A multi-UAV-multi-truck collaborative logistics distribution path planning method

Abstract

The present invention discloses a multi-drone-multi-truck collaborative logistics distribution path planning method, which belongs to the field of drone logistics technology. It includes the following steps: Step 1: Establish a mixed integer linear programming model for the multi-drone-multi-truck collaborative logistics distribution path planning problem; Step 2: Perform initial planning of the truck distribution path based on the K-Means algorithm and the genetic algorithm; Step 3: Design a path planning search operator, introduce a variable neighborhood search framework on the basis of the truck distribution route to jointly optimize the distribution paths of drones and trucks, and solve the constructed mixed integer linear programming model. The method provided by the present invention takes into account the different purchase costs of trucks and drones, reasonably optimizes the purchase quantity and use quantity of transportation tools, effectively reduces the total distribution cost, further optimizes the drone-truck distribution plan, and makes up for the shortcomings of the existing joint distribution models and methods.

Description

Technical Field

[0001] The present invention belongs to the technical field of drone logistics, and specifically relates to a multi-drone-multi-truck collaborative logistics distribution path planning method. Background Art

[0002] Unmanned aerial vehicles (UAVs) are aircraft that are remotely controlled or autonomously flown by a control station. In recent years, with the continuous development of UAV technology, UAVs have played an increasingly important role in both civil and military fields. The application of UAVs in the civil field involves infrastructure construction, agriculture, transportation logistics, safety and disaster management, and entertainment, and has also become a choice for future logistics and transportation tools. Compared with traditional delivery methods, UAVs have the characteristics of fast speed, no road restrictions, and low cost. These characteristics make UAVs have broad prospects in the current situation where the express delivery industry is developing rapidly and the "last mile" has become a problem in the delivery industry. On the other hand, low-altitude express delivery UAVs are limited by the size of the aircraft, and have the limitations of short flight time and small payload compared to truck delivery. Using UAVs only for round-trip delivery between warehouses and customers has limited improvement in the efficiency of express delivery. Using UAVs and trucks for delivery at the same time, allowing UAVs to take off and land, replenish goods, and other operations on trucks can achieve complementary advantages between the two. Therefore, UAV-truck joint delivery provides a new solution to the problem of terminal logistics delivery.

[0003] When drones and trucks are used for joint delivery, it is necessary to plan the delivery objects and order of drones and trucks, that is, to plan the paths of drones and trucks. Reasonable path planning can further improve the delivery efficiency and reduce the service cost on the basis of ensuring that drones and trucks can safely complete the delivery tasks of all users. Most existing methods consider the advantages of drone logistics delivery from the perspective of transportation time or transportation cost, but ignore the situation where the introduction of drones affects the purchase cost of delivery tools. However, in reality, the transportation cost is an order of magnitude different from the purchase cost of trucks and drones. The existing methods are still insufficient in reducing the service cost. Therefore, when performing drone-truck joint path planning, the purchase cost and transportation cost should be comprehensively considered to optimize the total cost of the path planning scheme. Summary of the invention

[0004] The technology of the present invention solves the problem: Overcoming the shortcomings of the prior art, providing a multi-UAV-multi-truck collaborative logistics distribution path planning method that comprehensively considers the purchase cost and distribution cost, and obtaining an executable and efficient distribution plan.

[0005] The present invention establishes a mixed integer linear programming model that can characterize the above-mentioned problem, and proposes a two-stage heuristic algorithm framework based on K-Means algorithm, genetic algorithm and variable neighborhood search algorithm, which makes up for the shortcomings of existing task planning models and methods.

[0006] The multi-UAV-multi-truck collaborative logistics distribution path planning provided by the present invention includes the following steps:

[0007] Step 1: Establish a mixed integer linear programming model for the multi-UAV-multi-truck collaborative delivery path planning problem;

[0008] Step 2: Initial planning of truck delivery routes based on K-Means algorithm and genetic algorithm;

[0009] Step 3: Design a path planning search operator, introduce a variable neighborhood search framework based on the truck delivery route to jointly optimize the delivery paths of drones and trucks, and solve the constructed mixed integer linear programming model.

[0010] The step 1 is specifically implemented as follows:

[0011] Step 1: Establish a mixed integer linear programming model for the multi-UAV-multi-truck collaborative delivery path planning problem:

[0012] Step 1.1 Scene setup:

[0013] Assume that the distribution network consists of a warehouse and several customer demand points, recorded as:

[0014] N c ={1,,2,…,n}

[0015] To distinguish between departure and return, the warehouse uses two numbers N0 (N n+1 ), where N0 represents the starting point of distribution, N n+1 It indicates the destination of the delivery;

[0016] Suppose the warehouse can store at most W trucks and U drones.

[0017] Take a single truck and a single drone serving a customer as an example, Figure 1 The drone-truck joint delivery scenario involved in the present invention is that the drone and the truck leave the warehouse together. While the truck is serving customers, the drone can follow the truck to serve together. It can also take off from the truck, carry the goods to serve a single customer, and then land on the truck at another location to complete the battery replacement and cargo loading, and prepare for the next delivery. During the delivery period, a truck can carry multiple drones. After completing the delivery to all customer service points, the truck and drone return to the warehouse.

