Unmanned aerial vehicle distribution scheduling method considering uncertain wind condition and random arrival time

Abstract

The invention belongs to the field of unmanned aerial vehicle distribution path optimization, and discloses an unmanned aerial vehicle distribution scheduling method considering an uncertain wind condition and random arrival time, and the method comprises the steps: calculating the travel time of an unmanned aerial vehicle based on an uncertain wind condition model, and constructing a nonlinear energy consumption function related to the load and travel time of the unmanned aerial vehicle; the minimum travel cost, the energy consumption cost and the penalty cost are used as objective functions, an unmanned aerial vehicle distribution scheduling optimization model is constructed, and the penalty cost is generated when unmanned aerial vehicle distribution exceeds a preset deadline; and solving the unmanned aerial vehicle distribution scheduling optimization model by adopting a tabu search algorithm to obtain an optimal unmanned aerial vehicle distribution scheduling scheme. According to the method, a high-quality distribution scheduling scheme can be obtained, and the solving efficiency is high.

Description

Technical Field

[0001] This invention belongs to the field of drone delivery route optimization, specifically involving a drone delivery scheduling method that takes into account uncertain wind conditions and random arrival times. Background Technology

[0002] The "last mile" delivery problem has become a major challenge facing the logistics industry. Traditional "last mile" delivery methods rely on ground transportation such as trucks, which suffer from low flexibility and high costs, especially when dealing with small-scale, geographically dispersed delivery needs. A more efficient and economical alternative is urgently needed. Drones, with their high flexibility, cost-effectiveness, and environmental friendliness, are widely regarded as a highly promising "last mile" delivery solution.

[0003] The drone delivery problem (DDP) is a variant of the vehicle routing problem (VRP), its core being the optimization of drones within the delivery system. Existing research shows that drone arrival times are highly susceptible to environmental factors, with wind uncertainty being the most critical. The presence of wind alters the drone's flight path and speed, causing fluctuations in arrival time. A tailwind helps the drone arrive at its destination earlier, while a headwind can reduce flight speed and prolong flight time, leading to delivery delays. Although some scholars have considered the impact of wind on drone delivery, most assume that wind speed and direction remain constant throughout the flight path or within a specific time period, neglecting the dynamic nature of wind changes.

[0004] Furthermore, considering battery capacity limitations, drone energy consumption is affected by payload, ultimately restricting its flight time and achievable delivery range. Some studies model drone energy consumption as a linear function of payload, neglecting the potential impact of uncertain wind conditions on flight time. This simplification may lead to risks such as delays in drone delivery missions and infeasible delivery routes. The increase in drone energy consumption is particularly pronounced under headwind conditions.

[0005] In summary, current research generally treats wind speed and direction as fixed parameters throughout the entire journey or a specific time period, neglecting the dynamic changes in wind conditions. This leads to insufficient responsiveness of drones to wind changes, limiting their applicability in complex real-world environments. Because drone energy consumption and arrival time are highly sensitive to environmental factors (such as uncertain wind conditions), achieving on-time delivery presents a challenge. To date, the uncertainty of the impact of wind conditions on drone arrival time has not been adequately modeled, restricting their widespread deployment in practical scenarios. Summary of the Invention

[0006] The purpose of this invention is to provide a drone delivery scheduling method that takes into account uncertain wind conditions and random arrival times, which can obtain high-quality delivery scheduling schemes and has high solution efficiency.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A drone delivery scheduling method that considers uncertain wind conditions and random arrival times includes:

[0009] The travel time of the UAV is calculated based on an uncertain wind condition model, and a nonlinear energy consumption function related to the UAV's payload and travel time is constructed.

[0010] A drone delivery scheduling optimization model is constructed with the objective function of minimizing travel cost, energy consumption cost, and penalty cost. The penalty cost is generated when the drone delivery exceeds the preset deadline.

[0011] The tabu search algorithm is used to solve the drone delivery scheduling optimization model to obtain the optimal drone delivery scheduling scheme.

[0012] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0013] Preferably, the uncertain wind condition model is constructed as follows:

[0014] Get Node The wind conditions at the location are represented as a wind vector. ,in Represents a node Wind speed at the location Represents a node The wind direction at your location;

[0015] wind speed Decomposed into components along the flight direction of the UAV. and the component perpendicular to the drone's flight direction. ,in Represents a node The path angle;

[0016] Under the influence of uncertain wind conditions, the ground speed and travel time of the drone are as follows:

[0017]

[0018]

[0019] In the formula, Represents a node and nodes Ground speed between For the drone's cruising airspeed, Represents a node and nodes Travel time between Represents a node and nodes The Euclidean distance between them.

