Furthermore, Basturk et al. [25] also applied ABC to function optimizations

with constraints and the simulation results had shown that this intelligent algorithm is superior to other heuristic algorithms such as ant colony optimization (ACO) kinase inhibitors [26], particle swarm optimization (PSO) [27], and artificial plant optimization (APO) [28] in 2006. In addition, the ABC algorithm has been also used to solve large-scale problems and engineering design optimization. Some representative applications are introduced as follows. Singh [29] applied the ABC algorithm for the leaf-constrained minimum spanning tree (LCMST) problem and compared the approach against GA, ACO, and tabu search. In literature [29], it was reported that the proposed algorithm was superior to the other methods in terms of solution qualities and computational time. Zhang et al. [30] developed the ABC clustering algorithm to optimally partition N objectives into K cluster and Deb’s rules were used to direct the search direction of each candidate. Pan et al. [31] used the discrete ABC algorithm to solve the lot-streaming flow shop scheduling problem with the criterion of total weighted earliness and tardiness

penalties under both the idling and no-idling cases. Samanta and Chakraborty [32] employed ABC algorithm to search out the optimal combinations of different operating parameters for three widely used nontraditional machining (NTM) processes, that is, electrochemical machining, electrochemical discharge machining, and electrochemical micromachining processes.

Chen and Ju [33] used the improved ABC algorithm to solve the supply chain network design under disruption scenarios. The computational simulations revealed the ABC approach is better than others for solving this problem. Bai [34] developed wavelet neural network (WNN) combined with a novel artificial bee colony for the gold price forecasting issue. Experimental results confirmed that the new algorithm converged faster than the conventional ABC when tested on some classical benchmark functions and was effective in improving modeling capacity of WNN regarding the gold price forecasting scheme. All these researches illustrated that the ABC algorithm has powerful ability to solve much more complex engineering problems [35, 36]. In the basic ABC algorithm, the colony of artificial bees contains three groups of bees: employed bees, onlookers, and scouts. Employed bees determine a food source within the neighborhood Batimastat of the food source in their memory and share their information with onlookers within the hive, while onlookers select one of the food sources according to this information. In addition, a bee carrying out random search is called a scout. In ABC algorithm, the first half of the colony consists of the employed bees and the remaining half includes the onlookers. There is only one employed bee corresponding to one food source.