Solving nonlinear equation systems and real-world engineering example via adaptive information migration and sharing evolutionary multitasking algorithm with cross-sampling

In practical engineering problems, nonlinear equation systems (NESs) are widely present, such as power systems and control systems. With the increase of system scale and the complexity of problems, solving these NESs becomes increasingly difficult. Although existing methods have proposed effective improvement methods from multiple perspectives, they still ignore the key issue that the implicit relationship between different NESs can promote the evolution of algorithms. Therefore, this paper proposes adaptive cross-sampling evolutionary multitasking algorithm framework, namely AC-MTNESs, to solve NESs. This framework establishes the implicit relationship between tasks through unified encoding method, and proposes an adaptive information migration and sharing selection mechanism, combined with fractional calculus methods, to more accurately capture the nonlinear relationship between NESs. In addition, to ensure that the algorithm maintains the level of population diversity, this work propose a cross-resource sampling strategy, which balances the exploration and exploitation capabilities of the algorithm by archiving roots that meet the accuracy threshold and reusing resources from different distributions to cross-generate offspring. Experiments verify the superiority of the algorithm on 30 standard and 18 complex NESs problem sets. The results show that AC-MTNESs outperforms existing methods. Furthermore, it also shows good application potential in practical problems of motor systems.