Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution

In numerical computation, locating multiple roots of nonlinear equations (NESs) in a single run is a challenging work. In order to solve the problem of population grouping and parameters settings during the evolutionary, a clustering-based adaptive speciation differential evolution, referred to as CASDE, is presented to deal with NESs. CASDE offers three advantages: 1) the clustering with dynamic clustering sizes is used to set clustering sizes for different problems; 2) adaptive parameter control at the niche level is proposed to enhance the search ability and efficiency; 3) re-initialization mechanism motivates the algorithm to search new roots and saves computing resources. To evaluate the performance of CASDE, we select 30 problems with different features as test suite. Experimental results indicate that the speciation clustering with dynamic clustering sizes, niche adaptive parameter control, and re-initialization mechanism when combined together in a synergistic manner can improve the ability to find multiple roots in a single run. Additionally, our method is also compared with other state-of-the-art methods, which is capable of obtaining better results in terms of peak ratio and success rate. Finally, two practical mechanical problems are used to verify the performance of CASDE, and it also demonstrates superior results.