INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL
ISSN 1841-9836, 13(4), 590-601, August 2018.

An ABC Algorithm with Recombination

X. You, Y. Ma, Z. Liu, M. Xie

Xuemei You*, Yinghong Ma, Zhiyuan Liu, Mingzhao Xie
Business School,
Shandong Normal University,
Shandong, 250014, P. R. China
*Corresponding author: sdxmyou@126.com yinghongma71@163.com
liuzhiyuan@sdnu.edu.cn

Abstract: Artificial bee colony (ABC) is an efficient swarm intelligence algorithm,
which has shown good exploration ability. However, its exploitation capacity needs
to be improved. In this paper, a novel ABC variant with recombination (called
RABC) is proposed to enhance the exploitation. RABC firstly employs a new search
model inspired by the updating equation of particle swarm optimization (PSO). Then,
both the new search model and the original ABC model are recombined to build a
hybrid search model. The effectiveness of the proposed RABC is validated on ten
famous benchmark optimization problems. Experimental results show RABC can
significantly improve the quality of solutions and accelerate the convergence speed.
Keywords: Artificial bee colony (ABC), recombination, hybrid search model, global
optimization.

1 Introduction

In recent years, swarm intelligence (SI) has become a research focus in optimization field.
The SI refers to establish mathematical model to simulate the social behaviors from nature. In
the past decades, different SI algorithms have been proposed, including ant colony optimization
(ACO) [8,17,25], particle swarm optimization (PSO) [22], artificial bee colony (ABC) [9], firefly
algorithm (FA) [20], hybrid algorithm (HA) [14], bat algorithm (BA) [2], and cuckoo search
(CS) [5,30].

Except PSO and ACO, ABC can be regarded as the most popular SI algorithm. The main
reason contains: 1) ABC has less control parameters than other SI algorithms; and 2) ABC has
powerful exploration ability. Due to the superiority of ABC, it has received much attention. In
the original ABC, individuals are divided into three types: i.e., employed bees, onlooker bees
and scouts. During the search, all individuals (bees) fly in the search space and try to improve
the food sources (find better solutions). Compared to other SI algorithms, ABC uses a different
search equation to generate new solutions. For the current solution, an individual (employed bee
or onlooker bee) randomly chooses a different solution in the population and uses their difference
to obtain a new solution by modifying one dimension. Based on this search mechanism, ABC
shows slow convergence speed and exploitation ability.

To strengthen the exploitation capacity, this paper presents a new ABC variant (called
RABC), which employs a recombination method between the original ABC search model and a
modified search model. For the latter model, it is inspired by the updating equation of PSO.
By combining the search information of the global best solution and previous best, RABC can
improve the exploitation ability. Experiment is validated on ten well-known benchmark prob-
lems. Simulation results of RABC are compared with the original ABC and two improved ABC
variants.

The rest of this paper is organized as follows. The original ABC is briefly introduced in
Section 2. A short review of recent progress on ABC is given in Section 3. In Section 4, our

Copyright ©2018 CC BY-NC



An ABC Algorithm with Recombination 591

proposed RABC is described. Section 5 presents the simulation results and discussions. Finally,
conclusion and future work are summarized in Section 6.

2 Artificial Bee Colony (ABC)

There are two famous SI optimization algorithms: PSO and ACO, which were developed
in the 1990s. Recently, different SI algorithms were proposed. Among these algorithms, ABC
becomes popular because of its superiorities [10]. In the original ABC, it consists of three types
of individuals: employed bees, onlooker bees and scouts. For all food sources (solutions), the
employed bees conduct the first round search around food sources and try to find new better
solutions. The onlooker bees conduct the second round search around some selected better food
sources. For a food source, if the above bees cannot find a better one to replace it after some
rounds search, the scout will randomly find a food source to replace it.

2.1 Population initialization

In the following, we will describe the original ABC in details. First, a initial population
consists of N food sources (solutions) {Xi|i = 1, 2, ...,N}, where Xi is the ith food source and
N is the population size. The initial food sources are randomly generated as follows.

xij = lowj + randj · (upj − lowj) (1)

where xij denotes the jth component for ith food source Xi, i = 1, 2, ...,N, j = 1, 2, ...,D; D
is the dimensional size; randj is a real random number between 0 and 1; upj and lowj are the
boundaries for the jth dimension.

