Scalable Inspection Planning via Flow-based Mixed Integer Linear Programming

TL;DR

This paper introduces a scalable MILP-based approach for inspection planning that reformulates the problem as a network flow, enabling efficient solutions at large scales in real-world scenarios.

Contribution

The authors present a novel flow-based MILP formulation and a specialized solver that significantly improves scalability and solution quality for inspection path planning.

Findings

Reduces optimality gaps by 30-50% on large instances.

Provides solutions for problems with up to 15,000 vertices.

Outperforms existing methods in runtime and solution quality.

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.