Artificial bee colony algorithm based on multi-population combination strategy

doi:10.11772/j.issn.1001-9081.2021010064

Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (11): 3113-3119.DOI: 10.11772/j.issn.1001-9081.2021010064

• Artificial intelligence • Previous Articles Next Articles

Artificial bee colony algorithm based on multi-population combination strategy

Wenxia LI, Linzhong LIU(), Cunjie DAI, Yu LI

School of Traffic and Transportation，Lanzhou Jiaotong University，Lanzhou Gansu 730070，China

Received:2021-01-13 Revised:2021-03-26 Accepted:2021-04-21 Online:2021-06-04 Published:2021-11-10
Contact: Linzhong LIU
About author:LI Wenxia， born in 1993， Ph. D. candidate. Her research interests include logistics supply chain management and algorithm optimization.
DAI Cunjie， born in 1982， Ph. D.， associate professor. His research interests include transportation network optimization.
LI Yu， born in 1990， Ph. D. candidate. Her research interests include logistics supply chain management.
Supported by:
the National Natural Science Foundation of China(71671079);the Gansu Natural Science Foundation(20JR5RA422);the Cooperation Project of Tianjin University-Lanzhou Jiaotong University Independent Innovation Fund(2020054)

基于多种群组合策略的人工蜂群算法

李文霞, 刘林忠(), 代存杰, 李玉

兰州交通大学交通运输学院，兰州 730070

通讯作者: 刘林忠
作者简介:李文霞（1993—），女，甘肃兰州人，博士研究生，主要研究方向：物流供应链管理及算法优化
代存杰（1982—），男，山东郓城人，副教授，博士，主要研究方向：交通网络优化
李玉（1990—），女，甘肃兰州人，博士研究生，主要研究方向：物流供应链管理。
基金资助:
国家自然科学基金资助项目(71671079);甘肃省自然科学基金资助项目(20JR5RA422);天津大学-兰州交通大学自主创新基金合作项目(2020054)

Abstract

Abstract:

In view of the disadvantages of the standard Artificial Bee Colony （ABC） algorithm such as weak development ability and slow convergence， a new ABC algorithm based on multi-population combination strategy was proposed. Firstly， the different-dimensional coordination and multi-dimensional matching update mechanisms were introduced into the search equation. Then， two combination strategies were designed for the hire bee and the follow bee respectively. The combination strategy was composed of two sub-strategies focusing on breadth exploration and depth development respectively. In the follow bee stage， the population was divided into free subset and non-free subset， and different sub-strategies were adopted by the individuals belonging to different subsets to balance the exploration and development ability of algorithm. The 15 benchmark functions were used to compare the proposed improved ABC algorithm with the standard ABC algorithm and other three improved ABC algorithms. The results show that the proposed algorithm has better optimization performance in both low-dimensional and high-dimensional problems.

Key words: Artificial Bee Colony (ABC) algorithm, update mechanism, combination strategy, population division, balance

摘要：

针对标准人工蜂群（ABC）算法存在开发能力弱、收敛速度慢的缺点，提出了一种基于多种群组合策略的ABC算法。首先，将异维协同和多维匹配的更新机制引入搜索方程；然后，针对雇佣蜂和跟随蜂分别设计了两种组合策略，组合策略是由侧重于广度探索和深度开发的两个子策略构成。在跟随蜂阶段，将种群划分为自由子集和非自由子集，并使属于不同子集的个体采用不同的子策略，从而平衡算法的探索与开发能力。通过15个标准测试函数将所提改进ABC算法与标准ABC算法和其他3种改进ABC算法进行仿真对比，结果表明所提算法在低维和高维问题中都具有更好的寻优性能。

关键词: 人工蜂群算法, 更新机制, 组合策略, 种群划分, 平衡

CLC Number:

TP301

Wenxia LI, Linzhong LIU, Cunjie DAI, Yu LI. Artificial bee colony algorithm based on multi-population combination strategy[J]. Journal of Computer Applications, 2021, 41(11): 3113-3119.

李文霞, 刘林忠, 代存杰, 李玉. 基于多种群组合策略的人工蜂群算法[J]. 《计算机应用》唯一官方网站, 2021, 41(11): 3113-3119.

