = ∑ i = 1 n x i + ∏ i = 1 n x i$	30	［-10，10］	0
$F 3 = ∑ i = 1 n ∑ i = 1 n x i 2$	30	［-100，100］	0
$F 4 = m a x i x i, - 1 < i < n$	30	［-100，100］	0
$F 5 (x) = ∑ i = 1 n - 1 100 x i + 1 - x i 2 2 + x i - 1 2$	30	［-30，30］	0
$F 6 (x) = ∑ i = 1 n [x i + 0.5] 2$	30	［-100，100］	0
$F 7 (x) = ∑ i = 1 n i x i 4 + r a n d o m 0,1$	30	［-1.28，1.28］	0
$F 8 (x) = ∑ i = 1 n - x i ⋅ s i n x i$	30	［-500，500］	-418.98d
$F 9 (x) = ∑ i = 1 n x i 2 - 10 c o s 2 π x i + 10$	30	［-5.12，5.12］	0
$F 10 (x) = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n c o s (2 π x i) + 20 + e$	30	［-32，32］	0
$F 11 (x) = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s x i / i + 1$	30	［-600，600］	0
$F 12 (x) = π n 10 s i n (π y 1) + ∑ i = 1 n - 1 y i - 1 2 1 + 10 s i n 2 (π y i + 1) + (y n - 1) 2 + μ (x i, 10,100,4); y i = 1 + x i + 1 / 4$	30	［-50，50］	0
$F 13 (x) = ∑ i = 1 n 0.1 s i n 2 (3 π x 1) + ∑ i = 1 n (x i - 1) 2 1 + s i n 2 (3 π x i + 1) + (x n - 1) 2 1 + s i n 2 (2 π x n) + ∑ i = 1 n μ (x i, 5,100,4)$	30	［-50，50］	0

Tab.1 Test functions

函数表达式	维度d	搜索区域	全局最优
$F 1 (x) = ∑ i = 1 n x i 2$	30	［-100，100］	0
$F 2 (x) = ∑ i = 1 n x i + ∏ i = 1 n x i$	30	［-10，10］	0
$F 3 = ∑ i = 1 n ∑ i = 1 n x i 2$	30	［-100，100］	0
$F 4 = m a x i x i, - 1 < i < n$	30	［-100，100］	0
$F 5 (x) = ∑ i = 1 n - 1 100 x i + 1 - x i 2 2 + x i - 1 2$	30	［-30，30］	0
$F 6 (x) = ∑ i = 1 n [x i + 0.5] 2$	30	［-100，100］	0
$F 7 (x) = ∑ i = 1 n i x i 4 + r a n d o m 0,1$	30	［-1.28，1.28］	0
$F 8 (x) = ∑ i = 1 n - x i ⋅ s i n x i$	30	［-500，500］	-418.98d
$F 9 (x) = ∑ i = 1 n x i 2 - 10 c o s 2 π x i + 10$	30	［-5.12，5.12］	0
$F 10 (x) = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n c o s (2 π x i) + 20 + e$	30	［-32，32］	0
$F 11 (x) = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s x i / i + 1$	30	［-600，600］	0
$F 12 (x) = π n 10 s i n (π y 1) + ∑ i = 1 n - 1 y i - 1 2 1 + 10 s i n 2 (π y i + 1) + (y n - 1) 2 + μ (x i, 10,100,4); y i = 1 + x i + 1 / 4$	30	［-50，50］	0
$F 13 (x) = ∑ i = 1 n 0.1 s i n 2 (3 π x 1) + ∑ i = 1 n (x i - 1) 2 1 + s i n 2 (3 π x i + 1) + (x n - 1) 2 1 + s i n 2 (2 π x n) + ∑ i = 1 n μ (x i, 5,100,4)$	30	［-50，50］	0

