Truck and unmanned aerial vehicle cooperative distribution method with flexible access of unmanned aerial vehicle for goods taking and delivery service

Abstract

The invention discloses a truck and unmanned aerial vehicle collaborative distribution method for flexible access of unmanned aerial vehicles with goods taking and delivering services. The method comprises the following steps: 1, constructing a target function with cost minimization as a target based on a distribution scene; 2, constructing a carbon emission constraint; 3, constructing a path constraint; 4, constructing a spatial constraint; 5, constructing a time constraint; 6, constructing a load constraint; and 7, solving the distribution model by using a gurobi solver to obtain a final distribution scheme. According to the method, the more comprehensive truck and unmanned aerial vehicle collaborative distribution model is constructed, and the optimal collaborative distribution scheme is generated, so that the distribution rationality and efficiency are greatly improved, the method is closer to the customer demand and the condition that the distribution is inseparable in reality, and the defects of an existing collaborative scheme are overcome.

Description

Technical Field

[0001] The present invention belongs to the field of operations research and path planning technology, and specifically is a truck-drone collaborative distribution method with flexible access by drones with pickup and delivery services based on mathematical modeling considerations. Background Art

[0002] With the rapid development of e-commerce, consumers have put forward higher requirements for logistics and distribution services. The traditional truck-based distribution model is limited by factors such as traffic congestion and complex distribution routes. It is inefficient and difficult to meet the demand for transportation speed and distribution efficiency. With its high efficiency, speed and flexibility, drones have gradually become an important technical means in the field of logistics and distribution. In particular, the truck and drone collaborative distribution model, as an emerging logistics solution, can give full play to the large-capacity transportation advantages of trucks and the fast and flexible characteristics of drones to jointly complete distribution tasks, achieve the optimal allocation of resources and thus improve distribution efficiency.

[0003] At present, most of the research on truck-drone collaborative delivery focuses on VRPD, that is, one truck is equipped with one drone, and the drone can only return to the truck from which it was launched. However, the issue of whether the drone's endurance during the delivery process is sufficient to continue to visit the next customer has not been fully considered. The truck-drone delivery model established by the existing method is relatively idealized and cannot handle the situation of maximizing resource utilization in practice. This leads to the unreasonable delivery plan generated by the existing model.

[0004] In summary, the existing truck-drone collaborative delivery methods have the following shortcomings:

[0005] 1. Environmental pollution constraints are not taken into account, and the generated distribution plan is not reasonable enough.

[0006] 2. The modeling is too idealistic and cannot be directly applied to actual delivery tasks. Summary of the invention

[0007] The present invention aims to address the deficiencies of the above-mentioned prior art and proposes a truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services, in order to effectively integrate green travel with path planning and generate an optimal or near-optimal collaborative delivery plan that not only meets the spatial constraints of the vehicle, but also takes into account the time constraints and the load limit of the vehicle, thereby improving the rationality and efficiency of delivery.

[0008] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0009] The truck-drone collaborative distribution method of the present invention, which has the advantages of flexible access by drones with pickup and delivery services, is applied to the collection of customer points. , the starting point of the warehouse 0, the end point of the warehouse n+1 and the truck set In the distribution scenario, each truck carries a collection of drones. ; Collected by customer points Together with the starting point 0 of the warehouse, it forms a set of nodes that the drone can launch. , collected by customer points The warehouse endpoint n+1 forms a collection of drone recyclable nodes The vehicle path planning method is carried out in the following steps:

[0010] Step 1: Use formula (1) to construct the objective function F of the truck-drone collaborative delivery model in which the drone visits multiple times and provides pickup and delivery services to customer points with the goal of minimizing the transportation distance:

[0011] (1)

[0012] In formula (1), Any truck Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let , Indicates drone Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let ; Any truck Nodes that can be launched from a drone Drive to a node where the drone can be recovered The distance Represents any drone Nodes that can be launched from a drone Drive to a node where the drone can be recovered distance; Indicates nodes that any drone can launch Arrived at the point where the drone can be recovered The path between them, E represents the path set;

[0013] Step 2: Construct carbon emission constraints for the truck-drone collaborative delivery model;

[0014] Step 3: Construct the path constraints of the truck-drone collaborative delivery model, including: truck path constraints, drone flight path constraints, and truck-drone collaborative path constraints;

[0015] Step 4: Construct the spatial constraints of the truck-drone collaborative delivery model;

[0016] Step 5: Construct the time constraints of the truck-drone collaborative delivery model;

[0017] Step 6: Construct load constraints for the truck-drone collaborative delivery model;

[0018] Step 7: Use the gurobi solver to solve the truck-drone collaborative delivery model and obtain the truck-drone collaborative delivery plan, including: the number of trucks and drones used, and the delivery path of each truck and each drone used.

