Solution of Nonlinear Systems of Equations via Metaheuristics

Abstract

A framework devoted to the solution of nonlinear systems of equations using grey wolf optimization algorithm (GWO) and a multi-objective particle swarm optimization algorithm (MOPSO) is presented in this work. Due to several numerical issues and very high computational complexity, it is hard to find the solution of such a complex nonlinear system of equations. It then explains that the problem of solution to a system of nonlinear equations can be simplified by viewing it as an optimization problem and solutions can be obtained by applying a nature inspired optimization technique. The results achieved are compared with classical as well as new techniques established in the literature. The proposed framework also seems to be very effective for the problems of system of non-linear equations arising in the various fields of science. For this purpose, the problem of neurophysiology application and the problem of combustion of hydrocarbons are considered for testing. Empirical results show that the presented framework is bright to deal with the high dimensional equations system.