A collaborative path planning method for vehicles and drones considering 3D loading constraints

Abstract

This invention discloses a vehicle-UAV collaborative path planning method considering three-dimensional loading constraints, including: employing two unloading modes: "first-in, last-out" and "unloading before loading." The "first-in, last-out" mode means that only goods located on the outermost layer of the vehicle can be delivered at a time, while the "unloading before loading" mode allows delivery of goods located on the inner layers of the vehicle. A mixed-integer linear programming model is constructed, including decision variables and auxiliary variables, optimization objectives, and constraints. A highly efficient hybrid metaheuristic solution method is designed to solve for the loading and delivery schemes. This invention is applied to the field of collaborative path planning, simultaneously considering the loading and delivery processes of goods. By employing the common "first-in, last-out" and "unloading before loading" modes in logistics delivery, it optimizes the main path of the delivery vehicle and the path of the UAV, significantly improving logistics delivery efficiency while meeting customer needs.

Description

Technical Field

[0001] This invention relates to the field of collaborative path planning technology, specifically a collaborative path planning method for vehicles and unmanned aerial vehicles that considers three-dimensional loading constraints. Background Technology

[0002] Modern logistics and distribution face a range of challenges, including the complex issue of simultaneously planning the loading and delivery of goods. Logistics companies must address these issues to efficiently deliver products from factories or distribution centers to customers. Loading and delivery are two critical phases in logistics and distribution. The loading phase requires consideration of the size, weight, characteristics, and loading sequence of the goods to facilitate subsequent unloading operations. The delivery phase requires determining the optimal routes so that delivery vehicles can effectively reach multiple customers and fulfill all order demands while minimizing delivery time.

[0003] In the field of logistics and delivery, unmanned aerial vehicles (UAVs) have shown great application opportunities due to their high efficiency and low cost, and have gradually become a new research hotspot. However, although scholars have proposed better methods for multi-UAV collaborative delivery, the limited endurance of UAVs makes it difficult to complete large-scale and long-distance delivery tasks.

[0004] The collaborative reconnaissance approach using vehicles and drones can compensate for the shortcomings of using drones alone, and has become a more popular research direction in recent years. Classic examples of this type of problem include the Flying Sidekick Traveling Salesman Problem (FSTSP) and the Traveling Salesman Problem with Drone (TSP-D).

[0005] In the Flying Assistant Traveling Salesman Problem (FSTSP), assuming a delivery drone leaves a vehicle, completes a delivery task, and then immediately returns, the problem is described using Mixed Integer Linear Programming (MILP). A heuristic method is proposed for solving the problem, and the proposed model and algorithm are evaluated and validated through a series of computational experiments. The heuristic algorithm first solves the TSP path of the vehicle based on all customer points, and then assigns each eligible customer to the drone's path or reassigns them to another location on the vehicle's path. In the Traveling Salesman Problem with Drones (TSP-D), unlike FTSSP, the drone can return to the node from which it was launched, and a novel mixed-integer programming model and corresponding heuristic algorithm are provided.

[0006] Considering the coordination between loading and delivery in logistics activities, the problem of simultaneously handling routing and loading / packaging has been extensively studied in many variations in recent years. In these problems, routing is only effective when certain loading constraints are met, and these can be classified as two-dimensional (2D) or three-dimensional (3D) loading constraints, depending on whether items can be stacked on top of other items. However, current research on logistics delivery separates the problem of vehicle loading and delivery from the problem of vehicle-drone collaboration, lacking real-world relevance. Summary of the Invention

[0007] To address the shortcomings of the existing technology, this invention provides a vehicle-UAV collaborative path planning method that considers three-dimensional loading constraints, taking into account both the loading and delivery process of goods, which can significantly improve logistics and delivery efficiency.

[0008] To achieve the above objectives, the present invention provides a vehicle-UAV cooperative path planning method considering three-dimensional loading constraints, comprising the following steps:

[0009] Step 1, Step 1, construct decision variables in the collaborative path planning process of vehicle and drone, wherein the decision variables determine the vehicle path, the drone path and the cargo loading location;

[0010] Step 2: Construct the optimization objective and constraints for vehicle-drone collaborative path planning. The optimization objective is to minimize delivery time. The constraints include vehicle path constraints, drone path constraints, vehicle-drone collaboration constraints, cargo stress resistance constraints, vehicle loading constraints, cargo first-in-last-out constraints, and cargo unloading and reloading constraints.

[0011] Step 3: Under the first-in-last-out (FILO) mode and the unloading-and-reloading mode respectively, the hybrid meta-heuristic solution method is used to calculate the cargo loading scheme and the delivery scheme. The FILO mode means that only cargo located on the outermost layer of the vehicle can be delivered each time, while the unloading-and-reloading mode means that cargo located on the inner layer of the vehicle can be delivered.

