# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 1 Introduction
Tabu search (TS) [25], harmony search optimization (HS) [26], teaching-learning-based optimization (TLBO) [27], JAYA [28], the group teaching optimization algorithm (GTOA) [29], the mother optimization algorithm (MOA) [30], the preschool education optimization algorithm (PEOA) [31], the learning cooking algorithm (LCA) [32], the imperialist competitive algorithm (ICA) [33], and the political optimizer (PO) [34] are representative algorithms reproducing human activities, behaviors, learning/education processes, social sciences, international strategies, and politics. Swarm intelligence-based algorithms represent the largest category in metaheuristic optimization. These algorithms mimic the social/individual behavior of animals (insets, terrestrial animals, birds and other flying animals, and aquatic animals) in reproduction, food search, hunting, migration, etc. Particle swarm optimization (PSO) [35], reproducing interactions between individuals of bird/fish swarms, is the most cited metaheuristic algorithm according to the Scopus database; in PSO, a population of candidate designs (the particles) are generated, and their positions and velocities are updated referring to the position of the leader(s) and the best positions of individual particles in each iteration. Insect behavior-inspired algorithms, for example, include ant colony optimization (ACO) [36], artificial bee colony (ABC) [37], the firefly algorithm (FFA) [38], and the ant lion optimizer (ALO) [39]. The grey wolf optimizer (GWO) [40], cyote optimization algorithm (COA) [41], snake optimizer (SO) [42], and snow leopard optimization algorithm (SLOA) [43] simulate the behavior of terrestrial animals. The GWO, reproducing the hunting behavior of grey wolves, is the 2 nd most cited algorithm in terms of citations/year after PSO. However, the GWO is preferred to PSO in view of its simpler formulation that does not include internal parameters except population size and a limit to the number of iterations. The bat algorithm (BA) [44], cuckoo search (CS) [45], crow search algorithm (CSA) [46], Harris hawks optimization (HHO) [47], and starling murmuration optimizer (SMO) [48] are inspired by flying animals like bats and birds. CS (reproducing the parasitic behavior of some cuckoo species that mix their eggs with those of other birds to guarantee the survival of their chicks) and HHO (reproducing the cooperative behavior of [PERSON] hawks in nature, specifically their surprise attacks during the chase) are the most cited MHAs of this sub-category. Last, the dolphin echolocation algorithm (DEA) [49], whale optimization algorithm (WOA) [50], salp swarm algorithm (SSA) [51], marine predators algorithm (MPA) [52], and giant revally optimizer (GTO) [53] reproduce social behavior, hunting strategy, swarming, and foraging of aquatic animals; WOA, SSA, and MPA are the most cited MHAs in this sub-category. Hybrid/improved/enhanced methods also were developed in the optimization literature by adding new equations in the original formulation or merging two or more MHAs. The goal always was finding the best balance between exploration and exploitation to minimize computational cost (i.e., the number of structural analyses or function evaluations required by the optimizer), improve robustness, and limit the number of internal parameters of the metaheuristic formulation. Hybrid metaheuristic algorithms may have a parallel or a serial architecture [54]. In the former case, the component algorithms are independently run on parallel computers, while in the latter case, they are sequentially executed on the same machine. Metaheuristic optimization algorithms are widely employed in various engineering fields such as, for example, the mechanical characterization of materials and structural identification [55], static and dynamic structural optimization [56; 57], damage identification [58], vehicle routing optimization [59], 3D printing process optimization [60], cancer classification [61], and image processing [62].