Figures/Tables 10

Fig. 1 Schematic diagram of multi-dimensional matching update

Fig. 2 Schematic diagram of different-dimensional single point update

Fig. 3 Population division

Fig. 4 Flow chart of MCABC algorithm

Tab. 1 Benchmark functions

函数编号	函数名称	搜索空间	最优值	可接受值
f ₁	Sphere	［ $-$ 100，100］	0	1E $- 8$
f ₂	SumSquares	［ $-$ 10，10］	0	1E $- 8$
f ₃	Step	［ $-$ 100，100］	0	1E $- 8$
f ₄	Quartic	［ $-$ 1.28，1.28］	0	1E $- 1$
f ₅	Rosenbrock	［ $-$ 10，10］	0	1E $- 1$
f ₆	Elliptic	［ $-$ 100，100］	0	1E $- 8$
f ₇	Schwefel2.22	［ $-$ 10，10］	0	1E $- 8$
f ₈	Schwefel2.21	［ $-$ 100，100］	0	1E+0
f ₉	Alpine	［ $-$ 10，10］	0	1E $- 8$
f ₁₀	Rastrigin	［ $-$ 5.12，5.12］	0	1E $- 8$
f ₁₁	Himmelblau	［ $-$ 5，5］	$-$ 78.3	$- 78$
f ₁₂	SumPower	［ $-$ 1，1］	0	1E $- 8$
f ₁₃	Schaffer	［ $-$ 100，100］	0	1E+0
f ₁₄	Ackley	［ $-$ 50，50］	0	1E $- 8$
f ₁₅	Griewank	［ $-$ 600，600］	0	1E $- 8$

Tab. 1 Benchmark functions

函数编号	函数名称	搜索空间	最优值	可接受值
f ₁	Sphere	［ $-$ 100，100］	0	1E $- 8$
f ₂	SumSquares	［ $-$ 10，10］	0	1E $- 8$
f ₃	Step	［ $-$ 100，100］	0	1E $- 8$
f ₄	Quartic	［ $-$ 1.28，1.28］	0	1E $- 1$
f ₅	Rosenbrock	［ $-$ 10，10］	0	1E $- 1$
f ₆	Elliptic	［ $-$ 100，100］	0	1E $- 8$
f ₇	Schwefel2.22	［ $-$ 10，10］	0	1E $- 8$
f ₈	Schwefel2.21	［ $-$ 100，100］	0	1E+0
f ₉	Alpine	［ $-$ 10，10］	0	1E $- 8$
f ₁₀	Rastrigin	［ $-$ 5.12，5.12］	0	1E $- 8$
f ₁₁	Himmelblau	［ $-$ 5，5］	$-$ 78.3	$- 78$
f ₁₂	SumPower	［ $-$ 1，1］	0	1E $- 8$
f ₁₃	Schaffer	［ $-$ 100，100］	0	1E+0
f ₁₄	Ackley	［ $-$ 50，50］	0	1E $- 8$
f ₁₅	Griewank	［ $-$ 600，600］	0	1E $- 8$

Tab. 2 Simulation results of five algorithms under low-dimensional functions （D=50）

