Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism

doi:10.21629/JSEE.2018.02.20

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (2): 405-414.doi: 10.21629/JSEE.2018.02.20

• Software Algorithm and Simulation • Previous Articles Next Articles

Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism

Chengli FAN(), Qiang FU*(), Guangzheng LONG(), Qinghua XING()

Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China

Received:2017-04-01 Online:2018-04-26 Published:2018-04-27
Contact: Qiang FU E-mail:ffq516@163.com;fuqiang_66688@163.com;lunggz@163.com;liuxqh@126.com
About author:FAN Chengli was born in 1988. She is a Ph.D. and a lecturer in Air force Engineering University. Her research interests include intelligent optimization algorithm, intelligent information processing, and military battle modeling & simulation. E-mail: ffq516@163.com|FU Qiang was born in 1988. He is a Ph.D. and a lecturer in Air Force Engineering University. His research interests include intelligent information processing, senor information fusion and multi-sensor task planning. E-mail: fuqiang_66688@163.com|LONG Guangzheng was born in 1975. He is a Ph.D. and an associate professor in Air Force Engineering University. His research interests include intelligent optimization algorithm, operation decision analysis and deep learning neural networks. E-mail: lunggz@163.com|XING Qianghua was born in 1966. She is a Ph.D. and a professor in Air Force Engineering University. Her research interests include operational research, cooperative control and optimization algorithms for military problems. E-mail: liuxqh@126.com
Supported by:
the National Natural Science Foundation of China(71771216);the National Natural Science Foundation of China(71701209);This work was supported by the National Natural Science Foundation of China (71771216; 71701209)

Abstract

Abstract:

Artificial bee colony (ABC) is one of the most popular swarm intelligence optimization algorithms which have been widely used in numerical optimization and engineering applications. However, there are still deficiencies in ABC regarding its local search ability and global search efficiency. Aiming at these deficiencies, an ABC variant named hybrid ABC (HABC) algorithm is proposed. Firstly, the variable neighborhood search factor is added to the solution search equation, which can enhance the local search ability and increase the population diversity. Secondly, inspired by the neuroscience investigation of real honeybees, the memory mechanism is put forward, which assumes the artificial bees can remember their past successful experiences and further guide the subsequent foraging behavior. The proposed memory mechanism is used to improve the global search efficiency. Finally, the results of comparison on a set of ten benchmark functions demonstrate the superiority of HABC.

Key words: artificial bee colony (ABC), hybrid artificial bee colony (HABC), variable neighborhood search factor, memory mechanism

Chengli FAN, Qiang FU, Guangzheng LONG, Qinghua XING. Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism[J]. Journal of Systems Engineering and Electronics, 2018, 29(2): 405-414.

Figures/Tables 7

Fig 1

Table 1

Table 2

Table 3

Table 4

Performance of HABC algorithm with different $M$ values"

Parameter	Function${f_1}$				Function${f_2}$				Function${f_3}$				Function${f_4}$				Function${f_1}$				Function${f_2}$				Function${f_7}$				Function${f_8}$				Function${f_9}$				Function${f_{10}}$
Parameter	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD
$M = 1$	0	6.05E-17	3.14E-17	1.70E-17	0.049 2	0.084 1	0.063 7	0.476 3	0	0	0	0	0	4.60E-15	2.72E-16	5.63E-18	0	5.14E-20	3.90E-20	5.03E-19	9.01E-16	3.62E-14	6.59E-15	1.75E-11	2.56E-14	3.52E-14	3.04E-14	2.26E-15	5.71E-08	5.71E-08	5.71E-08	2.08E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0
$M = 2$	0	6.24E-16	1.02E-16	3.46E-17	0.010 5	0.026 4	0.015 3	0.125 7	0	0	0	0	0	5.46E-16	1.25E-16	2.09E-18	0	2.37E-20	1.03E-21	4.52E-19	8.44E-16	3.07E-14	4.73E-15	6.06E-11	2.56E-14	3.52E-14	3.01E-14	2.28E-15	5.71E-08	5.71E-08	5.71E-08	5.64E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0
$M = 3$	0	2.79E-16	9.35E-17	2.25E-17	0.035 4	0.059 3	0.044 1	0.342 5	0	0	0	0	0	3.25E-15	1.37E-15	1.09E-17	0	7.06E-21	3.48E-21	5.77E-19	8.57E-16	5.84E-14	5.25E-15	3.94E-11	2.69E-14	3.77E-14		2.02E-15	5.71E-08	5.71E-08	5.71E-08	6.72E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0
$M = 5$	0	6.58E-16	4.87E-16	3.88E-17	0.009 6	0.062 6	0.042 9	0.289 8	0	0	0	0	0	4.43E-15	2.79E-15	2.72E-17	0	2.59E-20	1.79E-20	6.36E-19	8.89E-16	6.68E-14	5.46E-15	7.13E-11	2.56E-14	3.52E-14	3.06E-14	2.39E-15	5.71E-08	5.71E-08	5.71E-08	7.09E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0
$M = 10$	0	9.21E-16	6.64E-16	4.39E-17	0.057 0	0.087 2	0.075 2	0.301 5	0	0	0	0	0	6.94E-15	4.82E-15	4.63E-17	0	3.82E-20	2.26E-20	6.98E-19	9.23E-16	1.55E-14	6.03E-15	7.48E-11	2.56E-14	3.52E-14	3.37E-14	2.31E-15	5.71E-08	5.71E-08	5.71E-08	6.81E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0

