As a novel swarm intelligence algorithm, artificial bee colony (ABC) algorithm inspired by individual division of labor and information exchange during the process of honey collection has advantage of simple structure, less control parameters, and excellent performance characteristics and can be applied to neural network, parameter optimization, and so on. In order to further improve the exploration ability of ABC, an artificial bee colony algorithm with random location updating (RABC) is proposed in this paper, and the modified search equation takes a random location in swarm as a search center, which can expand the search range of new solution. In addition, the chaos is used to initialize the swarm population, and diversity of initial population is improved. Then, the tournament selection strategy is adopted to maintain the population diversity in the evolutionary process. Through the simulation experiment on a suite of unconstrained benchmark functions, the results show that the proposed algorithm not only has stronger exploration ability but also has better effect on convergence speed and optimization precision, and it can keep good robustness and validity with the increase of dimension.
Many important problems require optimization, including the traveling salesman problem, job shop scheduling, and neural network training [
As to further improve the performance of ABC algorithm, some scholars integrate the ABC algorithm and other intelligent optimization algorithms, and some improved hybrid optimization algorithms are proposed. Kıran and Gündüz [
In this paper, an artificial bee colony algorithm with random location updating (RABC) is proposed, the basic search equation is modified, which can expand the search range of new solution and further improve the exploration ability of ABC algorithm. Numerical simulation experiments are carried on some benchmark functions, and the results demonstrate the effectiveness of RABC. The rest of this paper is organized as follows. In Section
Bees in nature have three different roles while gathering nectar; they are, respectively, employed bees, onlooker bees, and scout bees. The three kinds of bees cooperate with each other to accomplish nectar collection. In addition, the basic behavior of bees can be divided into two categories, which are the recruitment of bees for food sources and the abandonment of a food source.
Food sources are equivalent to locations of solution in the optimization problem, and the quality of the food source is expressed by a fitness value. The primary task of the employed bees and the scout bees is to explore and exploit food sources. After watching the waggle dance of employed bees, onlooker bees determine the yield of the food source through the intensity and duration of the waggle dance and then choose the food source to collect nectar based on the yield, and the scout bees are randomly searching for food sources near the hive. The bees that have already found food sources are called the employed bees. The employed bees store some information about food sources; they match food sources one to one and share the information with other bees at certain probability. The number of the employed bees is the same as that of the onlooker bees, and the scout bee is only one.
The search process for food sources consists of three steps: (1) the employed bees find food sources and record the amount of nectar; (2) according to the nectar information provided by the employed bees, the onlooker bees select the food source to collect nectar; and (3) the scout bees are determined to search for new food sources.
Inspired by the bee swarm intelligent behavior of gathering nectar in nature, ABC algorithm is proposed by Karaboga. In the ABC algorithm, the complete search range of bee swarm represents the solution space of optimization problem. A location of a random food source corresponds to a stochastic solution of the optimization problem, and the nectar quantity of the food source represents the fitness value, which is used to describe quality of solutions. Therefore, the gathering nectar process is also the process of searching for the optimal solution.
Considering the global optimization problem
Employed Bees Phase
In this phase, each employed bee corresponds to the current food source
Onlooker Bees Phase
After all the employed bees have completed the search process, they will share the information of food sources with the onlooker bees in the dance area, and the onlooker bees will calculate the probability of each solution according to the following formula:
Scout Bees Phase
If a position cannot be improved further through a predetermined number of cycles
The above three phases will be repeated until the maximum iteration number MCN or the allowable value of error
The fitness function is used to measure nectar quality of solutions in ABC algorithm, and it is selected corresponding to optimization problem. If the optimization problem is to find the minimum value, the fitness function is deformation of the objective function
If the optimization problem is to find the maximum value, the fitness function is the objective function.
The greedy selection is performed in ABC algorithm, where
In ABC, the bee swarm relies on the information sharing among individuals to explore new food sources, and the algorithm has stronger randomness, so it is generally recognized that it has better global search ability. Therefore, some scholars have carried out research on how to improve the local search ability of ABC algorithm. The representative work is the global best (gbest) guided ABC proposed by Zhu (GABC). It is inspired by the particle swarm algorithm, and a search operator guided by the best solution is introduced to improve the exploit ability of the algorithm. Thus, the search equation is expressed as follow:
However, the main purpose of this paper is to further improve the global search ability of ABC algorithm and accelerate the convergence speed. In order to directly analyze the location of the new food source, the search range is analyzed taking the twodimensional plane space as an example. As shown in Figure
Search range of ABC.
In order to further expand the global search ability of ABC algorithm, we modify the search equation of ABC algorithm and propose an improved ABC algorithm with random location updating. This algorithm takes a random position of population as the search center, and thus the modified search equation is expressed as
In order to compare and analyze the search area of RABC algorithm, the same example in Figure
Search range of RABC.
Chaos is a nonlinear phenomenon and widely exists in nature. Generally, chaos is defined by a deterministic equation and can generate stochastic motion states. The generated chaotic sequence has the characteristics of randomness, ergodicity, and regularity, and it can traverse all the states in a certain range according to its own laws. In this paper, chaos is used to realize the initialization of population. At present, logistic is the most frequently used chaotic function, and its equation is as follows:
In the ABC algorithm, the selection probability of food source depends on the fitness value, and the food source with the higher fitness value has greater selection probability. In the early evolution stage, some superindividuals may be generated so that the evolution is easy to fall into the local extremum, and the premature convergence comes up. Tournament selection strategy is adopted based on the competition mechanism in this paper.
The framework of RABC Algorithm
Generate SN food sources
While
% Employed Bees Phase
Generate a new candidate solution
Update candidate solution
% Onlooker Bees Phase
Choose a food source
Generate a new candidate solution
Update candidate solution
% Scout Bees Phase
In this section, we use five typical benchmark functions to validate the comprehensive performance of the proposed algorithm, and the experiments were implemented on a computer with the main frequency of 3.6 GHz, memory 8G, Matlab R2013a, and Windows 7 operating system. Table
Typical benchmark functions.
Name  Function  Minimum  Range  Features 