[0020] Preferably, the objective function is constructed as follows:

[0021]

[0022] In the formula, Indicates a collection of drones. For set The serial number of the drone in the middle This represents the warehouse and all customer collections. Sets The node number, Represents a node and nodes Travel costs between As a binary variable, when the drone From node fly to node hour, The value is 1; otherwise The value is 0; This indicates the cost per kilowatt of electricity. Indicates drone From node To the node energy consumption This indicates that drone delivery has exceeded the node. The penalty cost incurred at the preset deadline. As a binary variable, when the drone Reaching the node Time exceeds node When the preset deadline is, The value is 1; otherwise The value of is 0.

[0023] Preferably, the execution process of the tabu search algorithm is as follows:

[0024] (1) Randomly generate an initial solution and set it as the optimal solution, and initialize the local iteration count and the global iteration count;

[0025] (2) Set an empty taboo list;

[0026] (3) Update the optimal solution based on the neighborhood operator;

[0027] (4) Update the local iteration count and determine whether the tabu search termination condition is met. If not, return to step (3) to execute; otherwise, execute step (5).

[0028] (5) Update the global iteration count and determine whether the algorithm execution termination condition is met. If not, return to step (2) to execute; otherwise, output the optimal solution as the optimal drone delivery scheduling scheme.

[0029] Preferably, the solution of the tabu search algorithm is represented by one or more two-dimensional matrices, where a two-dimensional matrix represents the delivery scheduling scheme of a drone.

[0030] The first dimension of the two-dimensional matrix is ​​the customer sequence layer, which represents the customer service order of the drone. The second dimension of the two-dimensional matrix is ​​the dynamic change layer, which represents the arrival time of the drone under the influence of uncertain wind conditions in the form of a binary tuple. In the binary tuple, the first element represents the location where the drone performs the delivery service, and the second element represents the time of arrival at the corresponding location.

[0031] Preferably, the tabu search algorithm integrates multiple neighborhood operators and updates the weights of each neighborhood operator after each round of global iteration.

[0032] Preferably, the various neighborhood operators include intra-segment exchange operators, relocation operators, 2-opt operators, inter-segment exchange operators, and segment exchange operators.

[0033] Preferably, the dynamic adjustment method for the tabu step size of the tabu search algorithm is as follows:

[0034]

[0035] In the formula, For the first Taboo step size for the next global iteration The initial forbidden step size, For the forbidden change in step size, This represents the number of times the current solution has been visited. This represents the global iteration count. To trigger the adjustment threshold.

[0036] Preferably, the method of updating the optimal solution based on the neighborhood operator includes:

[0037] (3-1) Update the taboo list;

[0038] (3-2) Select the neighborhood operator and generate a list of candidate solutions;

[0039] (3-3) Select the optimal solution from the candidate solution list as the current solution;

[0040] (3-4) Determine if the current solution is in the taboo list. If it is, proceed to step (3-5); otherwise, proceed to step (3-6).

[0041] (3-5) Determine whether the amnesty criterion is met. If yes, proceed to step (3-6); otherwise, select the suboptimal solution as the current solution and proceed to step (3-6).

[0042] (3-6) Update the optimal solution to the current solution.

[0043] This invention provides a drone delivery scheduling method that considers uncertain wind conditions and random arrival times. It takes into account the impact of uncertain wind conditions on probability distribution information, characterizing the impact of different wind conditions through drone travel time, thereby enhancing the model's feasibility in practical applications. Furthermore, a nonlinear energy consumption function for wind condition perception is constructed to account for delivery delays and path infeasibility issues that may be caused by energy consumption estimation errors. In addition, a penalty cost is set for exceeding the customer's delivery deadline to quantify customer satisfaction and consider the impact of delivery failures on the quality of drone delivery services, thus obtaining a high-quality drone delivery scheduling scheme with practical significance. Attached Figure Description

[0044] Figure 1 A flowchart of the drone delivery scheduling method of the present invention that takes into account uncertain wind conditions and random arrival times;

[0045] Figure 2 This is a schematic diagram of the wind triangle model of the present invention;

[0046] Figure 3 This is a flowchart of the tabu search algorithm of the present invention;

[0047] Figure 4 This is a schematic diagram of the two-dimensional encoding scheme of the present invention;

[0048] Figure 5 The graph shows the performance results of all algorithms in the experiment of this invention under different iteration numbers;

[0049] Figure 6 The graph shows the performance results of all algorithms in the experiment of this invention at different confidence levels. Detailed Implementation

[0050] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0052] This invention proposes a drone delivery scheduling problem considering uncertain wind conditions and random arrival times, which involves a homogeneous fleet of drones providing "last-mile" delivery services to a group of customers with different delivery deadlines. This problem allows for a certain degree of delivery delays, but requires the introduction of corresponding penalty costs to measure the decline in customer satisfaction. Due to the random influence of wind conditions, the arrival time of each drone is uncertain. To reduce the risk of delivery failures and better meet customers' requirements for on-time drone delivery, this invention introduces a wind-aware nonlinear energy consumption function to characterize the energy consumption characteristics of drones under uncertain conditions.

