A new hybrid algorithm based on chaotic maps for solving systems of nonlinear equations

This study attempts to present a new hybrid algorithm combining the capabilities of chaotic maps and the golden section search method to solve system of nonlinear equations. The proposed algorithm consists of two main stages. In the first stage, system of nonlinear equations is transformed into an unconstrained optimization problem. In the second stage, a bipartite experimental procedure is introduced (1) Chaotic reduction explores a sub-space to satisfy unimodal condition of the problem utilizing the chaotic maps as a global search. (2) The n-dimension golden section search method (GSS) is applied as a local search over the achieved search space to exploit the optimization problem. In order to study the performance of the proposed algorithm, eleven well-known problems are employed. The findings revealed that the approach is potentially capable of solving various types of systems of nonlinear equations with great precision. Moreover, the numerical results revealed that our model is an effective and efficient method in comparison with some state-of-the-art algorithms.