Truck-uav cooperative dynamic scheduling method and system in emergency logistics

Abstract

The application provides a truck-UAV collaborative dynamic scheduling method and system in emergency logistics, and relates to the technical field of UAV intelligent scheduling. A truck-UAV collaborative distribution network is constructed, each truck is equipped with a collaborative unit containing a large UAV and a small UAV; the network contains warehouses, hub points and demand points; a mixed integer programming model is established with the minimum total operating cost as the target, and the power management, service allocation, time window and collaborative feasibility as the constraints; a randomized greedy algorithm is used to solve the model, and the truck path and UAV task are decided synchronously in a single iteration to obtain the truck path scheme, UAV service allocation scheme and dynamic power scheduling scheme. Thus, the cost optimization and dynamic collaboration of emergency logistics scheduling are realized, and the efficiency and feasibility of emergency distribution are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent scheduling technology for unmanned aerial vehicles (UAVs), and in particular to a method and system for collaborative dynamic scheduling of trucks and UAVs in emergency logistics. Background Technology

[0002] Emergency logistics, as a core support for responding to major emergencies, relies on an efficient transportation network to achieve rapid response and precise coverage of supplies. Among these, the truck-drone collaborative delivery model, by integrating the advantages of large capacity and long endurance of ground vehicles with the flexible mobility and rapid delivery characteristics of drones, has become a key solution to overcome the bottlenecks of traditional single-mode ground transportation. The core of this model is to construct a collaborative network that includes the origin, transit and refueling nodes of supplies, and the receiving end of supplies. Through multi-dimensional decision optimization, it balances delivery efficiency, cost, and constraints to meet the dynamic and time-sensitive needs of emergency scenarios.

[0003] In recent years, extreme weather events, public health emergencies, and other emergencies have occurred frequently, highlighting problems such as road network damage at disaster sites and the spatial and temporal dispersion of demand. Traditional collaborative delivery models are no longer suitable for complex emergency scenarios. Although existing research has explored aspects such as truck-drone route planning and drone energy management, such as optimizing single-drone scheduling through branch-pricing-segmentation algorithms and handling energy consumption relationships through rule-based reasoning, there are still significant limitations in the face of the dynamic uncertainties and complexities of multi-device collaboration in emergency scenarios.

[0004] Specifically, existing collaborative scheduling models are mostly based on static environment assumptions, failing to effectively characterize the dynamic changes in road networks caused by disasters and the need for multi-drone collaborative obstacle avoidance; energy management strategies focus on conventional scenarios, with insufficient optimization in fast charging scheduling and dynamic power allocation under extreme conditions; solution algorithms often make separate decisions on truck routes and drone tasks, making it difficult to guarantee collaborative efficiency, and the weight setting in multi-objective optimization relies on subjective experience and lacks a dynamic adaptive mechanism, making it difficult to balance the practicality of the model with the feasibility of the solution, and failing to provide comprehensive and accurate decision support for emergency collaborative delivery. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a truck-drone collaborative dynamic scheduling method and system for emergency logistics, achieving cost optimization and dynamic collaboration in emergency logistics scheduling, and effectively improving the efficiency and feasibility of emergency delivery.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for dynamic scheduling of truck-drone collaboration in emergency logistics, comprising:

[0008] Construct a truck-drone collaborative delivery network, in which each truck is equipped with a collaborative unit containing both large and small drones; the network includes warehouses, hubs, and demand points;

[0009] With the goal of minimizing total operating costs, and constrained by power management, service allocation, time windows, and collaborative feasibility, a mixed integer programming model is established; the total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs.

[0010] A randomized greedy algorithm is used to solve the model, and the truck route and the drone mission are decided simultaneously in a single iteration to obtain the truck route scheme, the drone service allocation scheme and the dynamic power scheduling scheme.

[0011] Secondly, the present invention provides a truck-drone collaborative dynamic scheduling system for emergency logistics, comprising:

[0012] The network construction module is configured to build a truck-drone collaborative delivery network, in which each truck is equipped with a collaborative unit including large and small drones; the network includes warehouses, hubs, and demand points.

[0013] The planning model construction module is configured to establish a mixed integer programming model with the goal of minimizing total operating costs and constraints of power management, service allocation, time windows, and collaborative feasibility; the total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs;

[0014] The solution module is configured to solve the model using a randomized greedy algorithm, simultaneously deciding on truck routes and drone tasks in a single iteration to obtain truck route schemes, drone service allocation schemes, and dynamic power scheduling schemes.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the truck-drone collaborative dynamic scheduling method in emergency logistics described in the first aspect.

