FINDING ALL SOLUTIONS OF NONLINEAR SYSTEMS THROUGH A BIO-INSPIRED ALGORITHM

This work proposes solving systems of nonlinear equations by formulating them as optimization problems and using the polarization technique to find all solutions. The approach combines the global search method Differential Evolution (DE) with the local methods Hooke-Jeeves (HJ) and Quasi-Newton BFGS, creating hybrid methods (DE/HJ and DE/BFGS) to increase the robustness and efficiency of the DE method. The polarization technique is integrated into the methods to ensure the complete determination of the solutions. After numerical tests, an analysis will be carried out on the benefits of combining local searches with the global DE method.