算法	f₁				f₂				f₃
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	9.94E $-$ 16	6.88E $-$ 15	1.52E $-$ 16	1 461	6.92E $-$ 16	3.43E $-$ 13	1.49E-12	1 401	0.00E+00	3.65E+00	3.47E+00	342
GABC	6.94E $-$ 16	9.27E $-$ 16	6.94E $-$ 16	890	7.10E $-$ 16	8.88E-16	1.41E-16	846	0.00E+00	7.00E-01	6.57E-01	256
qABC	7.74E $-$ 16	9.98E $-$ 16	1.37E $-$ 16	1 049	7.75E $-$ 16	9.85E-16	8.37E-17	833	0.00E+00	2.00E-01	4.10E-01	232
CABC	4.59E $-$ 16	6.25E $-$ 16	1.20E $-$ 16	721	4.84E $-$ 16	6.01E-16	1.00E-16	682	0.00E+00	5.00E-02	2.24E-01	193
MCABC	1.84E-17	2.67E-17	3.84E-17	332	2.53E-16	3.71E-16	9.34E-17	523	0.00E+00	0.00E+00	0.00E+00	140
算法	f₄				f₅				f₆
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	2.16E-01	3.11E-01	4.74E-02	NaN	5.30E-04	2.76E-02	4.33E-02	3 332	6.59E-15	8.79E-15	1.32E $-$ 14	2 371
GABC	5.06E-02	9.16E-02	1.57E-02	2 182	7.90E-04	2.55E-01	5.91E-01	4 594	5.54E-16	8.39E-16	1.46E $-$ 16	1 365
qABC	4.07E-02	5.65E-02	9.54E-03	1 617	2.37E-04	1.82E-02	2.07E-02	2 382	6.67E-16	9.05E-15	3.66E $-$ 15	1 932
CABC	4.87E-02	6.56E-02	1.10E-02	1 256	1.47E-03	7.99E-02	1.51E-01	3 850	4.44E-16	6.01E-16	1.16E $-$ 16	1 095
MCABC	1.10E-02	1.62E-02	2.75E-03	189	1.47E-05	7.29E-01	2.23E+00	3 421	2.22E-17	3.27E-17	7.82E-17	419
算法	f₇				f₈				f₉
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	1.87E-13	2.21E-12	1.48E-13	2 269	5.50E+00	9.75E+00	2.27E+00	NaN	6.45E-10	2.76E-08	6.98E-08	4 818
GABC	2.05E-15	2.35E-15	1.56E-16	1 395	2.07E+00	2.85E+00	4.69E-01	NaN	1.37E-15	6.63E-07	2.73E-06	4 328
qABC	2.06E-15	2.45E-13	1.09E-14	1 411	2.89E+00	4.00E+00	6.16E-01	NaN	1.20E-15	2.52E-15	7.64E+16	1 247
CABC	1.11E-15	1.93E-15	2.52E-16	1 006	1.09E+00	1.46E+00	2.09E-01	NaN	1.20E-15	1.83E-15	2.37E-16	951
MCABC	7.28E-16	8.99E-16	1.60E-16	769	6.51E-05	1.79E-04	9.15E-05	1 548	5.55E-16	9.22E-16	1.43E-16	1 389
算法	f₁₀				f₁₁				f₁₂
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	0.00E+00	1.94E-11	8.71E-18	1 859	-7.83E+01	-7.83E+01	3.26E-15	760	2.19E-12	5.01E-11	1.56E-15	424
GABC	0.00E+00	0.00E+00	0.00E+00	1 410	-7.83E+01	-7.83E+01	0.00E+00	364	1.24E-17	3.91E-17	1.57E-18	255
qABC	0.00E+00	5.87E-17	8.71E-20	2 843	-7.83E+01	-7.83E+01	3.26E-15	479	1.67E-17	4.73E-17	1.73E-17	235
CABC	0.00E+00	0.00E+00	0.00E+00	1 483	-7.83E+01	-7.83E+01	3.26E-15	185	6.12E-18	2.90E-17	1.54E-17	240
MCABC	0.00E+00	0.00E+00	0.00E+00	691	-7.83E+01	-7.83E+01	0.00E+00	174	5.19E-19	4.95E-18	2.68E-20	356
算法	f₁₃				f₁₄				f₁₅
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	4.14E-01	4.53E-01	1.18E-02	1	7.63E-12	1.10E-11	3.09E-10	3 438	1.11E-16	1.99E-16	2.14E-17	1 714
GABC	3.12E-01	4.20E-01	3.59E-02	1	4.79E-13	5.91E-13	5.90E-15	2 124	0.00E+00	1.55E-16	1.85E-16	1 111
qABC	3.73E-01	4.38E-01	2.14E-02	1	4.79E-14	5.80E-13	6.01E-15	1 663	0.00E $+$ 00	1.60E-16	2.08E-16	1 029
CABC	3.12E-01	4.11E-01	3.52E-02	1	3.73E-14	6.39E-12	2.01E-12	2 552	0.00E+00	2.22E-17	4.55E-17	890
MCABC	1.26E-01	2.01E-01	4.16E-02	1	1.24E-15	2.22E-15	4.29E-16	1 855	0.00E+00	0.00E+00	0.00E+00	611

Tab. 2 Simulation results of five algorithms under low-dimensional functions （D=50）