Tab. 2 Comparison of results of different algorithms on test functions

函数类型	测试函数	指标	HDASDE	DA	DE	PSO	ABC	GWO
单峰函数	F₁	最优值	0.00E+00	4.38E+01	2.39E-12	5.77E-01	3.18E-03	3.63E-68
		平均值	0.00E+00	4.44E+02	7.35E-12	1.81E+00	1.50E-02	4.72E-65
		标准差	0.00E+00	2.71E+02	4.09E-12	1.09E+00	7.81E-03	1.59E-64
	F₂	最优值	0.00E+00	1.68E+00	5.41E-08	0.00E+00	8.74E-04	1.58E-39
		平均值	3.87E-35	9.07E+00	9.33E-08	1.00E+00	1.81E-03	3.34E-38
		标准差	2.45E-34	2.88E+00	2.61E-08	3.04E+00	8.67E-04	3.61E-38
	F₃	最优值	9.00E-19	1.04E+02	1.90E+04	5.49E+01	2.09E+04	1.45E-22
		平均值	8.03E-12	1.61E+03	2.87E+04	1.40E+02	2.84E+04	2.10E-17
		标准差	3.79E-11	1.09E+03	4.49E+03	6.91E+01	3.67E+03	6.83E-17
	F₄	最优值	0.00E+00	2.99E+00	1.94E-01	2.43E+00	4.78E+01	5.57E-18
		平均值	0.00E+00	9.22E+00	3.07E-01	5.83E+00	5.73E+01	2.24E-16
		标准差	0.00E+00	2.98E+00	5.75E-02	2.06E+00	3.99E+00	3.15E-16
	F₅	最优值	0.00E+00	2.06E+02	2.47E+01	4.65E+01	8.89E+02	2.53E+01
		平均值	3.00E+00	1.02E+04	2.95E+01	5.41E+02	2.05E+03	2.67E+01
		标准差	8.28E+00	1.06E+04	1.29E+01	3.48E+02	8.52E+02	7.66E-01
	F₆	最优值	0.00E+00	1.87E+00	2.19E-12	4.77E-01	3.66E-03	8.91E-06
		平均值	0.00E+00	3.46E+02	6.94E-12	1.46E+00	1.29E-02	4.96E-01
		标准差	0.00E+00	2.11E+02	4.26E-12	6.54E-01	5.92E-03	2.86E-01
多峰函数	F₇	最优值	1.24E-03	1.13E-02	1.48E-01	9.14E-04	7.89E-02	1.40E-04
		平均值	5.90E-03	1.03E-01	3.77E-01	3.70E+00	1.27E-01	5.69E-04
		标准差	2.26E-03	6.41E-02	1.03E-01	6.32E+00	2.65E-02	3.35E-04
	F₈	最优值	-1.26E+04	-8.02E+03	-1.17E+04	-8.99E+03	-6.13E+03	-7.87E+03
		平均值	-1.26E+04	-3.19E+03	-8.93E+03	-5.01E+03	-4.77E+03	-3.43E+03
		标准差	1.84E-12	1.14E+03	6.98E+02	8.77E+02	3.12E+02	9.01E+02
	F₉	最优值	0.00E+00	1.56E+01	7.00E+01	6.94E+01	1.89E+02	0.00E+00
		平均值	0.00E+00	4.17E+01	8.65E+01	1.26E+02	2.19E+02	1.39E-01
		标准差	0.00E+00	1.27E+01	6.67E+00	3.21E+01	1.11E+01	8.80E-01
	F₁₀	最优值	4.44E-15	4.12E+00	3.54E-07	3.07E-01	1.11E-01	7.99E-15
		平均值	4.44E-15	5.69E+00	6.35E-07	3.36E+00	6.31E-01	1.43E-14
		标准差	0.00E+00	1.10E+00	1.36E-07	9.09E-01	5.12E-01	2.61E-15
	F₁₁	最优值	0.00E+00	1.13E+00	6.72E-12	5.59E-02	2.33E-01	0.00E+00
		平均值	0.00E+00	4.00E+00	5.80E-10	1.57E-01	5.07E-01	2.45E-03
		标准差	0.00E+00	1.93E+00	1.66E-09	4.99E-02	1.23E-01	6.24E-03
	F₁₂	最优值	1.57E-32	5.42E-01	5.94E-13	9.54E-01	2.42E+01	2.45E-06
		平均值	1.57E-32	4.11E+00	2.04E-12	6.06E+00	1.03E+03	3.48E-02
		标准差	5.54E-48	2.38E+00	1.37E-12	4.07E+00	5.57E+03	2.33E-02
	F₁₃	最优值	1.35E-32	4.95E+00	1.45E-12	4.04E-01	3.30E+01	2.80E-05
		平均值	1.35E-32	6.32E+01	8.04E-12	5.54E+00	2.92E+03	3.91E-01
		标准差	5.54E-48	2.23E+02	5.11E-12	8.55E+00	4.71E+03	1.85E-01