[0018] Step 1.2 Model Assumptions:

[0019] Based on the definition of the problem scenario in step 1.1, this step makes assumptions before building the model, which are listed as follows:

[0020] 1. Due to the high purchase cost and the multiple delivery tasks after purchase, the purchase cost will be amortized by each delivery task during use. Therefore, when considering the transportation cost of delivery by means of transport, the number of times a truck or drone can be delivered before it is completely aged should be multiplied to make the calculation of transportation cost and purchase cost more reasonable;

[0021] 2. One truck can carry multiple drones, and drones can take off and land on different trucks;

[0022] 3. Trucks have a strong load capacity. It is assumed that trucks carry all the goods to be delivered when they leave the warehouse, and there is no need to restock them midway. The load capacity of drones is relatively weak. Therefore, it is assumed that a single drone can only serve one customer point during a single delivery process, and then needs to return to the truck for restocking;

[0023] 4. The drone can be replaced with a fully charged battery when it returns to the truck, and there are enough fully charged batteries on the truck.

[0024] Step 1.3 Parameter and variable settings:

[0025] In the logistics distribution model, the network mainly consists of warehouses N0(N n+1 ), customer demand node N c = {1,,2,…,n} and arcs between nodes, and the distance between nodes is d ij Represents, where if the truck can travel from node i to node j, then arc (i, j) ∈ A. Similarly, if the drone can travel from node i to node j, then arc (i, j) ∈ B. The delivery task is completed by trucks and drones, where the set of client nodes that can be served by drones is set to N U , the set of feasible paths (i, j, k) of the drone is set to E. In order to calculate the total cost of delivery, the purchase costs of the truck and the drone are set to F W 、F U , the transportation cost per unit distance traveled is C W , C U , a single truck and a single drone can be used T times after purchase, and the longest distance a drone can travel after a single takeoff is D U .

[0026] When designing a distribution plan, if a truck numbered w travels from node i to node j, then x ijw =1, if the drone numbered u travels from node i to node j, then y ijku = 1. Variable mi Records the order in which the i-th client node is accessed, z w 、z u The usage of the w-th truck and the u-th drone in the delivery plan are recorded respectively.

[0027] Step 1.4 Model construction:

[0028] The objective function of the present invention is to minimize the purchase cost and transportation cost required for truck and drone delivery. The purchase cost of the truck can be calculated by multiplying the number of trucks used in delivery by the unit price of the truck; the transportation cost of the truck can be calculated by multiplying the sum of the paths traveled by all trucks during the delivery process by the truck transportation cost per unit distance and then by the number of times it can be delivered before it is completely aged. The same calculation can be performed for drones. Therefore, the objective function of the model is shown in formula (1):

[0029]

[0030] In the overall distribution process, each truck must start from the warehouse and eventually return to the warehouse after completing the delivery task. It will only stop temporarily at the customer demand point, thus satisfying the flow balance constraint shown in formula (2):

[0031]

[0032] Due to the rationality of delivery, the truck will not wait for the drone to complete the delivery and return at the same customer point before going to the next customer point that needs to be delivered. Therefore, the same drone is limited to take off or land only once at each take-off and landing point, that is:

[0033]

[0034]

[0035] In the actual delivery process, a customer point is often only delivered by a truck or drone, without the need to split the goods between trucks and drones for separate delivery. Therefore, each demand point will only be visited once by a truck or drone, resulting in the following constraints:

[0036]

[0037] According to the model assumptions, drones can only take off and land on trucks. Therefore, if a drone takes off from customer i, serves customer j, and lands at point k, a truck must pass through i and k to meet the drone:

[0038]

[0039] Since the number of dispatched trucks and drones is required to calculate the total cost of dispatching trucks and drones in path planning, it is necessary to calculate z w and z u Two variables are constrained, where z w The constraints are as follows:

[0040]

[0041]

[0042] It can be seen from the above formula that constraints (7)-(8) determine the dispatch status of each truck. If the w-th truck does not serve any customer during the delivery process, then ∑ (i,j)∈A x ijw -1=0, constraint (7) makes z w =0; if it serves the customer, then ∑ (i,j)∈A x ijw -1≥1, constraint (8) makes z w = 1. For z u We can also create two constraints in the same way:

[0043]

[0044]

[0045] The path planning based on the current model may cause the truck to form a loop between customer points, so constraints need to be added to avoid this situation. The constraints are as follows:

[0046]

[0047]

[0048] For constraint (11), if the drone takes off from customer i, serves customer j, and lands at customer k, then m k -m i ≥1, the truck visits customer i and then customer k; if the drone has no take-off and landing process at customer i and customer k, then m k -m i ≥1-(n+2)=-n-1, n is the total number of customer points, that is, there is no special restriction on the access order of customer i and customer k.

[0049] Constraint (12) restricts trucks from traveling in a loop between customer points. If a path exists for truck w to travel from i to j, the value on the right side of the inequality is 0, and m i -m j+1≤0, customer i must be visited before customer j, which prevents trucks from traveling between customer points in a loop.

[0050] The drone is powered by batteries and has a power limit. Therefore, each drone has an upper limit on its single flight distance. From the time the drone takes off from the truck to the time it returns to the truck after delivery, the mileage of the drone cannot exceed this limit, that is:

[0051]

[0052] For an integer variable m i , which represents the order in which the i-th node is visited by the truck, namely:

[0053]

[0054] In addition, the 0-1 variable constraints in the model are as follows:

[0055]

[0056]

[0057]

[0058]

[0059] So far, a mixed integer linear programming model for the multi-UAV-multi-truck collaborative delivery path planning problem has been established.

[0060] Step 2: Initial planning of truck delivery routes based on K-Means algorithm and genetic algorithm:

[0061] In the present invention, the take-off and landing of the drone are all completed on the truck, that is, the flight path of the drone is generated on the path of the truck, so this step will generate a route for delivery only by trucks.

