A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles
Abstract
:1. Introduction and Motivation
1.1. Overview of the Trajectory Computation Problems and Existing Surveys
1.2. Motivation and Organization of This Review
2. Traveling Salesman Problem TSP
2.1. Delivery-Transportation
2.1.1. Delivery by 1-Truck 1-Drone
2.1.2. Delivery by 1-Truck and m-Drones
2.1.3. Delivery by n-Trucks and m-Drones
2.2. Logistics: Path Planning
2.3. Delay Tolerant Networks
2.4. Intelligence, Surveillance and Reconnaissance (ISR)
2.5. Monitoring, Tracking, Filming
3. Vehicle Routing Problem VRP
3.1. Delivery-Transportation
3.1.1. Delivery by Truck(s) and Drone(s)
3.1.2. Delivery by Drone(s)
3.2. Monitoring, Surveillance
3.3. Logistic: Task Assignment
3.4. Wildfire
4. Taxonomy of Routing Problems
- 1- UAV = 1; Only one UAV is used
- 2- UAV = m; A fleet of UAVs is deployed
- 3- UAV = 1, Truck = 1; One UAV works in tandem with one truck
- 4- UAV = m, Truck = 1; A fleet of UAVs working in tandem with one truck
- 5- UAV = m, Truck = n; A fleet of UAVs working in tandem with many trucks
- Extended variants of the Traveling Salesman Problem
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- 6- TSP-D: Traveling Salesman Problem with Drone. Given a number of target positions, one depot, one Drone and a cost metric, the objective of TSP-D is to determine a UAV’s tour that visits each target only once and returns to the depot such that the total tour cost (e.g., distance traveled or completion time) is minimized.
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- 7- mTSP-D: multiple Traveling Salesman Problem with Drones is a generalization of TSP-D in which more than one Drone is used. The objective of mTSP-D is to determine a set of m tours such that the total cost of all tours is minimized and each target is visited by only one Drone. When UAVs are working in tandem with trucks in delivery applications, the corresponding routing problem is called mTSP-D only if a fleet of trucks and a fleet of Drones are considered.
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- 8- ATSP-D: Asymmetric Traveling Salesman Problem with Drone is also a generalization of TSP-D in which the bi-direction cost between a pair of targets may not be identical like in TSP-D.
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- 9- CETSP-D: Close Enough Traveling Salesman Problem with Drone is a generalization of TSP-D where each target is identified by its neighborhood. Then, the objective CETSP-D is to determine a UAV’s tour that visits the neighborhood of each target only once and returns to the depot such that the total tour cost is minimized.
- Extended variants of the Vehicle Routing Problem
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- 10- VRP-D: Vehicle Routing Problem with Drone. VRP-D aims to determine a set of routes for a fleet of Drones that visit a set of targets such that the total routes cost is minimized.
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- 11- VRPTW-D: Vehicle Routing Problem with Time Window with Drone is a generalization of VRP-D where the service at each target starts at a given time called time window. This time window is specified at each target and is defined by the earliest and latest time of the service.
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- 12- CVRPTW-D: Capacitated Vehicle Routing Problem with Time Window with Drone is a generalization of VRPTW-D where each Drone has some capacity (e.g., payload capacity) and the total demand served by each Drone does not exceed its capacity.
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- 13- GVRP-D: Green Vehicle Routing Problem with Drone. GVRP-D is a variant of VRP-D that aims to reduce the number of Vehicles used by allowing the Drone to refuel its energy during its tour.
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- 14- MTVRP-D: Multi-Trip Vehicle Routing Problem is a variant of the GVRP-D that aims to cope with the limited payload capacity of UAVs. The GVRP-D cope with the limited energy of Drones; however, these flying vehicles might not be able to carry all the load to satisfy all customers on their routes. Then, they can return to the depot and perform multiple trips.
- 15- Transportation and delivery: such as parcel delivery
- 16- Communication: UAVs can be used as flying relay points to re-establish connectivity or data mules that pick up Data from one site and deliver it to another.
