Finding all solutions of nonlinear systems using a hybrid metaheuristic with Fuzzy Clustering Means

We apply a recently introduced hybrid metaheuristic to solve nonlinear systems of equations with multiple roots as an optimization problem. In this technique, first, the Luus–Jaakola random search method is used to explore the search space. Then, in order to find more than one root, the best solutions previously found are clustered using Fuzzy Clustering Means. Finally, multiple Nelder–Mead simplex instances are applied using these solutions as starting points for searching within their respective clusters’ domain. Our method is compared against other methodologies using benchmarks from the literature, and shows to perform well. Moreover, we successfully apply it to a real-world nonlinear system from the field of chemical engineering: the double retrograde vaporization problem.