[0016] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the truck-drone collaborative dynamic scheduling method in emergency logistics described in the first aspect.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] This invention addresses emergency logistics and delivery needs by constructing a truck-drone collaborative delivery network encompassing warehouses, hubs, and demand points. Each truck is equipped with both large and small drone collaborative units to accommodate the operational requirements of various delivery scenarios. A mixed-integer programming model is established with the goal of minimizing total operating cost. This model comprehensively constrains power management, service allocation, time windows, and collaborative feasibility, fully covering the core requirements of each stage of delivery. The total operating cost is integrated across truck travel, drone flight energy consumption, charging, and overtime penalty costs, achieving refined cost control. Simultaneously, a randomized greedy algorithm is employed to solve the model, simultaneously deciding on truck routes and drone tasks in a single iteration. This efficiently outputs multi-dimensional scheduling schemes, ensuring both dynamic adaptability and collaborative feasibility of scheduling decisions while significantly improving the overall efficiency of emergency logistics and delivery and reducing comprehensive operating costs.

[0019] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0021] Figure 1 This invention provides a main flowchart of a truck-drone collaborative dynamic scheduling method in emergency logistics.

[0022] Figure 2 This is a schematic diagram of a truck-drone cooperative mode provided in an embodiment of the present invention;

[0023] Figure 3 A flowchart of the greedy algorithm provided in an embodiment of the present invention;

[0024] Figure 4 This is a node distribution diagram of a 28-node test road network provided in an embodiment of the present invention;

[0025] Figure 5 The convergence curve of the 28-node objective function provided in this embodiment of the invention;

[0026] Figure 6 A schematic diagram illustrating the dynamic change of battery power for eight drones in the optimal solution provided in this embodiment of the invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] Example 1

[0029] like Figure 1As shown in the figure, this embodiment discloses a truck-drone collaborative dynamic scheduling method in emergency logistics, including the following steps:

[0030] S1: Construct a truck-drone collaborative delivery network, in which each truck is equipped with a collaborative unit containing both large and small drones; the network includes warehouses, hubs, and demand points;

[0031] S2: To minimize total operating costs, a mixed integer programming model is established, constrained by power management, service allocation, time windows, and collaborative feasibility. The total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs.

[0032] S3: The model is solved using a randomized greedy algorithm. In a single iteration, the truck route and the drone mission are decided simultaneously to obtain the truck route scheme, the drone service allocation scheme, and the dynamic power scheduling scheme.

[0033] Next, combined Figure 1 This embodiment provides a detailed description of a truck-drone collaborative dynamic scheduling method for emergency logistics.

[0034] (I) Problem Description

[0035] This embodiment relates to a convoy of multiple trucks. Each truck k is equipped with a heterogeneous drone cooperative unit, comprising one large drone and one small drone. These drones have different battery capacities ( ), flight speed ( ), load capacity ( and charge / discharge performance ( There are differences in the symbols to adapt to different task requirements; among them, the subscripts... Indicating large drones, This refers to a small drone.

[0036] The entire delivery network comprises three types of nodes: a central warehouse (node ​​0, the starting point for all trucks; node n+1, the virtual destination for all trucks), and a set of hub points. (Intermediate stations where trucks can safely dock and release drones), and a set of demand points D (final supply receiving points). Each demand point d is spatially associated with a specific hub point i, and its service must be provided by drones launched from that associated hub point.

[0037] The system's core operational logic is deeply driven by the dynamic power management of drones. Initially, all drones are fully charged in the warehouse. Trucks carrying drones and supplies move between hubs; their path planning is not pre-determined statically, but dynamically generated based on a decision-making loop of real-time power assessment and feedback, as illustrated in the diagram. Figure 2 As shown. The key components of this cycle include:

[0038] 1. Charging en route: The truck can charge the onboard drone while traveling to the next hub.

[0039] 2. Mission Execution and Power Consumption: Arrive at the Hub Point Afterwards, the drone can be dispatched to serve its associated demand point d. This round-trip flight will consume power, and the power consumption is related to the flight distance. Proportional.

[0040] 3. Charging during stops: During stops at hub points, not only can drones that are not performing missions (if their batteries are not fully charged) charge, but drones that have completed their missions can also use this time to replenish their batteries while waiting for another drone on the same vehicle to return.

