University of Tabriz Computational Methods for Differential Equations 2345-3982 10 1 2022 01 01 Design of normal distribution-based algorithm for solving systems of nonlinear equations 274 297 12208 10.22034/cmde.2020.37474.1658 EN Amir Khakbaz Department of Industrial Engineering, School of Engineering, Damghan University, Damghan, Iran. Journal Article 2019 12 23 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.  https://cmde.tabrizu.ac.ir/article_12208_c726ece3cd3b0a63225cf374943198ac.pdf