[0062] Step 2.1 K-Means algorithm realizes clustering of customer demand points according to spatial distribution:

[0063] In order to minimize the driving cost of the truck, this paper uses the K-Means algorithm to cluster customer points according to the spatial location distribution of customer demand points. This preprocessing is also helpful in reducing the time complexity of subsequent calculations.

[0064] Step 2.2 Generate a single truck delivery route based on genetic algorithm:

[0065] Based on the cluster labels assigned to each customer node in step 2.1, customers with the same label are delivered by the same truck. In this step, a genetic algorithm is used to plan the delivery route for each truck, making the truck's delivery route the shortest and the truck's transportation cost the lowest during the delivery process.

[0066] At this point, the path planning solution for delivery using only trucks required in the present invention has been established.

[0067] Step 3: Design a path planning search operator, introduce a variable neighborhood search framework based on the truck delivery route to jointly optimize the delivery paths of the drone and the truck, and solve the constructed mixed integer linear programming model:

[0068] After obtaining the initial feasible truck route, the variable neighborhood search algorithm (VNS) can be used to generate the multi-drone-multi-truck joint delivery path based on the truck delivery path. The present invention designs four neighborhood search operators to obtain the optimal solution of the joint delivery path. At the beginning of the algorithm, the first operator is repeatedly executed on the initial solution until the local optimal solution under the first operator is obtained, and then the second operator is executed. When a new optimal solution is found, it returns and executes the first operator again, and so on. The specific contents of the four operators are introduced below.

[0069] Step 3.1 UAV service customer point selection operator:

[0070] The goal of executing this operator is to convert as many customers who were originally delivered by trucks to drones as possible while reducing the total cost. When the operator is executed, it will detect the customer demand points served by each truck in turn. First, it will determine whether it can be served by drones, that is, whether the customer point is within the range of the drone's flight range and whether the required cargo weight is lower than the drone's load limit. If the customer is determined to meet the requirements, a feasible take-off and landing point will be assigned to the drone serving the customer point, and it will be calculated whether the customer point is better than the original solution after using drone delivery. If a new optimal solution is obtained, the customer point will be determined as the customer point served by the drone, and the previously set take-off and landing point will be used. It should be noted that customers who have been assigned to a drone service cannot be selected again. This operator is called multiple times at the beginning of the algorithm, so as to greedily generate solutions for joint delivery by drones and trucks.

[0071] Step 3.2 UAV take-off and landing point selection operator:

[0072] The new plan obtained by the above-mentioned operator only needs the delivery cost to be better than the initial cost to determine the take-off and landing points of the drone. Therefore, it cannot ensure that the current delivery plan is the global optimal solution. This operator will re-search the drone take-off and landing points for the drone service customer points based on the current truck delivery route. If the total delivery cost can be reduced again without changing the truck route, it will return to use the first operator again to optimize the current solution, and finally achieve the local optimal solution in the second neighborhood, and then execute the third operator.

[0073] Step 3.3 The drone customer clicks to put back the operator:

[0074] Since the greedy algorithm is used in the first operator to search for drone customer points, it is easy to fall into the local optimum, and after optimizing the take-off and landing points, it is impossible to determine which transportation tool is relatively better for the customer point to complete the delivery. Therefore, in this operator, each customer point delivered by drone needs to be reset to be delivered by truck, and it is evaluated whether the optimal solution at this time has been updated. If a better result is obtained, the point is converted into a node for truck delivery, and the first operator is returned to restart the neighborhood search.

[0075] Step 3.4 Truck visit order exchange operator:

[0076] Since the genetic algorithm is also a heuristic algorithm, it can only approximate the optimal solution but cannot guarantee that it will obtain the optimal solution. Therefore, the feasible solution obtained after the initial solution of the variable neighborhood search is solved by the above three operators is the upper bound of the current local optimal solution. In the fourth operator, the order of visits of any two customers served by the truck in the current truck delivery path is randomly exchanged, the total costs before and after the exchange are compared, and it is explored whether a new optimal solution can be found, so as to further approach the current local optimal solution.

[0077] Step 3.5: Perturbation function (Shake) operator:

[0078] The above four neighborhood search operators can get the local optimal solution of the current "drone-truck" joint delivery path planning. At this time, the Shake function needs to be used to jump out of the local optimal solution. The specific operation method is to randomly disrupt the order of all customers being visited while keeping the number of customers served by trucks and drones unchanged. Then re-plan the truck and drone delivery routes between all customers. After obtaining the new solution, the above four operators are used to obtain a new local optimal solution.

[0079] At this point, a satisfactory and required multi-UAV-multi-truck collaborative logistics distribution path planning scheme has been obtained.

[0080] The advantages and beneficial effects of the present invention are:

[0081] (1) This invention aims at the problem of multi-UAV-multi-truck collaborative logistics distribution path planning, establishes a combined optimization model that can accurately characterize the problem, takes into account a variety of practical factors, and makes the established model closer to the actual situation and has practical application value;

[0082] (2) The present invention proposes a two-stage heuristic algorithm framework based on K-Means algorithm, genetic algorithm and variable neighborhood search algorithm to effectively solve the above-mentioned multi-UAV-multi-truck collaborative logistics distribution path planning problem, and obtains a practical distribution plan. In the plan, the UAVs and trucks coordinate and carry out the distribution task in an orderly manner, and the overall distribution task is completed efficiently.