Tab. 2 Comparison of results of different algorithms on test functions

函数类型	测试函数	指标	HDASDE	DA	DE	PSO	ABC	GWO
单峰函数	F₁	最优值	0.00E+00	4.38E+01	2.39E-12	5.77E-01	3.18E-03	3.63E-68
		平均值	0.00E+00	4.44E+02	7.35E-12	1.81E+00	1.50E-02	4.72E-65
		标准差	0.00E+00	2.71E+02	4.09E-12	1.09E+00	7.81E-03	1.59E-64
	F₂	最优值	0.00E+00	1.68E+00	5.41E-08	0.00E+00	8.74E-04	1.58E-39
		平均值	3.87E-35	9.07E+00	9.33E-08	1.00E+00	1.81E-03	3.34E-38
		标准差	2.45E-34	2.88E+00	2.61E-08	3.04E+00	8.67E-04	3.61E-38
	F₃	最优值	9.00E-19	1.04E+02	1.90E+04	5.49E+01	2.09E+04	1.45E-22
		平均值	8.03E-12	1.61E+03	2.87E+04	1.40E+02	2.84E+04	2.10E-17
		标准差	3.79E-11	1.09E+03	4.49E+03	6.91E+01	3.67E+03	6.83E-17
	F₄	最优值	0.00E+00	2.99E+00	1.94E-01	2.43E+00	4.78E+01	5.57E-18
		平均值	0.00E+00	9.22E+00	3.07E-01	5.83E+00	5.73E+01	2.24E-16
		标准差	0.00E+00	2.98E+00	5.75E-02	2.06E+00	3.99E+00	3.15E-16
	F₅	最优值	0.00E+00	2.06E+02	2.47E+01	4.65E+01	8.89E+02	2.53E+01
		平均值	3.00E+00	1.02E+04	2.95E+01	5.41E+02	2.05E+03	2.67E+01
		标准差	8.28E+00	1.06E+04	1.29E+01	3.48E+02	8.52E+02	7.66E-01
	F₆	最优值	0.00E+00	1.87E+00	2.19E-12	4.77E-01	3.66E-03	8.91E-06
		平均值	0.00E+00	3.46E+02	6.94E-12	1.46E+00	1.29E-02	4.96E-01
		标准差	0.00E+00	2.11E+02	4.26E-12	6.54E-01	5.92E-03	2.86E-01
多峰函数	F₇	最优值	1.24E-03	1.13E-02	1.48E-01	9.14E-04	7.89E-02	1.40E-04
		平均值	5.90E-03	1.03E-01	3.77E-01	3.70E+00	1.27E-01	5.69E-04
		标准差	2.26E-03	6.41E-02	1.03E-01	6.32E+00	2.65E-02	3.35E-04
	F₈	最优值	-1.26E+04	-8.02E+03	-1.17E+04	-8.99E+03	-6.13E+03	-7.87E+03
		平均值	-1.26E+04	-3.19E+03	-8.93E+03	-5.01E+03	-4.77E+03	-3.43E+03
		标准差	1.84E-12	1.14E+03	6.98E+02	8.77E+02	3.12E+02	9.01E+02
	F₉	最优值	0.00E+00	1.56E+01	7.00E+01	6.94E+01	1.89E+02	0.00E+00
		平均值	0.00E+00	4.17E+01	8.65E+01	1.26E+02	2.19E+02	1.39E-01
		标准差	0.00E+00	1.27E+01	6.67E+00	3.21E+01	1.11E+01	8.80E-01
	F₁₀	最优值	4.44E-15	4.12E+00	3.54E-07	3.07E-01	1.11E-01	7.99E-15
		平均值	4.44E-15	5.69E+00	6.35E-07	3.36E+00	6.31E-01	1.43E-14
		标准差	0.00E+00	1.10E+00	1.36E-07	9.09E-01	5.12E-01	2.61E-15
	F₁₁	最优值	0.00E+00	1.13E+00	6.72E-12	5.59E-02	2.33E-01	0.00E+00
		平均值	0.00E+00	4.00E+00	5.80E-10	1.57E-01	5.07E-01	2.45E-03
		标准差	0.00E+00	1.93E+00	1.66E-09	4.99E-02	1.23E-01	6.24E-03
	F₁₂	最优值	1.57E-32	5.42E-01	5.94E-13	9.54E-01	2.42E+01	2.45E-06
		平均值	1.57E-32	4.11E+00	2.04E-12	6.06E+00	1.03E+03	3.48E-02
		标准差	5.54E-48	2.38E+00	1.37E-12	4.07E+00	5.57E+03	2.33E-02
	F₁₃	最优值	1.35E-32	4.95E+00	1.45E-12	4.04E-01	3.30E+01	2.80E-05
		平均值	1.35E-32	6.32E+01	8.04E-12	5.54E+00	2.92E+03	3.91E-01
		标准差	5.54E-48	2.23E+02	5.11E-12	8.55E+00	4.71E+03	1.85E-01

