Adaptive dual niching-based differential evolution with resource reallocation for nonlinear equation systems

Solving nonlinear equation systems (NESs) remains a challenging task in the numerical optimization community due to the multi-root nature of NESs. To locate multiple roots of NESs in a single run, an adaptive dual niching-based differential evolution with resource reallocation is developed. The novelty of the proposed algorithm mainly lies in: (i) two niching-based differential evolution (DE) including neighborhood-based crowding DE (NCDE) and neighborhood-based speciation DE (NSDE), are adaptively called through a population diversity dynamic capture mechanism; (ii) a novel resource reallocation strategy is proposed to release those found solutions; (iii) an efficient parameter adaptation approach is employed to alleviate the parameter setting pressure in NCDE and NSDE. Experimental results on thirty NESs and a new test set show that the proposed algorithm exhibits significant performance in terms of the root rate and success rate when compared with other well-established algorithms.