Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering

A novel optimization-based method for solving systems of nonlinear equations is proposed. The method employs Invasive Weed Optimization (IWO) for solving nonlinear systems and can find all real and complex roots of a system and also detect multiplicity. The proposed solver consists of two parts: a two-phase root-finder that detects the solutions of a system using IWO algorithm, and an alteration technique which creates repulsion areas around previously found roots. The proposed solver determines all solutions using successive runs of the two-phase root-finder along with the alteration technique. Several illustrative examples together with three examples of engineering applications are provided to demonstrate merits of our proposed algorithm in solving nonlinear equations systems. (C) 2011 Elsevier B.V. All rights reserved.