[0012] Compared with the prior art, the present invention has the following beneficial technical effects:

[0013] The proposed method for collaborative path planning between vehicles and drones, which considers three-dimensional loading constraints, takes into account both the loading and delivery process of goods. It also optimizes the main path of the delivery vehicle and the path of the drone for two common unloading modes in logistics and delivery: "first in, last out" and "unloading and then loading". This method can significantly improve logistics and delivery efficiency while meeting customer needs. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0015] Figure 1 This is a flowchart of a vehicle-UAV collaborative path planning method considering three-dimensional loading constraints in an embodiment of the present invention;

[0016] Figure 2 The location number of the goods in the carriage in this embodiment of the invention. Schematic diagram;

[0017] Figure 3 This is a schematic diagram of the unloading mode in an embodiment of the present invention, wherein (a) is a schematic diagram of the first-in-last-out mode and (b) is a schematic diagram of the unloading-then-loading mode;

[0018] Figure 4 This is a schematic diagram of the target access order in an embodiment of the present invention;

[0019] Figure 5 This is a schematic diagram of same-floor cargo exchange in an embodiment of the present invention;

[0020] Figure 6 This is a schematic diagram illustrating the exchange of goods with the same pressure resistance level in an embodiment of the present invention;

[0021] Figure 7 This is a schematic diagram of the additional time cost incurred due to loading and unloading of goods in an embodiment of the present invention, wherein (a) is a schematic diagram of the additional time cost of loading and unloading of goods 22, and (b) is a schematic diagram of the additional time cost of loading and unloading of goods 34.

[0022] Figure 8 The diagram below shows an example of a destruction operator in an embodiment of the present invention, wherein (a) is a schematic diagram of a deletion point that is not a takeoff / landing point, and (b) is a schematic diagram of a deletion point that is a takeoff / landing point;

[0023] Figure 9 The following is an example diagram of the repair operator in an embodiment of the present invention, wherein (a) is a schematic diagram of the target point being inserted into the vehicle path, and (b) is a schematic diagram of the target point being inserted into the drone path.

[0024] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0026] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0027] like Figure 1 The above describes a vehicle-UAV cooperative path planning method considering three-dimensional loading constraints disclosed in this embodiment, which mainly includes the following steps:

[0028] Step 1: Construct decision variables in the collaborative path planning process between vehicles and drones, where the decision variables determine the vehicle path, drone path, and cargo loading location;

[0029] Step 2: Construct the optimization objective and constraints for vehicle-drone collaborative path planning. The optimization objective is to minimize delivery time. The constraints include vehicle path constraints, drone path constraints, vehicle-drone collaboration constraints, cargo stress resistance constraints, vehicle loading constraints, cargo first-in-last-out constraints, and cargo unloading and reloading constraints.

[0030] Step 3: Under the first-in-last-out (FILO) mode and the unloading-and-reloading mode respectively, the hybrid meta-heuristic solution method is used to calculate the cargo loading scheme and the delivery scheme. The FILO mode means that only cargo located on the outermost layer of the vehicle can be delivered each time, while the unloading-and-reloading mode means that cargo located on the inner layer of the vehicle can be delivered.

[0031] The planning method in this embodiment takes into account both the loading and delivery process of goods, and optimizes the main path of the delivery vehicle and the path of the drone for the two common unloading modes in the logistics and distribution process, namely "first in, last out" and "unloading and then loading", which can significantly improve the efficiency of logistics and distribution while meeting the needs of customers.

[0032] In the vehicle-drone collaborative path planning method of this embodiment, a set of target points is defined. The goods needed by the customer group are loaded onto the vehicle in a certain order. The top of the vehicle can be opened for loading and unloading. One vehicle and multiple drones work together as delivery tools to complete the delivery task. The entire delivery process can be divided into two stages: cargo loading and cargo delivery.

[0033] During the cargo loading stage, when a vehicle loads multiple items of the same shape, the cargo compartment is divided into grids according to the shape of the cargo, and the cargo positions within the compartment are determined and numbered from top to bottom. ,like Figure 2 As shown. In this problem, the goods have different compressive strengths, and goods with lower compressive strength should be loaded on the upper level as much as possible. To simplify the problem, this embodiment uses compressive strength ratings. To quantify the resilience of goods, representing the target point. The required compression resistance rating of the goods; the stronger the compression resistance of the goods, the better. The larger.

[0034] During the cargo delivery phase, vehicles can carry multiple heterogeneous drones from the base (i.e., the warehouse), complete deliveries to all target points, and then return to the warehouse. While the vehicle is at a target point, the drones can take off from the vehicle to perform a delivery mission and then land on the vehicle at other target points to recharge or replace batteries.

[0035] Furthermore, the order of goods delivery is closely related to the order of goods loading. This embodiment considers two unloading modes: "first in, last out" and "unloading before loading." Figure 3 As shown. In the "first-in, last-out" mode, goods buried underneath cannot be unloaded. This means that only goods visible in the overhead view of the carriage can be unloaded. Once one item is unloaded, new items may be exposed. For example... Figure 3 As shown in (a), the lighter-colored goods are those currently available for delivery. After the delivery of goods 10 is completed, goods 22 are exposed. In the "unload and reload" mode, when the delivered goods are piled up underneath, the goods on top need to be unloaded and then loaded back into the vehicle from their original positions. Unloading and reloading goods takes a certain amount of time. Figure 3 As shown in (b), when delivering goods 22, goods 10 need to be unloaded and loaded back into the original position after delivery, but its position will be moved down one layer.

