Scalable Inspection Planning via Flow-based Mixed Integer Linear Programming

• URL: http://arxiv.org/abs/2603.16593v1
• Date: Tue, 17 Mar 2026 14:40:26 GMT
• Title: Scalable Inspection Planning via Flow-based Mixed Integer Linear Programming
• Abstract summary: Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest.<n>We present highly scalable Mixed Linear Programming (MILP) solutions for GIP that significantly advance the state-of-the-art in both runtime and solution quality.
• Score: 8.568142982906755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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