[0053] The model constructed in this invention consists of a delivery warehouse, a group of customers with defined needs and delivery deadlines, and a homogeneous fleet of drones with the same battery capacity. The basic assumptions of the model are as follows: (1) Each customer is visited only once; (2) A single drone can meet the delivery needs of a single customer at once; (3) All paths must start from the warehouse and eventually return to the warehouse; (4) Drones can return to the warehouse multiple times; (5) Customer service time and drone charging time in the warehouse are ignored; (6) Drones can start a new delivery task immediately after returning to the warehouse.

[0054] like Figure 1 As shown, this embodiment provides a drone delivery scheduling method that takes into account uncertain wind conditions and random arrival times, including the following steps:

[0055] Step 1: Calculate the travel time of the drone based on the uncertain wind condition model, and construct a nonlinear energy consumption function related to the drone's payload and travel time; and construct a drone delivery scheduling optimization model with the objective function of minimizing path travel cost, energy consumption cost and penalty cost.

[0056] Step 1-1, as follows Figure 2 The diagram shown illustrates the uncertain wind triangle, used to demonstrate the impact of wind on the flight trajectory and speed of a drone. For a given node... The wind conditions at its location can be represented as a wind vector. ,in Represents a node Wind speed at the location Represents a node The wind direction at the location. The average wind speed is denoted as... Variance is denoted as The average wind direction is denoted as Variance is denoted as . It can be decomposed into two parts: and , representing the components along the UAV's flight direction and perpendicular to the UAV's flight direction, respectively, where Represents a node The path angle is the angle between the line connecting the node and the UAV and the ground. Therefore, the actual flight speed of the UAV, i.e., the ground speed, can be calculated using formula (1). as follows:

[0057] (1)

[0058] In the formula, The airspeed of the UAV is its speed relative to the surrounding air. Due to uncertain wind conditions, the travel time of the UAV is uncertain and can be calculated using formula (2), where... For nodes and nodes Euclidean distance, Represents a node and nodes Travel time between.

[0059] (2)

[0060] Steps 1-2: This invention aims to minimize total costs, including travel costs, energy costs, and penalty costs. Under the opportunity constraint of meeting the delivery deadline, it ensures that the probability of delivery failure does not exceed a preset threshold. , This represents the confidence level. A penalty cost will be incurred if the actual arrival time exceeds the stipulated deadline, thus quantifying customer satisfaction.

[0061] To more accurately estimate the actual energy consumption of drones and reduce the risk of delivery delays and failures caused by underestimating actual energy consumption, a nonlinear function is used to model the energy consumption function, as shown in formula (3).

[0062] (3)

[0063] in, The energy consumption of the drone is a non-linear function of the payload; W is the weight of the drone's own frame (kg). The weight of the battery is in kg. Acceleration due to gravity (m / s²) 2 ), air fluid density (kg / m³) 3 ), Rotor area (m²) 2 ), For the number of rotors, For drones From node To the node The payload of each drone. The energy consumption of each drone is closely related to its travel time affected by wind conditions, which can be calculated by formula (4).

[0064] (4)

[0065] In the formula, For drones From node To the node Energy consumption.

[0066] Steps 1-3: In this embodiment, a nonlinear energy consumption function based on wind condition perception is introduced and extended with chance constraints. The final extended chance-constrained programming model is shown in equations (5)-(24).

[0067] The objective function is:

[0068] (5)

[0069] The constraints are:

[0070] (6)

[0071] (7)

[0072] (8)

[0073] (9)

[0074] (10)

[0075] (11)

[0076] (12)

[0077] (13)

[0078] (14)

[0079] (15)

[0080] (16)

[0081] (17)

[0082] (18)

[0083] (19)

[0084] (20)

[0085] (twenty one)

[0086] (twenty two)