[0036] To facilitate problem modeling and solving, this embodiment makes the following assumptions:

[0037] The vehicle has enough fuel to complete the entire delivery task;

[0038] A drone can deliver only one item per flight.

[0039] Since the delivery time of goods at each target point is the same, it is not considered in the model.

[0040] The vehicle delivery process does not affect the takeoff and landing of the drone, therefore the takeoff and landing time of the drone is not considered.

[0041] Without considering the impact of load on speed, the vehicle and the drone maintain a constant speed.

[0042] Drones can only take off or land when the vehicle is stationary;

[0043] For the safety of drones, vehicles should arrive at the drone's landing point first. In other words, drones are not allowed to wait for vehicles.

[0044] All goods required for each destination are packaged to a uniform size;

[0045] Simplify the pressure resistance constraints on goods, stipulating that goods with poor pressure resistance cannot be placed on lower layers with strong pressure resistance.

[0046] This embodiment constructs a mixed-integer linear programming model for solving the collaborative path planning of vehicles and drones considering three-dimensional loading constraints. The model includes decision variables, auxiliary variables, optimization objectives, and constraints.

[0047] Decision variables include those that determine the vehicle's route. Variables that determine the path of a drone and variables that determine the loading location of goods Specifically:

[0048] When the vehicle departs from the target point Drive to the destination hour, ,otherwise ;

[0049] When drones From the target point Drive to the destination hour, ,otherwise ;

[0050] If the target point The required goods are in the carriage When in position, ,otherwise .

[0051] To eliminate sub-loops and achieve vehicle-UAV collaboration, auxiliary variables reflecting the order in which target points are visited need to be introduced, including: target points Accessed sequential variables Target point With the target point Comparison variables based on access order The vehicle arrived at the target point. Time drones Reach the target point Time Among them, the target points visited by the drone, Same as its takeoff point, for example Figure 4 As shown. The auxiliary variable satisfies the following condition:

[0052] If the target point At the target point Delivery between ,otherwise Meanwhile, the auxiliary variables satisfy the following conditions:

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, The number of target points, Gathering at the arrival point of the transportation vehicle. For the set of target points, This indicates that the base is visited before all other target points. It is a set that includes the base and all target points. The time when the vehicle departs from the base. The time when the drone departs from the base. A collection of drones.

[0062] The optimization objective in this embodiment is to minimize delivery time, which includes vehicle travel time, drone travel time, and waiting time incurred by the vehicle or drone to achieve synchronization. It is assumed that the delivery time of goods is the same and is not considered in this embodiment.

[0063] The constraints in the mixed-integer linear programming model include vehicle path constraints, UAV path constraints, vehicle-UAV cooperation constraints, cargo stress resistance constraints, vehicle loading constraints, cargo first-in-last-out constraints, and cargo unloading and reloading constraints.

[0064] To ensure the feasibility of vehicle travel routes, this embodiment defines vehicle route constraints including:

[0065] The constraint that ensures vehicles depart from the base, complete all delivery tasks, and return to the base is:

[0066] ;

[0067] ;

[0068] Eliminating the constraints of the sub-loops is as follows:

[0069] ;

[0070] Constraints to maintain consistency between schedule and exit degree

[0071] ;

[0072] The lower bound for the time it takes for a vehicle to arrive at a target node is the sum of the time the vehicle departs from the previous node and the travel time between the two nodes. Therefore, the time constraint for the vehicle to arrive at the target node is:

[0073] ;

[0074] in, For vehicles from the target point Drive to the destination The time consumed It is an infinitely large positive number. The vehicles will gather at their starting point.

[0075] The drone collection in this embodiment It includes multiple heterogeneous drones, and the drone path constraints are defined as follows:

[0076] The constraint that each drone can only take off or land at the same point once is:

[0077] ;

[0078] ;

[0079] The delivery point for drones is specified as an auxiliary decision-making variable. The constraint that the takeoff point of the drone must be consistent with the following is:

[0080] ;

[0081] ;

[0082] Unlike the definition of vehicle arrival time, the drone arrival time uses a tight constraint to avoid situations where the drone waits for the vehicle. This ensures that the vehicle arrival time includes the potential waiting time for the drone, as follows:

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] in, For drones From the target point Drive to the destination The time consumed;

[0088] The drone's battery life constraint is:

[0089] ;

[0090] in, For drones Maximum battery life;

[0091] The drone path crossing constraint that ensures each drone can only take off again after landing is as follows:

[0092] ;

[0093] in, This is a collection of arrival points for vehicles.

[0094] The vehicle-drone cooperation constraints in this embodiment explain how vehicles and drones cooperate to complete collaborative delivery tasks, including:

[0095] Regardless of whether vehicle delivery or drone delivery is used, the constraint to ensure that each target is visited once is:

[0096] ;

[0097] in, This refers to the set of cargo locations within the carriage.