[0083] (3) The multi-drone-multi-truck collaborative logistics distribution path planning method proposed in this invention takes into account the purchase cost and transportation cost, which reduces the distribution cost and improves the distribution speed compared with the traditional distribution method. At the same time, considering the purchase cost, the logistics company can more reasonably purchase and retain the required number of drones and trucks. At the same time, with the further development of drone technology and the further reduction of unit distance transportation cost in the future, the transportation cost of drone delivery may be lower, and the advantages of drone logistics will be further highlighted. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 Schematic diagram of the multi-UAV-multi-truck collaborative logistics distribution path planning method of the present invention;

[0085] Figure 2 This is a flowchart of the multi-UAV-multi-truck collaborative logistics distribution path planning method of the present invention;

[0086] Figure 3 This is a schematic diagram of the K-Means algorithm flow chart of step 2 of a specific implementation example of the present invention;

[0087] Figure 4 This is a schematic diagram of a genetic algorithm flow chart of step 2 of a specific implementation example of the present invention;

[0088] Figure 5 It is a flowchart of step three of the specific implementation example of the present invention. DETAILED DESCRIPTION

[0089] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0090] The method provided by the present invention comprehensively considers the purchase cost and transportation cost of drones and trucks, reasonably allocates the number of drones and trucks, optimizes the distribution plan, and makes up for the shortcomings of the existing models and methods for drone-truck joint distribution problems.

[0091] like Figure 2 As shown, the implementation mode of the present invention is as follows:

[0092] Step 1: Establish a mixed integer linear programming model for the multi-UAV-multi-truck collaborative delivery path planning problem:

[0093] Step 1.1 Scene setup:

[0094] Assume that the distribution network consists of a warehouse and several customer demand points, recorded as:

[0095] N c ={1,,2,…,n}

[0096] To distinguish between departure and return, the warehouse uses two numbers N0 (N n+1 ), where N0 represents the starting point of distribution, N n+1 It indicates the destination of the delivery;

[0097] Suppose the warehouse can store at most W trucks and U drones.

[0098] Take a single truck and a single drone serving a customer as an example, Figure 1 The drone-truck joint delivery scenario involved in the present invention is that the drone and the truck leave the warehouse together. While the truck is serving customers, the drone can follow the truck to serve together. It can also take off from the truck, carry the goods to serve a single customer, and then land on the truck at another location to complete the battery replacement and cargo loading, and prepare for the next delivery. During the delivery period, a truck can carry multiple drones. After completing the delivery to all customer service points, the truck and drone return to the warehouse.

[0099] Step 1.2 Model Assumptions:

[0100] Based on the definition of the problem scenario in step 1.1, this step makes assumptions before building the model, which are listed as follows:

[0101] 5. Due to the high purchase cost and the fact that the vehicle will be used to complete multiple delivery tasks, the purchase cost will be amortized by each delivery task during use. Therefore, when considering the transportation cost of the vehicle, the number of times a truck or drone can be used for delivery before it is completely aged should be multiplied to make the calculation of transportation cost and purchase cost more reasonable;

[0102] 6. One truck can carry multiple drones, and drones can take off and land on different trucks;

[0103] 7. Trucks have a strong load capacity. It is assumed that trucks carry all the goods to be delivered when they leave the warehouse, and no restocking is required. UAVs have a weaker load capacity. Therefore, it is assumed that a single drone can only serve one customer point during a single delivery process, and then needs to return to the truck for restocking;

[0104] 8. The drone can be replaced with a fully charged battery when it returns to the truck, and there are enough fully charged batteries on the truck.

[0105] Step 1.3 Parameter and variable settings:

[0106] In the logistics distribution model, the network mainly consists of warehouses N0(N n+1 ), customer demand node N c = {1,,2,…,n} and arcs between nodes, and the distance between nodes is d ij Represents, where if the truck can travel from node i to node j, then arc (i, j) ∈ A. Similarly, if the drone can travel from node i to node j, then arc (i, j) ∈ B. The delivery task is completed by trucks and drones, where the set of client nodes that can be served by drones is set to N U , the set of feasible paths (i, j, k) of the drone is set to E. In order to calculate the total cost of delivery, the purchase costs of the truck and the drone are set to F W 、F U , the transportation cost per unit distance traveled is C W , C U , a single truck and a single drone can be used T times after purchase, and the longest distance a drone can travel after a single takeoff is D U .

[0107] The key elements and parameters required to build the model are shown in Table 1:

[0108] Table 1 Collections and parameters in the model

[0109]

[0110] When designing a distribution plan, if a truck numbered w travels from node i to node j, then x ijw =1, if the drone numbered u travels from node i to node j, then y ijku = 1. Variable m i Records the order in which the i-th client node is accessed, z w 、z u The usage of the w-th truck and the u-th drone in the delivery plan are recorded respectively. Table 2 shows all the variables involved in the model.

