A neighborhood information-based adaptive differential evolution for solving complex nonlinear equation system model

Nonlinear equation systems (NESs) widely exist in diverse fields, which have multiple equivalent roots in the search space. While several improved evolutionary algorithms (EAs) have been designed to solving NESs in recent years, they are ineffective to exploit the neighborhood information for evolution. This article thus develops a neighborhood information-based adaptive differential evolution (NIADE) to detect and track different roots in one run. It includes the following advantages: (i) a dynamic neighborhood size mechanism is designed to adjust the neighborhood size according to the state of evolution; (ii) a novel mutation strategy based on neighborhood information is introduced, which is beneficial to a completed search of the decision space; (iii) the neighborhood information is combined with adaptive parameter adjustment to enhance the search efficiency. The performance of NIADE is verified by solving the benchmark functions with different roots and different characteristics. The experimental results shows that NIADE has the ability to identify multiple roots simultaneously. Moreover, It achieves the better results than a number of existing advanced methods in terms of the success rate and root ratio.