摘要： 蚁群优化(ACO)算法被广泛应用于求解组合优化问题时，好的启发信息有助于快速收敛到高质量的解。现有神经蚁群优化算法，如深度蚁群优化(DeepACO)和生成流蚁群采样器(GFACS)利用深度强化学习自动化设计启发信息，显著提高了现有ACO算法的求解质量。然而，现有神经蚁群优化算法仅基于问题实例的静态特征生成启发信息，未考虑每只蚂蚁的部分解时序特征。这导致启发信息难以有效引导不同蚂蚁基于探索进程进行差异化搜索，丧失多样性。同时，现有神经蚁群优化算法采用图神经网络(GNN)聚合信息时，仅聚合节点特征，未考虑将边特征与节点特征融合后再聚合，导致GNN聚合的信息不够充分。为此，融合时序特征与边特征的神经蚁群优化(TEF-NACO)算法被提出。TEF-NACO算法通过循环神经网络(RNN)提取每只蚂蚁的时序特征，再与全局图结构信息融合。并且，在GNN的节点信息聚合阶段，充分考虑节点特征与边特征，以提升GNN的信息捕捉能力。同时，为损失函数添加基于边注意力的正则项以提高训练的稳定性。实验表明，TEF-NACO算法在24个组合优化任务中的最佳表现的数量超过ACO、DeepACO和GFACS的百分比分别为100%、87.5%和75%，平均精度提升分别为21.5%、3.4%和3.2%。

Abstract: The Ant Colony Optimization (ACO) algorithm is widely employed for solving combinatorial optimization problems, where effective heuristic information facilitates rapid convergence to high-quality solutions. The existing neural ant colony optimization algorithms, such as Deep Ant Colony Optimization(DeepACO) and Generative Flow Ant Colony Sampler(GFACS), leverage deep reinforcement learning to automatically design heuristic information, substantially enhancing the solution quality of existing ACO algorithms. However, the existing neural ant colony optimization algorithms generate heuristic information solely based on the static features of problem instances, neglecting the temporal characteristics of partial solutions constructed by individual ants. This limitation impedes the heuristic information from effectively guiding differentiated search behaviors among ants during the exploration process, thereby compromising population diversity. Moreover, when aggregating information via graph neural networks (GNN), the existing neural ant colony optimization algorithms only process node features without integrating edge features prior to aggregation, resulting in insufficient information capture by GNN. To address these issues, the Temporal Edge Feature enhanced Neural Ant Colony Optimization (TEF-NACO) algorithm is proposed. TEF-NACO extracts temporal features of each ant via a Recurrent Neural Network (RNN) and subsequently integrates them with global graph structural information. Furthermore, during the node aggregation phase of the GNN, both node and edge features are comprehensively incorporated to enhance the network’s information capture capacity. Additionally, an edge-attention-based regularization term is introduced into the loss function to improve training stability. The experiments show that the TEF-NACO algorithm achieves the best performance in 24 combinatorial optimization tasks, with the percentages exceeding those of ACO, DeepACO and GFACS being 100%, 87.5% and 75% respectively. The average accuracy improvement is 21.5%, 3.4% and 3.2% respectively.