[0019] The truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services described in the present invention is also characterized in that the carbon emission constraint is constructed using formula (2) in step 2:

[0020] (2)

[0021] In formula (2), represents the weighted average emission per vehicle unit, represents the carbon emissions per unit of drone, Represents the total carbon emissions from delivery.

[0022] Furthermore, the step three includes:

[0023] Step 3.1: Use equations (3) to (6) to construct the truck path constraints:

[0024] (3)

[0025] (4)

[0026] (5)

[0027] (6)

[0028] In formula (3) to formula (6), Truck Whether to pass through the starting point 0 of the warehouse to reach the node where the drone can be recycled If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Truck Whether from the customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let ;

[0029] Step 3.2: Use equations (7) to (9) to construct the UAV path constraints:

[0030] (7)

[0031] (8)

[0032] (9)

[0033] In formula (7) to formula (9), Indicates drone Whether to start from the starting point 0 of the warehouse and reach the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the truck k starts from the warehouse starting point 0 and reaches the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Whether it passes through the customer point Arrived at the point where the drone can be recovered , then let , otherwise let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Is it on truck k from customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let ;

[0034] Step 3.3: Use formula (10) to construct the truck-UAV collaborative path constraint:

[0035] (10).

[0036] Further, the step 4 comprises:

[0037] Step 4.1, Equation (11)-Equation (14) constructs the spatial constraints of the truck and the drone:

[0038] (11)

[0039] (12)

[0040] (13)

[0041] (14)

[0042] In formula (11) to formula (14), Truck Is it at the customer point? Launch a drone or recover a drone. If so, , otherwise, let 0;

[0043] Further, the step 5 comprises:

[0044] Step 5.1: Use equations (15)-(16) to construct the time constraint for the truck to travel from the drone launch node to the drone recovery node:

[0045] (15)

[0046] (16)

[0047] In formulas (15)-(16), Truck Arrival at the drone recovery node time, Truck Arrival of the drone launch node time, Indicates that drone d has reached the node where drones can launch time, Truck Nodes can be launched from drones Travel to time, X represents an integer;

[0048] Step 5.2: Use equations (17)-(18) to construct the time constraint for the drone to travel from the drone launch node to the drone recovery node:

[0049] (17)

[0050] (18)

[0051] In formulas (17)-(18), Indicates drone arrive node time, Indicates drone Arrival of the drone launch node time, Indicates drone Nodes can be launched from drones Drive to the drone recovery node time;

[0052] Step 5.3: Use equations (19)-(20) to construct the working time constraints of trucks and drones:

[0053] (19)

[0054] (20)

[0055] In formulas (19)-(20), A node indicating whether drone d is on truck k and can be launched from the drone Departure and arrival of drone recyclable nodes If so, then let , otherwise, let ; L represents an integer;

[0056] Step 5.4: Use equations (21)-(25) to construct the flight time constraint of the UAV:

[0057] (twenty one)

[0058] (twenty two)

[0059] (twenty three)

[0060] (twenty four)

[0061] (25)

[0062] In formulas (21)-(25), Indicates drone Take off from the truck and arrive at the customer point The accumulated flight time, Indicates drone From the last departure point The accumulated flight time, Indicates drone Take off from the truck and arrive at the drone recovery node The accumulated flight time, Indicates drone Take off from the truck and leave the drone recoverable node The accumulated flight time, Indicates the flight time of each drone.

