ORIGINAL ARTICLE Design of stochastic solvers based on genetic algorithms for solving nonlinear equations Muhammad Asif Zahoor Raja • Zulqurnain Sabir • Nasir Mehmood • Eman S. Al-Aidarous • Junaid Ali Khan Received: 16 February 2014 / Accepted: 14 July 2014 Ó The Natural Computing Applications Forum 2014 Abstract In the present study, a novel intelligent com- puting approach is developed for solving nonlinear equa- tions using evolutionary computational technique mainly based on variants of genetic algorithms (GA). The math- ematical model of the equation is formulated by defining an error function. Optimization of fitness function is carried out with the competency of GA used as a tool for viable global search methodology. Comprehensive numerical experimentation has been performed on number of benchmark nonlinear algebraic and transcendental equa- tions to validate the accuracy, convergence and robustness of the designed scheme. Comparative studies have also been made with available standard solution to establish the correctness of the proposed scheme. Reliability and effectiveness of the design approaches are validated based on results of statistical parameters. Keywords Genetic algorithm  Iterative techniques  Predictor–corrector method  Convergence analysis  Nonlinear equations 1 Introduction Many complex problems arising in Science and Engi- neering have function of nonlinear and transcendental nature, which can be expressed in the form of f(x) = 0 in single variable. The initial and boundary value problems arising in kinetic theory of gases, elasticity and other areas are reduced to nonlinear form in order to solve them. Due to their significant importance, many new numerical and analytical methods have been developed for these problems because it is not always possible to derive its exact solution by usual algebraic processes, for example, iterative numerical solvers based on Newton’s method [1–3], Taylor series, homotopy perturbation method and its various modified versions, quadrature formula, variational iteration method and decomposition method [4–8]. The performance of all of these methods is highly sensitive to initial start point of the algorithm. These algorithms work efficiently if start point is close to the solutions of the equation and normally fail otherwise. On the other hand, stochastic techniques based on viable global search methodologies have strength to solve these nonlinear equations effectively without prior knowledge of biased initial guess. Aim of this study was to provide an alternate, accurate and reliable platform for solving these problems by exploiting the strength of evolutionary computation mainly based on genetic algorithms. M. A. Z. Raja (&) Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan e-mail: Muhammad.asif@ciit-attock.edu.pk; rasifzahoor@yahoo.com Z. Sabir  N. Mehmood Department of Mathematics, Preston University Kohat, Islamabad Campus, Islamabad, Pakistan e-mail: zulqurnainsabir@gmail.com N. Mehmood e-mail: nasir.gcburewala@yahoo.com E. S. Al-Aidarous Department of Mathematics, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia e-mail: ealaidarous@kau.edu.sa J. A. Khan Hamdard Institute of Information Technology, Hamdard University, Islamabad Campus, Islamabad, Pakistan e-mail: junaid.ali@ciit-attock.edu.pk 123 Neural Comput & Applic DOI 10.1007/s00521-014-1676-z