# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 1 Introduction  
Optimization searches for the minimum or the maximum of an \(NDV\)-variables function \(W(\overrightarrow{X})\) subject to a set of \(N_{\text{CON}}\) inequality/equality constraint functions \(G(\overrightarrow{X})\) or \(H(\overrightarrow{X})\). Optimization problems may be iteratively solved with gradient based algorithms (GBAs) or metaheuristic algorithms (MHAs). GBAs formulate and solve a series of approximate sub-problems until the search process converges to the optimal solution; sub-problems are built by evaluating first-order and second-order derivatives of cost functions and constraints at the solution point found in the previous iteration. MHAs do not require gradients: local information provided by gradients in GBAs are replaced in MHAs by global information gathered from a population of candidate designs. Trial solutions of MHAs are randomly generated using a mathematical model inspired by evolutionary theory/processes, biology, physics, chemistry, mathematics, astronomy, astrophysics, herd behavior of animals, human behavior and activities, social sciences, etc. MHAs evaluate the new trial solutions randomly generated and then attempt to improve the design with respect to the previous iterations. Metaheuristic algorithms can inherently deal with highly nonlinear and non-convex optimization problems. The random search allows MHAs to explore larger portions of search space than GBAs without being trapped in local optima. This ability together with their straightforward software implementation made MHAs become the standard approach to the solution of complex engineering optimization problems. Exploration and exploitation are the two typical phases carried out in metaheuristic optimization. Exploration is the leading search mechanism in the early optimization stages where large perturbations are given to optimization variables to quickly find the best regions of the search space. Exploitation governs the search process as the optimizer converges toward the global optimum: local search is carried out in properly selected neighborhoods of the most promising solutions. Exploration and exploitation must be appropriately combined in metaheuristic optimization to fully search the design space and find the globally optimal solution with low computational effort. MHAs can be categorized in four groups: (i) evolutionary algorithms; (ii) science-based algorithms; (iii) human-based algorithms; (iv) swarm intelligence-based algorithms. Evolutionary algorithms such as genetic algorithms (GAs) [1,2], differential evolution (DE) [3,4], evolutionary programming (EP) [5], evolution strategies (ESs) [6], and biogeography-based optimization (BBO) [7] reproduce evolution theory and evolutionary processes. Science-based MHAs mimic laws of physics, chemistry, astronomy and astrophysics, and mathematics. Simulated annealing (SA) [8,9], charged system search (CSS) [10], magnetic charged system search (MCSS) [11], colliding bodies optimization (CBO) [12], water evaporation optimization (WAO) [13], thermal exchange optimization (TEO) [14], equilibrium optimizer (EO) [15], gases Brownian motion optimization (GBMO) [16], and Henry gas solubility optimization (HOSO) [17] are physics/chemistry-based MHAs that reproduce equilibrium conditions of mechanical, electro-magnetic, physical/chemical, or thermal systems subject to external perturbations. Ray optimization (RO) [18] and light spectrum optimizer (LSO) [19] reproduce optics laws to define search directions containing high-quality trial solutions. Big bang-big crunch optimization (BB-BC) [20] and the gravitational search algorithm (GSA) [21] are inspired by astronomy/astrophysics phenomena such as the expansion (big bang)--contraction (big crunch) cycles leading to the formation of new star-planetary systems and gravitational interactions between masses. Mathematics inspired the sine cosine algorithm (SCA) [22], the Runge-Kutta optimizer (RUN) [23], and the arithmetic optimization algorithm (AOA) [24].