AGSDE: Archive guided speciation-based differential evolution for nonlinear equations

Solving nonlinear equations (NEs) has been obtained considerable attentions in recent years. However, it is still a difficult problem to improve the efficiency of the algorithm to find multiple roots of NEs. Aiming to deal with this issue, an archive guided speciation-based differential evolution (AGSDE) is presented in this paper. It contains three main components: (i) an archive construction approach is used to save the historical individual with poor fitness values in the selection phase; (ii) a reusing historical individual mechanism is implemented to guide the evolution; (iii) a local search method for solving NEs is performed on different subpopulations to refine the accuracy of the candidate solutions. The performance of AGSDE is tested on 30 NEs problems with different characteristics. Experimental results of AGSDE are competitive with those of other state-of-the-art methods in terms of root rate and success rate. In addition, AGSDE also shows its superiority for solving the other 10 complex NEs problems.(c) 2022 Published by Elsevier B.V.

Automated summary

In this paper, an archive guided speciation-based differential evolution (AGSDE) is proposed to improve the efficiency of finding multiple roots of nonlinear equations (NEs). Experimental results show that AGSDE performs competitively with other state-of-the-art methods in terms of root rate and success rate, and demonstrates superiority in solving complex NEs problems.