Cellular Artificial Bee Colony algorithm with Gaussian distribution

Abstract

The Artificial Bee Colony (ABC) algorithm has shown competitive performance for handling various optimization problems. However, despite its strong global search ability, it suffers from a poor convergence rate and it loses the balance between exploitation and exploration. To compensate for this weakness, our paper proposes a cellular structured neighborhood, with Gaussian-based search equation and local attractor, and a redefined probability calculation for the ABC algorithm after an empirical analysis. The proposed algorithm is named as CGABC-Cellular neighborhood with Gaussian distribution ABC. The cellular automata (CA) model can keep individuals interact with specific neighbors while maintaining the population diversity. The Gaussian-based search equation combined with the local attractor can help exploit locally the search space, and the modified probability calculation based on rank sorting can make the selection of onlooker bees more robust and appropriate. Theoretical analysis are made to prove the global convergence of the CGABC algorithm based on the theory of probability metric spaces, and the results show that CGABC will converge to the global optimum. The proposed algorithm is tested on a set of benchmark functions and three real-world problems (the “Lennard Jones potential problem”, the “frequency-modulated sound wave synthesis problem” and the “feature selection problem”), and the results demonstrate that our proposed strategies help ABC achieve higher accuracy and faster convergence when compared with other ABC variants and swarm-based evolutionary algorithms (EAs).