[0087] In the formula, For the node set of all customers, , Total number of customers; For the collection of all customers and warehouses, ; For the assembly of homogeneous drone fleets, , The total number of drones; For set The serial number of the drone in the record; Sets or set The node sequence number in the middle; For nodes The demand; For drones From node To the node Load capacity; For drones From node The load capacity to the warehouse; This is the maximum payload of the drone; For nodes The delivery deadline; This is the maximum battery capacity for the drone; For the drone to reach the node Time; For nodes and nodes Travel costs between; Cost per kilowatt of electricity; Because of failure at node The penalty cost incurred for completing the delivery service before the delivery deadline; For drones Customers along the route The order of access should be determined to avoid the generation of sub-loops; For drones Customers along the route The order of access; It is an infinitely large number; For binary variables, 1 represents the drone. From node fly to node Otherwise, it is 0; For binary variables, 1 represents the drone. From node fly to node Otherwise, it is 0; For binary variables, 1 represents the drone. Fly from warehouse to node Otherwise, it is 0; For binary variables, 1 represents the drone. From node Fly to the warehouse, otherwise return 0; For binary variables, 1 represents the drone. From node Fly to the warehouse, otherwise return 0; For binary variables, 1 represents the drone. Reaching the node If the time exceeds its delivery deadline, then it is 0; otherwise, it is 0. For drones From node Energy consumption for returning to the warehouse; For drones Reaching the node Cumulative energy consumption; For drones Reaching the node Cumulative energy consumption; For drones From node Energy consumption at the warehouse.

[0088] Formula (5) represents the objective function, aiming to minimize the sum of total travel cost, energy cost, and penalty cost. Formulas (6)-(9) represent path feasibility constraints. Formula (6) ensures that each customer is visited exactly once. Formula (7) guarantees that the inflow and outflow at each node are conserved. Formula (8) limits the number of drones departing from the warehouse to the number returning to the warehouse to be equal. Formula (9) represents the sub-loop elimination constraint, i.e., if the drones... From the customer To the customer Then the customer The access order must be later than the customer's. .

[0089] Formulas (10)-(13) represent load constraints. Formula (10) stipulates that if the UAV... Not from node Go to node Therefore, its load on that path should be zero. Formula (11) ensures that the drone... Leave the customer Load at time Less than the customer The payload at that time. Formula (12) constrains the UAV. From node To the node The payload must not exceed the maximum payload limit after deducting the battery weight. Formula (13) prohibits drones from delivering any packages from customers back to the warehouse.

[0090] Formulas (14)-(16) represent energy consumption constraints. Formula (14) defines the energy consumption constraints for the UAV. fly to node Total energy consumption Formula (15) defines the unmanned aerial vehicle (UAV). From the customer Energy consumption for returning to the warehouse Formula (16) stipulates that if the drone No from the customer If the flight is to the warehouse, the energy consumption on that route is zero; otherwise, the total energy consumption on that route must not exceed its maximum battery capacity E.

[0091] The opportunity constraint, as shown in formula (17), indicates that the probability of the drone providing delivery service exceeding the customer's delivery deadline is less than... ,in This represents a probability function. Formulas (18)-(22) define the range of values ​​for the decision variables.

[0092] This embodiment makes and It follows a normal distribution. Define variables. Indicates that the drone has arrived at the customer's location. The difference between the time and the customer's delivery deadline also follows a normal distribution, i.e. ,in It is the expected value. It is variance. The definitions of expected value and variance are given in formulas (23) and (24).

[0093] (twenty three)

[0094] (twenty four)

[0095] To transform the chance constraint (Equation 17) into a solvable deterministic form, it is necessary to modify the variables. Standardize the distribution to make it conform to a standard normal distribution. The standardization process is shown in formula (25), where... Represents a probability function. The cumulative distribution function represents the normal distribution.

[0096] (25)

[0097] In the formula express The inverse function of, satisfying Formula (17) can be transformed into formula (26).

[0098] (26)

[0099] Since uncertain wind conditions can affect the arrival time of drones, this embodiment sets the expected arrival time equal to the travel time affected by wind condition changes, while setting the variance within a reasonable range. This assumption enables the proposed extended chance-constrained programming model to fully consider the mapping relationship between uncertain wind condition changes and probability distributions, thereby ensuring that chance constraints accurately reflect the effect of wind condition changes.

[0100] Step 2: Use the tabu search algorithm to solve the drone delivery scheduling optimization model to obtain the optimal drone delivery scheduling scheme. For example... Figure 3 As shown, the tabu search algorithm in this embodiment is executed as follows:

[0101] (1) Randomly generate an initial solution and set the initial solution as the optimal solution, and initialize the global iteration count and the local iteration count.

[0102] To account for the impact of uncertain wind conditions on the arrival time of the drone, this embodiment designs a two-dimensional encoding scheme, such as... Figure 4As shown in the diagram, this scheme uses a two-dimensional matrix to represent the dynamically changing arrival time of drones under the influence of uncertain wind conditions, thereby enabling rapid identification of delivery deadline violations. A solution contains multiple two-dimensional matrices (corresponding to the number of drones), and each two-dimensional matrix represents a drone path.

