Chemical equilibrium systems as numerical test problems
ACM Transactions on Mathematical Software (TOMS)
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Box-bisection for solving second-degree systems and the problem of clustering
ACM Transactions on Mathematical Software (TOMS)
A Method for Computing All Solutions to Systems of Polynomials Equations
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Optimization
Expert Systems with Applications: An International Journal
Clustering with a genetically optimized approach
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
A New Approach for Solving Nonlinear Equations Systems
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Random search techniques for optimization problems
Automatica (Journal of IFAC)
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Abstract: 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.