A New Hybrid Particle Swarm Optimization and Jaya Algorithm for Optimal Weight Design of a Gear Train

Optimization is essential in real-life mechanical engineering problems that mostly are nonlinear, depend on mixed decision variables, and are usually subject to constraints. However, most of the studied problems are modelled assuming continuous variables. A limited number of studies have been devoted to cases with mixed variables. Moreover, there is a lack of algorithm treating mixed variable problems properly. This article introduces a hybrid algorithm that can handle constrained problems depending on continuous or mixed variables. The proposed algorithm combines two meta-heuristics, Jaya and particle swarm optimization (PSO). PSO is one of the most popular methods to solve nonlinear problems, and Jaya is a novel parameter-free optimization algorithm. This new hybrid optimization algorithm is proposed in order to improve the convergence speed and to investigate what improvements it will bring to optimization problem solutions. The developed algorithm was used to tackle two minimization problems subject to nonlinear constraints. The first one relates to minimizing the weight of a gear and the second one concerns the minimization of a two-stage planetary gear train volume since they are widely used in power transmission systems. The developed algorithm proposes an easy and efficient way to deal with discrete, normalized, and integer variables. The obtained results are promising and show that the proposed algorithm gives much better results compared to other optimization methods that considered the examined problems, while satisfying the constraints. The algorithm has also proven to be fast in arriving to the optimal result in comparison with Jaya.