算法	f₁				f₂				f₃
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	9.94E $-$ 16	6.88E $-$ 15	1.52E $-$ 16	1 461	6.92E $-$ 16	3.43E $-$ 13	1.49E-12	1 401	0.00E+00	3.65E+00	3.47E+00	342
GABC	6.94E $-$ 16	9.27E $-$ 16	6.94E $-$ 16	890	7.10E $-$ 16	8.88E-16	1.41E-16	846	0.00E+00	7.00E-01	6.57E-01	256
qABC	7.74E $-$ 16	9.98E $-$ 16	1.37E $-$ 16	1 049	7.75E $-$ 16	9.85E-16	8.37E-17	833	0.00E+00	2.00E-01	4.10E-01	232
CABC	4.59E $-$ 16	6.25E $-$ 16	1.20E $-$ 16	721	4.84E $-$ 16	6.01E-16	1.00E-16	682	0.00E+00	5.00E-02	2.24E-01	193
MCABC	1.84E-17	2.67E-17	3.84E-17	332	2.53E-16	3.71E-16	9.34E-17	523	0.00E+00	0.00E+00	0.00E+00	140
算法	f₄				f₅				f₆
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	2.16E-01	3.11E-01	4.74E-02	NaN	5.30E-04	2.76E-02	4.33E-02	3 332	6.59E-15	8.79E-15	1.32E $-$ 14	2 371
GABC	5.06E-02	9.16E-02	1.57E-02	2 182	7.90E-04	2.55E-01	5.91E-01	4 594	5.54E-16	8.39E-16	1.46E $-$ 16	1 365
qABC	4.07E-02	5.65E-02	9.54E-03	1 617	2.37E-04	1.82E-02	2.07E-02	2 382	6.67E-16	9.05E-15	3.66E $-$ 15	1 932
CABC	4.87E-02	6.56E-02	1.10E-02	1 256	1.47E-03	7.99E-02	1.51E-01	3 850	4.44E-16	6.01E-16	1.16E $-$ 16	1 095
MCABC	1.10E-02	1.62E-02	2.75E-03	189	1.47E-05	7.29E-01	2.23E+00	3 421	2.22E-17	3.27E-17	7.82E-17	419
算法	f₇				f₈				f₉
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	1.87E-13	2.21E-12	1.48E-13	2 269	5.50E+00	9.75E+00	2.27E+00	NaN	6.45E-10	2.76E-08	6.98E-08	4 818
GABC	2.05E-15	2.35E-15	1.56E-16	1 395	2.07E+00	2.85E+00	4.69E-01	NaN	1.37E-15	6.63E-07	2.73E-06	4 328
qABC	2.06E-15	2.45E-13	1.09E-14	1 411	2.89E+00	4.00E+00	6.16E-01	NaN	1.20E-15	2.52E-15	7.64E+16	1 247
CABC	1.11E-15	1.93E-15	2.52E-16	1 006	1.09E+00	1.46E+00	2.09E-01	NaN	1.20E-15	1.83E-15	2.37E-16	951
MCABC	7.28E-16	8.99E-16	1.60E-16	769	6.51E-05	1.79E-04	9.15E-05	1 548	5.55E-16	9.22E-16	1.43E-16	1 389
算法	f₁₀				f₁₁				f₁₂
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	0.00E+00	1.94E-11	8.71E-18	1 859	-7.83E+01	-7.83E+01	3.26E-15	760	2.19E-12	5.01E-11	1.56E-15	424
GABC	0.00E+00	0.00E+00	0.00E+00	1 410	-7.83E+01	-7.83E+01	0.00E+00	364	1.24E-17	3.91E-17	1.57E-18	255
qABC	0.00E+00	5.87E-17	8.71E-20	2 843	-7.83E+01	-7.83E+01	3.26E-15	479	1.67E-17	4.73E-17	1.73E-17	235
CABC	0.00E+00	0.00E+00	0.00E+00	1 483	-7.83E+01	-7.83E+01	3.26E-15	185	6.12E-18	2.90E-17	1.54E-17	240
MCABC	0.00E+00	0.00E+00	0.00E+00	691	-7.83E+01	-7.83E+01	0.00E+00	174	5.19E-19	4.95E-18	2.68E-20	356
算法	f₁₃				f₁₄				f₁₅
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	4.14E-01	4.53E-01	1.18E-02	1	7.63E-12	1.10E-11	3.09E-10	3 438	1.11E-16	1.99E-16	2.14E-17	1 714
GABC	3.12E-01	4.20E-01	3.59E-02	1	4.79E-13	5.91E-13	5.90E-15	2 124	0.00E+00	1.55E-16	1.85E-16	1 111
qABC	3.73E-01	4.38E-01	2.14E-02	1	4.79E-14	5.80E-13	6.01E-15	1 663	0.00E $+$ 00	1.60E-16	2.08E-16	1 029
CABC	3.12E-01	4.11E-01	3.52E-02	1	3.73E-14	6.39E-12	2.01E-12	2 552	0.00E+00	2.22E-17	4.55E-17	890
MCABC	1.26E-01	2.01E-01	4.16E-02	1	1.24E-15	2.22E-15	4.29E-16	1 855	0.00E+00	0.00E+00	0.00E+00	611

