This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture to solve 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. 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和元启发式框架，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，并利用训练模型生成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。通过使用两种NDP变体和一个精确求解器作为基准，我们证明该框架能够在不到寻找最优解所需时间1%的条件下，提供与全局最优解差距在5%以内的解。此外，我们观察到许多有趣的研究方向，因此提出了一个关于该主题的简要研究议程。启发未来关键研究的核心观察是：利用GNN模型为遗传算法生成的推理结果进行适应度函数评估的时间仅为毫秒级，这提示我们存在机遇和需求，需要开发新型启发式算法，使其（1）能够有效处理神经网络提供的含噪声的适应度函数值，以及（2）能够利用显著增加的计算时间来有效（而非高效）探索搜索空间。这为专为AI驱动预测器设计的新一代元启发式算法开辟了新的途径。