- 17- Surveillance, monitoring, tracking: UAVs equipped with sensors can be used for area monitoring
- 18- Logistic processes: UAVs can be used for stock inventory in warehouses.
- 19- Disaster management: UAVs can be used in forest fire-fighting or for locating and tracking people or animals.
- 20- GA: Genetic algorithm
- 21- PSO: Particle Swarm Optimization Algorithm
- 22- ACO: Ant Colony Optimization Algorithm
- 23- Tabu Algorithm
- 24- Simulated Annealing algorithm
- 25- Smart Pool Search Algorithm
- 26- Exact Algorithm such as:
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- Branch and Bound
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- Branch and Cut
- 27- Local Search and dynamic programming such as:
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- GRASP: Greedy Randomized Adaptive Search Procedure
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- GVNS: General Variable Neighborhood Search
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- ALNS: Adaptive Large Neighborhood Search
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- Route First Cluster Second heuristic
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- Two Steps Approach
- 28- Constraint programming
5. Analysis of the Reviewed Papers
6. Conclusions and Future Directions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ADI | ADaptive Insertion |
ATSP | Asymmetric Traveling Salesman Problem |
CETSP | Close Enough Traveling Salesman Problem |
CNN | Convolutional Neural Network |
CPP | Coverage Path Planning |
CVRPTW | Capacitated Vehicle Routing Problem with Time Windows |
DC | Distribution Center |
DNN | Deep Neural Network |
DO | Deep Optimization |
DTN | Delay Tolerant Network |
DTP-TSP-D | Deadline Triggered Pigeon with Travelling Salesman Problem with Deadlines |
FCMURP | Fuel-Constrained Multiple-UAV Routing Problem |
FCURP | Fuel Constrained UAV Routing Problem |
FSTSP | Flying Sidekick Traveling Salesman Problem |
GA | Genetic Algorithm |
GA-ADI | Genetic Algorithm ADaptive Insertion |
GRASP | Greedy Randomized Adaptive Search Procedure |
GRP | Green Routing Problem |
GUAVRP | Green UAV Routing Problem |
GVNS | General Variable Neighborhood Search |
HGA | Hybrid Genetic Algorithm |
HGVNS | Hybrid General Variable Neighborhood Search |
IGA | Improved Genetic Algorithm |
ILP | Integer Linear Programming |
MILP | Mixed Integer Linear Programming |
MRT-Grid | Multiple RouTe algorithm with Grid |
MTDRP | Multi-Trip Drone Routing Problem |
mTSP | multiple Traveling Salesman Problem |
m-TSPD | multiple Traveling Salesman Problem with Drone |
MTVRP | Multi-Trip Vehicle Routing Problem |
PDSTSP | Parallel Drone Scheduling TSP |
PSO | Particle Swarm Optimization |
PSO-ACO | Particle Swarm Optimization based Ant Colony Optimization |
RP | Routing Problem |
SAA | Sample Average Approximation |
SDD | Same-day delivery |
SIRA | SIngle Route Algorithm |
SOCP | Second Order Cone Programming |
TSP | Traveling Salesman Problem |
TSP-D | Traveling Salesman Problem with Drone |
TSP-mD | Traveling Salesman Problem with multiple Drone |
TSP-LS | Traveling Salesman Problem Local Searches |
UAV | Unmanned Aerial Vehicle |
UAVRTOP | UAV Routing and Trajectory Optimization Problem |
VRP | Vehicle Routing Problem |
VRPD | Vehicle Routing Problem with Drone |
VRPTW | Vehicle Routing Problem with Time Windows |
TPH | Two-Phase Heuristic |
SPH | Single-Phase Heuristic |
VS-DP-VRP | Variable-Speed Dubins path Vehicle Routing Problem |
TSPLIB | Traveling Salesman Problem Library |
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Ref. | Vehicles | Routing Problem | Application | Approach | ||||||||||||||||||||||||
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TSP | VRP | |||||||||||||||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | |
[17] | × | × | × | × | ||||||||||||||||||||||||
[18] | × | × | × | × | ||||||||||||||||||||||||
[20] | × | × | × | × | × | |||||||||||||||||||||||
