# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 1 Introduction
However, in spite of the large diffusion of MHAs in engineering practice, some issues remain open in metaheuristic optimization: (i) no metaheuristic algorithm can always outperform all other MHAs in all optimization problems; (ii) MHAs may require a very large number of function evaluations (analyses) for completing optimization process; (iii) sophisticated algorithmic variants and hybrid MHAs combining multiple methods often increase the computational complexity of the optimizer also because of the presence of additional internal parameters that are difficult to be tuned. As a matter of fact, newly developed MHAs often added very little to the optimization field and stopped attracting potential users even after a rather short time from their release. The main objective of this study was to develop an efficient and robust hybrid metaheuristic algorithm for engineering optimization. Generally speaking, a hybrid optimizer should combine high-performance MHAs that complement each other in terms of exploration and exploitation. Furthermore, component algorithms should be versatile so as to successfully deal with as many different optimization problems as possible. Lastly, component algorithms should be simple enough in order to simplify the formulation of the hybrid optimizer and to limit the number of additional internal parameters governing the switch from one component algorithm to another. In view of this, the grey wolf optimizer (GWO) and the JAYA algorithms were selected in the present study and combined into the novel FHGWJA hybrid algorithm (the acronym stands for Fast Hybrid Grey Wolf JAYA) because they certainly satisfy the above-mentioned requisites. The GWO mimics the leadership hierarchy and hunting mechanism of grey wolves [40]. The leadership hierarchy is simulated by defining four types of grey wolves (\(\alpha\), \(\beta\), \(\delta\), and \(\omega\)). The hunting mechanism is simulated with different algorithmic operators that represent searching for prey, encircling prey, and attacking prey. The \(\alpha\) wolf is the group leader. The \(\beta\) wolf helps the \(\alpha\) in decision-making or other pack activities. The lowest ranking is represented by \(\omega\) wolves. The \(\delta\) wolves rank between the \(\alpha\)-\(\beta\) wolves and the \(\omega\) wolves. Alpha, beta, and delta wolves estimate the position of the prey, and other wolves randomly update their positions around the prey. As previously mentioned, the GWO is the 2 nd most cited metaheuristic algorithm after PSO according to the Scopus database. It was successfully applied to many fields because of its simple formulation and computational efficiency (see, for example, the surveys on GWO applications presented in [63; 64; 65]). However, the GWO may suffer from lack of exploitation, risk of stagnation especially in complex problems, and limited adaptability to variations in the problem landscape during the optimization process. Enhanced GWO formulations including (i) new operators to capture other characteristic behaviors of wolves (i.e., gaze cues learning [64] and dimension learning-based hunting [66]), (ii) Cauchy-Gaussian mutation (increasing the search range of leader wolves when they tend to the local optimal solution) along with greedy selection (to maintain population diversity) and improved search strategy considering average position of all individuals [67], (iii) chaotic grouping and dynamic regrouping of individuals to increase population diversity [68], (iv) optimization of initial population along with a nonlinear control parameter convergence strategy and nonlinear tuning strategy of parameters [69], and (v) update of wolves' positions with spiral movements [70], as well as (vi) hybrid algorithms combining GWO with other powerful MHAs (i.e., particle swarm optimization, biogeography-based optimization, differential evolution, Harris hawks optimization, and the whale optimization algorithm [71; 72; 73; 74; 75]) were proposed in order to overcome the above-mentioned limitations.