Differential Evolution with multi-stage parameter adaptation and diversity enhancement mechanism for numerical optimization

Differential Evolution (DE) is a powerful meta-heuristic algorithm for numerical optimization, however, it faces challenges such as improper parameter control, premature convergence, and population stagnation in complex problems. To address these issues, this paper proposes a Differential Evolution algorithm with multi-stage parameter adaptation and diversity enhancement mechanism (MD-DE). First, a multi-stage parameter adaptation scheme is designed, incorporating wavelet basis functions and Laplace distributions for parameter generation, and guiding parameter adjustment through a progressive Minkowski distance weighting strategy to balance exploration and exploitation. Second, a mutation strategy with dynamic dual archives is proposed, integrating potential information from promising but discarded solutions to enhance the diversity of donor vectors, thereby improving the perception of the fitness landscape. Finally, a hypervolume-based diversity metric is combined with a stagnation tracker to capture stagnant individuals, and a hierarchical intervention mechanism is employed to introduce perturbations, thereby enhancing the level of population diversity. To evaluate the performance of the proposed MD-DE, it was validated against five state-of-the-art DE variants on 87 benchmark functions from CEC2013, CEC2014, and CEC2017, as well as on real-world problems from CEC2011 and planetary gear design optimization problems. Experimental results demonstrate that our algorithm exhibits a high level of competitiveness.