2.2 Employed bee phase

For each food source Xi in the current population, each employed bee flies to its neighborhood
and tries to find a new solution Vi. This process can be described as below [9].

vij(t) = xij(t) + φij(xij(t) −xkj(t)) (2)

where j�[1,D] is a random index of the population; Xk is a randomly selected food source and
it is mutually different with Xi; t represents the iteration index; φij is a real random number in
the range [-1, 1].

The ABC employs a greedy selection method to determine whether the new candidate solution
(food source) Vi should be entered in the next generation. If Vi is better than Xi, then Xi is
updated by Vi; otherwise Xi is unchangeable. The greedy selection can accelerate the population
convergence.

2.3 Onlooker bee phase

The onlooker bees only fly to some selected food sources and search their neighborhood to find
new food sources. The selection of each food source Xi is related to its fitness quality. A better
food source has a higher selection probability. In the original ABC, the selection probability pi
for each food source Xi is defined by [9]:

pi =
fiti∑N
i=1 fiti

(3)



592 X. You, Y. Ma, Z. Liu, M. Xie

where fiti is the fitness value of Xi. When Xi is selected, the onlooker bee searches the neigh-
borhood of Xi and obtain a new solution Vi according to Eq.(2).

Similar to the employed bees, the same greedy selection is utilized by the onlooker bees to
determine whether the new solution Vi should be entered in the next generation.

2.4 Scout bee phase

If the employed or onlooker bees cannot improve the quality of Xi in limit iterations, Xi may
be stagnated. Then, a scout bee re-initializes Xi according to Eq.(1).

3 A brief review of ABC

Although the original ABC has shown good performance, it still has some drawbacks. To
tackle these issues, many improved ABCs have been proposed. In this section, a brief review of
recent advance on ABC is presented.

Karaboga and Akay [10] compared ABC with some evolutionary algorithms on a number
of benchmark problems. Simulation results demonstrate ABC is competitive to those compared
algorithms. Zhu and Kwong [32] proposed a new ABC called GABC , which introduced the global
best individual into the original solution search equation. Akay and Karaboga [1] designed a new
parameter MR to adjust the probability of dimension perturbation. Results demonstrate the
modified approach can accelerate the search. Wang et al. [23] combined multi-strategy ensemble
learning and ABC. It aims that multiple strategies can effectively balance the global and local
search. Inspired by Gaussian DE [21], Zhou et al. [31] introduced Gaussian sampling into ABC
to obtain good performance. Cui et al. [4] used a ranking method to choose the parent solutions
when generating new solutions. Simulation results show the ranking based ABC is very effective.
In [6], Cui et al. developed another version of ABC, which employs a dynamic population
mechanism. During the search, the population size is not fixed and dynamically updated. In [3],
Chen et al. combined teaching learning based optimization into ABC, and proposed an improved
ABC variant to optimize the parameters estimation of photovoltaic.

To improve the exploitation, Xiang et al. [26] used a grey relational model to choose the
neighbor individuals. Then, the DE mutation operator is employed to generate new candidate
solutions. In [27], Xiang et al. proposed another ABC variant based on the cosine similarity. To
select some good neighbor individuals, a novel solution search model is designed. The frequency
of parameters perturbation is also modified to share more search information between different
solutions. Simulation results on twenty-four benchmark functions show that the proposed Cos-
ABC is competitive. Yaghoobi and Esmaeili [29] designed an improved ABC by using three new
strategies: chaos theory, multiple searches, and modified perturbation. Song et al. [18] presented
an improved ABC based on objective function value information, which employs two modified
solution search models. The objective function value is incorporated to adjust the step size.
Experiments on thirty test functions show the proposed approach is better than other six ABCs.
Li et al. [13] designed a new gene recombination operation to accelerate the convergence of ABC.
Some good solutions in the population are chosen to generate offspring through the gene recom-
bination. Results demonstrate the gene recombination operation can effectively strengthen the
exploitation capacity of ABC. Kong et al. [12] presented a new ABC variant with two strategies:
elite group guidance and combined breadth-depth search. The proposed algorithm was verified
on twenty-two benchmark functions. Sulaiman et al. [19] presented a robust ABC to balance
exploitation and exploration. Experiments on 27 test functions and economic environmental
dispatch (EED) problems show the effectiveness of the approach.