[0111] Table 2 Variables in the model

[0112]

[0113] Step 1.4 Model construction:

[0114] The objective function of this model is to minimize the purchase cost and transportation cost required for truck and drone delivery. The purchase cost of the truck can be calculated by multiplying the number of trucks used in delivery by the unit price of the truck; the transportation cost of the truck can be calculated by multiplying the sum of the paths traveled by all trucks during the delivery process by the truck transportation cost per unit distance and then by the number of deliveries that can be made before it is completely aged. The same calculation can be performed for drones. Therefore, the objective function of the model is shown in formula (1):

[0115]

[0116] In the overall distribution process, each truck must start from the warehouse and eventually return to the warehouse after completing the delivery task. It will only stop temporarily at the customer demand point, thus satisfying the flow balance constraint shown in formula (2):

[0117]

[0118] Due to the rationality of delivery, the truck will not wait for the drone to complete the delivery and return at the same customer point before going to the next customer point that needs to be delivered. Therefore, the same drone is limited to take off or land only once at each take-off and landing point, that is:

[0119]

[0120]

[0121] In the actual delivery process, a customer point is often only delivered by a truck or drone, without the need to split the goods between trucks and drones for separate delivery. Therefore, each demand point will only be visited once by a truck or drone, resulting in the following constraints:

[0122]

[0123] According to the model assumptions, drones can only take off and land on trucks. Therefore, if a drone takes off from customer i, serves customer j, and lands at point k, a truck must pass through i and k to meet the drone:

[0124]

[0125] Since the number of dispatched trucks and drones is required to calculate the total cost of dispatching trucks and drones in path planning, it is necessary to calculate z w and z u Two variables are constrained, where z w The constraints are as follows:

[0126]

[0127]

[0128] It can be seen from the above formula that constraints (7)-(8) determine the dispatch status of each truck. If the w-th truck does not serve any customer during the delivery process, then ∑ (i，j)∈A x ijw -1=0, constraint (7) makes z w =0; if it serves the customer, then ∑ (i，j)∈A x ijw -1≥1, constraint (8) makes z w = 1. For z u We can also create two constraints in the same way:

[0129]

[0130]

[0131] The path planning based on the current model may cause the truck to form a loop between customer points, so constraints need to be added to avoid this situation. The constraints are as follows:

[0132]

[0133]

[0134] For constraint (11), if the drone takes off from customer i, serves customer j, and lands at customer k, then m k -m i ≥1, the truck visits customer i and then customer k; if the drone has no take-off and landing process at customer i and customer k, then m k -m i ≥1-(n+2)=-n-1, n is the total number of customer points, that is, there is no special restriction on the access order of customer i and customer k.

[0135] Constraint (12) restricts trucks from traveling in a loop between customer points. If a path exists for truck w to travel from i to j, the value on the right side of the inequality is 0, and m i -m j +1≤0, customer i must be visited before customer j, which prevents trucks from traveling between customer points in a loop.

[0136] The drone is powered by batteries and has a power limit. Therefore, each drone has an upper limit on its single flight distance. From the time the drone takes off from the truck to the time it returns to the truck after delivery, the mileage of the drone cannot exceed this limit, that is:

[0137]

[0138] For an integer variable m i , which represents the order in which the i-th node is visited by the truck, namely:

[0139]

[0140] In addition, the 0-1 variable constraints in the model are as follows:

[0141]

[0142]

[0143]

[0144]

[0145] So far, a mixed integer linear programming model for the multi-UAV-multi-truck collaborative delivery path planning problem has been established.

[0146] Step 2: Initial planning of truck delivery routes based on K-Means algorithm and genetic algorithm:

[0147] In the present invention, the take-off and landing of the drone are all completed on the truck, that is, the flight path of the drone is generated on the path of the truck, so this step will generate a route for delivery only by trucks.

[0148] Step 2.1 K-Means algorithm realizes clustering of customer demand points according to spatial distribution:

[0149] In order to minimize the driving cost of the truck, this paper uses the K-Means algorithm to cluster customer points according to the spatial location distribution of customer demand points. This preprocessing is also helpful in reducing the time complexity of subsequent calculations. The K-Means algorithm flow chart is as follows Figure 3 As shown in the figure, assuming that the number of dispatched vehicles is w, the algorithm flow for clustering customer demand points is as follows:

[0150] Step 1 Randomly specify w points as the centers of the clusters;

[0151] Step 2: Allocate customer demand points to the center they are closest to;

[0152] Step 3: Calculate the average location of customer demand points of w clusters as the new cluster center point;

[0153] Step 4 determines whether the termination condition is met. If so, return to Step 2, otherwise the algorithm ends.

[0154] Step 2.2 Generate a single truck delivery route based on genetic algorithm:

[0155] Based on the cluster labels assigned to each customer node in step 2.1, customers with the same label are delivered by the same truck. In this step, a genetic algorithm is used to plan the delivery route for each truck, making the truck's delivery route the shortest and the truck's transportation cost the lowest during the delivery process. The genetic algorithm flow chart is as follows: Figure 4 As shown, the process is described as follows:

[0156] Step 1 Randomly generate q path planning solutions as the initial solution set p * , that is, the initial population of the genetic algorithm, and set the genetic generation number a, crossover probability b and mutation probability c in the algorithm;

[0157] Step 2 Calculate the truck delivery cost of all solutions in the current solution set. The lower the cost, the higher the fitness, and find the optimal solution s in the solution set. * , whose cost is f * , and preserve it to the next generation of population;

[0158] Step 3 Use the roulette method to determine the q individuals in the new population p;

[0159] Step 4: Determine whether each individual in the new population crosses over according to the crossover probability b. If so, randomly generate a crossover point, exchange the routes after the crossover point, and generate a new population.

[0160] Step 5: Determine whether each individual in the new population mutates according to the mutation probability c. If it mutates, randomly select two customer demand points, exchange their access order, and generate a new population p.

[0161] Step 6 Calculate the truck delivery cost of all solutions for the new population p and find the optimal solution s in the solution set, whose cost is f. If f <f * , then the optimal solution s is retained to the next generation population, and s * =s,f * =f, otherwise, s * With f * constant;

[0162] Step 7 determines whether the genetic generation has reached a. If not, return to Step 3; if it has, end the algorithm.

[0163] Step 8 The final truck single delivery route solution is s * .

