# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 1 Introduction
JAYA [28] utilizes the most straightforward search scheme amongst all MHAs consisting of only one equation to perturb optimization variables: to approach the population's best solution and move away from the worst solution, thus achieving a significant convergence capability. JAYA is a very versatile algorithm with a large number of applications documented in the literature [76; 77]. JAYA has an inherently hybrid nature combining basic features of evolutionary algorithms (the survival of fittest individual) and swarm-based algorithms where the swarm normally follows the leader in the search of the optimal solution. These characteristics make JAYA a very good candidate component of new hybrid metaheuristic algorithms. Similar to the GWO, JAYA may present a rather weak exploitation phase. Furthermore, JAYA uses only one equation to perturb optimization variables involving only the best and the worst individuals of the population: this may produce stagnation and also limit the exploration phase. To overcome these issues, improved JAYA formulations using subpopulations [78], or involving also the current average solution and the historical solutions (a population of candidate solutions initially generated besides the standard population and permuted in the optimization process according to a probabilistic criterion) [79], were developed. Fuzzy clustering competitive learning, experience learning, and Cauchy mutation mechanisms were also implemented [80] to effectively utilize population information, speed up the convergence rate, improve the balance between exploiting the previously visited regions and exploring new regions of search space in the search process, and reduce the risk of being trapped into local optimum by fine-tuning the quality of the so-far best solution. The high computational cost is another issue in JAYA optimization. In [81; 82], it was attempted to reduce the number of analyses and increase convergence speed by directly rejecting heavier designs than population individuals, but this strategy missed the global optimum in many structural optimization problems. Similarly, in [83], the population was updated not only if the new trial solutions improve the individuals currently stored in the population but also if they have the same values for the cost function or penalized cost function. In [84], generation of trial designs also relied on two randomly selected individuals \(\overset{\rightarrow}{X_{m}}\) and \(\overset{\rightarrow}{X_{n}}\), and the perturbation equation varied if \(m>n\) or \(m<n\) as well as if \(W(\overset{\rightarrow}{X_{m}})<W(\overset{\rightarrow}{X_{n}})\) or \(W(\overset{\rightarrow}{X_{m}})>W(\overset{\rightarrow}{X_{n}})\). JAYA was also hybridized with other efficient MHAs such as, for example, harmony search optimization [56], genetic algorithms [85], crow search [86], the Rao-1 optimizer [87], teaching-learning-based optimization [88], and differential evolution [89]. The main features of the novel FHGWJA algorithm developed in this study and the advancements with respect to the state-of-the-art can be summarized as follows:  
1. GWO and JAYA were simply merged into FHGWJA without complicating the algorithmic structure resulting from the hybridization process: this is a significant step further with respect to the above-mentioned studies where performance improvements achieved with the GWO and JAYA variants often were problem-sensitive and entailed complicated optimization formulations that were not easy to reproduce;
2. FHGWJA utilizes elitist and repair strategies to generate high-quality candidate solutions that always have a significantly high probability of improving the current best record. The movements assigned to optimization variables in the perturbation process may be adjusted according to a rank-proportional variation strategy. This approach is more effective than those adopted in the GWO/JAYA variants proposed in the literature that do not guarantee each new trial solution be better than the current best record.