[0103] The first dimension is the customer sequence layer (the beginning and end of the sequence represent warehouses, and the middle represents the customer service order), indicating the customer service order for drones. Figure 4 For example, the drone departs from the warehouse (node ​​0), serves customers 2, 3, and 1 sequentially, and finally returns to the warehouse. The second dimension is a dynamically changing layer, recording arrival times under uncertain wind conditions as tuples (arrival times are the sequential sums of travel times). This layer uses a binary encoding structure to characterize the actual arrival time of the drone during flight, where D represents the warehouse and C represents the customer. For example, [C, 324] indicates that the drone will arrive at the corresponding customer's location at the 324th second to provide delivery service. The arrival time of the drone departing from the warehouse is set to 0 seconds, and the return time to the warehouse is set to 2000 seconds. This layer's data can be dynamically updated as the drone flies along the planned route; that is, when the customer service order in the customer sequence layer of the solution changes, the corresponding arrival time will also be dynamically adjusted to reflect the impact of uncertain wind conditions on flight time in real time.

[0104] (2) Set an empty list of taboos and parameters.

[0105] (3) Update the optimal solution based on the neighborhood operator.

[0106] (3-1) Update the taboo list.

[0107] (3-2) Select the neighborhood operator and generate a list of candidate solutions.

[0108] To accelerate the convergence speed of the tabu search algorithm, this embodiment introduces five neighborhood operators in the customer sequence layer: intra-segment swap operator, relocation operator, 2-opt operator, inter-segment swap operator, and segment swap operator. The intra-segment swap operator swaps the order of two nodes on the same path. The relocation operator re-inserts a node from one position in a path into another position on the same path. The 2-opt operator reverses the path segment between two nodes on the same path. The inter-segment swap operator swaps nodes on two different paths. The segment swap operator swaps segments on two paths. Whenever any of these operators is applied in the first dimension (customer sequence layer), the corresponding dynamically changing layer (binary array) in the second dimension is also updated synchronously. Furthermore, the arrival time of the drones at each customer changes accordingly with the dynamic changes in wind conditions.

[0109] Furthermore, this embodiment introduces two adaptive mechanisms in the tabu search algorithm design: one is the dynamic adjustment of the neighborhood operator weights, and the other is the adaptive modification of the tabu step size.

[0110] Regarding the dynamic adjustment of neighborhood operator weights, each neighborhood operator is assigned an equal initial weight in the initial stage. After each round of global iteration, the weights of the neighborhood operators are updated and adjusted, and the adjustment formula is shown in (27).

[0111] (27)

[0112] in, The weight of each neighborhood operator is the probability of it being selected. Update the coefficients for weights. The number of times the neighborhood operator is used. This represents the cumulative score of the neighborhood operator.

[0113] Setting the tabu step size too short may cause the algorithm to get stuck in a local optimum, while setting it too long may lead to reduced search efficiency and increased computational overhead. Therefore, this embodiment adaptively adjusts the tabu step size based on the number of times a solution is accessed, as shown in formula (28). When the number of times a solution is accessed exceeds a preset threshold, the tabu step size in the current iteration is dynamically increased.

[0114] (28)

[0115] in, Let be the current tabu step size in the t-th global iteration. The initial forbidden step size, This is the forbidden step size increment for each adjustment. This represents the number of times the current solution has been visited. To represent the global iteration count of the tabu search algorithm, The threshold for determining whether step size adjustment is triggered.

[0116] (3-3) Select the best solution from the candidate solution list as the current solution.

[0117] (3-4) Determine whether the current solution is in the taboo list. If yes, proceed to step (3-5); otherwise, proceed to step (3-6).

[0118] (3-5) Determine whether the amnesty criterion is met. If yes, proceed to step (3-6); otherwise, select the suboptimal solution as the current solution and proceed to step (3-6).

[0119] (3-6) Update the optimal solution to the current solution. When updating the optimal solution, compare the objective function value of the current solution with that of the historical optimal solution, and update according to the objective function value.

[0120] (4) Determine whether the tabu search termination condition is met (increment the number of local iterations by 1 after each execution of step (3), and determine whether the number of local iterations exceeds the local threshold in step (4). If it exceeds the threshold, the condition is not met; otherwise, the condition is met). If the condition is not met, return to step (3) to execute; otherwise, execute step (5).

[0121] (5) Update the global iteration count (increase by 1) and determine whether the algorithm execution termination condition is met (e.g., if the global iteration count exceeds the global threshold, it is not met; otherwise it is met). If it is not met, return to step (2) to execute; otherwise, output the optimal solution as the optimal drone delivery scheduling scheme.

