Autonomous data detection and inspection with a fleet of UAVs

Consider an area of interest A , where a set of n sites lie. Two kinds of information can be captured from each site: light and heavy information. A fleet of m homogeneous UAVs, each one equipped with a battery B , is available at a common depot, where the flight mission of each UAV starts and finishes. The problem we consider focuses on a single flight of the fleet of UAVs and aims at collecting their light information from all sites (that can be retrieved, not necessarily passing over each site, but simply "close"to it). At the same time, the fleet will have to select a limited number of sites from which to collect their heavy information. Flying among sites and acquiring information from them (both light and heavy) has a battery cost. On the other hand, a profit is associated with the action of acquiring heavy information from a site. We refer to the extraction of light and heavy information from a site as to weakly or strongly cover the site. The aim of the problem consists of retrieving light information from all sites while maximizing the overall profit, keeping the battery consumption of each UAV within B . In this paper, we model this real -life situation as a new combinatorial optimization problem that we call m3DIP, for which we provide a mixed integer programming model. Given the high degree of complexity of the problem, in this way we are not able to provide a solution in a reasonable time. To address larger instances we propose a matheuristic in which we exploit a path -based algorithm filled with only a subset of feasible cycles (paths) provided by different heuristics. The output indicates which path to select and the set of nodes to be strongly and weakly covered by each trip. We compare our matheuristic with the results obtained by every single heuristic on a large set of instances, showing that the matheuristic strongly outperforms them. An interesting insight is that even paths provided by a heuristic with very bad performances can be useful if combined with paths provided by other heuristics and if the coverage decisions are reoptimized by the matheuristic. We also show the benefit of adding fictitious additional points that UAVs can visit to weakly cover a subset of sites, without actually visiting none of them.