Optimizing Line Segment Inspection with Limited-Range Drones

Optimization problems with drones are widely studied in a variety of civilian tasks, mainly due to their ability to traverse rough terrains and to carry cameras and other sensors for surveillance tasks. The limited battery life of these aerial robots poses challenges in operational research. In this paper, we address the following optimization problem. We are given a set of line segments (e.g. tubes in a solar plant) to inspect by drones. The objective is to detect broken pipes using artificial intelligence and path planning must be carried out efficiently. On the one hand, the limited capacity of the batteries necessitates periodic visits (tours) to a fixed base station. However, it is desirable to allocate a set of tours for each drone to ensure that the segments are covered as quickly as possible, aiming to minimize the makespan, which is the maximum time spent by any drone. We are able to prove that this optimization problem is strongly NP-hard even when the segments are positioned on a line and the scenario involves only two drones. Then, approximation algorithms are proposed. Our computational experiments demonstrate that the proposed algorithm achieves near-optimal performance across diverse operational scenarios.