Lie Group-Based Optimization of the Greater Cane Rat Algorithm

Optimizing algorithms, due to their importance, are widely applied in fields such as engineering design, logistics management, and machine learning. However, most current models have potential shortcomings, such as the complexity of parameter tuning and the difficulty in balancing accuracy and computational performance for large-scale data. To address these issues, we propose an improved Greater Cane Rat Algorithm based on the Lie Group intrinsic mean (LGGCRA). This al-gorithm leverages the Lie Group intrinsic mean to replace the reproduction coefficient in GCRA and incorporates a Lie Group kernel function to enhance model robustness. Specifically, we introduce the Lie Group intrinsic mean to improve the population updating process, introduce the Lie Group kernel function to enhance diversity and robustness, and utilize Lie Group manifold space distance to replace the traditional Euclidean distance, better capturing the search paths in real-world scenarios. Our approach enhances global search capability, reduces the complex-ity of parameter tuning, and improves accuracy and convergence speed. We selected the representative and challenging CEC2022 dataset and also tested our algorithm on twenty-three classical benchmark problems, conducting extensive experiments. Our algorithm was compared with state-of-the-art models, and the results show that our algorithm has certain advantages in terms of accuracy, convergence speed, and robustness.