## 3 Nature-Inspired Global Optimization Methods
### Firefly Algorithm Method  
[PERSON] proposed the Firefly Algorithm (FFA) [29] which was inspired by the flashing lights of fireflies. Almost all of the firefly species use flashing lights as an attraction communication signal between females and males. The recurring flash, the flashing rate, and the time delay between flashes are the key concepts used among fireflies to share information. Although the mechanism of flashing lights in fireflies is still largely unclear, it is obvious that this signaling system helps fireflies find food, protect themselves, and attract their prey. FFA has become one of the most efficient global optimization algorithms and has been used in many real-life problems [29]. In FFA, the objective function is connected to the flashing light. In other words, the brightness is proportional to the best solution of an optimization problem. Brightness will assist fireflies to travel to shinier and more attractive positions in order to find the global best solution. There are three important rules in the FFA procedure:  
* Fireflies are socially oriented insects, and regardless of their sex, all of them move towards more attractive and brighter fireflies. * The amount of attraction of a firefly is proportionate to its brightness; hence, a firefly that has less brightness will travel toward one that has higher brightness. The attractiveness decreases as the space from the other firefly rises since air absorbs light. If there is no brighter firefly in the vicinity, fireflies will travel randomly in the design space. * The brightness (light intensity) of a firefly is specified by the objective function value of the optimization problem. In the firefly method, there are two essential keys: the variation of the light density and the formulation of the attractiveness. FFA assumes that the attraction of a firefly is determined by its shine, which is always connected with the value of the objective function: \(I(x)\propto f(x)\), where \(I(x)\) is the brightness of a firefly at position \(x\) and \(f(x)\) is the value of the objective function. \(\beta\) is defined as the attractiveness of a firefly \(i\) to firefly \(j\), which is affected by the distance between them. \(\beta_{0}\) is the attractiveness at \(r=0\), where \(r\) is the space between two fireflies. Coefficient \(\gamma\) is the fixed light absorption value. Over the iterations, fireflies converge to the local optimal solutions. The global solution can then be obtained by comparing the local solutions. Implementation of FFA is often easier than other nature-based GO algorithms such as PSO, BA and ACO. FFA is reasonably efficient in solving many continuous complex optimization problems that are challenging to other powerful GO algorithms such as GA and PSO [30]. The Firefly algorithm has gained much attention, and, due to its simplicity, many modifications on the FFA have been achieved. Some instances of the attention that the Firefly algorithm has received are: [PERSON] and [PERSON] [31] compared the performance and the effectiveness of FFA in dealing with nonlinear optimization problems against GA. [PERSON] et al. [32] employed FFA in solving continuous practical global optimization problems in dynamic environments. [PERSON] et al. [33] implemented a hybrid FFA for solving multi-objective continuous/discrete GO problems. [PERSON] et al. [34] used FFA to find the optimum design of structure design problems. [PERSON] et al. [35] modified FFA to deal with image processing optimization problems. [PERSON] [36] employed FFA to solve many complicated GO problems such as TSP. [PERSON] and [PERSON] [37] considered the optimal choice range of FFA parameters in different numeric experiments. [PERSON] and [PERSON] [38] improved FFA by adjusting the parameter controller in order to balance the exploitation and exploration of the algorithm. [PERSON] et al. [39] introduced a hybrid algorithm by combining the Fuzzy C-Means (FCM) with FFA to improve the clustering accuracy with global optimum solutions. [PERSON] et al.