International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3247 2020 2020 Department of Mathematics, Faculty of Education College for Pure Sciences, Babylon University, Babylon, Iraq; Department of Mathematical Sciences, College of Liberal Arts and Sciences, Northern Illinois University, DeKalb, USA Ahmed Ahmed The aim of this study is to compare common and previously used numerical algorithms for nonlinear problems under different conditions. This study proposes a parallel implementation of two free derivative optimization methods, Powell's method and Nelder-Mead's method, combined with two restart strategies to achieve a global search. In terms of total time, the Powell method converges faster than the Nelder-Mead method. The final function value obtained by the Powell method is slightly lower. Both are optimization techniques used to find the minimum of an objective function in multidimensional space, without requiring derivatives. Also, we extend our results to apply to some neutrosophic non-linear problems under different neutrosophic-based conditions with many examples that explain the validity of our approach. 2025 2025 115 122 10.54216/IJNS.250311 https://www.americaspg.com/articleinfo/21/show/3247