Tab. 3 Simulation results of 5 algorithms under high-dimensional functions （D=100）

算法	f₁				f₇
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	3.27E-15	5.99E-15	3.10E-15	3 264	2.47E-09	4.10E-09	1.19E-09	4 842
GABC	1.85E-15	2.24E-15	1.76E-16	1 941	5.84E-14	6.23E-14	2.51E-15	2 976
qABC	1.86E-15	6.27E-13	1.92E-12	2 154	4.52E-12	2.00E-10	8.77E-10	2 966
CABC	2.07E-15	2.27E-15	1.84E-16	1 491	4.09E-14	4.58E-14	2.80E-16	2 108
MCABC	5.25E-16	7.80E-16	1.49E-16	615	2.27E-15	2.88E-15	2.78E-16	1 637
算法	f₁₀				f₁₅
算法	Best	Mean	Std	Minc	Best	Mean	Std	Minc
ABC	3.41E-13	1.00E-08	3.06E-11	4 487	8.88E-16	5.14E-15	1.31E-14	3 201
GABC	0.00E+00	1.08E-13	7.80E-14	3 062	1.11E-16	6.93E-16	6.24E-16	2 077
qABC	4.54E-13	1.05E-10	1.21E-11	4 978	4.44E-16	9.15E-11	4.09E-10	1 795
CABC	0.00E+00	6.48E-12	2.65E-10	2 735	0.00E+00	4.21E-16	7.22E-16	1 692
MCABC	0.00E+00	6.82E-14	5.71E-14	1 686	0.00E+00	2.22E-17	4.55E-17	1 253

