Fuzzy neighborhood-based differential evolution with orientation for nonlinear equation systems.

Solving nonlinear equation systems (NESs) plays a vital role in science and engineering. Systems of nonlinear equations typically have more than root. Most of the classical methods cannot locate multiple roots in a single run. Finding these multiple roots in a single run is a difficult task in numerical computation. To effectively and reliably find the multiple roots of NES simultaneously, we propose a fuzzy neighborhood-based differential evolution with orientation (FNODE). FNODE is novel for two reasons: (1) it hasan improved fuzzy neighborhood, where the sub-populations are generated according to the fuzzy rule and the distribution of individuals; and (2) an orientation-based mutation is used, where the orientation information of the neighborhood individual’s migration is integrated into the mutation to produce promising offspring. To evaluate the performance of FNODE, we used 30 NESs with diverse features as the test suite. The experimental results demonstrate that FNODE is capable of successfully solving most of the problems in the test suite and provide better results than the other methods.