Drone arc routing problems

Abstract

In this article, we present some drone arc routing problems (Drone ARPs) and study their relation with well‐known postman ARPs. Applications for Drone ARPs include traffic monitoring by flying over roadways, infrastructure inspection such as by flying along power transmission lines, pipelines or fences, and surveillance along linear features such as coastlines or territorial borders. Unlike the postmen in traditional ARPs, drones can travel directly between any two points in the plane without following the edges of the network. As a consequence, a drone route may service only part of an edge, with multiple routes being used to cover the entire edge. Thus the Drone ARPs are continuous optimization problems with an infinite number of feasible solutions. In order to solve them as a discrete optimization problem, we approximate each curve in the plane by a polygonal chain, thus allowing the vehicle to enter and leave each curve only at the points of the polygonal chain. If the capacity of the vehicles is unlimited, the resulting problem is a rural postman problem (RPP). We propose an algorithm that iteratively solves RPP instances with an increasing number of points of the polygonal chain and present results on several sets of instances. We also briefly discuss the case in which the drones have limited capacity and several drones are needed.

Arc routing problems: A review of the past, present, and future

“…Hence, the segments define the set of required edges of the transformed graph and the set of nonrequired edges defines a complete graph with costs given by the Euclidean distances. The drone RPP is introduced in Campbell et al [40]. Given a set of lines, each one with an associated service cost, and a point called the depot, and assuming that the cost of deadheading between any two points is the Euclidean distance, the drone RPP consists of finding a minimum cost tour starting and ending at the depot and traversing all the given lines.…”

Traffic Patrolling Routing Problem with Drones in an Urban Road System

“…Chow et al [22] proposed the deterministic multiperiodic arc inventory routing problem and deployed a drone for traffic monitoring in view of the monitoring requirements of traffic big data. Campbell et al [31] established the arc routing problem of drones to solve the application of side targets in the access network. When drone capacity is limited, multiple drones should be considered for joint execution.…”

Future directions in drone routing research

“…For some reviews, see Chung et al [11], Khoufi et al, [23], and Otto et al [32]. Much of this research extends TSP and VRP models, though there is some work on arc routing with drones as well (e.g., [7,10]). The purpose of this article is not to summarize the rapidly growing drone routing research, but rather to raise some questions to stimulate new and better drone routing research in directions that we think will prove interesting and fruitful.…”