[0122] In summary, this embodiment extends and improves upon the basic tabu search algorithm in the following four aspects: (1) A two-dimensional encoding scheme is designed to effectively represent the complex solution structure in the model; (2) The tabu search algorithm is embedded in an iterative framework to prevent getting stuck in a loop search; (3) An adaptive mechanism is introduced to dynamically adjust the search strategy of the tabu search algorithm, thereby improving the diversity of solutions and the efficiency of global search; (4) Multiple neighborhood operators are integrated to expand the exploration range of the solution space and improve the search quality. The improved algorithm in this embodiment is referred to as the improved IATS algorithm.

[0123] Furthermore, this invention evaluates the solution performance of the proposed IATS algorithm through numerical experiments. To comprehensively evaluate the performance of the IATS algorithm, this experiment selects 21 test cases and compares the IATS algorithm with five baseline algorithms, including the basic Tabu Search (TS) algorithm, the Adaptive Tabu Search (ATS) algorithm, the Adaptive Large Neighborhood Search (ALNS) algorithm, the Iterated Local Search (ILS) algorithm, and the Natural Survivor Method Modified Differential Evolution (NSM-MadDE) algorithm. All experiments were conducted on a personal computer running Windows 11, equipped with a 12th generation Intel® Core™ i5-12450H 2.00GHz processor and 16 GB of memory.

[0124] I. Benchmark Example:

[0125] Since existing benchmark instances are mostly built based on uncertain scenarios, they are not applicable to the drone delivery scheduling (DDPST-UW) problem proposed in this invention, which considers uncertain wind conditions and random arrival times. Therefore, before evaluating the performance of the proposed IATS algorithm, this experiment simulates a real delivery scenario and generates a new set of test instances. Specifically, combining drone endurance, payload limitations, and actual operational data from major logistics companies such as UPS and Amazon, this experiment sets the drone delivery range to a rectangular area of ​​4.8 × 3.2 square kilometers. Customer demand follows a uniform distribution in the interval [0.45, 2.27] kg. The wind speed at each customer point follows a Weibull distribution with a scale parameter of 10 m / s and a shape parameter of 2, and the wind direction follows a uniform distribution in the interval [0, 360). In addition, the cost per unit flight distance of the drone is set to $1 / km.

[0126] The delivery mission was carried out by drones equipped with four 14.8-volt lithium polymer batteries. The cruising airspeed of each drone was set to 20 meters per second. The relevant parameter settings for the drones are shown in Table 1.

[0127] Table 1. UAV Parameter Settings

[0128]

[0129] The warehouse coordinates are set to (0, 0). To test the algorithm performance under different test instance sizes, the number of customers is set to 50, 75, 100, 125, 150, 175, and 200; the number of drones is set to 5, 6, and 7 respectively. Instance "C050_5" represents using 5 drones to provide delivery service to 50 customers. Additionally, the confidence level in the model... The value is set to 0.9. Considering the impact of wind on the drone's arrival time, this experiment sets the expected arrival time for each customer to be 0.9. The time variance is set to a random variable within [1, 4], and the penalty cost is set to $10.

[0130] II. Parameter Settings:

[0131] To evaluate the performance of the proposed IATS algorithm, this experiment compares its performance with four other baseline algorithms. The parameter settings of the baseline algorithms are shown in Table 2.

[0132] Table 2 Parameter settings for all algorithms

[0133]

[0134] As shown in Table 2 and These represent the weight update coefficients and scores of the neighborhood operators in the IATS and ALNS algorithms, respectively. This is the threshold used in the IATS algorithm to determine whether the taboo step size needs to be increased. This is the increment of the taboo step size when the number of repeated visits to the solution exceeds this threshold. and These represent the cooling rate in the Simulated Annealing (SA) algorithm and the operator removal ratio in the ALNS algorithm, respectively. This is the initial tabu step size in the IATS algorithm, the basic TS algorithm, and the ATS algorithm. and These represent the initial iteration counts for single-point movement and two-point movement in the ATS algorithm, respectively. and The number of iterations at which the current move method is stopped if single-point or two-point moves fail to improve the current solution. This refers to the number of tabu search iterations in the basic TS algorithm and the embedded IATS algorithm. This represents the number of neighborhood operators in the ILS algorithm.

[0135] To determine the appropriate number of iterations, this experiment selects instance "C100_5" as the test object to evaluate the performance of all algorithms under different number of iterations. Figure 5 Experimental results show that the proposed IATS algorithm has a faster convergence speed than other algorithms. Specifically, the optimal solution obtained by the IATS algorithm within 100 iterations is better than the results obtained by the other five algorithms within 300 iterations, indicating that the algorithm has stronger local search capabilities.

[0136] Given that the convergence performance of each algorithm tends to find the optimal solution within 300 iterations, to ensure the fairness of the algorithm comparison, the number of iterations for all algorithms was uniformly set to 300 in this comparative experiment. Each algorithm was run independently 20 times, and the average value was taken as the final experimental result for performance comparison analysis.