[0098] The requirement is that both the takeoff and landing points of the drone should be subject to vehicle access constraints, as follows:

[0099] ;

[0100] ;

[0101] The constraint requiring that the order of visits to the UAV takeoff point in the vehicle's access path precedes the landing point is:

[0102] ;

[0103] The constraint to ensure time synchronization at the drone's takeoff point is:

[0104] ;

[0105] ;

[0106] The constraint to ensure time synchronization at the drone landing point is:

[0107] ;

[0108] ;

[0109] The cargo compression resistance constraints and vehicle loading constraints in this embodiment are specifically as follows:

[0110] The constraint that each location can load at most one cargo, and that all cargoes are loaded, is as follows:

[0111] ;

[0112] ;

[0113] Tight loading constraints stipulate that goods are loaded from the bottom of the car body upwards to prevent gaps from forming at the bottom of the car body.

[0114] ;

[0115] Compression restraints ensure that goods with poor compression resistance are always placed on top of or on the same layer as goods with high compression resistance during loading.

[0116] ;

[0117] in, This refers to the collection of cargo locations within the carriage. For the collection of goods.

[0118] When goods are delivered, this embodiment constructs corresponding constraints for the two commonly used delivery operation modes: "unloading and reloading not allowed" ("first-in, last-out") and "unloading and reloading allowed," including:

[0119] The first-in, last-out (LIFO) constraint links the loading sequence of goods to the delivery route. Lower-level goods can only be delivered after the goods above them have been delivered. It is defined as follows:

[0120] ;

[0121] in, This refers to the number of goods that can be loaded on each level of the carriage;

[0122] Cargo is subject to unloading and reloading constraints. Under these constraints, goods located on lower levels can be delivered before goods located on upper levels, but this incurs additional loading and unloading time costs. The time required for each item to be unloaded and reloaded is... ,use This indicates the quantity of goods that need to be unloaded and reloaded upon arrival at a certain location.

[0123] In practical implementation, the following formula can be used to replace the time constraint for the vehicle to reach the target point in the vehicle path constraint:

[0124] ;

[0125] ;

[0126] ;

[0127] The first two equations of the UAV arrival time tight constraint in the UAV path constraint can be replaced by the following equation:

[0128] ;

[0129] ;

[0130] ;

[0131] Among them, symbols Indicates taking The integer part, It can represent The total number of layers below the location. The reason for setting only one boundary for the drone path constraint is: There may be multiple items on top of the cargo. Each Each corresponds to a constraint condition. The constraint that takes the longest time should be satisfied.

[0132] After constructing the mixed-integer linear programming model, although the exact solution for the vehicle-UAV collaborative path planning can be obtained directly using the mathematical programming optimizer Gurobi, the solution becomes extremely slow as the problem size increases. Therefore, to accelerate the solution process, this embodiment employs a two-stage metaheuristic solution method, which can significantly improve solution efficiency while obtaining a relatively satisfactory solution. Thus, the specific calculation process for the cargo loading and delivery schemes in this embodiment under the cargo first-in-last-out mode and the cargo unloading and reloading permitted mode is as follows:

[0133] Step 301: Obtain the initial cargo loading plan for all goods;

[0134] Step 302: Iteratively optimize the initial cargo loading plan to obtain the cargo loading plan;

[0135] Step 303: Based on the cargo loading plan, optimize the delivery plan under the cargo first-in-last-out mode and the cargo unloading and reloading mode respectively to obtain the delivery plan.

[0136] In step 301, during the process of constructing the initial cargo loading plan, the cargo is loaded sequentially from the bottom of the carriage according to the order of pressure resistance from high to low. The specific implementation process includes the following steps:

[0137] Step 301.1: Obtain the set of cargo locations in the carriage. Goods collection ,in, This refers to the number of cargo spaces in the carriage. For the quantity of goods, and ;

[0138] Step 301.2: Select any cargo location in the lowest corner of the carriage as the current cargo location;

[0139] Step 301.3: Randomly select one cargo from all currently unloaded cargo with the highest pressure resistance rating and load it into the current cargo location;

[0140] Step 301.3: Determine if any storage locations on the same floor and adjacent to the current storage location are empty.

[0141] If so, use the adjacent storage location as the current storage location;

[0142] Otherwise, the storage location located on the upper level and adjacent to the current storage location will be used as the current storage location;

[0143] Step 301.4, determine whether all goods have been loaded:

[0144] If so, output the current loading plan as the initial cargo loading plan;

[0145] Otherwise, return to step 301.3.

[0146] After obtaining the initial cargo loading plan, this embodiment uses a tabu search algorithm to optimize it, thereby obtaining the cargo loading plan. The specific implementation process includes the following steps:

[0147] Step 302.1, obtain the maximum number of iterations. Compared with the initial cargo loading plan and let the current iteration number Current solution Current optimal solution ;

[0148] Step 302.2, apply the commutation operator to the current solution. After modification, several candidate solutions were obtained. A set;

[0149] For condition 302.3, select the optimal solution from the candidate solution set. Determine if the taboo list exists. :

[0150] If so, proceed to step 302.4;

[0151] Otherwise, proceed to step 302.5;

[0152] Step 302.4, Determine Does the amnesty rule apply?

