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 LuusJaakola 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 NelderMead 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.
nonlinear systems metaheuristics fuzzy clustering global optimization