An ABC Algorithm with Recombination 593

4 ABC with recombination (RABC)

In Section 2, it can be seen that ABC mainly uses Eq.(2) to find new food sources (solutions)
during the iterations. From Eq.(2), the new solution Vi is very similar to its parent solution Xi,
because they are different on only one dimension. Based this search mechanism, ABC shows
powerful exploration ability, but its convergence speed is slow. To improve this case, some
researchers introduced some good search experiences into ABC to accelerate the search. In [32],
the global best solution is used to improve the search equation. Results show the modification
can significantly improve the performance.

PSO is a successful SI optimization algorithm. The original PSO references has more than
100,000 citations. The main advantages of PSO focus on fast convergence speed and strong
search ability. In PSO, each individual (also called particle) flies to its previous best (pbest) and
the global best (gbest) found so far. So, PSO takes full advantage of the search experiences of
those best individuals. The PSO updating model is defined by [11].

vij(t + 1) = w ·vij(t) + c1r1(pbestij(t) −xij(t)) + c2r2(gbestj(t) −xij(t)) (4)

where Vi and Xi are the velocity and position, respectively; w�[0, 1] is inertia weight; c1 and c2
are two learning factors; r1,r2�[0, 1] are two random numbers.

In this paper, a new solution updating equation is proposed inspired by PSO. However, this
paper is not the first time to introduce PSO model into ABC. In [32], a gbest guided ABC
(GABC) was proposed. In [28], Xiang et al. used the gbest and an elitist method to modify
the solution search model. Liu [16] used pbest to update the employed bees and gbest to the
onlooker bees. In [15], Li et al. defined a modified model as follows.

vij(t) = w ·xij(t) + 2φij(xij(t) −xkj(t))Φ1 + ϕij(gbestj(t) −xkj(t))Φ2 (5)

where Φ1 and Φ2 are two positive values; φij and ϕij are two random numbers in [0,1].
Differs from these existing models, we design a new one by taking full advantage of pbest and

gbest. The detailed model is defined as follows.

vij(t) = w ·xij(t) + r1(pbestij(t) −xij(t)) + r2(gbestj(t) −xij(t)) (6)

where j is a randomly selected dimension index, r1,r2�[0, 1] are two random numbers, and the
weight factor w�[0, 1].

Based on Eq.(6), we propose an alternative model by combining the original ABC model.
The recombined model is described as below.

vij(t) =

{
xij(t) + φij(xij(t) −xkj(t)), ifrand(0, 1) < pr
w ·xij(t) + r1(pbestij(t) −xij(t)) + r2(gbestj(t) −xij(t)), Otherwise.

(7)

where rand(0, 1)�[0, 1] is a random value, and pr�[0, 1] is the probability rate.
In our approach RABC, both employed and onlooker bees use Eq. 6 to generate new solutions

during iterations. Like the original ABC, a greedy selection method is also utilized to accelerate
the search.

In comparison to the original ABC, RABC adds a probability parameter pr to control the
usage of pbest and gbest. When pr is large, bees mainly use the original ABC model to generate
new solutions. Then, RABC is similar to ABC. When pr is small, bees mainly employ the
modified model to generate new solutions. Then, more search experiences of pbest and gbest are
utilized in the search process. Therefore, pr plays an significant role in balancing exploration and



594 X. You, Y. Ma, Z. Liu, M. Xie

exploitation in RABC. Moreover, RABC only modifies the search model, and does not employ
other operations. So, ABC and RABC have the same computational time complexity.

5 Experimental study

5.1 Test functions

In this paper, ten famous classical benchmark functions are utilized to validate the perfor-
mance of RABC. These functions were early used in many optimization papers [24]. The dimen-
sion D is set to 30 in the experiments. Table 1 briefly describes the ten benchmark problems.
All functions should be minimized and their mathematical definitions are listed as below.

f1: Sphere

f1(x) =
∑D

i=1 x
2
i

f2: Schwefel 2.22

f2(x) =
∑D

i=1 |xi| +
∏D
i=1 xi

f3: Schwefel 1.2

f3(x) =
∑D

i=1(
∑i

j=1 xj)
2

f4: Schwefel 2.21

f4(x) = maxi(|xi|, 1 ≤ i ≤ D)

f5: Rosenbrock

f5(x) =
∑D−1

i=1 [100(xi+1 −x
2
i )