[0153] If so, proceed to step 302.5;

[0154] Otherwise, After removing it from the candidate solution set, return to step 302.3;

[0155] Step 302.5, Determine Is it superior to :

[0156] If so, let = , = Then proceed to step 302.6;

[0157] Otherwise, greedily select one of the candidate solutions from the current set of candidate solutions as the current solution. ;

[0158] Step 302.6, change the current Add to the taboo list, and make and determine Is it true or false?

[0159] If so, output the current... As a cargo loading scheme;

[0160] Otherwise, return to step 302.2.

[0161] In the specific implementation of step 302.4, the conditions for satisfying the pardon rule can be adaptively set according to needs. For example, when the same solution is tabooed and the number of consecutive occurrences exceeds a threshold, the pardon rule is satisfied. And / or when the solution is tabooed and the number of iterations in which it has not occurred consecutively exceeds a threshold, the pardon rule is satisfied, etc. In addition, the taboo table in this embodiment has a certain length limit. When the number of tabooed solutions exceeds a set threshold, the taboos of some solutions in the taboo table are lifted, for example, the better 10% are lifted.

[0162] It is worth noting that in step 302.5, the judgment is made... and When finding a better solution, respectively... and The corresponding loading scheme is obtained through the optimization process of subsequent steps 303.1A-303.4A or 303.1B-303.2B, and then the corresponding delivery scheme is calculated. and The target value (i.e., delivery time) for the corresponding delivery plan. and The solution with the smaller objective value is better.

[0163] In the specific implementation process, this embodiment designs two exchange operators that satisfy the cargo compression resistance constraint: a cargo exchange operator for goods on the same level and a cargo exchange operator for goods with the same compression resistance level. Each time, one operator is randomly selected to exchange the positions of two goods, thereby generating a new neighbor solution. Wherein:

[0164] The same-level cargo exchange operator refers to randomly selecting two goods located on the same level of a carriage and exchanging their positions. For example... Figure 5 As shown, cargo 1 and cargo 2 are located on the same floor. Regardless of whether their compressive strength ratings are the same, exchanging their positions will not violate the compressive strength constraints of the cargo.

[0165] The same pressure resistance level cargo exchange operator refers to randomly selecting two goods of the same pressure resistance level and exchanging their positions each time. For example... Figure 6 As shown, goods of the same color have the same compressive strength rating. Although goods 1 and goods 2 are located on different layers, exchanging their positions still satisfies the compressive strength constraints of the goods.

[0166] From the perspective of picking up goods, two exchange operators are used: same-level goods exchange and goods exchange of the same pressure resistance level. This allows any two states to reach each other within a finite step size, thus ensuring the diversity of information.

[0167] In the specific implementation of step 303, the optimization process of the delivery plan under the first-in-last-out (FIFO) mode is similar to the path planning problem of dynamic demand. The optimization process only considers the currently deliverable target points and does not consider the goods underneath or the already delivered target points. After each delivery, the vehicle may expose new goods. The newly exposed goods are regarded as new demand and are inserted into the current delivery plan with a greedy strategy, and the delivery plan is re-optimized. Therefore, the optimization process of the delivery plan under the FIFO mode in this embodiment is as follows:

[0168] Step 303.1A: Obtain the set of target points corresponding to the goods currently located on the top layer of the carriage. And generate the target point set. The initial delivery plan;

[0169] Step 303.2A, in the target point set Based on the initial delivery plan, optimization was performed using an adaptive large neighborhood search iterative framework with fusion annealing mechanism to obtain the target point set. Current delivery plan;

[0170] Step 303.3A, the simulated vehicle is based on the target point set. The current delivery plan proceeds to the next destination and delivers the goods;

[0171] Step 303.4A: Determine whether all goods in the carriage have been delivered.

[0172] If so, the output of the simulated vehicle's route is the delivery plan;

[0173] Otherwise, return to step 303.1A.

[0174] As for optimizing the delivery plan under the cargo unloading and reloading mode, it can be done by optimizing all goods at once. The specific implementation process includes the following steps:

[0175] Step 303.1B: Obtain the set of target points corresponding to all goods in the carriage. And generate the target point set. The initial delivery plan;

[0176] Step 303.2B, in the target point set Based on the initial delivery plan, an optimized delivery plan is obtained by using an adaptive large neighborhood search iterative framework with a fusion annealing mechanism.

[0177] It is worth noting that when a vehicle or drone is picking up goods, if the goods are underneath other goods, the goods on top of the goods to be delivered need to be temporarily unloaded, retrieved, and then reloaded into the vehicle. The additional time cost incurred due to unloading and reloading is calculated per item, with the time spent unloading and reloading each item being [calculated as follows]. .like Figure 7 As shown, at the current moment, the additional time cost for loading and unloading goods 22 is... The additional time cost for loading and unloading goods 34 is 2. .

[0178] In the specific implementation of steps 303.1A and 303.1B, the process of obtaining the initial delivery plan is the same. Both are based on a greedy strategy to generate the initial delivery plan. First, a vehicle-only delivery route is generated by finding the nearest neighbor. Then, the delivery method of some target points is greedily changed to be carried out by drones, and their take-off and landing points are determined. The specific implementation process is as follows:

[0179] Step 401: Based on all target points in the current target point set, simulate a vehicle departing from the base and sequentially selecting the nearest target point for delivery until all target points have been delivered, thus generating a delivery route;

[0180] Step 402: Based on the current delivery route, calculate the time cost increment resulting from changing all vehicle delivery points to drone delivery, and obtain the minimum time cost increment. and its corresponding target points ;

[0181] Step 403, Determine Is it true or false?

