Binary Artificial Bee Colony optimization using bitwise operation

doi:10.1016/j.cie.2014.08.016

Computers & Industrial Engineering

Volume 76, October 2014, Pages 360-365

https://doi.org/10.1016/j.cie.2014.08.016 Get rights and content

Highlights

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Proposes a novel Binary Artificial Bee Colony optimization (BitABC) algorithm.
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BitABC has a similar framework to the original ABC.
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BitABC uses a bitwise operation for the movements of the bees.

Abstract

Artificial Bee Colony (ABC) algorithm has been applied to many scientific and engineering problems for its easy of use and efficiency. However, the original ABC technique cannot be used in a binary search space directly. This paper proposes an effective binary ABC algorithm, or BitABC, that has a similar framework to the original ABC but uses a bitwise operation for the movements of the employed bees and onlooker bees. Experiments have been carried out by comparing BitABC with three binary ABC variants, DisABC, normABC, and BinABC, and the most used binary search technique, GA, on a set of 13 selected benchmark functions. Results show that the proposed BitABC performs better than, or at least comparable to, the other algorithms in terms of the final solution accuracy, convergence speed, and robustness.

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. $v_{ij} = x_{ij} \land (ϕ_{ij} & (x_{ij} | x_{kj}))$ 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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In the real world, many optimization problems are discrete and very complex to solve. Some of them are in the class of NP-hard problems and their search spaces grow exponentially with the problem size. As a result, an exhaustive search will be impractical using exact algorithms. In the last decades, meta-heuristic algorithms as approximate algorithms have shown superior performance in solving these problems. The majority of these algorithms have been designed for continuous search spaces and are not able to solve binary optimization problems. Therefore, a transfer function is applied to convert the continuous search space to the binary one. The performance of such binary algorithms depends on their ability of exploration, exploitation and transfer function. Several transfer functions have been introduced so far but they have shown poor exploration and exploitation in solving some problems. In this study, a novel adaptive transfer function, based on two linear functions, is proposed to overcome the shortcomings of existing transfer functions. The proposed method called upgrade transfer function (UTF) adapts itself during running the algorithm to switch from exploration to exploitation. This capability also covers disadvantages of metaheuristic algorithms in terms of poor exploration and exploitation. The performance of UTF has been evaluated by three discrete optimization problems: function optimization, feature selection and the 0–1 multi-knapsack problem (MKP). The results of binary particle swarm optimization (BPSO), binary artificial bee colony (BABC) and several improved BPSO and BABC have been compared with those of UTF–BPSO and UTF–BABC using function optimization problems. Also, the efficiency of UTF–BPSO and UTF–BABC and some binary meta-heuristic algorithms such as binary salp swarm algorithm (BSSA) and binary gray wolf optimization (bGWO), binary dragon algorithm (BDA), binary multi-neighborhood artificial bee colony (BMNABC), binary hybrid topology particle swarm optimization quadratic interpolation (BHTPSO-QI), binary ant lion optimizer (bALO) and binary gravitational search algorithm (BGSA) have been evaluated by feature selection problems. Moreover, UTF and seventeen transfer functions have been applied in original PSO, ABC, SSA and GWO algorithms to solve low and high dimensions 0–1 MKP benchmark instances. The results showed that the new transfer function significantly enhances the performance of algorithms to achieve the best solution in the binary search space.

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^☆: This manuscript was processed by Area Editor Mitsuo Gen.

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Binary Artificial Bee Colony optimization using bitwise operation☆

Highlights

Abstract

Introduction

Section snippets

Artificial Bee Colony algorithm

The proposed Binary Artificial Bee Colony algorithm

Benchmark test functions

Conclusions

Acknowledgment

Information Sciences

Computers & Industrial Engineering

Applied Mathematics and Computation

Applied Soft Computing

Applied Soft Computing

Aerospace Science and Technology

Applied Soft Computing

Simulated annealing based artificial bee colony algorithm for global numerical optimization

Applied Mathematics and Computation

Performance evaluation of artificial bee colony optimization and new selection schemes

Memetic Computing

Ant system: Optimization by a colony of cooperating agents

IEEE Transactions on Agents Systems, Man, and Cybernetics-Part B, Cybernetics

A new optimizer using particle swarm theory

Binary differential evolution strategies

IEEE Congress on Evolutionary Computation (CEC)

Network models and optimization: Multiobjective genetic algorithm approach