Abstract
To address the issues of uneven initial distribution and limited search accuracy with the traditional divergent quantum-inspired differential search (DCS) algorithm, a hybrid multi-strategy variant, termed DQDCS, is proposed. This improved version overcomes these limitations by integrating the refined set strategy and clustering process for population initialization, along with the double Q-learning model to balance exploration and exploitation This enhanced version replaces the conventional pseudo-random initialization with a refined set generated through a clustering process, thereby significantly improving population diversity. A novel position update mechanism is introduced based on the original equation, enabling individuals to effectively escape from local optima during the iteration process. Additionally, the table reinforcement learning model (double Q-learning model) is integrated into the original algorithm to balance the probabilities between exploration and exploitation, thereby accelerating the convergence towards the global optimum. The effectiveness of each enhancement is validated through ablation studies, and the Wilcoxon rank-sum test is employed to assess the statistical significance of performance differences between DQDCS and other classical algorithms. Benchmark simulations are conducted using the CEC2019 and CEC2022 test functions, as well as two well-known constrained engineering design problems. The comparison includes both recent state-of-the-art algorithms and improved optimization methods. Simulation results demonstrate that the incorporation of the refined set and clustering process, along with the table reinforcement learning model (double Q-learning model) mechanism, leads to superior convergence speed and higher optimization precision.