Gbest-guided artificial bee colony algorithm for numerical function optimization

Artificial bee colony (ABC) algorithm invented recently by Karaboga is a biological-inspired optimization algorithm, which has been shown to be competitive with some conventional biological-inspired algorithms, such as genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO). However, there is still an insufficiency in ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by PSO, we propose an improved ABC algorithm called gbest-guided ABC (GABC) algorithm by incorporating the information of global best (gbest) solution into the solution search equation to improve the exploitation. The experimental results tested on a set of numerical benchmark functions show that GABC algorithm can outperform ABC algorithm in most of the experiments. By now, there have been several kinds of biological-inspired optimization algorithms, such as genetic algorithm (GA) inspired by the Darwinian law of survival of the fittest [1,2], particle swarm optimization (PSO) inspired by the social behavior of bird flocking or fish schooling [3,4], ant colony optimization (ACO) inspired by the foraging behavior of ant colonies [5], and Biogeography-Based Optimization (BBO) inspired by the migration behavior of island species [6]. By simulating the foraging behavior of honey bee swarm, Karaboga [7] recently invented a new kind of optimization algorithm called artificial bee colony (ABC) algorithm for numerical function optimization. A set of experimental results on function optimization [8–11] show that ABC algorithm is competitive with some conventional biological-inspired optimization algorithms, such as GA, differential evolution (DE) [12], and PSO. Since its invention in 2005, ABC algorithm has been applied to solve many kinds of problems besides numerical function optimization. In [13], Singh applied ABC algorithm for the Leaf-Constrained Minimum Spanning Tree (LCMST) problem. The experimental results presented in [13] show that comparing with GA, ACO and Tabu Search (TS), ABC algorithm can obtain better quality solutions of the LCMST problem in shorter time. Karaboga [14] used ABC algorithm to design Infinite Impulse Response (IIR) filters. And the performance of ABC algorithm was compared with that of a conventional optimization algorithm (LSQ-nonlin) [15] and PSO algorithm in the designs of IIR filters. According to their experimental results, ABC algorithm can be an alternative to design low-and high-order digital IIR filters [14]. Rao et al. [16] also applied ABC algorithm to solve the distribution system loss minimization problem. Their simulation results on the optimization of distribution network configuration show that ABC algorithm outperforms GA, DE …