[0164] At this point, the path planning solution for delivery using only trucks required in the present invention has been established.

[0165] Step 3: Design a path planning search operator, introduce a variable neighborhood search framework based on the truck delivery route to jointly optimize the delivery paths of drones and trucks, and solve the constructed mixed integer linear programming model:

[0166] After obtaining the initial feasible truck route, the variable neighborhood search algorithm (VNS) can be used to generate the multi-drone-multi-truck joint delivery path based on the truck delivery path. The present invention designs four neighborhood search operators to obtain the optimal solution of the joint delivery path. At the beginning of the algorithm, the first operator is repeatedly executed on the initial solution until the local optimal solution under the first operator is obtained, and then the second operator is executed. When a new optimal solution is found, it returns and executes the first operator again, and so on. The overall process of step three is as follows Figure 5 As shown in the figure, the specific contents of the four operators are introduced below.

[0167] Step 3.1 UAV service customer point selection operator:

[0168] The goal of executing this operator is to convert as many customers who were originally delivered by trucks to drones as possible while reducing the total cost. When the operator is executed, it will detect the customer demand points served by each truck in turn. First, it will determine whether it can be served by drones, that is, whether the customer point is within the range of the drone's flight range and whether the required cargo weight is lower than the drone's load limit. If the customer is determined to meet the requirements, a feasible take-off and landing point will be assigned to the drone serving the customer point, and it will be calculated whether the customer point is better than the original solution after using drone delivery. If a new optimal solution is obtained, the customer point will be determined as the customer point served by the drone, and the previously set take-off and landing point will be used. It should be noted that customers who have been assigned to a drone service cannot be selected again. This operator is called multiple times at the beginning of the algorithm, so as to greedily generate solutions for joint delivery by drones and trucks.

[0169] Step 3.2 UAV take-off and landing point selection operator:

[0170] The new plan obtained by the above-mentioned operator only needs the delivery cost to be better than the initial cost to determine the take-off and landing points of the drone. Therefore, it cannot ensure that the current delivery plan is the global optimal solution. This operator will re-search the drone take-off and landing points for the drone service customer points based on the current truck delivery route. If the total delivery cost can be reduced again without changing the truck route, it will return to use the first operator again to optimize the current solution, and finally achieve the local optimal solution in the second neighborhood, and then execute the third operator.

[0171] Step 3.3 The drone customer clicks to put back the operator:

[0172] Since the greedy algorithm is used in the first operator to search for drone customer points, it is easy to fall into the local optimum, and after optimizing the take-off and landing points, it is impossible to determine which transportation tool is relatively better for the customer point to complete the delivery. Therefore, in this operator, each customer point delivered by drone needs to be reset to be delivered by truck, and it is evaluated whether the optimal solution at this time has been updated. If a better result is obtained, the point is converted into a node for truck delivery, and the first operator is returned to restart the neighborhood search.

[0173] Step 3.4 Truck visit order exchange operator:

[0174] Since the genetic algorithm is also a heuristic algorithm, it can only approximate the optimal solution but cannot guarantee that it will obtain the optimal solution. Therefore, the feasible solution obtained after the initial solution of the variable neighborhood search is solved by the above three operators is the upper bound of the current local optimal solution. In the fourth operator, the order of visits of any two customers served by the truck in the current truck delivery path is randomly exchanged, the total costs before and after the exchange are compared, and it is explored whether a new optimal solution can be found, so as to further approach the current local optimal solution.

[0175] Step 3.5: Perturbation function (Shake) operator:

[0176] The above four neighborhood search operators can get the local optimal solution of the current "drone-truck" joint delivery path planning. At this time, the Shake function needs to be used to jump out of the local optimal solution. The specific operation method is to randomly disrupt the order of all customers being visited while keeping the number of customers served by trucks and drones unchanged. Then re-plan the truck and drone delivery routes between all customers. After obtaining the new solution, the above four operators are used to obtain a new local optimal solution.

[0177] Specifically, after determining the operation of each operator, the corresponding algorithm steps are described as follows:

[0178] Step 1: Set the maximum number of neighbors in the algorithm N = 4, the maximum number of iterations K, and record the current optimal solution s * , the cost value is f * ;

[0179] Step 2 uses the variable neighborhood descent search algorithm and four neighborhood search operators to obtain the current local optimal solution s and the cost f of the optimal solution;

[0180] Step 3 Compare f * and the value of f, if f <f * , then let s * =s,f * =f;

[0181] Step 4: Determine whether the number of iterations reaches K. If so, terminate the algorithm and obtain the optimal solution s. * , the minimum cost is f * , otherwise continue to Step 5;

[0182] Step 5 obtains a new solution through the Shake function and returns to Step 2.

[0183] At this point, a satisfactory and required multi-UAV-multi-truck collaborative logistics distribution path planning scheme has been obtained.

[0184] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned implementation examples, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the implementation examples of the present invention.