Fig. 5 Boxplots of unimodal function test

Fig. 6 Boxplots of multimodal function test

Tab.3 Wilcoxon signed-rank test

测试函数	DA	DE	PSO	ABC	GWO
（-/+/=）	13/0/0	13/0/0	12/1/0	13/0/0	10/2/1
F₁	-	-	-	-	-
F₂	-	-	+	-	-
F₃	-	-	-	-	+
F₄	-	-	-	-	-
F₅	-	-	-	-	-
F₆	-	-	-	-	-
F₇	-	-	-	-	+
F₈	-	-	-	-	-
F₉	-	-	-	-	-
F₁₀	-	-	-	-	-
F₁₁	-	-	-	-	=
F₁₂	-	-	-	-	-
F₁₃	-	-	-	-	-

Fig. 7 Partial function convergence curve comparison

Fig. 8 Three-bar truss structure

Tab.4 Optimal values obtained by different algorithms in solving three-bar truss design problem

算法	优化变量		最优值
算法	A₁	A₂	最优值
DA	0.784 043	0.421 509	263.911 867
DE	0.784 405	0.420 460	263.909 439
ABC	0.788 689	0.408 325	263.907 749
GWO	0.787 470	0.411 678	263.898 126
PSO	0.788 714	0.408 137	263.895 843
GOA	0.788 897	0.407 619	263.895 881
ALO	0.788 662	0.408 283	263.895 843
MGWO-Ⅲ	0.788 693	0.408 199	263.895 860
MGWO-Ⅱ	0.788 861	0.407 724	263.895 880
GWO-Ⅰ	0.788 561	0.408 571	263.895 890
SCA	0.789 068	0.407 162	263.898 380
MVO	0.788 993	0.407 351	263.895 940
GSA	0.777 622	0.448 853	264.829 960
CS	0.788 670	0.409 020	263.971 600
ERDSSA	0.795 000	0.395 000	264.300 000
HDASDE	0.788 668	0.408 265	263.895 843