[0063] Further, the step 6 comprises:

[0064] Step 6.1: Use equations (26) and (27) to construct the delivery load constraints of the truck at the node:

[0065] (26)

[0066] (27)

[0067] In formula (26)-formula (27), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at customer point of delivery load, Indicates drone At the customer point Delivery load after transshipment, Indicates customer point The delivery demand;

[0068] Step 6.2: Use equations (28) and (29) to construct the truck's pickup load constraints at the node:

[0069] (28)

[0070] (29)

[0071] In formula (28)-formula (29), Truck Arrival at the drone recovery node of pickup load, Truck Arrival at customer point of pickup load, Indicates drone At the customer point Pick-up load after transshipment, Indicates customer point The demand for pickup;

[0072] Step 6.3: Use equations (30) and (31) to construct the delivery and pickup load constraints when the truck leaves the warehouse:

[0073] (30)

[0074] (31)

[0075] In formula (30)-formula (31), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at the drone recovery node of pickup load, Truck Delivery load at warehouse origin 0, Truck Pickup load at warehouse starting point 0;

[0076] Step 6.4: Use equation (32) to construct the maximum truck load constraint:

[0077] (32)

[0078] In formula (32), Truck Arrival at customer point of delivery load, Truck Arrival at customer point of pickup load, Truck Maximum load capacity;

[0079] Step 6.5: Use equations (33) and (34) to construct the delivery and pickup load constraints for the drone to reach the drone's recyclable node after serving the customer point:

[0080] (33)

[0081] (34)

[0082] In formula (33)-formula (34), Indicates drone Arrival at the drone recovery node of delivery load, Indicates drone At the customer point Delivery load after transshipment, Indicates drone Arrival at the drone recovery node of pickup load, Indicates drone At the node Pick-up load after transshipment;

[0083] Step 6.6: Use equations (35) and (36) to construct the constraint that all tasks are completed and packages are unloaded before the drone returns to the truck and starts a new visit:

[0084] (35)

[0085] (36)

[0086] In formula (35)-formula (36), Truck Is it in the drone recyclable node? Launch or recover the drone, if so, , otherwise, let ; Indicates that the drone is in the drone recyclable node Pick-up load after transshipment, Truck Is it in the drone recyclable node? Launch or recover the drone, if so, , otherwise, let ;

[0087] Step 6.7: Use equations (37) to (40) to construct the constraint that the package is not transferred when the drone is flying alone:

[0088] (37)

[0089] (38)

[0090] (39)

[0091] (40)

[0092] In formula (37) to formula (40), Indicates drone Arrival at customer point of delivery load, Indicates drone Arrival at customer point of pickup load;

[0093] Step 6.8: Use formula (41) to construct the maximum load constraint of the UAV:

[0094] (41)

[0095] In formula (41), Indicates the maximum payload of UAV d.

[0096] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the planning method, and the processor is configured to execute the program stored in the memory.

[0097] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes any step of the planning method when executed by a processor.

[0098] Compared with the prior art, the present invention has the following beneficial effects:

[0099] 1. By constructing a more comprehensive truck-UAV collaborative delivery model, the present invention can rationally plan the delivery routes of trucks and UAVs, reduce invalid delivery time and distance, and thus greatly improve delivery efficiency.

[0100] 2. The present invention takes carbon emission constraints into consideration. Environmental issues have become a serious problem faced by most companies. Considering green delivery can provide better services to customers, which is in line with the concept of green travel.

[0101] 3. The present invention expands the problem of truck-drone collaboration, allowing a truck to carry multiple drones and the drones to provide pick-up and delivery services to multiple customers in one flight. It fully considers the actual situation and better utilizes the advantages of drones, thereby avoiding wasting drone flight time or multiple round trips to the same customer point, and improving the utilization efficiency and delivery efficiency of drones.

[0102] 4. The present invention constructs a mixed integer programming model and solves it with the gurobi solver to obtain a delivery plan with high delivery efficiency. The plan makes full use of the use of drones, improves the quality of delivery services and customer satisfaction, while taking into account the development concept of green travel and reducing environmental pollution. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 A schematic diagram of a truck-drone collaborative delivery network that is flexibly accessed by drones with pickup and delivery services in the present invention;

[0104] Figure 2 A schematic diagram of the paths of trucks and drones in the present invention;

[0105] Figure 3 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0106] In this embodiment, a truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services is based on the distribution scenario to establish a target function, model the minimization of transportation distance as the goal, and construct carbon emission constraints; then, construct path constraints, including truck path constraints, drone flight path constraints, and truck-drone collaborative path constraints, to ensure the rationality of the distribution path; then, construct space constraints, rules for trucks and drones to arrive at and leave nodes; then, establish relevant constraints for delivery time calculation, calculate the arrival time of trucks and drones and the endurance of drones, and then establish load constraints for trucks and drones, including delivery and pickup load constraints for trucks at nodes, delivery and pickup load constraints for drones that finish serving nodes and start new visits, and maximum load constraints for trucks and drones, to ensure the rationality of package delivery; finally, use the gurobi solver to solve the model to obtain the final distribution plan. Specifically, Figure 3 As shown, the method comprises the following steps:

[0107] Step 1: Construct a scene: In this embodiment, it is applied to a scene composed of a set of customer points. , the starting point of the warehouse 0, the end point of the warehouse n+1 and the truck set In the distribution scenario, each truck carries a collection of drones. ; Collected by customer points Together with the starting point 0 of the warehouse, it forms a set of nodes that the drone can launch. , collected by customer points The warehouse endpoint n+1 forms a collection of drone recyclable nodes :

[0108] The warehouse starts at 0 and contains k trucks of the same model. , each truck carries the same type of drone , any truck can be launched from the drone node Drive to the drone recovery node The distance is recorded as , time is recorded as , any UAV can launch a node from the UAV Drive to the drone recovery node The distance is recorded as , time is recorded as ; Let the flight time of each drone be ; The maximum load of each truck and the maximum load of each drone are recorded as ;

[0109] See also Figure 1 , Figure 1 0 represents the warehouse, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 represent customer points 1-12 respectively. There are three different types of customers: customers who only need delivery, customers who only need pickup, and customers who need both pickup and delivery. Trucks The path is 0→1→3→5→4→0, and the truck The path is 0→7→10→12→0, the truck The flight paths of the drones carried are 1→2→3, 3→6→7, and the trucks The flight paths of the carried drones are 7→8→9→10, 10→11→1.

[0110] Step 2: Extract delivery information: Based on the delivery network, obtain the delivery information of the customer nodes to be served, including node location, customer point distance, customer point demand, truck driving speed, drone flight speed, flight time of any drone, and maximum load capacity of trucks and drones.

[0111] Step 3: Use formula (1) to construct the objective function F of the truck-drone collaborative delivery model in which the drone visits multiple times and provides pickup and delivery services to customer points with the goal of minimizing the transportation distance:

[0112] (1)

[0113] In formula (1), Any truck Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let , Indicates drone Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let ; Any truck Nodes that can be launched from a drone Drive to a node where the drone can be recovered The distance Represents any drone Nodes that can be launched from a drone Drive to a node where the drone can be recovered distance; Indicates nodes that can be launched by any drone Arrived at the point where the drone can be recovered The path between them, E represents the path set.

[0114] Step 4: Use formula (2) to construct the carbon emission constraints of the truck-drone collaborative delivery model:

[0115] (2)

[0116] In formula (2), represents the weighted average emission per vehicle unit, represents the carbon emissions per unit of drone, Represents the total carbon emissions from delivery.

[0117] Step 5: Construct the path constraints of the truck-drone collaborative delivery model, including: truck path constraints, drone flight path constraints, and truck-drone collaborative path constraints, including:

[0118] Step 5.1: Use equations (3) to (6) to construct the truck path constraints:

[0119] (3)

[0120] (4)

[0121] (5)

[0122] (6)

[0123] In formula (3) to formula (6), Truck Whether to pass through the starting point 0 of the warehouse to reach the node where the drone can be recycled If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Truck Whether from the customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let .

[0124] Step 5.2: Use equations (7) to (9) to construct the UAV path constraints:

[0125] (7)

[0126] (8)

[0127] (9)

[0128] In formula (7) to formula (9), Indicates drone Whether to start from the starting point 0 of the warehouse and reach the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the truck k starts from the warehouse starting point 0 and reaches the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Whether it passes through the customer point Arrived at the point where the drone can be recovered , then let , otherwise let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Is it on truck k from customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let .

[0129] Step 5.3: Use formula (10) to construct the truck-UAV collaborative path constraint:

[0130] (10)

[0131] Step 6: Construct the spatial constraints of the truck-drone collaborative delivery model, including:

[0132] Step 6.1, Equation (11)-Equation (14) constructs the spatial constraints of the truck and the drone:

[0133] (11)

[0134] (12)

[0135] (13)

[0136] (14)

[0137] In formula (11) to formula (14), Truck Is it at the customer point? Launch a drone or recover a drone. If so, , otherwise, let 0.

[0138] Step 7: Construct the time constraints of the truck-drone collaborative delivery model, including:

[0139] Step 7.1: Use equations (15)-(16) to construct the time constraint for the truck to travel from the drone launch node to the drone recovery node:

[0140] (15)

[0141] (16)

[0142] In formulas (15)-(16), Truck Arrival at the drone recovery node time, Truck Arrival of the drone launch node time, Indicates that drone d has reached the node where drones can launch time, Truck Nodes can be launched from drones Travel to time, X represents an integer.