[19] | × | × | × | × | ||||||||||||||||||||||||
[21] | × | × | × | × | × | |||||||||||||||||||||||
[22] | × | × | × | × | ||||||||||||||||||||||||
[27] | × | × | × | × | ||||||||||||||||||||||||
[23] | × | × | × | × | ||||||||||||||||||||||||
[24] | × | × | × | × | ||||||||||||||||||||||||
[25] | × | × | × | × | × | |||||||||||||||||||||||
[28] | × | × | × | × | × | × | ||||||||||||||||||||||
[29] | × | × | × | × | ||||||||||||||||||||||||
[30] | × | × | × | × | ||||||||||||||||||||||||
[31] | × | × | × | × | ||||||||||||||||||||||||
[32] | × | × | × | × | ||||||||||||||||||||||||
[33] | × | × | × | × | ||||||||||||||||||||||||
[34] | × | × | × | × | ||||||||||||||||||||||||
[36] | × | × | × | × | ||||||||||||||||||||||||
[35] | × | × | × | × | ||||||||||||||||||||||||
[37] | × | × | × | × | ||||||||||||||||||||||||
[38] | × | × | × | × | ||||||||||||||||||||||||
[39] | × | × | × | × | ||||||||||||||||||||||||
[40] | × | × | × | × | × | |||||||||||||||||||||||
[41] | × | × | × | × | × | |||||||||||||||||||||||
[42] | × | × | × | × | × | |||||||||||||||||||||||
[43] | × | × | × | × | ||||||||||||||||||||||||
[44] | × | × | × | × | ||||||||||||||||||||||||
[45] | × | × | × | × |
Year | Ref. | Scope | Approach | Simulation Parameters | Metrics | Simulation Results |
---|---|---|---|---|---|---|
2016 | [17] | • Improve Truck and Drone schedule for Parcel Delivery • RP: TSP-D | • IP • First-cluster second procedure • Minimum Spanning tree | • Instance from [46] • 30 instances • 100 km km square region • 1 depot • 10, 12, 100 nodes • 1 UAV • 1 Truck | • Saving time compared to delivery by truck only • The number of drone nodes • The number of truck nodes • The travel distance of the truck and the drone • The waiting time of both the drone and the truck | • An optimal solution to the TSP is a —approximation to the TSP-D. • The benefits of combining a truck and a drone are time savings, on average between a factor and 2. • Using the exact partitioning outperforms the greedy heuristic. • The heuristics that use the exact partitioning (TSP-ep) show consistent savings of about and the greedy heuristic (TSP-gp) of approximately . • The greedy approaches (TSP-gp-swap and TSPgp-all) are extremely fast and solve all the instances with 100 nodes within a few seconds. |
2017 | [18] | • Maximize Drone coverage in Parcel Delivery • RP: TSP-D | • IP (same in [17]) • The Greedy Randomized Adaptive Search Procedure (GRASP) including en route drone operations | • Benchmark instances by [46] • 15 km km, 30 km×30 km, 50 km ×50 km square regions • 1 depot • 10, 20 and 50 nodes • 1 UAV • 1 Truck • UAV endurance= 30 min • UAV speeds = 40 or 60 km/h • The truck speed = 40 km/h • The en route operation cost = 1 min | • The percentage of savings over the TSP solution • The percentage of battery savings related to the remaining endurance for each operation • The waiting time | • With regards to the savings over TSP solution, the en-route operations seem to be less useful when the drone is faster than the truck. When truck and drone have the same speed, the obtained result is improved due to the en-route operation. • Battery savings and waiting times are significantly improved. • The average increase of in battery savings using en-route operations. |
2015 | [20] | • Find the optimal customer assignments for a UAV working in tandem with delivery truck • PR: TSP-D | • IP • Savings • Nearest neighbor • Sweep | • 72 instances • 8-miles square region • 10 nodes • 1 depot • 1 UAV • 1 Truck • UAV endurance = 20–40 min • UAV speed = 15,25,30 mile/h • Truck speed 25 miles/h | • Running time • Solution quality: minimizing delivery time. | • The IP approach outperformed all other heuristics in terms of solution quality. However, it is not scalable. • Savings heuristic performed well in terms of running time (fraction of second) • Nearest and Sweep are not competitive in terms of solution quality. |