[0182] If so, set the target point The delivery method was changed to drone delivery, and the delivery routes and available time windows for drone assemblies were updated.

[0183] Otherwise, output the current delivery route as the initial delivery plan.

[0184] It is worth noting that in step 402, when calculating the time cost increment caused by changing all vehicle delivery points to drone delivery, if there is a vehicle delivery point for which the drone has no available time window during the calculation, then the vehicle delivery point will be removed from this iteration, that is, the time cost increment of the vehicle delivery point will not be calculated.

[0185] In the specific implementation of steps 303.2A and 303.2B, the process of obtaining the delivery plan is the same. This embodiment optimizes the initial delivery plan by designing a fusion algorithm that temporarily disregards loading constraints, called the Annealed Adaptive Large-Scale Neighborhood Search Algorithm. When designing this algorithm, various constraints caused by loading, such as cargo location, pressure resistance, unloading method, and unloading order, are relaxed, and only the delivery path of the goods is considered, simplifying the problem to an MFSTSP problem. The algorithm adopts an adaptive large-scale neighborhood search iterative framework with a fusion annealing mechanism. On the one hand, it adaptively adjusts the operator scores and weights to improve the efficiency of solving complex problems; on the other hand, through the Metropolis criterion, it accepts poor solutions with a certain probability, improving the algorithm's exploration ability and avoiding getting trapped in local optima, thereby improving the algorithm's performance. The specific implementation process of optimizing the cargo delivery plan using this Annealed Adaptive Large-Scale Neighborhood Search Algorithm is as follows:

[0186] Step 501, Obtain the initial temperature Termination temperature Cooling coefficient Compared with the initial delivery plan And construct two destruction operators and two repair operators;

[0187] Step 502, Initialize the current solution Current optimal solution Current temperature The scores of all four operators are 0, and the weights of all four operators are 0.5, i.e., operator scores. = And initialization, i.e., operator weights = ;

[0188] Step 503, based on operator weights The roulette wheel selection operator is used to destroy and repair the current solution, generating neighboring solutions. ;

[0189] Step 504, determine neighboring solutions Is it better than the current solution? :

[0190] If so, let and in the neighbor's solution Update when better than the current best solution ;

[0191] Otherwise, judge based on the Metropolis criterion. Whether it is accepted or not, if it is accepted then ,otherwise ;

[0192] Step 505, based on the current solution Update operator score Then update the period based on the operator weights. Determine whether to use operator score Update operator weights;

[0193] Step 506, Determine Is it true or false?

[0194] If so, output the current optimal solution. As a delivery solution;

[0195] Otherwise, let Then, return to step 503.

[0196] In the process of calculating the delivery plan, this embodiment designs an adaptive operator selection method. The probability of an operator being selected is adjusted based on the optimization effect of each operator, so that the better the operator performs, the higher its score and weight, and the greater the probability of the operator being used. Specifically, the adaptive process mainly includes two parts: 1. Updating the operator score based on the effect of the neighboring solutions generated by the operator. 2. When the number of iterations reaches the specified weight update cycle, updating the operator's selection weight based on the operator's score and clearing the weight score; otherwise, the weight is not updated. That is, the specific implementation process of step 505 is as follows:

[0197] First, based on the current solution Update operator score Specifically:

[0198] Get the current score of the currently selected destruction operator. And the current score of the previously selected repair operator. :

[0199] If the neighbor solves Updated to the current solution ,but , ;

[0200] If the neighbor solves Updated to the current solution ,but , ;

[0201] If the neighbor solves Not updated to the current solution It has not been updated to the current solution. ,but , ;

[0202] in, , , All of these are bonus points for operator scores, and ;

[0203] Then, based on the operator weight update period Determine whether to use operator score Update the operator weights, specifically:

[0204] Get the previous inner iteration count of the currently selected destruction operator or repair operator. ;

[0205] make = After adding 1, check = Is it true or false?

[0206] If so, update the weights of the destruction operator or the repair operator as follows: ,in, , The weights of the disruptive or repairing operator before and after the update are given. This is the current score for the destruction operator or the repair operator. This represents the number of times the damage operator or repair operator is used. To control the impact factors of the weight change rate, the inner iteration count and operator score of the destruction operator or the repair operator are updated as follows: , ;

[0207] Otherwise, do not update the operator weights and output the current weights. and .

[0208] In this embodiment, the destruction operator is used to delete from the current solution. Target point nodes ( (Randomly generated within a given range), the repair operator is used to insert the deleted target node into a different position than before, generating a new neighbor solution. To address this characteristic, this embodiment designs two types of repair operators and a destruction operator.

