A significant biomimetic numerical optimization approach for solving complex Non-linear problems

Abstract

One of the hard problems in the modern world of high-level science and engineering is to find the solution of non-linear equations. A wide range of real-life applications such as climate prediction, chemical reactions, physical phenomenon, spacecraft trajectory determination, finance and economic modeling etc. exhibits non-linear dynamics in nature. A new numerical optimization solver has been proposed in this paper. The suggested method is an algorithm that combines numerical iterative method with meta-heuristic algorithms for tackling intricate Non-linear system of equations (NSE). The techniques that are used in constructing the proposed method include; Newton fourth order variation and Coati Optimization Algorithm (COA). The COA is used in order to conduct an effective global exploration of the solution space, and the fourth-order iterative approach helps to achieve quick and precise convergence at the local search stage. This combination of methods results in the increased efficiency of the computation process and accuracy of the solution process. The stability, reliability and efficiency of the proposed approach has been verified by the applicability to large and complex non-linear system of equations, which contain optimization benchmark functions and a single real-life application of Economic modeling. Comparative analyses are thoroughly done against a number of state-of-the-art metaheuristic algorithms, which include the Slime Mould Optimization Algorithm (SMA),  Pelican Optimization Algorithm (POA), Walrus Optimization Algorithm (WOA) and the original COA. The findings of the numerical simulations show that the proposed strategy always demonstrates high performance in a variety of measures, including lower computational time, fewer converge iterations, and better fitness function values. This parametric study of the suggested method makes it a prospective instrument in terms of the optimization of complex systems and the accuracy of the solutions.