Chaotic Enhanced Genetic Algorithm for Solving the Nonlinear System of Equations

Abstract

Many engineering and scientific models are based on the nonlinear system of equations (NSEs), and their effective solution is critical for development in these domains. NSEs can be modeled as an optimization problem. So, the goal of this paper is to propose an optimization method, to solve the NSEs, which is called a chaotic enhanced genetic algorithm (CEGA). CEGA is a chaotic noise-based genetic algorithm (GA) that improves performance. CEGA will be configured so that it uses a new definition which is chaotic noise to overcome the drawbacks of optimization methods such as lack of diversity of solutions, the imbalance between exploitation and exploration, and slow convergence of the best solution. The goal of chaotic noise is to reduce the number of repeated solutions and iterations to speed up the convergence rate. In the chaotic noise, the chaotic logistic map is utilized since it has been used by numerous researchers and has proven its efficiency in increasing the quality of solutions and providing the best performance. CEGA is tested using many well-known NSEs. The suggested algorithm's results are compared to the original GA to prove the importance of the modifications introduced in CEGA. Promising results were obtained, where CEGA’s average percentage of improvement was about 75.99, indicating that it is quite effective in solving NSEs. Finally, comparing CEGA’s results with previous studies, statistical analysis by Friedman and Wilcoxon’s tests demonstrated its superiority and ability to solve this kind of problem.