References 30

1	HOLLAND J H. Genetic algorithms［J］. Scientific American， 1992， 267（1）：66-73. 10.1038/scientificamerican0792-66
2	AYDIN M E， FOGARTY T C. A distributed evolutionary simulated annealing algorithm for combinatorial optimisation problems［J］. Journal of Heuristics， 2004， 10（3）：269-292. 10.1023/b:heur.0000026896.44360.f9
3	李晓磊，路飞，田国会，等. 组合优化问题的人工鱼群算法应用［J］. 山东大学学报（工学版）， 2004， 34（5）：64-67.
	LI X L， LU F， TIAN G H， et al. Applications of artificial fish school algorithm in combinatorial optimization problems［J］. Journal of Shandong University （Engineering Science）， 2004， 34（5）：64-67.
4	GANDOMI A H， YANG X S， ALAVI A H. Cuckoo search algorithm： a metaheuristic approach to solve structural optimization problems［J］. Engineering with Computers， 2013， 29（1）：17-35. 10.1007/s00366-011-0241-y
5	DERELI S. A novel approach based on average swarm intelligence to improve the whale optimization algorithm［J］. Arabian Journal for Science and Engineering， 2022， 47（2）：1763-1776. 10.1007/s13369-021-06042-3
6	MIRJALILI S. Dragonfly algorithm： a new meta-heuristic optimization technique for solving single-objective， discrete， and multi-objective problems［J］. Neural Computing and Applications， 2016， 27（4）：1053-1073. 10.1007/s00521-015-1920-1
7	THARWAT A， GABEL T， HASSANIEN A E. Parameter optimization of support vector machine using dragonfly algorithm［C］// Proceedings of the 2017 International Conference on Advanced Intelligent Systems and Informatics， AISC 639. Cham： Springer， 2018： 309-319. 10.1007/978-3-319-64861-3_29
8	NAIR S P， MARY LINDA M. An efficient maximum power point tracking in hybrid solar and wind energy system： a combined MDA-RNN technique［J］. Journal of Intelligent and Fuzzy Systems， 2019， 37（4）：5495-5514. 10.3233/jifs-190591
9	SALAM M A， ZAWBAA H M， EMARY E， et al. A hybrid dragonfly algorithm with extreme learning machine for prediction［C］// Proceedings of the 2016 International Symposium on INnovations in Intelligent SysTems and Applications. Piscataway： IEEE， 2016： 1-6. 10.1109/inista.2016.7571839
10	MAFARJA M M， ELEYAN D， JABER I， et al. Binary dragonfly algorithm for feature selection［C］// Proceedings of the 2017 International Conference on New Trends in Computing Sciences. Piscataway： IEEE， 2017： 12-17. 10.1109/ictcs.2017.43
11	BHESDADIYA R H， PANDYA M H， TRIVEDI I N， et al. Price penalty factors based approach for combined economic emission dispatch problem solution using dragonfly algorithm［C］// Proceedings of the 2016 International Conference on Energy Efficient Technologies for Sustainability. Piscataway： IEEE， 2016： 436-441. 10.1109/iceets.2016.7583794
12	MARGARITA A D C， NOE O S， HINOJOSA S， et al. A multi-level thresholding method for breast thermograms analysis using dragonfly algorithm［J］. Infrared Physics and Technology， 2018， 93：346-361. 10.1016/j.infrared.2018.08.007
13	SCREE RANJINI K S， MURUGAN S. Memory based hybrid dragonfly algorithm for numerical optimization problems［J］. Expert Systems with Applications， 2017， 83：63-78. 10.1016/j.eswa.2017.04.033