Table 4

Table 5

Fig 2

References 12

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Updateindex	Optimalneighborhood	Randomneighborhood	Updatingcoefficient
1	$x_{lbest(i)}^j (1)$	$k_i^j (1)$	$\phi _i^j (1)$
2	$x_{lbest(i)}^j (2)$	$k_i^j (2)$	$\phi _i^j (3)$
$ \vdots $	$ \vdots $	$ \vdots $	$ \vdots $
$M$	$x_{lbest(i)}^j(M)$	$k_i^j(M)$	$\phi _i^j (M)$

Function	Formula	Feature	Interval	Optimum	$ D $
Sphere	${f_1}(x) = \sum\limits_{i = 1}^D {x_i^2} $	US	[–100, 100]	0	30
Rosenbrock	${f_2}(x) = \sum\limits_{i = 1}^{D - 1} {(100(} {x_{i + 1}} - x_i^2{)^2} + {({x_i} - 1)^2})$	UN	[–30, 30]	0	30
Rastrigin	${f_3}(x) = \sum\limits_{i = 1}^D {(x_i^2 - 10\cos (} 2\pi {x_i}) + 10)$	MS	[–5.12, 5.12]	0	30
Griewank	${f_4}(x) = \frac{1}{{4000}}\sum\limits_{i = 1}^D {x_i^2} - \prod\limits_{i = 1}^D {\cos } \left( {\frac{{{x_i}}}{{\sqrt i }}} \right) + 1$	MN	[–600, 600]	0	30
Schaffer	${f_5}(x) = 0.5 + {\sin ^2}(\sqrt {\sum\limits_{i = 1}^2 {x_i^2} } ) - 0.5/(1 + 0.001(\sqrt {\sum\limits_{i = 1}^2 {x_i^2} } ))$	MN	[–100, 100]	0	2
Dixon-Price	${f_6}(x) = {({x_1} - 1)^2} + \sum\limits_{i = 2}^D {i{{(2x_i^2 - {x_{i - 1}})}^2}} $	UN	[-10, 10]	0	30
Ackley	${f_7}(x) = - 20\exp \left( { - 0.2\sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {x_i^2} } } \right) - \exp \left( {\frac{1}{n}\sum\limits_{i = 1}^n {\cos } 2\pi {x_i}} \right) + 20 + e$	MN	[–32, 32]	0	30
Schwefel	${f_8}(x) = - 418.9828D - \sum\limits_{i = 1}^D {({x_i}\sin (} \sqrt {\|{x_i}\|} ))$	MS	[–500, 500]	0	30
Six Hump Camel Back	${f_9}(x) = 4x_1^2 - 2.1x_1^4 + \frac{1}{{3x_1^6}} + {x_1}{x_2} - 4x_2^2 + 4x_2^4$	MN	[–5, 5]	–1.031 63	2
Branin	${f_{10}}(x) = {({x_2} - \frac{{5.1}}{{4{\pi ^2}}}x_1^2 + \frac{5}{\pi }{x_1} - 6)^2} + 10(1 - \frac{1}{{8\pi }})\cos {x_1} + 10$	MS	[?5, 10] × [0, 15]	0.397 89	2

