A knowledge transfer-based adaptive differential evolution for solving nonlinear equation systems

Solving nonlinear equation systems (NESs) is an important yet challenging task in the field of numerical computation. It aims to locate multiple roots in a single run. However, the existing methods lack effective knowledge transfer. In this article, a knowledge transfer-based adaptive differential evolution is proposed to deal with NESs. Its main features are: (i) knowledge transfer between two niching techniques (crowding and speciation) is carried out to balance diversity and convergence; (ii) the variation characteristics of population diversity and convergence are used to judge knowledge transfer intensity; (iii) a knowledge transfer mechanism is designed to ensure that reasonable individuals are selected for the transfer to supplement the deficiencies of crowding and speciation; (iv) a parameter adaptation with niching level is introduced to improve search efficiency. Experiments on classical 30 NES problems have demonstrated that the proposed approach can outperform the state-of-the-art algorithms, in terms of root ratio and success rate.