Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical robotics. To alleviate the problem's complexity, recent methods rely on sampling-based methods to obtain a more manageable (discrete) graph inspection planning (GIP) problem. Unfortunately, GIP still remains highly difficult to solve at scale as it requires simultaneously satisfying POI-coverage and path-connectivity constraints, giving rise to a challenging optimization problem, particularly at scales encountered in real-world scenarios. In this work, we present highly scalable Mixed Integer Linear Programming (MILP) solutions for GIP that significantly advance the state-of-the-art in both runtime and solution quality. Our key insight is a reformulation of the problem's core constraints as a network flow, which enables effective MILP models and a specialized Branch-and-Cut solver that exploits the combinatorial structure of flows. We evaluate our approach on medical and infrastructure benchmarks alongside large-scale synthetic instances. Across all scenarios, our method produces substantially tighter lower bounds than existing formulations, reducing optimality gaps by 30-50% on large instances. Furthermore, our solver demonstrates unprecedented scalability: it provides non-trivial solutions for problems with up to 15,000 vertices and thousands of POIs, where prior state-of-the-art methods typically exhaust memory or fail to provide any meaningful optimality guarantees.

翻译：巡检规划旨在计算机器人利用传感器检测给定兴趣点集的最短路径。该问题广泛存在于从制造业到医疗机器人的各类应用中。为降低问题复杂度，近期方法依赖基于采样的技术来构建更易处理的（离散）图巡检规划问题。然而，图巡检规划在大规模场景中仍极具求解难度，因其需同时满足兴趣点覆盖与路径连通性约束，形成极具挑战性的优化问题，尤其在真实场景的规模下。本研究提出针对图巡检规划的高度可扩展混合整数线性规划解法，在求解速度与解质量两方面均显著提升现有技术水平。我们的核心洞见在于将问题的核心约束重构为网络流模型，从而构建高效的混合整数线性规划模型，并开发出能利用流组合结构的专用分支剪切求解器。我们在医疗与基础设施基准测试及大规模合成实例上评估了该方法。在所有场景中，我们的方法均产生比现有公式更紧凑的下界，在大规模实例上将最优性差距缩小30-50%。此外，我们的求解器展现出前所未有的可扩展性：可针对包含多达15000个顶点与数千个兴趣点的问题提供非平凡解，而现有最先进方法通常内存耗尽或无法提供任何有意义的优化性保证。