Hybridization of Grasshopper Optimization Algorithm with Genetic Algorithm for Solving System of Non-Linear Equations

A novel algorithm for optimization in this article, called hybrid grasshopper optimization algorithm (GOA) with genetic algorithm (GA): hybrid-GOA-GA, is proposed for solving the system of non-linear equations (SNLEs). First, the SNLEs are converted into an optimization problem. Then, the optimization problem is solved by hybrid-GOA-GA. In the hybrid-GOA-GA, a population of randomized solutions is initialized. These solutions, by GOA, are looking for an optimal solution for SNLE in the domain of optimization problem. During this process, the evolution of these solutions is carried out by GA. Hybrid-GOA-GA integrates the merits of both GOA and GA; where GOA's exploitability and GOA's exploration potential are combined. Furthermore, hybrid-GOA-GA has good capability for escaping from local optima with faster convergence. The hybrid-GOA-GA has been tested by eight benchmarks problems which include different applications. Additionally, the effect of changing the initial intervals of the variables on the efficiency of the proposed algorithm is discussed. Also, the computational cost of the proposed algorithm is studied and compared with other methods. The results show that the hybrid-GOA-GA algorithm is superior to other algorithms, and return the best solution of SNLEs. Finally, in terms of accuracy, the effect of changing initial intervals and computational cost, the proposed approach is competitive and better in most benchmark problems compared to other methods. So, we can say that hybrid-GOA-GA is effective to solve a SNLEs.