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 two NDP variants and an exact solver as benchmark, we show that our proposed framework can provide solutions within 5% gap of the global optimum results given less than 1% of the time required for finding the optimal results. Our framework can be utilized within an expert system for infrastructure planning to intelligently determine the best infrastructure management decisions. 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 observe many interesting future directions, thus we propose a brief research agenda for this topic. The key observation inspiring influential future research was that fitness function evaluation time using the inferences made by the GNN model for the genetic algorithm 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 neural networks, and 2) can use the significantly higher computation time provided to them 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混合深度学习-元启发式框架，用于解决道路网络设计问题（NDPs）。我们训练了一个图神经网络（GNN）来近似求解用户均衡（UE）交通分配问题，并利用该训练模型的推理结果计算遗传算法（GA）的适应度函数评估，从而近似求解NDPs。以两种NDP变体及一个精确求解器作为基准，我们证明所提出的框架能够在少于寻找最优结果所需时间1%的条件下，提供与全局最优结果差距在5%以内的解。该框架可应用于基础设施规划的专家系统中，智能地确定最佳基础设施管理决策。鉴于框架的灵活性，它可轻松适配许多其他可建模为图上的双层问题的决策问题。此外，我们观察到许多有趣的未来研究方向，因此提出了该主题的简要研究议程。其中关键观察是，使用GNN模型为遗传算法推理得到的适应度函数评估时间仅为毫秒量级，这催生了具有影响力的未来研究，并指出了两个新方向：1）开发能妥善处理神经网络提供的含噪适应度函数值的启发式算法；2）利用显著增加的计算时间进行搜索空间的有效（而非高效）探索。这为面向人工智能驱动的预测器而设计的新型元启发式方法开辟了新道路。