Fig. 5 Fifty-dimensional convergence graph of 4 benchmark functions

Fig. 6 One hundred-dimensional convergence graph of 4 benchmark functions

Tab. 4 Running time comparison of different algorithms

算法	时间	算法	时间	算法	时间
ABC	16.59	qABC	25.02	MCABC	19.33
GABC	27.41	CABC	24.11

References 27

1	HOLLAND J H. Adaptation in Natural and Artificial Systems： an Introductory Analysis with Applications to Biology， Control， and Artificial Intelligence ［M］. Cambridge： MIT Press， 1992： 22-29. 10.7551/mitpress/1090.001.0001
2	COLORNI A， DORIGO M， MANIEZZO V. Distributed optimization by ant colonies ［C］// Proceedings of the 1991 European Conference on Artificial Life. Amsterdam： Elsevier Publishing Company， 1991： 134-142. 10.1007/978-3-642-77489-8_14
3	KENNEDY J， EBERHART R C. Particle swarm optimization ［C］// Proceedings of the 1995 International Conference on Neural Networks. Piscataway： IEEE， 1995： 1942-1948. 10.1109/icnn.1995.488968
4	KARABOGA D. An idea based on honey bee swarm for numerical optimization： Technical Report-TR06 ［R］. Kayseri： Erciyes University， 2005.
5	曲志坚，张先伟，曹雁锋，等.基于自适应机制的遗传算法研究［J］.计算机应用研究，2015，32（11）：3222-3225，3229. 10.3969/j.issn.1001-3695.2015.11.004
	QU Z J， ZHANG X W， CAO Y F， et al. Research on genetic algorithm based on adaptive mechanism ［J］. Application Research of Computers， 2015， 32（11）：3222-3225， 3229. 10.3969/j.issn.1001-3695.2015.11.004
6	陆庆伟.一种改进的多种群遗传算法在车间布局的应用［J］.价值工程，2019，38（17）：206-208.
	LU Q W. Application of an improved multi-population genetic algorithm in workshop layout ［J］. Value Engineering， 2019， 38（17）： 206-208.
7	裴焱栋，顾克江.面向对象编码技术下的大个体问题的遗传算法［J］.南京师大学报（自然科学版），2015，38（1）：86-90. 10.3969/j.issn.1001-4616.2015.01.013
	PEI Y D， GU K J. Gene algorithm for long individual problems in object-oriented coding method ［J］. Journal of Nanjing Normal University （Natural Science Edition）， 2015， 38（1）： 86-90. 10.3969/j.issn.1001-4616.2015.01.013
8	姚俊峰，梅炽，彭小奇，等.混沌遗传算法及其应用［J］.系统工程，2001，19（1）：70-74. 10.3969/j.issn.1001-4098.2001.01.016
	YAO J F， MEI C， PENG X Q， et al. A new optimization approach — chaos genetic algorithm ［J］. Systems Engineering， 2001， 19（1）： 70-74. 10.3969/j.issn.1001-4098.2001.01.016
9	易正俊，李勇霞，易校石.自适应蚁群算法求解最短路径和TSP问题［J］.计算机技术与发展，2016，26（12）：1-5. 10.3969/j.issn.1673-629X.2016.12.001
	YI Z J， LI Y X， YI X S. Solving of shortest path problem and TSP with adaptive ant colony algorithm ［J］. Computer Technology and Development， 2016， 26（12）： 1-5. 10.3969/j.issn.1673-629X.2016.12.001
10	游晓明，刘升，吕金秋.一种动态搜索策略的蚁群算法及其在机器人路径规划中的应用［J］.控制与决策，2017，32（3）：552-556. 10.13195/j.kzyjc.2016.0005
	YOU X M， LIU S， LYU J Q. Ant colony algorithm based on dynamic search strategy and its application on path planning of robot ［J］. Control and Decision， 2017， 32（3）： 552-556. 10.13195/j.kzyjc.2016.0005
11	袁小平，蒋硕.基于分层自主学习的改进粒子群优化算法［J］.计算机应用，2019，39（1）：148-153. 10.11772/j.issn.1001-9081.2018061342
	YUAN X P， JIANG S. Improved particle swarm optimization algorithm based on hierarchical autonomous learning ［J］. Journal of Computer Applications， 2019， 39（1）： 148-153. 10.11772/j.issn.1001-9081.2018061342
12	EL-GALLAD A， EL-HAWARY M， SALLAM A， et al. Enhancing the particle swarm optimizer via proper parameters selection ［C］// Proceedings of the 2002 IEEE Canadian Conference on Electrical and Computer Engineering. Piscataway： IEEE， 2002： 792-797. 10.1109/ccece.2002.1013043
13	周文峰，梁晓磊，唐可心，等.具有拓扑时变和搜索扰动的混合粒子群优化算法［J］.计算机应用，2020，40（7）：1913-1918.
	ZHOU W F， LIANG X L， TANG K X， et al. Hybrid particle swarm optimization algorithm with topological time-varying and search disturbance ［J］. Journal of Computer Applications， 2020， 40（7）： 1913-1918.
