## 3 Nature-Inspired Global Optimization Methods
### Artificial Bee Colony Method  
The Artificial Bee Colony (ABC) method, presented by [PERSON] in 2005 [PERSON] (2005), was inspired by the search behaviour of bee colonies. Honeybees use several mechanisms, such as a waggle dance, to locate food sources. The waggle dance technique is used by scout bees to share information about the source of food. Bees can quickly and precisely modify their search pattern and search space in accordance to the updated information received from other bees. In the ABC method, artificial bees are classified into three different groups: employed bees, onlooker bees, and lastly, scout bees. Each of these groups is assigned different tasks in the ABC procedure. The employed bee's task is to visit and collect information about a source of nectar and then share it with other bees in the hive. In the ABC algorithm, the number of employed bees and the number of food sources are equal since each employed bee is linked with only one source of nectar. The onlooker bees receive the data regarding the sources of nectar from the employed bees, and then the onlooker bees select one of the sources and start to transfer the food to the hive. The scout bees fly in random directions and have the responsibility of finding new sources of nectar. In the ABC method, the possible solution corresponds to the nectar source location in which the fitness of the solution mainly depends on \begin{table}
\begin{tabular}{c c} \hline
**Symbol** & **Description** \\ \hline _NFE_ & Number of Function Evolution \\ \(D\) & Dimensional \\ _CPU_ & Computation time \\ _GO_ & Global Optimization \\ TSP & Travelling Salesman problem \\ \(a\) & Step size in CSA \\ _\(\gamma\)_ & Scaling factor to control the step size in FFA \\ _\(\beta\)_ & Attractiveness of firefly in FFA \\ _\(\lambda\)_ & Wavelengths in BA \\ _\(p\)_ & Switch probability \\ _\(N\)_ & population size \\ \hline \end{tabular}
\end{table} 
Table 1: Symbols and Notations. the related nectar amount. Furthermore, the total number of best obtained solutions is also identical to the number of employed bees or equivalent onlooker bees. In the ABC method, a number of parameters including population size \(N\), number of cycles (iterations), and the exploration parameter limit should be set prior to running the optimization. The number of cycles (iterations) and the parameter limits are equally important, and, to obtain the best results, should be set to their optimal values. It must be noted that in the ABC method, employed bees apply a local search to each nectar source, whereas the onlooker bees will likely update better food sources. Therefore, in the ABC algorithm, the employed bees are responsible for diversification whereas the onlooker bees are used for condensation. By implementing these three groups of bees (employed, onlooker and scout), the ABC algorithm easily escapes from minimums and improves its search efficiency. The ABC algorithm is competitive with other nature-inspired algorithms [20]; its implementation is relatively easy, and it requires only a few tuning control parameters to be set. Due to the high efficiency of the ABC method, many researchers have used their own points of view to utilize ABC for different purposes. For instance, [PERSON] and [PERSON] [21], inspired by differential evolution (DE), developed a search strategy ABC/best/1 with a new chaotic initialization method with a subsequent improvement of the exploitation ability of ABC. [PERSON] and [PERSON] [22] developed a global best- (gbest-) guided ABC algorithm (GABC) to improve the search ability as well as the efficiency by using the gbest solution with the original search formula of the ABC algorithm. [PERSON] et al. [23] presented a modified ABC method (I-ABC) using the best-so-far solution, inertia weight, and coefficients to improve the search efficiency. [PERSON] et al. [24] presented an improved search equation that causes the solution to directly converge towards the best-so-far solution rather than through a randomly selected path.