Abstract
Nonlinear equations represent highly complex systems and their solutions by conventional methods have high computational complexity. Methods like Bisection, Regula Falsi, Newton–Raphson, Secant, Muller, etc., are used to solve such problems. This work find gaps in the existing methods and justifies the applicability of Genetic Algorithm to the problem. A Genetic Algorithm-based method has been proposed, which is more efficient and produces better results as compared to the existing methods.
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Abd-El-Wahed, W.F., Mousa, A.A., El-Shorbagy, M.A.: Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems. J. Comput. Appl. Math. 235, 1446–1453 (2011)
Bianchini, M., Fanelli, S.: Optimal algorithms for well-conditioned nonlinear systems of equations. IEEE Trans. Comput. 50(7), 689–698 (2001)
Chang, W.D.: An improved real-coded genetic algorithm for parameters estimation of nonlinear systems. Mech. Syst. Signal Process. 20, 236–246 (2006)
Effati, S., Nazemi, A.R.: A new method for solving a system of the nonlinear equations. Appl. Math. Comput. 168, 877–894 (2005)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Grosan, C., Abraham, A.: A new approach for solving nonlinear equations systems. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Humans 38(3), 698–714 (2008)
Guessan, A.N.: Analytical existence of solutions to a system of nonlinear equations with application. J. Comput. Appl. Math. 234, 297–304 (2010)
Holland, J.: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1975)
Ji, Z., Li, Z., Ji, Z.: Research on genetic algorithm and data information based on combined framework for nonlinear functions optimization. Proc. Eng. 23, 155–160 (2011)
Joshi, G., Krishna, M.B.: Solving system of non-linear equations using genetic algorithm. In: International Conference on Advances in Computing, Communications and Informatics (ICACCI) (2014)
Konaka, A., Coitb, D.W., Smith, A.E.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab. Eng. Syst. Saf. 91, 992–1007 (2006)
Mastorakis, N.E.: Solving non-linear equations via genetic algorithms. In: Proceedings of the 6th WSEAS International Conference on Evolutionary Computing, pp. 24–28. Lisbon, Portugal (2005)
McCall, J.: Genetic algorithms for modelling and optimization. J. Comput. Appl. Math. 184, 205–222 (2005)
Mousa, A.A., El-Desoky, I.M.: GENLS: Co-evolutionary algorithm for nonlinear system of equations. Appl. Math. Comput. 197, 633–642 (2008)
Nie, P.: An SQP approach with line search for a system of nonlinear equations. Math. Comput. Modell. 43, 368–373 (2006)
Pourrajabian, A., Ebrahimi, R., Mirzaei, M., Shams, M.: Applying genetic algorithms for solving nonlinear algebraic equations. Appl. Math. Comput. 219, 11483–11494 (2013)
Raja, M.A.Z., Sabir, Z., Mehmood, N., Al-Aidarous, E.S., Khan, J.A.: Design of stochastic solvers based on genetic algorithms for solving nonlinear equations. Neural Comput. Appl. 26, 1–23 (2015)
Ren, H., Wua, L., Bi, W., Argyros, I.K.: Solving nonlinear equations system via an efficient genetic algorithm with symmetric and harmonious individuals. Appl. Math. Comput. 219, 10967–10973 (2013)
Rovira, A., Valdés, M., Casanova, J.: A new methodology to solve non-linear equation systems using genetic algorithms. Application to combined cycle gas turbine simulation. Int. J. Numer. Meth. Eng. 63, 1424–1435 (2005)
Zhang, X., Wu, Z.: Study neighborhood field optimization algorithm on nonlinear sorptive barrier design problems. Neural Comput. Appl. (2015)
Bhasin, H., Mehta, S.: On the applicability of diploid genetic algorithms. AI Soc. 31(2), 265–274 (2015)
Bhasin, H., Behal G., Aggarwal, N., Saini, R.K., Choudhary, S.: On the applicability of diploid genetic algorithms in dynamic environments. Soft Comput. 20(9), 3403–3410 (2015)
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Mangla, C., Bhasin, H., Ahmad, M., Uddin, M. (2017). Novel Solution of Nonlinear Equations Using Genetic Algorithm. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Industrial Mathematics and Complex Systems. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3758-0_17
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DOI: https://doi.org/10.1007/978-981-10-3758-0_17
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