[0209] The destruction operator is deleted from the current path. For each target point node, this embodiment designs two deletion methods: 1. When the node to be deleted is a drone access point or a vehicle access point that is not a drone takeoff / landing point, it can be directly deleted from the path, such as... Figure 8 As shown in (a); 2. When deleting a node that is a vehicle access node for drone takeoff / landing, after deletion, a greedy strategy is adopted to find the node closest to the drone among the current vehicle access points as the new takeoff / landing point for the drone, such as... Figure 8 As shown in (b). After clarifying the node deletion method, the following two destruction operators are designed:

[0210] Random destruction operator: random selection Target nodes are removed from the current path scheme.

[0211] Greedy destruction operator: Calculates the time cost reduction when each target point is deleted in turn, deletes the target point that saves the most time, until all targets are deleted. Target nodes.

[0212] The repair operator re-inserts deleted nodes into the current path, with two insertion methods: 1. Insert the node into the vehicle path, such as... Figure 9As shown in (a); 1. Designate the node as a new UAV access node and find suitable take-off and landing points for it, such as Figure 9 As shown in (b).

[0213] Two repair operators were then designed:

[0214] Greedy repair operator: For deleted For each node, calculate the time cost of inserting each node into all possible positions in turn, and insert the node with the smallest time increment into its optimal position until all nodes are re-inserted into the path.

[0215] Regret-correcting operator: When inserting a node, it may reduce the number of available insertion positions for subsequent nodes, resulting in greater time costs. Therefore, unlike the greedy correction operator, this operator focuses on the impact of the currently inserted node on subsequent insertions. To indicate the insertion of a node The degree of "regret" is considered, and nodes with higher regret values ​​are prioritized for insertion into the path. This gives the repair operation a more global perspective. The regret value is calculated as follows:

[0216]

[0217] in, , Representing nodes respectively The delivery time increments generated by inserting the optimal and suboptimal locations are therefore available. Approximate representation of nodes The additional time cost incurred when inserting the suboptimal position when the optimal position is occupied.

[0218] It is worth noting that during the stage of using destruction and repair operators to destroy and repair the solution, two types of solutions that do not meet the constraints may be generated: 1. The takeoff or landing point of the UAV path is deleted; 2. When a target point is inserted into the vehicle path, the waiting time for the UAV after takeoff becomes longer, thus violating the UAV's endurance constraint. In summary, both types of infeasible solutions originate from the UAV path. When an infeasible solution is generated, a solution correction method is used to modify it into a feasible solution, specifically:

[0219] Find the target point that makes the solution infeasible for drone access, and use the two nearest vehicle access points as its take-off and landing points. If the drone path is feasible, accept the path; otherwise, greedily insert the target point into the vehicle path.

[0220] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A vehicle-UAV cooperative path planning method considering three-dimensional loading constraints, characterized in that, Includes the following steps: Step 1: Construct decision variables in the collaborative path planning process between vehicles and drones, wherein the decision variables determine the vehicle path, the drone path, and the cargo loading location; Step 2: Construct the optimization objective and constraints for vehicle-drone collaborative path planning. The optimization objective is to minimize delivery time. The constraints include vehicle path constraints, drone path constraints, vehicle-drone collaboration constraints, cargo stress resistance constraints, vehicle loading constraints, cargo first-in-last-out constraints, and cargo unloading and reloading constraints. Step 3: Under both the first-in-last-out (FILO) and unloading-only-reloading (UNI) modes, a hybrid metaheuristic approach is used to calculate the loading and delivery schemes. The FILO mode allows delivery only of goods located on the outermost layer of the vehicle at a time, while the UNI mode allows delivery of goods located on the inner layers of the vehicle. Specifically, this includes: Step 301: Obtain the initial cargo loading plan for all goods; Step 302: Iteratively optimize the initial cargo loading plan to obtain the optimized cargo loading plan; Step 303: Based on the optimized cargo loading plan, further optimization is performed under both the first-in-last-out cargo mode and the cargo unloading-and-reloading mode to obtain the delivery plan, specifically including: In the first-in, last-out (LIFO) goods mode, the optimization process of the delivery plan is as follows: Step 303.1A: Obtain the set of target points corresponding to the goods currently located on the top layer of the carriage. And generate the target point set. The initial delivery plan; Step 303.2A, in the target point set Based on the initial delivery plan, optimization was performed using an adaptive large neighborhood search iterative framework with fusion annealing mechanism to obtain the target point set. Current delivery plan; Step 303.3A, the simulated vehicle is based on the target point set. The current delivery plan proceeds to the next destination and delivers the goods; Step 303.4A: Determine whether all goods in the carriage have been delivered. If so, the simulated vehicle's driving route is the delivery plan. Otherwise, return to step 303.1A; Under the cargo unloading and reloading mode, the optimization process of the delivery plan is as follows: Step 303.1B: Obtain the set of target points corresponding to all goods in the carriage. And generate the target point set. The initial delivery plan; Step 303.2B, in the target point set Based on the initial delivery plan, the optimization is carried out, and the delivery plan is obtained by adopting an adaptive large neighborhood search iterative framework with fusion annealing mechanism; The process of obtaining the delivery plan is as follows: Step 501, Obtain the initial temperature Termination temperature Cooling coefficient Compared with the initial delivery plan And construct two destruction operators and two repair operators; Step 502, Initialize the current solution Current optimal solution Current temperature The scores of all four operators are 0, that is: operator scores = And the weights of the four operators are initialized to 0.5, i.e., the operator weights are... = ; Step 503, based on operator weights The roulette wheel selection operator is used to destroy and repair the current solution, generating neighboring solutions. ; Step 504, determine neighboring solutions Is it better than the current solution? : If so, let and in the neighbor's solution Update when better than the current best solution ; Otherwise, judge based on the Metropolis criterion. Whether it is accepted or not, if it is accepted then ,otherwise ; Step 505, based on the current solution Update operator score Then update the period based on the operator weights. Determine whether to use operator score Update operator weights; Step 506, Determine Is it true or false? If so, output the current optimal solution. As the aforementioned delivery solution; Otherwise, let Then, return to step 503.

2. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to claim 1, characterized in that, In step 1, the decision variables include variables that determine the vehicle's route. Variables that determine the path of a drone and variables that determine the loading location of goods Specifically: When the vehicle departs from the target point Drive to the destination hour, ,otherwise ; When drones From the target point Drive to the destination hour, ,otherwise ; If the target point The required goods are in the carriage When in position, ,otherwise .

3. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to claim 1, characterized in that, Step 301 specifically includes: Step 301.1: Obtain the set of cargo locations in the carriage. Goods collection ,in, This refers to the number of cargo spaces in the carriage. For the quantity of goods, and ; Step 301.2: Select any cargo location in the lowest corner of the carriage as the current cargo location; Step 301.3: Randomly select one cargo from all currently unloaded cargo with the highest pressure resistance rating and load it into the current cargo location; Step 301.4: Determine if any storage locations on the same floor and adjacent to the current storage location are empty. If so, use the adjacent storage location as the current storage location; Otherwise, the storage location located on the upper level and adjacent to the current storage location will be used as the current storage location; Step 301.5: Determine if all goods have been loaded. If so, output the current loading plan as the initial cargo loading plan; Otherwise, return to step 301.

3.

4. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to claim 3, characterized in that, Step 302 specifically includes: Step 302.1, obtain the maximum number of iterations. Compared with the initial cargo loading plan and let the current iteration number Current solution Current optimal solution ; Step 302.2, apply the commutation operator to the current solution. After modification, several candidate solutions were obtained. A set; Step 302.3: Select the optimal solution from the candidate solution set. Determine if the taboo list exists. : If so, proceed to step 302.4; Otherwise, proceed to step 302.5; Step 302.4, determine Does the amnesty rule apply? If so, proceed to step 302.5; Otherwise, After removing it from the candidate solution set, return to step 302.3; Step 302.5, Determine Is it superior to : If so, let = , = Then proceed to step 302.6; Otherwise, greedily select one of the candidate solutions from the current set of candidate solutions as the current solution. ; Step 302.6, change the current Add to the taboo list, and make and determine Is it true or false? If so, output the current... As a cargo loading scheme; Otherwise, return to step 302.

2.

5. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to claim 4, characterized in that, The exchange operator includes: Same-level cargo exchange operator: Each time, two goods located on the same level of the carriage are randomly selected and their positions are exchanged; Same pressure resistance level goods exchange operator: Each time, randomly select two goods with the same pressure resistance level and exchange their positions.

6. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to any one of claims 1 to 5, characterized in that, The process of obtaining the initial delivery plan is as follows: Step 401: Based on all target points in the current target point set, simulate a vehicle departing from the base and sequentially selecting the nearest target point for delivery until all target points have been delivered, thus generating a delivery route; Step 402: Based on the current delivery route, calculate the time cost increment resulting from changing all vehicle delivery points to drone delivery, and obtain the minimum time cost increment. and its corresponding target points ; Step 403, Determine Is it true or false? If so, set the target point The delivery method was changed to drone delivery, and the delivery routes and available time windows for drone assemblies were updated. Otherwise, output the current delivery route as the initial delivery plan.

7. The vehicle-UAV cooperative path planning method considering three-dimensional loading constraints according to any one of claims 1 to 5, characterized in that, In step 505, the step of determining the current solution... Update operator score Specifically: Get the current score of the currently selected destruction operator. And the current score of the previously selected repair operator. : If the neighbor solves Updated to the current solution ,but , ; If the neighbor solves Updated to the current solution ,but , ; If the neighbor solves Not updated to the current solution It has not been updated to the current solution. ,but , ; in, , , All of these are bonus points for operator scores, and ; The operator weight update period Determine whether to use operator score Update the operator weights, specifically: Get the previous inner iteration count of the currently selected destruction operator or repair operator. ; make = After adding 1, determine = Is it true or false? If so, update the weights of the destruction operator or the repair operator as follows: ,in, , The weights of the disruptor or repair operator before and after the update are given. This is the current score for the destruction operator or the repair operator. This represents the number of times the damage operator or repair operator is used. To control the impact factors of the weight change rate, the inner iteration count and operator score of the breaking or repairing operator are updated as follows: , ; Otherwise, do not update the operator weights and output the current weights. and .

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