Sphere 

0  (−100,100)  Unimodal 
Rosenbrock 

0  (−50,50)  Unimodal 
Rastrigin 

0  (−5.12,5.12)  Multimodal 
Ackley 

0  (−32.768,32.768)  Multimodal 
Griewank 

0  (−600,600)  Multimodal 
A series of experiments on the benchmark function are performed, and the results are compared and analyzed among ABC, GABC, and RABC; it mainly includes accuracy, convergence speed, and dimension expansion. For a fair comparison among ABCs, they are tested using the same settings of the parameters. The number of the employed bees is the same as that of the onlooker bees. The maximum number of function evaluation is set to 300000; thus, the maximum iterations’ cycle is 5000, and the size of population SN = 60. In addition, all the benchmark functions are tested when the dimension
For each benchmark function, every algorithm runs 30 times independently, and the performance of each algorithm is evaluated by calculating the best value, the worst value, the mean value, and the standard deviation (SD). Note that the SD is mainly used to evaluate the stability of convergence accuracy for each algorithm. Table
Result comparisons of ABCs at
Function  Algorithm  Best  Worst  Mean  SD 


ABC  1.3343 
5.5490 
2.9340 
1.2284 
GABC  8.0766 
7.5958 
5.1502 
1.7824  
RABC 








ABC  6.7942 
2.3206 
1.6657 
3.3657 
GABC  2.5497 
1.6969 
7.1468 
3.9955  
RABC  3.4317 







ABC  3.3160 
4.2417 
3.9589 
1.9607 
GABC  4.5768 
4.4127 
1.2709 
1.0648  
RABC  5.0743 







ABC  6.7080 
1.6450 
1.0683 
2.8482 
GABC  7.0690 
6.7093 
1.5803 
1.6938  
RABC 








ABC  1.4731 
9.4283 
5.7262 
2.0506 
GABC  0.00 
0.00 
0.00 
0.00  
RABC 




Result comparisons of ABCs at
Function  Algorithm  Best  Worst  Mean  SD 


ABC  1.9289 
3.0586 
2.5029 
2.4108 
GABC  8.3306 
3.3362 
9.2300 
8.0450  
RABC 








ABC  5.7439 
9.1878 
7.6453 
8.3811 
GABC  1.6008 
8.2963 
2.5306 
2.3158  
RABC 








ABC  8.1959 
1.0394 
9.9539 
4.3577 
GABC  2.8785 
1.0569 
5.2517 
2.0834  
RABC 








ABC  1.3725 
1.5174 
1.4491 
4.0077 
GABC  1.5230 
5.8137 
3.0739 
8.9919  
RABC 








ABC  1.5337 
2.1861 
1.8835 
1.6630 
GABC  9.7595 
2.8826 
1.3889 
3.9773  
RABC 




As can be seen from Table
Figures
Evolution curves at the sphere function. (a)
Evolution curves at the Rosenbrock function. (a)
Evolution curves at the Rastrigin function. (a)
Evolution curves at the Ackley function. (a)
Evolution curves at the Griewank function. (a)
In summary, whether for unimodal or multimodal functions, RABC not only has stronger exploration ability, but also has better effect on convergence speed and optimization precision. As the dimension of the optimization problem increases, it can also keep good robustness and validity.
This paper presents an artificial bee colony algorithm with random location updating, and the search equation of this algorithm takes a random position in swarm population as the search center. In contrast to ABC, the search range of new solution is further expanded, which can enhance the exploration ability. Besides this, the chaos is used to initialize the swarm population, and diversity of initial population is improved. Then the tournament selection strategy is adopted to maintain the population diversity in the evolutionary process. The results of the simulation experiment on a suite of unconstrained benchmark functions demonstrate that RABC not only has stronger exploration ability but also has better effect on convergence speed and optimization precision, and it can keep good robustness and validity with the increase of dimension.
As an extension of this paper, the proposed algorithm will be further studied in theory; for instance, the global convergence of this algorithm will be verified using the convergence criterion of stochastic search algorithm and the properties of the Markov chain, and the moving trajectory of bees will also be studied according to the theory of nonlinear dynamic. In addition, from the perspective of practical application, the fusion of the proposed algorithm with other optimization algorithms and the selection of its own parameters will also be the next research contents.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported in part by the National Natural Science Foundation of China (U1604151), Outstanding Talent Project of Science and Technology Innovation in Henan Province (174200510008), Program for Scientific and Technological Innovation Team in the Universities of Henan Province (16IRTSTHN029), Science and Technology Project of Henan Province (182102210094), Natural Science Project of the Education Department of Henan Province (18A510001), and the Fundamental Research funds of the Henan University of Technology (2015QNJH13 and 2016XTCX06).