2 + (xi − 1)2]

f6: Step

f6(x) =
∑D

i=1(bxi + 0.5c)
2

f7: Quartic with noise

f7(x) =
∑D

i=1 ix
4
i + rand(0, 1)

f8: Schwefel 2.26

f8(x) =
∑D

i=1 −xi sin(
√
|xi|)

f9: Rastrigin

f9(x) =
∑D

i=1[x
2
i − 10 cos(2πxi) + 10]

f10: Ackley

f10(x) = −20 ·exp(−0.2 ·
√

1
D

∑D
i=1 x

2
i ) −exp(

1
D

∑D
i=1 cos(2πxi)) + 20 + e



An ABC Algorithm with Recombination 595

Table 1: Search range and global optimum for the benchmark problems.

Functions Search range Global optimum
f1 [-100,100] 0
f2 [-10,10] 0
f3 [-100,100] 0
f4 [-100,100] 0
f5 [-30,30] 0
f6 [-100,100] 0
f7 [-1.28,1.28] 0
f8 [-500,500] −418.98 ·D
f9 [-5.12,5.12] 0
f10 [-32,32] 0

Table 2: PComputational results of RABC with different pr values.

Functions pr = 0.1 pr = 0.3 pr = 0.5 pr = 0.7 pr = 0.9
Mean Mean Mean Mean Mean

f1 5.94E-75 6.51E-57 6.75E-48 7.46E-40 4.35E-33
f2 8.78E-36 9.61E-33 1.54E-26 8.44E-20 5.65E-14
f3 5.87E+03 6.40E+03 6.32E+03 5.56E+03 5.83E+03
f4 1.47E+00 3.37E+00 9.89E+00 1.84E+01 3.32E+01
f5 2.74E+01 2.54E+01 2.31E+01 1.61E+01 1.43E-01
f6 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
f7 2.79E-02 2.25E-02 3.59E-02 4.57E-02 1.06E-01
f8 -10925.2 -12545.9 -12569.5 -12569.5 -12569.5
f9 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00
f10 2.90E-14 3.26E-14 2.55E-14 2.89E-14 1.73E-12



596 X. You, Y. Ma, Z. Liu, M. Xie

Sensitivity analysis of the parameter pr

According to Eq.(7), a new parameter pr is introduced in our approach RABC. As mentioned
in Section 4, pr is beneficial for balancing the exploration and exploitation. A large pr is good
for exploration and a small pr is helpful for exploitation. So, how to choose a suitable pr is
worthy to be investigated.

To analyze the parameter pr, we try to test different pr on the benchmark set. The parameter
pr is set to 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. For other parameters N and limit, they are
set to 50 and 100, respectively. The termination criterion for running an algorithm is maximum
number of function evaluations (MaxFEs). When the number of function evaluations reaches
to MaxFEs, the algorithm is stopped. According to the literature [23], MaxFEs is equal to
1.5E+05. For each parameter pr, RABC is run 25 trials.

Table 2 displays the results of RABC with different pr, where "Mean" is the mean best
function value. As seen, when pr = 0.1, RABC outperforms other pr values on two functions f1
and f2. For functions f3 −f5, all pr values cannot help RABC find good solutions. on function
f3, pr = 0.7 is slightly better than other pr values, and pr = 0.1 is better on function f4. For
function f5, pr = 0.9 can find reasonable solution, while other pr values fail. All pr values
and find the global optimum on f6 and f9. When pr > 0.3, RABC can converge to the global
optimum, but RABC with pr = 0.1 and 0.3 falls into local minima. For function f7, RABC
with pr = 0.2 is better than other pr values. When pr = 0.5, RABC achieves better results on
function f10. From the above analysis, RABC with a fixed pr value cannot obtain better results
than other pr values. So, it is not easy to select which pr is suitable for the benchmark set.

In order to choose the relatively best pr, Friedman test is used to calculate the mean rank
of each pr on the benchmark set. Table 3 shows the mean rank values of RABC with different
pr values. As shown, RABC with pr = 0.1 achieves the best mean rank. It demonstrates that
pr = 0.1 is the relatively best choice among five different pr values. In the following experiment,
pr = 0.1 is used for RABC.

