Design of normal distribution-based algorithm for solving systems of nonlinear equations

Khakbaz, Amir

doi:10.22034/cmde.2020.37474.1658

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	Design of normal distribution-based algorithm for solving systems of nonlinear equations
Computational Methods for Differential Equations
مقاله 20، دوره 10، شماره 1، فروردین 2022، صفحه 274-297 اصل مقاله (1014.75 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.37474.1658
نویسنده
Amir Khakbaz
Department of Industrial Engineering, School of Engineering, Damghan University, Damghan, Iran.
چکیده
In this paper, a completely new statistical-based approach is developed for solving the system of nonlinear equations. The developed approach utilizes the characteristics of the normal distribution to search the solution space. The normal distribution is generally introduced by two parameters, i.e., mean and standard deviation. In the developed algorithm, large values of standard deviation enable the algorithm to escape from a local optimum, and small values of standard deviation help the algorithm to find the global optimum. In the following, six benchmark tests and thirteen benchmark case problems are investigated to evaluate the performance of the Normal Distribution-based Algorithm (NDA). The obtained statistical results of NDA are compared with those of PSO, ICA, CS, and ACO. Based on the obtained results, NDA is the least time-consuming algorithm that gets high-quality solutions. Furthermore, few input parameters and simple structure introduce NDA as a user friendly and easy-to-understand algorithm.
کلیدواژه‌ها
Normal distribution-based Algorithm (NDA)؛ Nonlinear equations؛ Numerical optimization؛ Meta-heuristic

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Design of normal distribution-based algorithm for solving systems of nonlinear equations