Binary Artificial Bee Colony optimization using bitwise operation☆
Introduction
In recent years, a new swarm intelligence-based optimization algorithm, called Artificial Bee Colony (ABC), has greatly attracted the attention of researchers. The ABC algorithm was first proposed by Karaboga in 2005 for finding near-optimal solutions to numerical optimization problems (Akay and Karaboga, 2012, Karaboga, 2005, Karaboga and Akay, 2009a). It shares many similarities to other swarm intelligence techniques such as Particle swarm optimization (PSO) and Ant Colony Optimization (ACO). All swarm intelligence-based techniques have a common feature. That is, they mimic the group behavior of animals or insects in the nature. PSO is inspired by the social behavior of bird flocking or fish schooling (Eberhart and Kennedy, 1995, Jia et al., 2011) and ACO takes inspiration from the behavior of real ant colonies (Dorigo, Maniezzo, & Colorni, 1996), while ABC simulates the foraging behavior of honey bees. So far, ABC algorithm has been successfully applied to many scientific and engineering fields. Karaboga, Akay, and Ozturk (2007) tested ABC algorithm on neural network training and got a comparable result. Mohan and Baskaran (2011) employed an Artificial Bee Colony system for ad-hoc network routing protocol. Other uses of ABC algorithm include data mining, wireless sensor networks, air vehicle path planning, design and manufacturing etc. (Ozturk et al., 2011, Shukran et al., 2011, Xu et al., 2010, Yildiz, 2013).
Artificial Bee Colony algorithm has been studied comprehensively and a lot of improved variants of ABC algorithm have been developed recently (Diwold et al., 2011, Karaboga and Akay, 2009b, Karaboga et al., 2012). Karaboga and Akay (2009b) made a thorough investigation on the foraging behavior of honey bees. In (Karaboga and Akay, 2009a, Karaboga and Basturk, 2008), the performance of ABC algorithm was compared to Differential Evolution (DE), PSO, Evolutionary Algorithm (EA), and Evolution Strategies (ES) upon a large set of numerical benchmark test functions. Akay and Karaboga (2012) presented a modified Artificial Bee Colony algorithm for real-parameter optimization. Wu, Hao, and Xu (2011) described an improved ABC algorithm to enhance the global search ability of basic ABC algorithm. Tsai, Pan, Liao, & Chu, 2009 introduced an enhanced interactive ABC algorithm (IABC) for numerical optimization problems. Chen, Sarosh, and Dong (2013) proposed an improved Artificial Bee Colony algorithm based on simulated annealing for global numerical optimization. Except mentioned above, more improved variants of ABC algorithm can be found in (Karaboga et al., 2012).
Since ABC algorithm was originally proposed for solving real-parameter problems, most studies on improving the ABC algorithm were developed in continuous search space. However, there are many binary optimization problems where the initial ABC algorithm cannot be implemented directly. Besides, for easy of hardware logic implementation, continuous optimization problems are usually solved in a binary number space. But, unfortunately, only a few researches pay their attentions to the binary ABC algorithm. Kashan, Nahavandi, and Kashan (2012) proposed a binary version of ABC (DisABC), in which the vector subtraction operator in the original ABC algorithm was replaced by a new differential expression which employs a measure of dissimilarity between binary vectors. Based on the concept of Binary PSO and binary DE, Pampara and Engelbrecht (2011) also proposed three binary version of ABC algorithm, called binary ABC (binABC), angle-modulated ABC (AMABC), and normalized ABC (normABC), respectively. Wang, Li, and Ren (2010) applied a binary ABC to intrusion detection systems to obtain the optimum feature selection.
In Jia, Duan, and Khan (2013), we have proposed a binary DE algorithm, which used a logic operation, and its results showed a better performance on test functions. Based on the binary DE conception, in this paper, we proposed a novel binary version of ABC algorithm, or BitABC, with a similar framework to the original ABC algorithm. Different from the normABC, binABC, and DisABC, the real arithmetic operation in original ABC was replaced by a bitwise operation. Compared with other binary variants of ABC algorithm and Genetic Algorithm (GA), the proposed BitABC algorithm shows a better performance in terms of search ability, convergence speed, and robustness.
Section snippets
Artificial Bee Colony algorithm
Artificial Bee Colony algorithm shares many similarities to other swarm intelligence-based techniques such as PSO and ACO. The system is randomly initialized with a population in the search space. In the ABC system, the population consists of three groups of bees: employed bees, onlooker bees and scouts. Each bee in the colony stands for a solution to the problem and searches for optima by updating generations.
The main phases of ABC algorithm are as follows:
The proposed Binary Artificial Bee Colony algorithm
This section proposes a novel Artificial Bee Colony algorithm for binary optimization. In the proposed binary ABC algorithm, a binary bitwise operation takes the place of the real arithmetic operation used in the original ABC system.
In the binary ABC algorithm, a new food source for an employed bee or an onlooker bee is produced by the following equation.where, ‘^’ stands for a ‘xor’ operator, ‘&’ stands for a ‘and’ operator, and ‘|’ represents a ‘or’ operator in a binary
Benchmark test functions
Experiments are carried out over a set of 13 widely used benchmark functions listed in Appendix A. These functions are taken from Yao, Liu, and Lin (1999) each with different characteristics. Most of them are also used for the comparison of other binary optimization algorithms (Engelbrecht and Pampara, 2007, Jia et al., 2013, Pampara and Engelbrecht, 2011). Among these benchmarks, F1–F4 are unimodal functions, F5 is the Rosenbrock function which is unimodal function for D = 2 and multimodal
Conclusions
ABC is a recently developed swarm intelligence-based optimization technique. Due to its ease of implementation, ABC has been applied to many scientific and engineering problems. However, the ABC cannot be used to binary optimization problems directly. In this paper, we proposed a simple but effective binary ABC algorithm, or BitABC, that has a similar structure to original ABC but uses bitwise operations.
Comparisons have been carried out on a set of 13 selected benchmarks. Results show that the
Acknowledgment
This paper is partially supported by the National Nature Science Foundation of China (Grant Nos. U1204606, 41373101, and 61304131).
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