[0143] Step 7.2: Use equations (17) and (18) to construct the time constraint for the UAV to travel from the UAV launch node to the UAV retrievable node:

[0144] (17)

[0145] (18)

[0146] In formulas (17)-(18), Indicates drone arrive node time, Indicates drone Arrival of the drone launch node time, Indicates drone Nodes can be launched from drones Drive to the drone recovery node time.

[0147] Step 7.3: Use equations (19)-(20) to construct the working time constraints of trucks and drones:

[0148] (19)

[0149] (20)

[0150] In formulas (19)-(20), A node indicating whether drone d is on truck k and can be launched from the drone Departure and arrival of drone recyclable nodes If so, then let , otherwise, let ; L represents an integer.

[0151] Step 7.4: Use equations (21)-(25) to construct the flight time constraint of the UAV:

[0152] (twenty one)

[0153] (twenty two)

[0154] (twenty three)

[0155] (twenty four)

[0156] (25)

[0157] In formulas (21)-(25), Indicates drone Arrival at the customer point from the last takeoff The accumulated flight time, Indicates drone From the last departure point The accumulated flight time, Indicates drone Arrival at the drone recovery node from the last takeoff The accumulated flight time, Indicates drone Departing the drone recyclable node from the last takeoff The accumulated flight time, Indicates the flight time of each drone.

[0158] Step 8: Construct the load constraints of the truck-drone collaborative delivery model, including:

[0159] Step 8.1: Use equations (26) and (27) to construct the delivery load constraints of the truck at the node:

[0160] (26)

[0161] (27)

[0162] In formula (26)-formula (27), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at customer point of delivery load, Indicates drone At the customer point Delivery load after transshipment, Representation Node delivery needs.

[0163] Step 8.2: Use equations (28) and (29) to construct the truck's pickup load constraints at the node:

[0164] (28)

[0165] (29)

[0166] In formula (28)-formula (29), Truck Arrival at the drone recovery node of pickup load, Truck Arrival at customer point of pickup load, Indicates drone At the customer point Pick-up load after transshipment, Indicates customer point Pickup demand.

[0167] Step 8.3: Use equations (30) and (31) to construct the delivery and pickup load constraints when the truck leaves the warehouse:

[0168] (30)

[0169] (31)

[0170] In formula (30)-formula (31), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at the drone recovery node of pickup load, Truck Delivery load at warehouse origin 0, Truck Pickup load at warehouse origin 0.

[0171] Step 8.4: Use equation (32) to construct the maximum load constraint of the truck:

[0172] (32)

[0173] In formula (32), Truck Arrival at customer point of delivery load, Truck Arrival at customer point of pickup load, Truck Maximum load capacity.

[0174] Step 8.5: Use equations (33) and (34) to construct the delivery and pickup load constraints for the drone to reach the drone's recyclable node after serving the customer point:

[0175] (33)

[0176] (34)

[0177] In formula (33)-formula (34), Indicates drone Arrival at the drone recovery node of delivery load, Indicates drone At the customer point Delivery load after transshipment, Indicates drone Arrival at the drone recovery node of pickup load, Indicates drone At the node Pick-up load after transshipment.

[0178] Step 8.6: Use equations (35) and (36) to construct the constraint that all tasks are completed and packages are unloaded before the drone returns to the truck and starts a new visit:

[0179] (35)

[0180] (36)

[0181] In formula (35)-formula (36), Truck Is it in the drone recyclable node? Launch or retrieve the drone, and if so, order , otherwise, let ; Indicates that the drone is in the drone recyclable node Pick-up load after transshipment, Truck Is it in the drone recyclable node? Launch or retrieve the drone, and if so, order , otherwise, let .

[0182] Step 8.7: Use equations (37) to (40) to construct the constraint that the package will not be transferred when the drone is flying alone:

[0183] (37)

[0184] (38)

[0185] (39)

[0186] (40)

[0187] In formula (37) to formula (40), Indicates drone Arrival at customer point of delivery load, Indicates drone Arrival at customer point of pickup load.

[0188] Step 8.8: Use formula (41) to construct the maximum load constraint of the UAV:

[0189] (41)

[0190] In formula (41), Indicates the maximum payload of UAV d.