Parameter	Function${f_1}$				Function${f_2}$				Function${f_3}$				Function${f_4}$				Function${f_5}$				Function${f_6}$				Function${f_7}$				Function${f_8}$				Function${f_9}$				Function${f_{10}}$
Parameter	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD	Best	Worse	Mean	SD
${l_{\max }} = 1$	4.81E-15	3.53E-14	6.17E-15	4.72E-18	0.099 7	0.114 1	0.103 5	0.582 8	0	0	0	0	2.27E-15	5.01E-15	3.44E-15	7.67E-18	0	6.13E-19	3.78E-19	1.36E-18	5.03E-14	2.67E-13	8.52E-14	1.33E-09	4.09E-14	7.51E-14	5.19E-14	3.68E-14	1.34E-07	5.06E-07	3.91E-07	3.63E-12	–1.011 2	–1.004 1	–1.010 3	3.31E-15	0.399 6	0.436 7	0.411 1	0
${l_{\max }} = 3$	2.96E-15	4.89E-15	3.04E-15	6.51E-18	0.046 2	0.072 9	0.056 6	0.339 4	0	0	0	0	4.08E-16	7.36E-16	5.80E-16	4.11E-18	0	3.85E-20	0.92E-20	7.70E-18	6.16E-15	5.29E-14	9.67E-15	5.05E-10	2.27E-14	3.39E-14	3.18E-14	5.54E-15	7.60E-08	9.23E-08	8.04E-08	7.71E-13	1.025 5	–1.020 8	–1.023 5	1.70E-15	0.398 8	0.418 2	0.405 8	0
${l_{\max }} = 5$	0	6.24E-16	1.02E-16	3.46E-17	0.010 5	0.026 4	0.015 3	0.125 7	0	0	0	0	0	5.46E-16	1.25E-16	2.09E-18	0	2.37E-20	1.03E-20	4.52E-19	8.44E-16	3.07E-14	4.73E-15	6.06E-11	2.56E-14	3.52E-14	3.01E-14	2.28E-15	5.71E-08	5.71E-08	5.71E-08	5.64E-13	–1.031 6	–1.031 6	–1.031 6	6.78E-16	0.397 9	0.397 9	0.397 9	0

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Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism

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Function	Algorithm	Best	Worst	Median	Mean	SD
${f_1}$	ABC	2.81E-16	5.39E-15	3.87E-16	4.64E-16	5.35E-17
	qABC	2.04E-16	3.77E-15	3.12E-16	4.64E-16	7.82E-17
	HABC	0	6.24E-16	2.54E-16	1.02E-16	3.46E-17
${f_2}$	ABC	0.093 2	0.141 1	0.125 9	0.108 8	0.190 6
	qABC	0.138 6	0.250 7	0.184 3	0.177 8	0.407 0
	HABC	0.010 5	0.026 4	0.018 9	0.015 3	0.125 7
${f_3}$	ABC	0	0	0	0	0
	qABC	0	0	0	0	0
	HABC	0	0	0	0	0
${f_4}$	ABC	2.38E-16	8.25E-16	4.04E-16	4.96E-16	7.38E-17
	qABC	2.11E-16.	7.73E-16	3.95E-16	4.66E-16	6.35E-17
	HABC	0	5.46E-16	2.28E-16	1.25E-16	2.09E-18
${f_5}$	ABC	5.69E-19	8.77E-18	5.35E-18	1.85E-18	1.01E-17
	qABC	3.16E-09	6.02E-08	4.40E-08	1.21E-08	4.31E-08
	HABC	0	2.37E-20	1.92E-20	1.03E-20	4.52E-19
${f_6}$	ABC	3.52E-12	1.19E-10	4.76E-11	5.29E-11	7.85E-10
	qABC	4.80E-12	2.52E-10	6.31E-11	5.52E-11	1.47E-10
	HABC	8.44E-16	3.07E-14	5.26E-15	4.73E-15	6.06E-11
${f_7}$	ABC	2.74E-14	3.89E-14	3.05E-14	3.26E-14	3.51E-15
	qABC	2.95E-14	4.13E-14	3.27E-14	3.60E-14	3.72E-15
	HABC	2.56E-14	3.52E-14	2.99E-14	3.01E-14	2.28E-15
${f_8}$	ABC	5.71E-08	5.71E-08	5.71E-08	5.71E-08	3.32E-13
	qABC	5.71E-08	5.71E-08	5.71E-08	5.71E-08	7.83E-13
	HABC	5.71E-08	5.71E-08	5.71E-08	5.71E-08	5.64E-13
${f_9}$	ABC	–1.031 6	–1.031 6	–1.031 6	–1.031 6	6.78E-16
	qABC	–1.031 6	–1.031 6	–1.031 6	–1.031 6	6.78E-16
	HABC	–1.031 6	–1.031 6	–1.031 6	–1.031 6	6.78E-16
${f_{10}}$	ABC	0.397 9	0.397 9	0.397 9	0.397 9	0
	qABC	0.397 9	0.397 9	0.397 9	0.397 9	0
	HABC	0.397 9	0.397 9	0.397 9	0.397 9	0