Differential Evolution Algorithm with Dynamic Neighborhood

The present paper introduces a novel differential evolution algorithm, the core purpose of which is to overcome the common problems of slow convergence and local optimisation in traditional algorithms. This algorithm adopts the adaptive variation strategy and combines the local search mechanism driven by individual fitness difference. It inherits the advantages of traditional differential evolution algorithm, significantly speeds up the convergence speed and enhances the global search efficiency, thus opening up a new effective way for solving optimisation problems. The proposed DE algorithm employs a novel dynamic neighborhood selection method, which significantly enhances the algorithm's ability to avoid local optimal traps and promote fast convergence. Firstly, the ring topology of the population is constructed and a generation mechanism with appropriate dynamic neighbourhood radius is designed to alleviate the information cocoon effect during the interaction of neighbourhood individuals. Secondly, in accordance with the principle of Chebyshev's theorem, the cluster is divided into elite groups and ordinary groups, and the appropriate mutation strategy is selected according to the individual objective function value. In order to achieve equilibrium between search and utilisation capabilities, the algorithm must be capable of both rapid convergence and the avoidance of local optima. In addition, the efficacy of the algorithm must be verified. To this end, 30 complex problems from the CEC2014 test set have been selected for detailed experimentation. These results were then compared with those obtained from a number of exceptional differential evolution algorithm variants. The experimental data provide comprehensive verification of the proposed algorithm's efficacy in addressing complex problems, ensuring stable execution and facilitating rapid convergence. These findings underscore the algorithm's overall efficiency and lay the foundation for further exploration and practical applications in related domains.