A decomposition-based differential evolution with reinitialization for nonlinear equations systems

Abstract

Solving nonlinear equations systems (NESs) is one of the most important challenges in numerical computation, especially to find multiple roots in one run. In this paper, a decomposition-based differential evolution with reinitialization is proposed to tackle this challenging task. The main advantages of our method are: (i) an improved parameter-free decomposition technique is exploited to partition the population into numerous sub-populations to locate multiple roots of NESs; (ii) to enhance the search ability of optimization algorithm, a sub-population control strategy is presented to control the number of solutions in the sub-populations; and (iii) the sub-population reinitialization mechanism is proposed to enrich the population diversity. To evaluate the performance of our approach, thirty NES problems with different characteristics are selected as the test suite. Moreover, to further indicate the superiority of our method, ten complex NESs with many roots are also tested. Experimental results show that the proposed approach can locate multiple roots in a single run. In addition, it is able to obtain better results compared with other state-of-the-art methods in terms of both root rate and success rate.