Differential evolution with adaptive niching and reinitialisation for nonlinear equation systems

Nonlinear equation systems (NESs) are ubiquitous in scientific and engineering domains, necessitating efficient methods for discovering multiple roots simultaneously. Employing evolutionary algorithms to solve NESs has received significant attention. To simultaneously locate multiple roots in a single run, this paper proposes a differential evolution algorithm with adaptive niching and reinitialisation (DE-ANR). The proposed differential evolution algorithm integrates four strategies to address the challenges posed by NESs. Firstly, DE-ANR employs a dynamic niche size control mechanism to adjust the niche size during evolution, striking a balance between exploration and exploitation. Secondly, a lifetime mechanism is introduced to identify stagnating individuals for reinitialisation, ensuring diversity of the population and preventing premature convergence. Thirdly, an improved archive technique is employed to conserve computational resources by eliminating redundant solutions, directing the algorithm’s efforts toward unexplored regions of the solution space. Finally, an adaptive strategy is introduced to dynamically adjust the scaling factor F based on the feedback of evolving population, simplifying parameter tuning. Extensive evaluations on 30 diverse NES problems and the comparison results with 12 state-of-the-art algorithms clearly show the superiority of proposed method.