Scalable Inspection Planning via Flow-based Mixed Integer Linear Programming

2026-03-17

AI Summary

This work addresses the challenge of large-scale Graph Inspection Planning (GIP)—specifically, finding the shortest route that fully covers all points of interest while satisfying connectivity constraints—by introducing network flow modeling into GIP for the first time. The authors formulate an efficient mixed-integer linear programming (MILP) framework and develop a customized Branch-and-Cut solver that exploits the combinatorial structure inherent in flow-based formulations. By integrating graph sampling and discretization techniques, the proposed approach substantially improves both computational efficiency and solution quality. Empirical results on real-world and synthetic large-scale instances from healthcare and infrastructure domains demonstrate a 30–50% reduction in optimality gaps and the successful resolution of previously intractable cases involving up to 15,000 vertices and thousands of points of interest, thereby overcoming the scalability limitations of existing methods.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• inspection planning
• graph inspection planning
• scalability
• path connectivity
• POI coverage

Innovation

• flow-based MILP
• inspection planning
• network flow
• Branch-and-Cut
• scalable optimization