Table 3: Mean rank of RABC with different pr values.

RABC Mean rank
pr = 0.1 2.70
pr = 0.3 3.00
pr = 0.5 2.80
pr = 0.7 2.90
pr = 0.9 3.60

Comparison of RABC and other well-known ABC algorithms

In this section, we compare RABC with the standard ABC and two other well-known ABCs.
The compared algorithms are listed as below.

• ABC [9]

• GABC GABC [32]

• MABC [7]

• Our approach RABC



An ABC Algorithm with Recombination 597

In the following experiments, all algorithms use the same population size and stopping con-
dition. Both N and limit are set to 100. MaxFEs is equal to 1.5E+05. The parameter C is
equal to 1.5 in GABC [32]. In MABC, the probability P is set to 0.7 by the suggestions of [7].
The parameter pr in RABC is equal to 0.1 based on experimental study. Each algorithm is run
25 trial on each function.

Table 4 presents the results among RABC, ABC, GABC, and MABC on the ten benchmark
functions, where "Mean" indicates the mean best function value. From the table, RABC out-
performs the standard ABC on 7 functions, while ABC is better than RABC on f5 and f8. For
the last function f6, all ABCs can find the global optimum zero. Compared to GABC, RABC
achieves better solutions on 5 functions. GABC performs better than RABC on 3 functions. Be-
sides the function f6, RABC, GABC, MABC can converge to the global minima on f9. MABC
is better than RABC on 2 functions, but RABC outperforms MABC on six functions.

Table 4: Comparison results among RABC, ABC, GABC and MABC.

Functions ABC GABC MABC RABC
Mean Mean Mean Mean

f1 9.67E-16 6.86E-16 2.98E-40 5.94E-75
f2 2.36E-10 1.39E-15 2.13E-21 8.78E-36
f3 9.21E+03 4.29E+03 1.01E+04 5.87E+03
f4 3.73E+01 1.91E+01 5.71E+00 1.47E+00
f5 1.21E+00 6.77E-01 2.27E-01 2.74E+01
f6 0.00E+00 0.00E+00 0.00E+00 0.00E+00
f7 1.68E-01 7.98E-02 4.02E-02 2.79E-02
f8 -12332.6 -12569.5 -12569.5 -10925.2
f9 5.33E-14 0.00E+00 0.00E+00 0.00E+00
f10 1.65E-09 3.97E-14 3.26E-14 2.90E-14

Fig.1 lists the convergence graphs of RABC and three other ABCs on six test functions.
As shown, RABC converges faster than MABC, GABC, and ABC on f1, f2, f4, f9 and f10 on
the whole search process. For function f3, RABC is faster than other three algorithms at the
beginning of the search. GABC is faster than RABC at the last stage. Because RABC converges
to a local minima when FEs reaches to 3.0E+04. For function f10, RABC converges much faster
than other three algorithms at the beginning and middle stages. The convergence curves of
RABC, MABC, and GABC are similar at the last stage of the search.



598 X. You, Y. Ma, Z. Liu, M. Xie

0 30000 60000 90000 120000 150000
-200

-150

-100

-50

0

50

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
1
)

 ABC
 GABC
 MABC

f1

0 30000 60000 90000 120000 150000
-90

-60

-30

0

30

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
2
)

 ABC
 GABC
 MABC

f2

0 30000 60000 90000 120000 150000
8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
3
)

 ABC
 GABC
 MABC

f3

0 30000 60000 90000 120000 150000
0

2

4

6

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
4
)

 ABC
 GABC
 MABC

f4

0 30000 60000 90000 120000 150000
-40

-30

-20

-10

0

10

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
9
)

 ABC
 GABC
 MABC

f9

0 30000 60000 90000 120000 150000
-40

-30

-20

-10

0

10

B
es

t f
un

ct
io

n 
va

lu
e 

(L
og

)

FEs (f
10

)

 ABC
 GABC
 MABC
 RABC

f10

Figure 1: The convergence graphs of four ABCs on six selected functions.