14	SAYED G I， THARWAT A， HASSANIEN A E. Chaotic dragonfly algorithm： an improved metaheuristic algorithm for feature selection［J］. Applied Intelligence， 2019， 49（1）：188-205. 10.1007/s10489-018-1261-8
15	SINGH P， MEENA N K， YANG J， et al. Modified dragonfly optimisation for distributed energy mix in distribution networks［J］. Energies， 2021， 14（18）： No.5690. 10.3390/en14185690
16	CUI X T， LI Y， FAN J H， et al. A hybrid improved dragonfly algorithm for feature selection［J］. IEEE Access， 2020， 8：155619-155629. 10.1109/access.2020.3012838
17	张水平，高栋. 基于随机替换和混合变异的蜻蜓算法［J］. 科学技术与工程， 2020， 20（22）：9108-9115. 10.3969/j.issn.1671-1815.2020.22.038
	ZHANG S P， GAO D. Dragonfly algorithm based on random replacement and hybrid mutation［J］. Science Technology and Engineering， 2020， 20（22）：9108-9115. 10.3969/j.issn.1671-1815.2020.22.038
18	STORN R， PRICE K. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces［J］. Journal of Global Optimization， 1997， 11（4）：341-359. 10.1023/a:1008202821328
19	汤安迪，韩统，徐登武，等. 混沌多精英鲸鱼优化算法［J］. 北京航空航天大学学报， 2021， 47（7）：1481-1494.
	TANG A D， HAN T， XU D W， et al. Chaos multi-elite whale optimization algorithm［J］. Journal of Beijing University of Aeronautics and Astronautics， 2021， 47（7）：1481-1494.
20	LÜ Q Z， JIANG J H， YU R Q， et al. A genetic algorithm based on prepotency evolution using chaotic initiation used for network training［J］. Journal of Chemical Information and Computer Sciences， 2003， 43（4）：1132-1137. 10.1021/ci020068t
21	KAUR G， ARORA S. Chaotic whale optimization algorithm［J］. Journal of Computational Design and Engineering， 2018， 5（3）：275-284. 10.1016/j.jcde.2017.12.006
22	LIANG J J， SUGANTHAN P N. Dynamic multi-swarm particle swarm optimizer［C］// Proceedings of the 2005 IEEE Swarm Intelligence Symposium. Piscataway： IEEE： 2005： 124-129.
23	WOLPERT D H， MACREADY W G. No free lunch theorems for optimization［J］. IEEE Transactions on Evolutionary Computation， 1997， 1（1）：67-82. 10.1109/4235.585893
24	SAREMI S， MIRJALILI S， LEWIS A. Biogeography-based optimisation with chaos［J］. Neural Computing and Applications， 2014， 25（5）：1077-1097. 10.1007/s00521-014-1597-x
25	RAHNAMAYAN S， TIZHOOSH H R， SALAMA M M A. Opposition-based differential evolution［J］. IEEE Transactions on Evolutionary Computation， 2008， 12（1）： 64-79. 10.1109/tevc.2007.894200
26	KARABOGA D， BASTURK B. On the performance of Artificial Bee Colony （ABC） algorithm［J］. Applied Soft Computing， 2008， 8（1）： 687-697. 10.1016/j.asoc.2007.05.007
27	KENNEDY J， EBERHART R. Particle swarm optimization［J］. Proceedings of the 1995 International Conference on Neural Networks - Volume 4. Piscataway： IEEE，1995： 1942-1948.
28	MIRJALILI S， MIRJALILI S M， LEWIS A. Grey wolf optimizer［J］. Advances in Engineering Software， 2014， 69：46-61. 10.1016/j.advengsoft.2013.12.007
29	刘景森，袁蒙蒙，李煜. 基于改进樽海鞘群算法求解工程优化设计问题［J］. 系统仿真学报， 2021， 33（4）：854-866.
	LIU J S， YUAN M M， LI Y. Solving engineering optimization design problem based on improved salp swarm algorithm［J］. Journal of System Simulation， 2021， 33（4）：854-866.
30	BRÜTTING J， DESRUELLE J， SENATORE G， et al. Design of truss structures through reuse［J］. Structures， 2019， 18： 128-137. 10.1016/j.istruc.2018.11.006

