ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator being conditioned on the current solution. We also discuss important considerations such as the size of the operator portfolio and the impact of the choice of operator scales. Notably, our approach can also save significant time and labour costs for handcrafting problem-specific operator portfolios.

翻译：ALNS是一种在解决组合优化问题中具有显著效率的流行元启发式算法。然而，尽管对ALNS进行了长达16年的深入研究，其内置的自适应层能否高效选择算子以改进当前解仍是一个悬而未决的问题。在本研究中，我们将算子选择问题建模为马尔可夫决策过程，并提出了一种基于深度强化学习与图神经网络的实用方法。实验结果表明，由于算子选择依赖于当前解状态，所提方法在性能上优于经典的ALNS自适应层。我们还探讨了关键影响因素，如算子池的规模以及算子选择尺度的作用。值得注意的是，该方法可显著节省针对特定问题手工设计算子池所需的时间与人力成本。