Fireworks explosion based artificial bee colony for numerical optimization☆
Introduction
Nowadays, numerical optimization has become a hot issue in the field of both science and engineering. These problems are also getting more and more complicated due to the characteristics such as nonlinear, discontinuous, non-convex and non-differentiable [1]. Traditional gradient-based methods often become incapable due to their strict use conditions and local convergence. In recent decades, taking inspiration from different natural phenomenon, many meta-heuristic algorithms (MHAs) have been developed by scholars from all over the world. Some major MHAs include genetic algorithm [2], [3] , differential evolution [4], [5], particle swarm optimization [6], [7], [8], ant colony optimization [9] and artificial bee colony (ABC) [10]. These algorithms have also been widely applied to solve numerical optimization problems and have shown excellent performance [11], [12], [13].
ABC is a swarm optimization algorithm that simulates the intelligent foraging behavior of honey bees [14]. ABC uses three types of bees, i.e., employed bees, onlookers and scouts, to search for good solutions. Compared with other MHAs, ABC has with few parameters and strong exploration abilities. Due to its simplicity, easy implementation and good performance, ABC has attracted wide attentions and also been applied to solve various real-world optimization problems such as job-shop scheduling problem [15], vehicle routing problem [16], transit network design [17] and photovoltaic parameters estimation [18].
Although ABC has shown competitive performance on many problems compared with other algorithms such as PSO and GA, it still has some weakness that it is unsatisfactory at exploitation [19]. However, an efficient search process should have good balance between global exploration and local exploitation, i.e., favor exploration at the beginning and switch to exploitation with the iteration increases. Therefore, developing new search mechanisms to enhance ABC’s exploration–exploitation balance is crucial to its performance improvement for complex optimization problems.
Fireworks algorithm (FWA) is a relatively new MHA proposed by Tan et al. [20]. The main productive operator of FWA is the fireworks explosion search, which generates new individuals around several well-distributed promising individuals [21]. The new individuals with better fitness will replace the old ones.
In this paper, by incorporating the fireworks explosion search into ABC, we propose a fireworks explosion based artificial bee colony (FW-ABC) framework. Specifically, the proposed FW-ABC framework consists of two search stages, namely bee search stage and fireworks explosion search stage. When the three bee search phases (i.e., employed, onlooker, and scout) are completed, a fireworks explosion search is implemented to exploit the promising regions. Five individuals with good distribution are selected from the populations, and new individuals are generated around these individuals. By incorporating the FW-ABC framework into the existing ABC algorithms, six FW-ABC algorithms are developed. Experimental results on CEC2014 benchmark functions [22] demonstrate that the fireworks explosion search is beneficial to enhance the performances of the ABC algorithms.
The structure of this paper is organized as follows. Section 2 reviews the research works of ABC algorithms. In Section 3, the FW-ABC algorithms are presented in detail. Section 4 analyzes and discusses the experimental results. Finally, the conclusion is drawn in Section 5.
Section snippets
Literature survey
In recent years, many improved ABC algorithms have been developed to enhance the performance. These algorithms can be divided into the following three categories.
(1) Introduction of new search equations. The search equations in ABC are used to determine the search directions and generate the new solutions. Many new search equations have been designed to enhance the ABC’s search ability. Inspired by PSO, Zhu et al. [19] proposed a gbest-guided ABC (GABC) which introduces the global best solution
Basic ABC
ABC is a swarm optimization algorithm that mimics forging behavior of honey bee. In ABC, the swarm consists of three types of bees: employed bees, onlookers and scouts [36]. The first half of the colony is the employed bees, while the other half is the onlooker bees. Different types of bees are responsibility for different tasks. The employed bees are responsible for finding better food sources, collecting the information about the quality of food source, and then passing the food information
Experimental results and analysis
We evaluate the performance of the FW-ABC algorithms on the CEC2014 benchmark functions [22]. These functions includes four groups: (1) unimodal functions (F01–F03); (2) simple multimodal functions (F04–F16); (3) hybrid functions (F17–F22); and (4) composition functions (F23–F30). The experiments are conducted with and , where D is the problem dimension. Based on the recommendation in [22], the maximum number of functional evaluations is set as MaxFES 104 D. All the compared
Conclusion
In this paper, a novel fireworks explosion based artificial bee colony (FW-ABC) framework has been proposed to enhance the performance of ABC for complex optimization problem. In the FW-ABC, three bee search phases are first utilized to search the solution space, and then fireworks explosion search is implemented to search around potential food sources for better exploitation. Specifically, it firstly selects five individuals based on their distances to each other, and fireworks explosion
Acknowledgments
This work was partly supported by the Natural Science Foundation of Jiangsu Province (BK 20160540).
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No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.knosys.2019.105002.