Claims

1. A multi-UAV-multi-truck collaborative logistics distribution path planning method, characterized in that: The following steps are involved: Step 1: Establish a mixed integer linear programming model for multi-UAV-multi-truck collaborative logistics distribution path planning problem; Step 2: Initial planning of truck delivery routes based on K-Means algorithm and genetic algorithm; Step 3: Design a path planning search operator, introduce a variable neighborhood search framework based on the truck delivery route to jointly optimize the delivery paths of drones and trucks, and solve the constructed mixed integer linear programming model; The step 1 is specifically implemented as follows: Step 1.1 Scene setup: Assume that the distribution network consists of a warehouse and several customer demand points, recorded as: N C ={1,,2,...,n} To distinguish between departure and return, the warehouse uses two numbers N0 (N n+1 ), where N0 represents the starting point of distribution, N n+1 It indicates the destination of the delivery; Assume that the warehouse can store at most W trucks and U drones; Step 1.2 Model definition: Based on the definition of the problem scenario in step 1.1, define the following before building the model: 1) When considering the transportation costs of delivery by transport, multiply the number of times a truck or drone will make deliveries before it becomes completely obsolete to make the transportation and acquisition costs reasonable; 2) One truck can carry multiple drones, and the drones take off and land on different trucks; 3) The truck carries all the goods to be delivered when it leaves the warehouse, and there is no need to restock during the journey. A single drone can only serve one customer point during a single delivery process, and then needs to return to the truck for restocking; 4) The drone can be replaced with a fully charged battery when it returns to the truck, and there are spare batteries on the truck; Step 1.3 Parameter and variable settings: In the logistics distribution model, the network consists of warehouses N0(N n+1 ), customer demand node N c = {1,,2,…,n} and arcs between nodes, and the distance between nodes is d ij Represented as follows: If a truck travels from node i to node j, then arc (i, j) ∈ A; if a drone travels from node i to node j, then arc (i, j) ∈ B; the delivery task is completed by trucks and drones, where the set of client nodes served by the drone is set to N U , the set of feasible paths (i, j, k) of the drone is set to E; the purchase costs of the truck and the drone are set to F W 、F U , the transportation cost per unit distance traveled is C W , C U , a single truck and a single drone can be used T times after purchase, and the longest distance a drone can travel after a single takeoff is D U ; When designing a distribution plan, if a truck numbered w travels from node i to node j, then x ijw =1, if the drone numbered u travels from node i to node j, then y ijku =1; variable m i Records the order in which the i-th client node is accessed, z w 、z u The usage of the w-th truck and the u-th drone in the delivery plan are recorded respectively; Step 1.4 Model construction: The objective function of the model is to minimize the purchase cost and transportation cost required for truck and drone delivery. The purchase cost of the truck can be calculated by multiplying the number of trucks used in delivery by the unit price of the truck. The transportation cost of the truck is calculated by multiplying the sum of the paths traveled by all trucks during the delivery process by the truck transportation cost per unit distance and then by the number of deliveries that can be made before it is completely aged, thereby establishing the objective function. In the overall distribution process, each truck must start from the warehouse and eventually return to the warehouse after completing the delivery task. It will only stop temporarily at the customer demand point, thus satisfying the flow balance constraint shown in formula (2): Limit the same drone to take off or land only once at each take-off and landing point, that is: In the actual delivery process, a customer point is often only delivered by a truck or a drone, without the need to split the goods between trucks and drones for separate delivery. Therefore, each demand point will only be visited once by a truck or a drone, resulting in the following constraints: According to the model assumptions, drones can only take off and land on trucks. Therefore, if a drone takes off from customer i, serves customer j, and lands at point k, a truck must pass through i and k to meet the drone: Since the number of dispatched trucks and drones is required to calculate the total cost of dispatching trucks and drones in path planning, w and z u Two variables are constrained, where z w The constraints are as follows: Constraints (7)-(8) determine the dispatch status of each truck. If the wth truck does not serve any customer during the delivery process, then Σ (i,j)∈A x ijw -1=0, constraint (7) makes z w =0; if the customer is served, then Σ (i,j)∈A x ijw -1≥1, constraint (8) makes z w =1; for z u In the same way, we create two constraints: The path planning based on the current model may cause the truck to form a loop between customer points, so constraints need to be added to avoid this situation. The constraints are as follows: For constraint (11), if the drone takes off from customer i, serves customer j, and lands at customer k, then The truck visits customer i and then customer k; if the drone has no take-off and landing process at customer i and customer k, then m k -m i ≥1-(n+2)=-n-1, n is the total number of customer points, that is, there is no special restriction on the access order of customer i and customer k; Constraint (12) restricts trucks from traveling in a loop between customer points. If a path exists for truck w to travel from i to j, the value on the right side of the inequality is 0, and m i -m j +1≤0, customer i must be visited before customer j to avoid trucks traveling between customer points in a loop; The drone is powered by batteries and has a power limit. Therefore, each drone has an upper limit on its single flight distance. From the time the drone takes off from the truck to the time it returns to the truck after delivery, the mileage of the drone cannot exceed this limit, that is: For an integer variable m i , which represents the order in which the i-th node is visited by the truck, namely: In addition, the 0-1 variable constraints in the model are as follows:

2. The multi-UAV-multi-truck collaborative logistics distribution path planning method according to claim 1 is characterized by: The step 2 is specifically implemented as follows: Step 2.1 K-Means algorithm realizes clustering of customer demand points according to spatial distribution: Cluster customer points according to the spatial location distribution of customer demand points using the K-Means algorithm; Step 2.2 Generate a single truck delivery route based on genetic algorithm: Based on the clustering label assigned to each customer node in step 2.1, customers with the same label are delivered by the same truck; a genetic algorithm is used to plan the delivery route for each truck, making the truck's delivery route the shortest and the truck's transportation cost the lowest during the delivery process.