14	谭继安，关继夫.基于人工蜂群算法的分布式入侵攻击检测系统［J］.计算机应用与软件，2019，36（3）：326-333. 10.3969/j.issn.1000-386x.2019.03.058
	TAN J A， GUAN J F. Distributed intrusion detection system of networks based on artificial bee colony algorithm ［J］. Computer Applications and Software， 2019， 36（3）： 326-333. 10.3969/j.issn.1000-386x.2019.03.058
15	刘紫微，徐元铭，童岩.基于Kriging模型的复合材料圆管吸能优化研究［J］.飞机设计，2017，37（5）：27-33.
	LIU Z W， XU Y M， TONG Y. Study of optimization for energy absorption of composite tubes based on dynamic Kriging method ［J］. Aircraft Design， 2017， 37（5）： 27-33.
16	廖伍代，朱范炳，王海泉，等.基于人工蜂群优化的K均值聚类算法［J］.计算机测量与控制，2018，26（4）：136-138，156.
	LIAO W D， ZHU F B， WANG H Q， et al. A K-means clustering algorithm based on artificial bee colony optimization ［J］. Computer Measurement & Control， 2018， 26（4）： 136-138， 156.
17	穆晓芳，邓红霞，李晓宾，等.基于人工蜂群算法的两阶段图像隐写分析算法［J］.计算机科学，2019，46（6）：174-179. 10.11896/j.issn.1002-137X.2019.06.026
	MU X F， DENG H X， LI X B， et al. Two-phase image steganalysis algorithm based on artificial bee colony algorithm ［J］. Computer Science， 2019， 46（6）： 174-179. 10.11896/j.issn.1002-137X.2019.06.026
18	向万里，安美清，何瑞春，等.基于搜索能力均衡的人工蜂群算法［J］.计算机工程与应用，2014，50（23）：51-55. 10.3778/j.issn.1002-8331.1305-0076
	XIANG W L， AN M Q， HE R C， et al. Improved artificial bee colony algorithm based on balance of searching ability ［J］. Computer Engineering and Applications， 2014， 50（23）： 51-55. 10.3778/j.issn.1002-8331.1305-0076
19	KIRAN M S， FINDIK O. A directed artificial bee colony algorithm ［J］. Applied Soft Computing， 2015， 26： 454-462. 10.1016/j.asoc.2014.10.020
20	孟红云，位冰可.基于精英解和随机个体邻域信息的改进人工蜂群算法［J］.控制与决策，2020，35（9）：2169-2174.
	MENG H Y， WEI B K. An improved artificial bee colony algorithm based on elite solution and random individual neighborhood information ［J］. Control and Decision， 2020， 35（9）： 2169-2174.
21	JADON S S， TIWARI R， SHARMA H， et al. Hybrid artificial bee colony algorithm with differential evolution ［J］. Applied Soft Computing， 2017， 58： 11-24. 10.1016/j.asoc.2017.04.018
22	魏锋涛，岳明娟，郑建明.基于改进邻域搜索策略的人工蜂群算法［J］.控制与决策，2019，34（5）：965-972. 10.13195/j.kzyjc.2017.1506
	WEI F T， YUE M J， ZHENG J M. Artificial bee colony algorithm based on improved neighborhood search strategy ［J］. Control and Decision， 2019， 34（5）： 965-972. 10.13195/j.kzyjc.2017.1506
23	包敏泽，胡秀婷，谢玉莹，等.基于人工蜂群算法的p-center问题求解算法［J］.计算机工程与科学，2020，42（6）：1127-1133. 10.3969/j.issn.1007-130X.2020.06.022
	BAO M Z， HU X T， XIE Y Y， et al. A p-center problem solving algorithm based on artificial bee colony algorithm ［J］. Computer Engineering and Science， 2020， 42（6）： 1127-1133. 10.3969/j.issn.1007-130X.2020.06.022
24	林凯，陈国初，张鑫.多交互式人工蜂群算法及其收敛性分析［J］.计算机应用，2017，37（3）：760-765. 10.11772/j.issn.1001-9081.2017.03.760
	LIN K， CEHN G C， ZHANG X. Multiple interactive artificial bee colony algorithm and its convergence analysis ［J］. Journal of Computer Applications， 2017， 37（3）： 760-765. 10.11772/j.issn.1001-9081.2017.03.760
25	ZHU G P， KWONG S. Gbest-guided artificial bee colony algorithm for numerical function optimization ［J］. Applied Mathematics and Computation， 2010， 217（7）： 3166-3173. 10.1016/j.amc.2010.08.049
26	KARABOGA D， GORKEMLI B. A quick Artificial Bee Colony （qABC） algorithm and its performance on optimization problems ［J］. Applied Soft Computing， 2014， 23： 227-238. 10.1016/j.asoc.2014.06.035
27	GAO W F， LIU S Y， HUANG L L. A novel artificial bee colony algorithm based on modified search equation and orthogonal learning ［J］. IEEE Transactions on Cybernetics， 2013， 43（3）： 1011-1024. 10.1109/tsmcb.2012.2222373

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Artificial bee colony algorithm based on multi-population combination strategy

基于多种群组合策略的人工蜂群算法

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