Exact methods for the traveling salesman problem with multiple drones

Drone delivery is drawing increasing attention in last-mile delivery. Effective solution methods to solve decision-making problems arising in drone delivery allow to run and assess drone delivery systems. In this paper, we focus on delivery systems with a single traditional vehicle and multiple drones working in tandem to fulfill customer requests. We address the Traveling Salesman Problem with Multiple Drones (TSP-MD) and investigate the modeling challenges posed by the presence of multiple drones, which have proven to be hard to handle in the literature. We propose a compact Mixed-Integer Linear Programming (MILP) model to formulate the TSP-MD and several families of valid inequalities. Moreover, we illustrate an exact decomposition approach based on the compact MILP and a branch-and-cut algorithm. We show that this exact approach can solve instances with up to 24 customers to proven optimality, improving upon existing exact methods that can solve similar problems with up to ten customers only

Parallel drone scheduling vehicle routing problems with collective drones

We study last-mile delivery problems where trucks and drones collaborate to deliver goods to final customers. In particular, we focus on problem settings where either a single truck or a fleet with several homogeneous trucks work in parallel to drones, and drones have the capability of collaborating for delivering missions. This cooperative behaviour of the drones, which are able to connect to each other and work together for some delivery tasks, enhance their potential, since connected drone has increased lifting capabilities and can fly at higher speed, overcoming the main limitations of the setting where the drones can only work independently. In this work, we contribute a Constraint Programming model and a valid inequality for the version of the problem with one truck, namely the \emph{Parallel Drone Scheduling Traveling Salesman Problem with Collective Drones} and we introduce for the first time the variant with multiple trucks, called the \emph{Parallel Drone Scheduling Vehicle Routing Problem with Collective Drones}. For the latter variant, we propose two Constraint Programming models and a Mixed Integer Linear Programming model. An extensive experimental campaign leads to state-of-the-art results for the problem with one truck and some understanding of the presented models' behaviour on the version with multiple trucks. Some insights about future research are finally discussed

An ACO-Inspired, Probabilistic, Greedy Approach to the Drone Traveling Salesman Problem

In recent years, major companies have done research on using drones for parcel delivery. Research has shown that this can result in significant savings, which has led to the formulation of various truck and drone routing and scheduling optimization problems. This paper explains and analyzes a new approach to the Drone Traveling Salesman Problem (DTSP) based on ant colony optimization (ACO). The ACO-based approach has an acceptance policy that maximizes the usage of the drone. The results reveal that the pheromone causes the algorithm to converge quickly to the best solution. The algorithm performs comparably to the MIP model, CP model, and EA of Rich & Ham (2018), especially in instances with a larger number of stops

Trajectory Design of Laser-Powered Multi-Drone Enabled Data Collection System for Smart Cities

This paper considers a multi-drone enabled data collection system for smart cities, where there are two kinds of drones, i.e., Low Altitude Platforms (LAPs) and a High Altitude Platform (HAP). In the proposed system, the LAPs perform data collection tasks for smart cities and the solar-powered HAP provides energy to the LAPs using wireless laser beams. We aim to minimize the total laser charging energy of the HAP, by jointly optimizing the LAPs’ trajectory and the laser charging duration for each LAP, subject to the energy capacity constraints of the LAPs. This problem is formulated as a mixed-integer and non-convex Drones Traveling Problem (DTP), which is a combinatorial optimization problem and NP-hard. We propose an efficient and novel search algorithm named DronesTraveling Algorithm (DTA) to obtain a near-optimal solution. Simulation results show that DTA can deal with the large scale DTP (i.e., more than 400 data collection points) efficiently. Moreover, the DTA only uses 5 iterations to obtain the nearoptimal solution whereas the normal Genetic Algorithm needs nearly 10000 iterations and still fails to obtain an acceptable solution

A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Drone

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.Comment: Technical Report. 34 pages, 5 figure

On The Continuous Coverage Problem for a Swarm of UAVs

Unmanned aerial vehicles (UAVs) can be used to provide wireless network and remote surveillance coverage for disaster-affected areas. During such a situation, the UAVs need to return periodically to a charging station for recharging, due to their limited battery capacity. We study the problem of minimizing the number of UAVs required for a continuous coverage of a given area, given the recharging requirement. We prove that this problem is NP-complete. Due to its intractability, we study partitioning the coverage graph into cycles that start at the charging station. We first characterize the minimum number of UAVs to cover such a cycle based on the charging time, the traveling time, and the number of subareas to be covered by the cycle. Based on this analysis, we then develop an efficient algorithm, the cycles with limited energy algorithm. The straightforward method to continuously cover a given area is to split it into N subareas and cover it by N cycles using N additional UAVs. Our simulation results examine the importance of critical system parameters: the energy capacity of the UAVs, the number of subareas in the covered area, and the UAV charging and traveling times.We demonstrate that the cycles with limited energy algorithm requires 69%-94% fewer additional UAVs relative to the straightforward method, as the energy capacity of the UAVs is increased, and 67%-71% fewer additional UAVs, as the number of subareas is increased.Comment: 6 pages, 6 figure