Adaptive Large Neighborhood Search (ALNS) is a widely used heuristic method for solving combinatorial optimization problems. ALNS explores the solution space by iteratively using destroy and repair operators with probabilities, which are adjusted by an adaptive mechanism to find optimal solutions. However, the classic ALNS adaptive mechanism does not consider the interaction between destroy and repair operators when selecting them. To overcome this limitation, this study proposes a novel adaptive mechanism. This mechanism enhances the adaptability of the algorithm through a Dual Actor-Critic (DAC) model, which fully considers the fact that the quality of new solutions is jointly determined by the destroy and repair operators. It effectively utilizes the interaction between these operators during the weight adjustment process, greatly improving the adaptability of the ALNS algorithm. In this mechanism, the destroy and repair processes are modeled as independent Markov Decision Processes to guide the selection of operators more accurately. Furthermore, we use Graph Neural Networks to extract key features from problem instances and perform effective aggregation and normalization to enhance the algorithm's transferability to different sizes and characteristics of problems. Through a series of experiments, we demonstrate that the proposed DAC-ALNS algorithm significantly improves solution efficiency and exhibits excellent transferability.

翻译：自适应大邻域搜索（ALNS）是一种广泛应用于组合优化问题求解的启发式方法。该方法通过迭代使用具有概率的破坏与修复算子来探索解空间，其概率由自适应机制进行调整以寻找最优解。然而，经典ALNS的自适应机制在选择算子时未考虑破坏算子与修复算子之间的交互作用。为克服这一局限，本研究提出了一种新型自适应机制。该机制通过双Actor-Critic（DAC）模型增强算法的自适应性，充分考虑了新解质量由破坏与修复算子共同决定的事实，在权重调整过程中有效利用算子间的交互作用，显著提升了ALNS算法的适应能力。在此机制中，破坏过程与修复过程被建模为独立的马尔可夫决策过程，以更精确地指导算子选择。此外，我们采用图神经网络从问题实例中提取关键特征，并进行有效的聚合与归一化处理，从而增强算法对不同规模及特征问题的可迁移性。通过一系列实验，我们证明所提出的DAC-ALNS算法在求解效率上取得显著提升，并展现出优异的可迁移性能。