[0137] III. Experimental Results:

[0138] To evaluate the performance of the IATS algorithm, a comparative experiment was conducted on 21 instances, and the results are shown in Table 3 (including a continuation of Table 3). Table 3 provides three statistical indicators: mean, best, and worst, labeled "Mean," "Best," and "Worst," respectively. As shown in Table 3, in 18 of the 21 instances, the IATS algorithm proposed in this invention outperformed the other five baseline algorithms on average, indicating that the algorithm still possesses strong solution capabilities even with increased instance size and complexity. In the instances "C075_5," "C075_6," and "C100_6," the basic TS algorithm slightly outperformed the IATS algorithm on average. From the perspective of the best value, the IATS algorithm achieved a better best value than the other five baseline algorithms in 19 of the 21 instances. Overall, the IATS algorithm improved the average performance of all other algorithms by approximately 5% across the 21 instances. Regarding the worst-case scenario, the IATS algorithm outperformed the other five algorithms in achieving the worst-case scenarios on 11 instances. In conclusion, the IATS algorithm proposed in this invention demonstrates high effectiveness in solving the DDPST-UW problem.

[0139] Table 3. Comparison of the average, best, and worst values ​​of the six algorithms.

[0140]

[0141] Table 3 (Continued) Comparison of the average, best, and worst values ​​of the six algorithms

[0142]

[0143] Important values ​​in Table 3 and Table 3 (continued) are indicated by bold text, and "↓" indicates that the smaller the value, the better.

[0144] To further evaluate the robustness of the proposed IATS algorithm under uncertainty conditions, this experiment tested its performance at confidence levels ranging from 0.70 to 0.90, and a comparative experiment was conducted based on the example "C100_5". Figure 6 The results show that, at all confidence levels, the IATS algorithm consistently yields solutions superior to other algorithms. Furthermore, the total cost curve of the IATS algorithm exhibits smaller fluctuations, indicating stronger stability and controllability when facing delivery failure risks.

[0145] To further verify the effectiveness and scalability of the iterative framework proposed in this invention, it was further applied to the simulated annealing algorithm and the Variable Neighborhood Search (VNS) algorithm, respectively. In Tables 4 (including continued Table 4) and 5, SA w / i and VNS w / i represent the SA algorithm and the VNS algorithm integrated with the iterative framework, respectively. As shown in Table 4, the SA algorithm with the integrated iterative framework outperformed the average of its base algorithm in 17 out of 21 instances, achieving a better optimal value, indicating that the iterative framework significantly improves the performance of the SA algorithm. Similarly, the VNS algorithm with the integrated iterative framework outperformed the base VNS algorithm in all instances, further verifying the universality and robustness of the iterative framework.

[0146] Table 4. Comparison of the average, best, and worst values ​​of the five algorithms.

[0147]

[0148] Table 4 (Continued) Comparison of the average, best, and worst values ​​of the five algorithms

[0149]

[0150] Important values ​​in Table 4 and Table 4 (continued) are indicated by bold text, and "↓" indicates that the smaller the value, the better.

[0151] Table 5 shows the standard deviation and CPU computation time of the five algorithms. In 21 instances, the SA algorithm with the integrated iterative framework had a smaller standard deviation in 12 instances than the basic SA algorithm; and in all instances, its CPU computation time was shorter than the basic SA algorithm, indicating that the SA algorithm with the integrated iterative framework has significant advantages in improving solution robustness and computational efficiency. The VNS algorithm with the integrated iterative framework had a smaller standard deviation in 11 instances and a shorter CPU computation time in 18 instances, indicating that the VNS algorithm with the integrated iterative framework has significant advantages in improving solution robustness and computational efficiency.

[0152] Table 5. Standard deviations and CPU computation times of the five algorithms

[0153]

[0154] Important values ​​in Table 5 are indicated by bold, and "↓" indicates that the smaller the value, the better.

[0155] This invention addresses the DDPST-UW problem by constructing an extended opportunity-constrained programming model to more realistically depict actual drone delivery scenarios. In this model, wind conditions at the customer's location are dynamically changing. By considering the impact of wind condition changes on drone arrival time, this invention effectively reduces the risk of delivery delays and failures caused by flight time uncertainty. Furthermore, this invention constructs a wind-aware nonlinear energy consumption function, overcoming the problem of traditional linear approximation energy consumption functions underestimating actual energy consumption, thus providing a more accurate estimate of the drone's actual energy consumption and improving the reliability of drone delivery. This invention also introduces a penalty cost function to quantify customer satisfaction and consider the impact of delivery failures on the quality of drone delivery services. To efficiently solve the model, this invention proposes an IATS algorithm based on a two-dimensional coding scheme. This algorithm integrates an adaptive mechanism and multiple neighborhood operators to enhance its search capability. Experimental results show that the proposed IATS algorithm can obtain high-quality solutions to the DDPST-UW problem while possessing higher solution efficiency.

