Solving nonlinear equation systems based on evolutionary multitasking with neighborhood-based speciation differential evolution

Locating multiple roots of nonlinear equation systems (NESs) remains a challenging and meaningful task in the numerical optimization community. Although a large number of NES-solving approaches have been put forward, they can only find the roots of one NES at a time. In this paper, we develop a novel NES-solving algorithm based on evolutionary multitasking referred to as EMNES, the goal of which is to effectively find the multiple roots of multiple different NESs simultaneously in a single run through knowledge sharing and transfer. Specifically, firstly a NES-solving framework based on evolutionary multitasking is proposed. Then an efficient multi-task evolutionary algorithm based on neighborhood-based speciation differential evolution for NESs is designed. Finally, combining Gaussian distribution and uniform distribution, a novel resource release strategy is proposed to release the found roots to improve resource utilization and increase population diversity. Numerous experimental results reveal that the proposed EMNES algorithm can achieve a higher root rate and success rate when compared with several well-established algorithms on thirty NESs. Furthermore, simulation results on a more complex test set show that the proposed EMNES is able to locate more roots than most comparison algorithms.