2015 | [20] | •Minimize the latest time that a UAV or a truck returns to the depot •RP: TSP-D | •MILP •Savings heuristic •Nearest neighbor •PMS subproblem: binary integer programming formulation to obtain optimal PMS solutions and the popular longest processing time (LPT) first heuristic | •720 instances •8-mile square region • nodes • of nodes are UAV-eligible according to weight •1 Depot • UAVs •1 Truck •UAV-Truck speed = 25 miles/h •UAV endurance = 30 min | •Running time •Solution quality •Delivery time •Speed versus endurance | •The solutions obtained via the LPT first heuristic were often identical in quality to those obtained when the IP formulation was used to solve the PMS subproblems optimally. •The LPT first heuristic is generally faster than the IP approach to solving the PMS subproblems. •The LPT first heuristic appears to provide near-optimal solutions to the PMS subproblems. •Delivery-by-drone systems may be made more efficient by utilizing faster UAVs, even at the expense of reduced flight endurance. |
2018 | [19] | •Minimize the delivery completion time •RP: TSP-D | •TSP-LS (Local Searches) •GRASP | •65 instances •100 km×100 km, 500 km× 500 km, 1000 km×1000 km •1 depot • nodes •UAV-Truck speed = 40 Km/h •UAV endurance = 20 min • of customers can be served by UAV | • min-time: completion time (time of delivery, achievement) • min-cost: drone time tour + truck time tour + waiting time | •GRASP outperforms TSP-LS in terms of solution quality. •The running time is slower with GRASP. |
2018 | [21] | •Minimize the latest time that a UAV or a truck returns to the depot •RP: TSP-D | •Hybrid Genetic Algorithm (HGA) | •Instance sets from [19,20] •72 instances of 10 nodes from [20] •60 instances of 50 and 100 nodes from [19] •1 Depot •1 UAV •1 Truck •UAV-truck speed = 40 Km/h •UAV endurance = 20–40 min | • min-time: completion time (time of delivery, achievement) • min-cost: drone time tour + truck time tour + waiting time | •For min-cost TSP-D, the average objective values of solutions of HGA are even better than those of the best solutions of GRASP found in most instances. •HGA can improve existing best-known solutions by and on average for 50 and 100 nodes instances, respectively. •HGA performs better in large instances (i.e., 100 node instances). However, for two instances, GRASP performs better. •Regarding run time, HGA is to 2 times slower than GRASP due to its more complex design. This result is acceptable since it still can deliver significantly better results in less than 1 min for 50-node instances and less than 5 min for 100-node instances. •For min-time TSP-D, HGA can also improve the existing best-known solutions found by GRASP on all instances but not as significantly as in min-cost TSP-D. •HGA performs approximately times slower than GRASP but can still deliver better solutions in less than 1 min and 5 min for 50 and 100 node instances, respectively. •For min-time TSP-D, HGA can also improve the existing best-known solutions found by GRASP on all instances but not as significantly as in min-cost TSP-D. •HGA performs approximately times slower than GRASP but can still deliver better solutions in less than 1 min and 5 min for 50 and 100 node instances, respectively. |
2018 | [27] | •Minimize the time needed to satisfy all delivery requests •RP: TSP-D | •Constraint Programming (CP) •Variable orderings heuristics (VOH) | •120 instances •8-mile square region •20, 50 and 100 nodes •[1–2] Depots •[1–3] Trucks •[1–2] UAVs •UAV is 30 percent faster than the truck •UAV endurance= 14 miles | •Minimize the maximum completion time •Run time | •The computational study demonstrates the merit of both streamlining drop-pickup tasks and integrating multiple-depot. •CP is a promising technology for the UAVs scheduling problem. •CP proves optimality for larger test instances. |
