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.