This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic assignment problem and use inferences made by the trained model to calculate fitness function evaluations of a genetic algorithm (GA) to approximate solutions for NDPs. Using three test networks, two NDP variants and an exact solver as benchmark, we show that on average, our proposed framework can provide solutions within 1.5% gap of the best results in less than 0.5% of the time used by the exact solution procedure. Our framework can be utilized within an expert system for infrastructure planning to determine the best infrastructure planning and management decisions under different scenarios. Given the flexibility of the framework, it can easily be adapted to many other decision problems that can be modeled as bi-level problems on graphs. Moreover, we foreseen interesting future research directions, thus we also put forward a brief research agenda for this topic. The key observation from our research that can shape future research is that the fitness function evaluation time using the inferences made by the GNN model was in the order of milliseconds, which points to an opportunity and a need for novel heuristics that 1) can cope well with noisy fitness function values provided by deep learning models, and 2) can use the significantly enlarged efficiency of the evaluation step to explore the search space effectively (rather than efficiently). This opens a new avenue for a modern class of metaheuristics that are crafted for use with AI-powered predictors.

翻译：本研究提出了一种具有双层架构的深度学习-元启发式混合框架，用于解决道路网络设计问题（NDPs）。我们训练图神经网络（GNN）以近似用户均衡（UE）交通分配问题的解，并利用训练模型的推理结果计算遗传算法（GA）的适应度函数评估值，从而近似求解NDPs问题。通过三个测试网络、两种NDP变体及精确求解器的基准测试表明，本框架在平均情况下能够在精确求解流程所需时间的0.5%以内，提供与最优解偏差不超过1.5%的解决方案。该框架可嵌入基础设施规划专家系统，用于确定不同情景下的最优规划与管理决策。鉴于其灵活特性，该框架可便捷适配至其他可建模为图上双层问题的决策场景。此外，我们预判了有趣的未来研究方向，并提出了针对该主题的简要研究议程。本研究的核心发现在于：使用GNN模型推理进行适应度函数评估的时间仅为毫秒级，这揭示了两大机遇与需求：其一，需要能有效处理深度学习模型提供的含噪适应度函数值的新型启发式算法；其二，应充分利用评估步骤效率的显著提升来有效（而非仅高效）探索搜索空间。这为构建适用于人工智能预测器的现代元启发式算法开辟了新路径。