2018 | [22] | •Minimize the delivery time •RP: TSP-D | •MIP •Hybrid General Variable Neighborhood Search (HGVNS) | •Instances from [47]: •32 km × 32 km square region •1 Depot •1 UAV •1 truck •UAV speed = 80.47 km/h •Truck speed = 56.32 km/h •UAV endurance = 24 min •The percentage of feasible drone customers is •Instance from [17] •TSPLIB instances: •25 instances •[51–200] nodes • and of nodes eligible to UAV delivery | •Solution quality •Completion time •Run time •Gap between the average solution and the best-known solution found in the literature | •Collaborative work of truck and drone can drastically decrease delivery times up to •In the instances introduced in [47], HGVNS improved the solution of the majority instances, achieving an improvement up to . •In the instance proposed in [17], the best improvement occurred in one instance with 75 nodes (also called customers) where the drone traveled twice as fast as the truck and the least improvements were observed for instances where both vehicles presented the same speed. •In the instances based on the TSPLIB instances, the best solution found in these instances shows an improvement of when over the optimal TSP tour value. |
• to are truck-only nodes. •UAV speed = 40 km/h •Truck speed = 40 km/h •UAV endurance = 40 min | ||||||
2018 | [23] | •Minimize the delivery completion time •RP: TSP-D | •MILP •An iterative two-step heuristic •Single-start two-step •Multi-start two-step | •Instance of [20]: •10, 20 nodes •UAV speed = 25 miles/h •UAV endurance = 30 min •1 Depot •1 Truck •1,2,3 UAVs •Instance TSPLIB: •UAV speed 1, 2, 3, 4 or 5 times faster than truck •1,2,3,4,5,6 UAVs | •Completion time •Running time •Percentage of UAV-eligible nodes •UAV speed •Number of UAVs •Solution quality | •With regards to the instance from [20]: •The average completion time value decreases when the number of drones increases. •The proposed scheme is optimal with a single UAV while it is not when using several UAVs. •With regards to TSPLIB instance: •Quick convergence towards good-quality solutions. |
2019 | [25] | •Minimize the delivery time •RP: mTSP-D | •MILP •Adaptive Insertion Heuristic (ADI) •ADI-GA •ADI-Kmeans-NN •ADI-Random | •185 test instances •2,25,50 nodes •1000 unit×1000 unit square region •1 Depot •n UAVs •m Trucks •UAV speed is 1.5 times faster than the truck speed •large instance: TSPLIB from [48] | •Minimizes the arrival time of drones and trucks at the depot •Run time | •In small size instance, GA-ADI reached the optimal solution significantly faster than the CPLEX Optimizer. •By comparing the results of the mTSPD with TSP and FSTSP, the delivery time can be significantly improved by using multiple drones in the route planning. •The total time to complete the delivery by using one truck and multiple drones is faster than the total delivery time using the truck alone and around faster than the total delivery time using one truck and one drone. •In large instances, the effect of drones becomes less significant once the number of trucks increases. •Allowing multiple drones in delivery operations can significantly accelerate deliveries. •The runtime increases once the number of trucks increases in different instances. •The runtime of the ADI heuristic rises quickly as the number of nodes increases. •The use of multiple drones and trucks along with ADI provides shorter delivery completion time than simply using trucks alone, multiple trucks and a single truck-drone in operation. |
2017 | [28] | •Minimize the UAV tour time •RP: TSP-D | •Improved Genetic Algorithm (IGA) •Particle-Swarm Optimization based Ant Colony Optimization algorithm (PSO-ACO) •Ant Colony Optimization (ACO) | •10,20,30,40,50 nodes • square region •1 UAV | •Shortest path •Optimal solution | •With the increasing of the number of nodes, IGA and PSO-ACO can obtain shorter paths compared with the contrast ACO method. •IGA and PSO-ACO algorithms can obtain more reasonable and effective solutions for the problem of UAV path planning. |