3. The multi-UAV-multi-truck collaborative logistics distribution path planning method according to claim 1 is characterized by: The step three is specifically implemented as follows: Step 3.1 UAV service customer point selection operator: The goal of executing this operator is to convert customers who were originally delivered by trucks to those delivered by drones under the premise of reducing the total cost. When the operator is executed, it will detect the customer demand points served by each truck in turn, and first determine whether it can be served by drones, that is, whether the customer point is within the range of the drone's cruising range and whether the required cargo weight is lower than the drone's load limit. If it is determined that the customer meets the requirements, a feasible take-off and landing point will be specified for the drone serving the customer point, and it will be calculated whether the solution after using drone delivery for the customer point is better than the original solution. If a new optimal solution is obtained, the customer point will be determined as the customer point served by the drone, and the previously set take-off and landing point will be used. Step 3.2 UAV take-off and landing point selection operator: The drone take-off and landing point selection operator will re-search the drone take-off and landing points for the drone service customer points based on the current truck delivery route. If the total delivery cost is reduced again without changing the truck route, it will return to optimize the current solution using the first operator again, and finally reach the local optimal solution in the second neighborhood, and then execute the drone customer point return operator; Step 3.3 The drone customer clicks to put back the operator: Reset each customer point delivered by drone to one delivered by truck, and evaluate whether the optimal solution at this time has been updated. If a better result is obtained, convert it to a node delivered by truck, return to the drone service customer point selection operator, and restart the neighborhood search; Step 3.4 Truck visit order exchange operator: The feasible solution obtained by the above three operators after the initial solution of the variable neighborhood search is the upper bound of the current local optimal solution. In the truck visit order exchange operator, the order of visits of any two customers served by the truck in the current truck delivery path is randomly exchanged, and the total cost before and after the exchange is compared. It is also explored whether a new optimal solution can be found, thereby approaching the current local optimal solution. Step 3.5 Perturbation function operator: The above four neighborhood search operators are used to obtain the local optimal solution for the current "drone-truck" joint delivery path planning. At this time, the Shake function needs to be used to jump out of the local optimum. The specific operation method is to randomly disrupt the order of visiting all customers while keeping the number of customers served by trucks and drones unchanged; then re-plan the truck and drone delivery routes between all customers; after obtaining the new solution, the above four operators are used to obtain a new local optimal solution.

4. The multi-UAV-multi-truck collaborative logistics distribution path planning method according to claim 1 is characterized by: When designing a distribution plan, if a truck numbered w travels from node i to node j, then x ijw =1, if the drone numbered u travels from node i to node j, then y ijku =1; variable m i Records the order in which the i-th client node is accessed, z w 、z u The usage of the w-th truck and the u-th drone in the delivery plan are recorded respectively; The K-Means algorithm is used to cluster customer points according to their spatial location distribution. Preprocessing is also helpful in reducing the time complexity of subsequent calculations. Assuming that the number of dispatched vehicles is w, the algorithm flow for clustering customer demand points is as follows: Step 1 Randomly specify w points as the centers of the clusters; Step 2: Allocate customer demand points to the center they are closest to; Step 3: Calculate the average location of customer demand points of w clusters as the new cluster center point; Step 4 determines whether the termination condition is met. If so, return to Step 2, otherwise the algorithm ends.

5. The multi-UAV-multi-truck collaborative logistics distribution path planning method according to claim 2 is characterized by: Step 2.2 Generate a single truck delivery route based on genetic algorithm: Based on the clustering labels assigned to each customer node in step 2.1, customers with the same label are delivered by the same truck; a genetic algorithm is used to plan the delivery route for each truck, so that the truck's delivery route is the shortest and the truck's transportation cost during the delivery process is the lowest; the genetic algorithm process is as follows: Step 1 Randomly generate q path planning solutions as the initial solution set p * , that is, the initial population of the genetic algorithm, and set the genetic generation number a, crossover probability b and mutation probability c in the algorithm; Step 2 Calculate the truck delivery cost of all solutions in the current solution set. The lower the cost, the higher the fitness, and find the optimal solution s in the solution set. * , whose cost is f * , and preserve it to the next generation of population; Step 3 Use the roulette method to determine the q individuals in the new population p; Step 4: Determine whether each individual in the new population crosses over according to the crossover probability b. If so, randomly generate a crossover point, exchange the routes after the crossover point, and generate a new population. Step 5: Determine whether each individual in the new population mutates according to the mutation probability c. If it mutates, randomly select two customer demand points, exchange their access order, and generate a new population p. Step 6 Calculate the truck delivery cost of all solutions for the new population p and find the optimal solution s in the solution set, whose cost is f. If f <f * , then the optimal solution s is retained to the next generation population, and s * =s,f * =f, otherwise, s * With f * constant; Step 7 determines whether the genetic generation has reached a. If not, return to Step 3; if it has, end the algorithm. Step 8 The final truck single delivery route solution is s * ; At this point, the required routing plan for delivery using only trucks is established.

6. The multi-UAV-multi-truck collaborative logistics distribution path planning method according to claim 3 is characterized by: After determining the operation of each operator, the corresponding algorithm steps are described as follows: Step 1: Set the maximum number of neighbors in the algorithm N = 4, the maximum number of iterations K, and record the current optimal solution s * , the cost value is f * ; Step 2 uses the variable neighborhood descent search algorithm and four neighborhood search operators to obtain the current local optimal solution s and the cost f of the optimal solution; Step 3 Compare f * and the value of f, if f <f * , then let s * =s,f * =f; Step 4: Determine whether the number of iterations reaches K. If so, terminate the algorithm and obtain the optimal solution s. * , the minimum cost is f * , otherwise continue to Step 5; Step 5: Get a new solution through the Shake function and return to Step 2; At this point, the required multi-UAV-multi-truck collaborative logistics distribution path planning solution that meets the conditions is obtained.

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