An ABC Algorithm with Recombination 599

6 Conclusion

In order to strengthen the exploitation ability of ABC, a new ABC variant with recombination
(called RABC) is proposed in this paper. RABC firstly employs a new search model inspired by
the updating equation of PSO. Then, both the new search model and the original ABC model
are recombined to build a hybrid search model. A set of ten famous benchmark optimization
problems are tested in the experiments. Results show RABC performs better than ABC, MABC,
and GABC on most test functions.

The parameter pr aims to control the frequency of using pbest and gbest. How to choose the
best pr is studied in the experiments. Results show that RABC with a fixed pr value cannot
obtain better results than other pr values. The statistical test demonstrates that pr = 0.1 is the
relatively best choice among five different pr values. However, a fixed pr is not a good choice. A
dynamic pr may be more suitable. This will be studied in the future work.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 71701115,
71471106, 61502284, and 71704098), the Natural Science Foundation of Shandong Province (Nos.
ZR2017MF058 and ZR2016GQ03), and the Higher School Science and Technology Foundation
of Shandong Province (No. J17KA172).

Bibliography

[1] Akay, B.; Karaboga, D. (2012); A modified Artificial bee colony algorithm for real-parameter
optimization, Information Sciences, 192, 120-142, 2012.

[2] Cai, X.; Wang, H.; Cui, Z.; Cai, J.; Xue, Y.; Wang, L.(2018); Bat algorithm with triangle-
flipping strategy for numerical optimization, International Journal of Machine Learning and
Cybernetics, 9(2), 199-215, 2018.

[3] Chen, X.; Xu, B.; Mei, C.; Ding, Y.; Li, K. (2018); Teaching Clearning Cbased artificial bee
colony for solar photovoltaic parameter estimation, Applied Energy, 212, 1578-1588, 2018.

[4] Cui, L.; Li, G.; Wang, Z.; Lin, Q.; Chen, J.; Lu, N.; Lu, J. (2017); A ranking-based adaptive
artificial bee colony algorithm for global numerical optimization, Information Sciences, 417,
169-185, 2017.

[5] Cui, Z.H.; Sun, B.; Wang, G.G.; Xue, Y.; Chen, J.J. (2017); A novel oriented cuckoo search
algorithm to improve DV-Hop performance for cyber-physical systems, Journal of Parallel
and Distributed Computing, 103, 42-52, 2017.

[6] Cui, L.; Li, G.; Zhu, Z.; Lin, Q.; Chen, J. (2017); A novel artificial bee colony algorithm
with an adaptive population size for numerical function optimization, Information Sciences,
414, 53-67, 2017.

[7] Gao, W.; Liu, S. (2012); A modified artificial bee colony algorithm, Computers & Operations
Research, 39, 687-697, 2012.

[8] Huang, P.; Lin, F.; Xu, L.J.; Kang, Z.L.; Zhou, J.L.; Yu, J.S. (2017); Improved ACO-
bsed seep coverage scheme considering data delivery, International Journal of Simulation
Modelling, 16(2), 289-301, 2017.



600 X. You, Y. Ma, Z. Liu, M. Xie

[9] Karaboga, D. (2005); An idea based on honey bee swarm for numerical optimization, Tech-
nical Report-TR06, Erciyes University, engineering Faculty, Computer Engineering Depart-
ment, 2005.

[10] Karaboga, D.; Akay, B. (2009); A comparative study of artificial bee colony algorithm,
Applied Mathematics and Computation, 214, 108-132, 2009.

[11] Kennedy, J.; Eberhart, R. (1995); Particle swarm optimization, Proceedings of IEEE Inter-
national Conference on Neural Networks, 1942-1948, 1995.

[12] Kong, D.; Chang, T.; Dai, W.; Wang, Q.; Sun, H. (2018); An improved artificial bee
colony algorithm based on elite group guidance and combined breadth-depth search strategy,
Information Sciences, 442-443, 54-71, 2018.

[13] Li, G.; Cui, L.; Fu, X.; Wen, Z.; Lua, N.; Lu, J. (2017); Artificial bee colony algorithm
with gene recombination for numerical function optimization, Applied Soft Computing, 52,
146-159, 2017.

[14] Li, J.; Pan, Q.; Xie, S.; Wang, S. (2011); A Hybrid Artificial Bee Colony Algorithm for Flex-
ible Job Shop Scheduling Problems, International Jotrnal of Computers Communications &
Control, 6(2), 286-296, 2011.