2018 | [29] | •Ensure network communication in a DTN context •RP: TSP-D | •Deadline Triggered Pigeon with Travelling Salesman Problem Deadlines (DTP-TSP-D) •Single Route Algorithm (SIRA) •Multiple route algorithm (MRT-Grid) | • square region •25 nodes •5,15 UAVs •UAV speed= 1 unit of distance per unit of time | •Delivery ratio •Average delay | •The DTP-TSPD outperforms the other schemes in terms of delivery ratio, although it does not always present the best average delay. •DTP-TSP-D average delay is not significantly affected by using more UAVs in the network. |
2014 | [30] | •Data gathering from target location with UAV energy refueling •RP: ATSP-D | •MIP •Approximation algorithm (Approx) •Improvement heuristic | •50 instances •5,10,15,20,25 nodes •5000 unit×5000 unit square region •5 Depots •1 UAV = Fixed-wing •Maximum fuel capacity = 4500 units •UAV speed constant •UAV Minimum turning radius = 100 units •UAV turning angle [0, 2] | •Solution quality | •The average quality of the solutions produced by the improvement heuristic is much superior compared to the average quality of the solutions found by the approximation algorithm. •Using the feasible solution produced by the heuristic as a starting point, the CPLEX Optimizer was able to improve the quality of the solution further. •For instances with 25 targets and 5 depots, the CPLEX Optimizer was further able to improve the average solution quality of the instances to . •The proposed algorithms can be effectively used in conjunction with standard optimization software like the CPLEX Optimizer in order to obtain high-quality solutions for the FCURP. |
2018 | [34] | •Minimize the delivery time •RP: VRP-D | •Two-Phase Heuristic (TPH) •Single-Phase Heuristic (SPH) | •TSPLIB instance: •1 Depot •3 Trucks •1 UAV per Truck | •Solution quality | •The TPH provides better results than the SPH in most cases and there are a few cases where the SPH produces better or competitive results. •Good VRPD solutions can be constructed by using a two-stage heuristic, starting from good VRP solutions. |
2018 | [35] | •Minimize the delivery time •RP: VRP-D | •Policy Function Approximation (PFA): •Policy 1: •Policy 2: •Policy 3: | •300, 400, 500 and 800 expected orders •Depot ≥ 1 •[1–20] UAVs •[1–5] Trucks •UAV speed = 40Km •Truck speed = 20Km | •Solution quality (served/requests) | •PFA is effective both in a geography in which customers are more tightly clustered around the depot as well as one in which the customer distribution is more heterogeneous. •Comparisons to other threshold-type benchmark policies reveal that the districting by the proposed PFA is highly beneficial in significantly increasing the expected number of services by the fleets. •Using the PFA, a combination of drones and vehicles may reduce operational resources required to serve the majority of customers. |
2018 | [37] | CVRPTW | •Mathematic model | •Time window [0.1, 0.5] h •Number of node [5,10] •UAV: md4-1000 model •UAV payload = 1.2 kg •UAV endurance = 70 min •UAV speed= 13 m/s | •The fleet size •The traveled distance •The energy consumption •Impact of the Time Window | •Delivering in short time windows requires an important number of batteries. •The number of batteries needed may exceed the fleetâ™s size. •Three problem classes are proposed: 1-minimizing the distance traveled 2-minimizing the number of UAVs and 3-minimizing the number of batteries used. •Based on the three proposed cases, we can evaluate the fleet and battery sizes and the necessary energy consumption to deliver a defined set of customers during a defined time window. |
2017 | [39] | •Minimize the delivery time with UAV refueling •RP: GVRP-D | •MILP •Multi Objective Smart Pool Search (MOSPOOLS) Matheuristic | •Lower layer: •1 km×1 km square region •10 nodes •Upper layer •5 km×5 km square region •25 nodes •Common parameters: •UAV capacity in [0.3 5] kg •UAV speed = [20 120] km •3 inter layer/supporting points •Depot = 5 recharging points | •Minimizes seven objective functions: •Total traveled distance •UAVs maximum speed •Number of used UAVs •Makespans of the last collected and delivered package •Average time spent with each package •Maximize batteries load at the end of the schedule. | •By minimizing the last collect, the model minimized the last delivered with high correlation between both objectives. •If the schedule finishes with more charged batteries, then the solutions run higher distances. •Using more drones resulted in schedules that finish earlier. |