[1]	Dahai LI, Meixin ZHAN, Zhendong WANG. Enhanced sparrow search algorithm based on multiple improvement strategies [J]. Journal of Computer Applications, 2023, 43(9): 2845-2854.
[2]	Jian LIN, Jingxuan YE, Wenwen LIU, Xiaowen SHAO. Multimodal differential evolution algorithm for solving capacitated vehicle routing problem [J]. Journal of Computer Applications, 2023, 43(7): 2248-2254.
[3]	Junxing XIANG, Yonghong WU. Hybrid salp swarm and butterfly optimization algorithm combined with neighborhood centroid opposition-based learning [J]. Journal of Computer Applications, 2023, 43(3): 820-826.
[4]	Zhongrui QIU, Hong MIAO, Chengbi ZENG. Improved slime mould algorithm with multi-strategy fusion [J]. Journal of Computer Applications, 2023, 43(3): 812-819.
[5]	Qingqing NIE, Dingsheng WAN, Yuelong ZHU, Zhijia LI, Cheng YAO. Hydrological model based on temporal convolutional network [J]. Journal of Computer Applications, 2022, 42(6): 1756-1761.
[6]	Xiaoping XU, Yangli TANG, Feng WANG. Artificial cooperative search algorithm for solving traveling salesman problems [J]. Journal of Computer Applications, 2022, 42(6): 1837-1843.
[7]	Rongrong DAI, Honghui LI, Xueliang FU. Data center flow scheduling mechanism based on differential evolution and ant colony optimization algorithm [J]. Journal of Computer Applications, 2022, 42(12): 3863-3869.
[8]	Xin YONG, Yuelin GAO, Yahua HE, Huimin WANG. Improved firefly algorithm based on multi-strategy fusion [J]. Journal of Computer Applications, 2022, 42(12): 3847-3855.
[9]	ZHANG Xiangfei, LU Yuming, ZHANG Pingsheng. Constrained multi-objective optimization algorithm based on coevolution [J]. Journal of Computer Applications, 2021, 41(7): 2012-2018.
[10]	TANG Andi, HAN Tong, XU Dengwu, XIE Lei. Path planning method of unmanned aerial vehicle based on chaos sparrow search algorithm [J]. Journal of Computer Applications, 2021, 41(7): 2128-2136.
[11]	CAI Ruiguang, ZHANG Desheng, XIAO Yanting. Parameter independent weighted local mean-based pseudo nearest neighbor classification algorithm [J]. Journal of Computer Applications, 2021, 41(6): 1694-1700.
[12]	JIA Heming, JIANG Zichao, LI Yao, SUN Kangjian. Simultaneous feature selection optimization based on improved spotted hyena optimizer algorithm [J]. Journal of Computer Applications, 2021, 41(5): 1290-1298.
[13]	Zhisheng SHAO, Guofu ZHANG, Zhaopin SU, Lei LI. Dynamic testing resource allocation algorithm based on software architecture and generalized differential evolution [J]. Journal of Computer Applications, 2021, 41(12): 3692-3701.
[14]	LI Erchao, YANG Rongrong. Multi-objective estimation of distribution algorithm with adaptive opposition-based learning [J]. Journal of Computer Applications, 2021, 41(1): 15-21.
[15]	LI Kewen, MA Xiangbo, HOU Wenyan. Enhanced fireworks algorithm with adaptive merging strategy and guidance operator [J]. Journal of Computer Applications, 2021, 41(1): 81-86.

Hybrid dragonfly algorithm based on subpopulation and differential evolution

基于亚群和差分进化的混合蜻蜓算法

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 12

References 30

Related Articles 15

Recommended Articles

Metrics