[15] Li, G.; Niu, P.; Xiao, X. (2012); Development and investigation of efficient artificial bee
colony algorithm for numerical function optimization, Applied Soft Computing, 12(1), 320-
332, 2012.

[16] Liu, J.J.; Zhu, H.Q.; Ma, Q.; Zhang, L.L.; Xu, H.L. (2015); An artificial bee colony algo-
rithm with guide of global & local optima and asynchronous scaling factors for numerical
optimization, Soft Computing, 37, 608-618, 2015.

[17] Rajput, U.; Kumari, M. (2017); Mobile robot path planning with modified ant colony
optimisation, International Journal of Bio-Inspired Computation, 9(2), 106-113, 2017.

[18] Song, X.; Yan, Q.; Zhao, M. (2017); An adaptive artificial bee colony algorithm based on
objective function value information, Applied Soft Computing, 55, 384-401, 2017.

[19] Sulaiman, N.; Mohamad-Saleh, J.; Abro, A.G. (2017); Robust variant of artificial bee colony
(JA-ABC4b) algorithm, International Journal of Bio-Inspired Computation, 10(2), 99-108,
2017.

[20] Wang, H.;Wang, W.; H. Sun, H.; Rahnamayan, S. (2016); Firefly algorithm with random
attraction, International Journal of Bio-Inspired Computation, 8(1), 33-41, 2016.

[21] Wang, H.; Rahnamayan, S.; Sun, H.; Omran, M.G.H. (2013); Gaussian bare-bones differen-
tial evolution, IEEE Transactions on Cybernetics, 43(2), 634-647, 2013.

[22] Wang, H.; Wu, Z.; Rahnamayan, S.; Liu, Y.; Ventresca, M. (2011); Enhancing parti-
cle swarm optimization using generalized opposition-based learning, Information Sciences,
181(20), 4699-4714, 2011.

[23] Wang, H.; Wu, Z.J.;Rahnamayan, S.; Sun, H.; Liu, Y.; Pan, J.S. (2014); Multi-strategy
ensemble artificial bee colony algorithm, Information Sciences, 279, 587-603, 2014.

[24] H. Wang; H. Sun; C, Li; S. Rahnamayan; J.S. Pan; Diversity enhanced particle swarm
optimization with neighborhood search, Information Sciences, 223, 119-135, 2013.



An ABC Algorithm with Recombination 601

[25] Wu, J.; Wu, G.D.; Wang, J.J. (2017); Flexible job-shop scheduling problem based on hybrid
ACO algorithm, International Journal of Simulation Modelling, 16(3), 497-505, 2017.

[26] Xiang, W.; Li, Y.; Meng, X.; Zhang, C.; An, M. (2017); A grey artificial bee colony algo-
rithm, Applied Soft Computing, 60, 1-17, 2017.

[27] Xiang, W.; Li, Y.; He, R.; Gao, M.; An, M. (2018); A novel artificial bee colony algorithm
based on the cosine similarity, Computers & Industrial Engineering, 115, 54-68, 2018.

[28] Xiang, Y.; Peng, Y.M.; Zhong, Y.B.; Chen, Z.Y.; Lu, X.W.; Zhong, X.J. (2014); A particle
swarm inspired multi-elite artificial bee colony algorithm for real-parameter optimization,
Computational Optimization and Applications, 57, 493-516, 2014.

[29] Yaghoobi, T.; Esmaeili, E. (2017); An improved artificial bee colony algorithm for global
numerical optimisation, International Journal of Bio-Inspired Computation, 9(4), 251-258,
2017.

[30] Zhang, M.; Wang, H.; Cui, Z.; Chen, J. (2017); Hybrid Multi-objective cuckoo search with
dynamical local search, Memetic Computing, doi: 10.1007/s12293-017-0237-2, 2017.

[31] Zhou, X.; Wu, Z.; Wang, H.; Rahnamayan, S. (2016); Gaussian bare-bones artificial bee
colony algorithm[J], Soft Computing, 20(3), 907-924, 2016.

[32] Zhu, G.; Kwong, S. (2010); Gbest-guided artificial bee colony algorithm for numerical func-
tion optimization, Applied Mathematics and Computation, 217, 3166-3173, 2010.