2017 | [40] | •Minimize the delivery cost while reusing UAVs •RP: MTVRP-D and GVRP-D | •MILP •Simulated Annealing (SA) heuristic | •100 random instances •Small area 0.25 km×0.25 km •[6 8] nodesâ“delivery locations •Large area 1 km × 1 km •1 depot •UAV capacity = 3 kg •UAV speed = 6 m/s •[125 500] nodes •UAV: Multirotor helicopter | •Energy consumption •Delivery time •Run time | •Minimize cost in dollars or delivery time while considering battery weight, payload weight and drone reuse •Increasing battery and payload weight can noticeably increase energy consumption, which in turn reduces flight time. •To minimize the cost or the delivery time for UAVs deliveries, the payload weight, battery weight and flight time should be considered. •The energy consumption increases at an approximately linear rate with battery and payload weight. •UAVs consume approximately the same power regardless of being in hover or flying at a constant speed. •SA implementations find near-optimal solutions to small instances of the DDPs and provide consistent results for larger instances. •Reusing UAVs to perform multiple trips is an essential strategy for reducing costs. •Optimizing battery weight is an effective strategy for reducing the total cost and overall delivery time. |
2018 | [41] | •Minimize the traveling distance while performing refueling •RP: GVRP-D | •Two-stage stochastic optimization problem •Two-stage stochastic program •Sample average approximation (SAA) •Tabu search-based heuristic | •100 unit × 100 unit square region •5 Instances of 10 nodes •120 instances of 20,30 nodes •1 Depot •4 refueling sites •UAVs number in 3,4,5 •UAV capacity in 2.25, 2.5, 2.75, 3 | •Minimum travel costs for UAV routes •Fuel consumption •Run time | •The solutions obtained with the heuristic are computationally efficient and not very different from the solutions for deterministic models and that they are also very robust in the face of uncertainty. |
2016 | [43] | •Optimize UAV task assignment •RP: VRP-D | •MILP •Novel Ant Colony Optimization metaheuristic approach (ACO) | •60 test instances. • NM2 (square nautical miles of less than 100 nodes • NM2 for larger instances. •UAV speed = 60 knots •UAV number [6,12] | •Maximize the total score of covered interest points | •Most instances are found difficult to solve optimally. •Ant colony optimization metaheuristic can provide the best-known or close to the best-known solution in a short time. |
2018 | [44] | •Optimize UAV task allocation and path planning •RP: VRP-D | •GA based optimization algorithm | •Airspeed = 10 ms •Minimum turning radius = 200 m •3 targets •1,2 UAV s | •Minimizing the time required for UAVs to visit all the targets and return to the starting point | •The allocation of tasks and the planning of the route are integrated and optimized under the influence of the wind, the result of which is the best possible solution in the wind. •The actual flight time will be reduced by in the presence of wind. |
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Khoufi, I.; Laouiti, A.; Adjih, C. A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles. Drones 2019, 3, 66. https://doi.org/10.3390/drones3030066
Khoufi I, Laouiti A, Adjih C. A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles. Drones. 2019; 3(3):66. https://doi.org/10.3390/drones3030066
Chicago/Turabian StyleKhoufi, Ines, Anis Laouiti, and Cedric Adjih. 2019. "A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles" Drones 3, no. 3: 66. https://doi.org/10.3390/drones3030066