[0191] Step 9: The objective function F and all constraints constitute a truck-drone collaborative delivery model that considers multiple visits by drones and pick-up and delivery services to customers, and use the gurobi solver to solve it to obtain the final delivery plan, including: the number of trucks and drones used, the specific delivery path of each truck and each drone used, and the participants. Figure 2 The example shown: Figure 2 0 represents the warehouse start point, 13 represents the warehouse end point, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 represent customer points 1-12 respectively. There are three different types of customers: customers who only need delivery, customers who only need pickup, and customers who need both pickup and delivery. Trucks The path is 0→1→3→5→4→13. The path is 0→7→10→12→13, the truck The flight paths of the drones carried are 1→2→3, 3→6→7, and the trucks The flight paths of the carried drones are 7→8→9→10, 10→11→12.

[0192] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the planning method, and the processor is configured to execute the program stored in the memory.

[0193] In this embodiment, a computer-readable storage medium stores a computer program, wherein the computer program executes the steps of the planning method when executed by a processor.

[0194] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services, characterized in that: is applied to a collection of customer points , the starting point of the warehouse 0, the end point of the warehouse n+1 and the truck set In the distribution scenario, each truck carries a collection of drones. ; Collected by customer points Together with the starting point 0 of the warehouse, it forms a set of nodes that the drone can launch. , collected by customer points The warehouse endpoint n+1 forms a collection of drone recyclable nodes The vehicle path planning method is carried out in the following steps: Step 1: Use formula (1) to construct the objective function F of the truck-drone collaborative delivery model in which the drone visits multiple times and provides pickup and delivery services to customer points with the goal of minimizing the transportation distance: (1) In formula (1), Any truck Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let , Indicates drone Whether it passes through a node where the drone can launch Arrived at the point where the drone can be recovered If so, then let , otherwise, let ; Any truck Nodes that can be launched from a drone Drive to a node where the drone can be recovered The distance Represents any drone Nodes that can be launched from a drone Drive to a node where the drone can be recovered distance; Indicates nodes that can be launched by any drone Arrived at the point where the drone can be recovered The path between them, E represents the path set; Step 2: Construct carbon emission constraints for the truck-drone collaborative delivery model; Step 3: Construct the path constraints of the truck-drone collaborative delivery model, including: truck path constraints, drone flight path constraints, and truck-drone collaborative path constraints; Step 4: Construct the spatial constraints of the truck-drone collaborative delivery model; Step 5: Construct the time constraints of the truck-drone collaborative delivery model; Step 6: Construct load constraints for the truck-drone collaborative delivery model; Step 7: Use the gurobi solver to solve the truck-drone collaborative delivery model and obtain the truck-drone collaborative delivery plan, including: the number of trucks and drones used, and the delivery path of each truck and each drone used.

2. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services according to claim 1, characterized in that: In the second step, the carbon emission constraint is constructed using formula (2): (2) In formula (2), represents the weighted average emission per vehicle unit, represents the carbon emissions per unit of drone, Represents the total carbon emissions from delivery.

3. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services according to claim 2, characterized in that: The step three comprises: Step 3.1: Use equations (3) to (6) to construct the truck path constraints: (3) (4) (5) (6) In formula (3) to formula (6), Truck Whether to pass through the starting point 0 of the warehouse to reach the node where the drone can be recycled If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Truck Whether from the customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let ; Truck Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let ; Step 3.2: Use equations (7) to (9) to construct the UAV path constraints: (7) (8) (9) In formula (7) to formula (9), Indicates drone Whether to start from the starting point 0 of the warehouse and reach the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the truck k starts from the warehouse starting point 0 and reaches the node where the drone can be recovered If so, then let , otherwise, let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure to the warehouse end point n+1, if so, then let , otherwise, let ; Indicates drone Whether the node can be launched from the drone Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Whether it passes through the customer point Arrived at the point where the drone can be recovered , then let , otherwise let ; Indicates drone Is there a node on truck k that can be launched from the drone? Departure and arrival at customer point If so, then let , otherwise, let ; Indicates drone Is it on truck k from customer point Departure and arrival at the node where the drone can be recovered If so, then let , otherwise, let ; Step 3.3: Use formula (10) to construct the truck-UAV collaborative path constraint: (10)。 4. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services according to claim 3, characterized in that: The step 4 comprises: Step 4.1, Equation (11)-Equation (14) constructs the spatial constraints of the truck and the drone: (11) (12) (13) (14) In formula (11) to formula (14), Truck Is it at the customer point? Launch a drone or recover a drone. If so, , otherwise, let 0.

5. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services according to claim 4, characterized in that: The step 5 comprises: Step 5.1: Use equations (15)-(16) to construct the time constraint for the truck to travel from the drone launch node to the drone recovery node: (15) (16) In formulas (15)-(16), Truck Arrival at the drone recovery node time, Truck Arrival of the drone launch node time, Indicates that drone d has reached the node where drones can launch time, Truck Nodes can be launched from drones Travel to time, X represents an integer; Step 5.2: Use equations (17)-(18) to construct the time constraint for the drone to travel from the drone launch node to the drone recovery node: (17) (18) In formulas (17)-(18), Indicates drone arrive node time, Indicates drone Arrival of the drone launch node time, Indicates drone Nodes can be launched from drones Drive to the drone recovery node time; Step 5.3: Use equations (19)-(20) to construct the working time constraints of trucks and drones: (19) (20) In formulas (19)-(20), A node indicating whether drone d is on truck k and can be launched from the drone Departure and arrival of drone recyclable nodes If so, then let , otherwise, let ; L represents an integer; Step 5.4: Use equations (21) to (25) to construct the flight time constraint of the UAV: (21) (22) (23) (24) (25) In formulas (21)-(25), Indicates drone Take off from the truck and arrive at the customer point The accumulated flight time, Indicates drone From the last departure point The accumulated flight time, Indicates drone Take off from the truck and arrive at the drone recovery node The accumulated flight time, Indicates drone Take off from the truck and leave the drone recoverable node The accumulated flight time, Indicates the flight time of each drone.

6. A truck-drone collaborative delivery method with flexible access by drones for pickup and delivery services according to claim 5, characterized in that: The step 6 comprises: Step 6.1: Use equations (26) and (27) to construct the delivery load constraints of the truck at the node: (26) (27) In formula (26)-formula (27), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at customer point of delivery load, Indicates drone At the customer point Delivery load after transshipment, Indicates customer point The delivery demand; Step 6.2: Use equations (28) and (29) to construct the truck's pickup load constraints at the node: (28) (29) In formula (28)-formula (29), Truck Arrival at the drone recovery node of pickup load, Truck Arrival at customer point of pickup load, Indicates drone At the customer point Pick-up load after transshipment, Indicates customer point The demand for pickup; Step 6.3: Use equations (30) and (31) to construct the delivery and pickup load constraints when the truck leaves the warehouse: (30) (31) In formula (30)-formula (31), Truck Arrival at the drone recovery node of delivery load, Truck Arrival at the drone recovery node of pickup load, Truck Delivery load at warehouse origin 0, Truck Pickup load at warehouse starting point 0; Step 6.4: Use equation (32) to construct the maximum truck load constraint: (32) In formula (32), Truck Arrival at customer point of delivery load, Truck Arrival at customer point of pickup load, Truck Maximum load capacity; Step 6.5: Use equations (33) and (34) to construct the delivery and pickup load constraints for the drone to reach the drone's recyclable node after serving the customer point: (33) (34) In formula (33)-formula (34), Indicates drone Arrival at the drone recovery node of delivery load, Indicates drone At the customer point Delivery load after transshipment, Indicates drone Arrival at the drone recovery node of pickup load, Indicates drone At the node Pick-up load after transshipment; Step 6.6: Use equations (35) and (36) to construct the constraint that all tasks are completed and packages are unloaded before the drone returns to the truck and starts a new visit: (35) (36) In formula (35)-formula (36), Truck Is it in the drone recyclable node? Launch or recover the drone, if so, , otherwise, let ; Indicates that the drone is in the drone recyclable node Pick-up load after transshipment, Truck Is it in the drone recyclable node? Launch or recover the drone, if so, , otherwise, let ; Step 6.7: Use equations (37) to (40) to construct the constraint that the package is not transferred when the drone is flying alone: (37) (38) (39) (40) In formula (37) to formula (40), Indicates drone Arrival at customer point of delivery load, Indicates drone Arrival at customer point of pickup load; Step 6.8: Use formula (41) to construct the maximum load constraint of the UAV: (41) In formula (41), Indicates the maximum payload of UAV d.

7. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the planning method described in any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the planning method according to any one of claims 1 to 6 are executed.

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