Modified grasshopper optimization algorithm-based genetic algorithm for global optimization problems: the system of nonlinear equations case study

Abstract

Grasshopper optimization algorithm (GOA) is one of the promising optimization algorithms for optimization problems. However, it has the main drawback of trapping into a local minimum, which causes slow convergence or inability to detect a solution. Several modifications and combinations were suggested to overcome this problem. This paper presents a modified grasshopper optimization algorithm (MGOA)-based genetic algorithm to overcome this problem. Modifications rely on certain mathematical assumptions and varying the domain of the control parameter, Cmax, to escape from the local minimum and move the search process to an improved point. Parameter C is one of the essential parameters in GOA, where it balances the exploration and exploitation of the search space. These modifications aim to speed up the convergence rate by reducing the repeated solutions and the number of iterations. Both the original GOA and the proposed algorithms are tested with 19 main test functions to investigate the influence of the proposed modifications. In addition, the algorithm will be applied to solve five different cases of nonlinear systems with different types of dimensions and regularity to show the reliability and efficiency of the proposed algorithm. Promising results are achieved compared to the original GOA. The proposed approach shows an average percentage of improvement of 96.18 as illustrated in the detailed results.