[0156] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0157] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A drone delivery scheduling method considering uncertain wind conditions and random arrival times, characterized in that, The drone delivery scheduling method that considers uncertain wind conditions and random arrival times includes: The travel time of the UAV is calculated based on an uncertain wind condition model, and a nonlinear energy consumption function related to the UAV's payload and travel time is constructed. A drone delivery scheduling optimization model is constructed with the objective function of minimizing travel cost, energy consumption cost, and penalty cost. The penalty cost is generated when the drone delivery exceeds the preset deadline. The tabu search algorithm is used to solve the drone delivery scheduling optimization model to obtain the optimal drone delivery scheduling scheme.

2. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 1, characterized in that, The uncertain wind condition model is constructed as follows: Get Node The wind conditions at the location are represented as a wind vector. ,in Represents a node Wind speed at the location Represents a node The wind direction at your location; wind speed Decomposed into components along the flight direction of the UAV. and the component perpendicular to the drone's flight direction. ,in Represents a node The path angle; Under the influence of uncertain wind conditions, the ground speed and travel time of the drone are as follows: ； ； In the formula, Represents a node and nodes Ground speed between For the drone's cruising airspeed, Represents a node and nodes Travel time between Represents a node and nodes The Euclidean distance between them.

3. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 1, characterized in that, The objective function is constructed as follows: ； In the formula, Indicates a collection of drones. For set The serial number of the drone in the middle This represents the warehouse and all customer collections. Sets The node number, Represents a node and nodes Travel costs between As a binary variable, when the drone From node fly to node hour, The value is 1; otherwise The value is 0; This indicates the cost per kilowatt of electricity. Indicates drone From node To the node energy consumption This indicates that drone delivery has exceeded the node. The penalty cost incurred at the preset deadline. As a binary variable, when the drone Reaching the node Time exceeds node When the preset deadline is, The value is 1; otherwise The value of is 0.

4. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 1, characterized in that, The execution process of the tabu search algorithm is as follows: (1) Randomly generate an initial solution and set it as the optimal solution, and initialize the local iteration count and the global iteration count; (2) Set an empty taboo list; (3) Update the optimal solution based on the neighborhood operator; (4) Update the local iteration count and determine whether the tabu search termination condition is met. If not, return to step (3) to execute. Otherwise, proceed to step (5); (5) Update the global iteration count and determine whether the algorithm execution termination condition is met. If not, return to step (2) to execute; otherwise, output the optimal solution as the optimal drone delivery scheduling scheme.

5. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 1 or 4, characterized in that, The solution of the tabu search algorithm is represented by one or more two-dimensional matrices, where a two-dimensional matrix represents the delivery scheduling scheme of a drone. The first dimension of the two-dimensional matrix is ​​the customer sequence layer, which represents the customer service order of the drone. The second dimension of the two-dimensional matrix is ​​the dynamic change layer, which represents the arrival time of the drone under the influence of uncertain wind conditions in the form of a binary tuple. In the binary tuple, the first element represents the location where the drone performs the delivery service, and the second element represents the time of arrival at the corresponding location.

6. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 4, characterized in that, The tabu search algorithm integrates multiple neighborhood operators and updates the weights of each neighborhood operator after each round of global iteration.

7. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 6, characterized in that, The various neighborhood operators include intra-segment exchange operators, relocation operators, 2-opt operators, inter-segment exchange operators, and segment exchange operators.

8. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 4, characterized in that, The dynamic adjustment method for the tabu step size of the tabu search algorithm is as follows: ； In the formula, For the first Taboo step size for the next global iteration The initial forbidden step size, For the forbidden change in step size, This represents the number of times the current solution has been visited. This represents the global iteration count. To trigger the adjustment threshold.

9. The drone delivery scheduling method considering uncertain wind conditions and random arrival times according to claim 4, characterized in that, The method of updating the optimal solution based on the neighborhood operator includes: (3-1) Update the taboo list; (3-2) Select the neighborhood operator and generate a list of candidate solutions; (3-3) Select the optimal solution from the candidate solution list as the current solution; (3-4) Determine if the current solution is in the taboo list. If it is, proceed to step (3-5); otherwise, proceed to step (3-6). (3-5) Determine whether the amnesty criterion is met. If yes, proceed to step (3-6); otherwise, select the suboptimal solution as the current solution and proceed to step (3-6). (3-6) Update the optimal solution to the current solution.

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