[0041] 4. Feasibility Screening and Next Stop Decision: After all drone missions at the current hub point have concluded and all possible charging has been completed, the system will determine the next stop based on the drones' updated battery status. The next accessible hub point j is assessed and selected. The selection principle is: when the truck arrives at j, it must be ensured that at least one drone has sufficient power to support the round-trip flight from j to one of its associated demand points, with a safety return margin (determined by a safety power ratio). (Regulations). This principle ensures that every step of the path is feasible.

[0042] In addition, the system must meet strict service requirements: all demand points must be fully covered and served only once; each truck can access any hub point at most once; the same drone can serve only one demand point at the same hub point. Specifically, some severely affected demand points are given priority (…). ), and has a latest service time ( ).

[0043] The system operates according to a dynamic decision-making mechanism driven by priorities and timeliness. Each requirement point... Priority attribute and its latest service time It is embedded in a heuristic scoring function for real-time evaluation. When dynamically constructing truck routes, the algorithm prioritizes routes that serve points of immediate need (i.e.,...). And nearby The pivot point is given a higher selection probability, thus implicitly guiding the path to prioritize high-time-sensitive tasks.

[0044] This embodiment aims to minimize total costs, including truck operating costs, drone flight costs, drone charging costs, and overtime penalty costs. Key decisions include: (1) the order in which trucks access hub points; (2) the allocation of service relationships between drones from each hub point to demand points; and (3) dynamic energy management based on power consumption and charging. To facilitate the solution of this problem, the following assumptions are made:

[0045] 1. The charging and discharging behavior of drone batteries is deterministic, and the impact of random factors such as battery degradation and ambient temperature on the battery capacity is not considered;

[0046] 2. The emergency relief supplies being transported are light and small items, so the load-bearing constraints of the truck can be ignored, and only its volume and capacity limitations need to be considered;

[0047] 3. All supplies will be loaded at the warehouse at the start of the mission, and no replenishment will be carried out during transportation;

[0048] 4. The truck's driving speed and the drone's flight speed are both constant, and the drone flies along a straight path between the hub point and the demand point.

[0049] In summary, this embodiment constructs a mixed integer programming model with the goal of minimizing total cost. It embeds dynamic decision-making logic through a carefully designed constraint system and reasonably abstracts uncertainty, thereby laying a solid model foundation for subsequent algorithm design and system analysis.

[0050] (II) Model Construction

[0051] Construct a mixed-integer programming model as follows:

[0052]

[0053] The objective function (1) of the model aims to minimize the total operating cost of the system, which consists of four parts:

[0054] The first part is the cost of truck travel, which is proportional to the total distance the truck travels in the route network; Let k be the cost per unit distance traveled by truck. , For the set of all available trucks; Let i be the set of truck path nodes; i and j are truck path nodes; Let i be the distance traveled between truck path nodes i and j; This means that if truck k travels from truck path node i to truck node j, and If the value is 1, then the value is 1; otherwise, the value is 0.

[0055] The second part is the energy consumption cost of drone flight, which is determined by the amount of battery discharge when the drone flies back and forth to perform delivery tasks; For the set of demand points, For the set of hub points, For large drone collections, ; , These respectively indicate that if drones u and v are assigned to truck k, and If the value is 1, then the value is 1; otherwise, the value is 0. These represent the unit discharge cost for large and small drones, respectively. , ; , These represent the conditions if drones u and v are at hub point i serving demand point d, and If the value is 1, then the value is 1; otherwise, the value is 0. Let i be the flight distance between hub point i and demand point d. ; , The discharge rates are for large and small drones, respectively.

[0056] The third part is the cost of charging drones, which covers the costs of all charging activities, including charging the truck while it is in motion, charging the standby drones while it is parked, and replenishing the power of the returning drones during mission breaks. , These are the charging cost coefficients for large drones and small drones, respectively. A collection of small drones, ; , The charging rates for large and small drones are respectively. For trucks The speed of travel; , These are the maximum battery capacities for large and small drones, respectively. , These represent the battery levels of drones u and v when they leave hub point i; , These represent the conditions if drones u and v are assigned to truck k, and If the value is 1, then the value is 1; otherwise, the value is 0. The time when the truck leaves hub point i; Let k be the time it takes for truck k to reach hub point i; , The flight speeds of large and small drones are respectively. , These represent the battery levels of drones u and v when they reach hub point i;

[0057] The fourth part is the timeout penalty cost, which imposes a linear delay penalty on high-priority requests that fail to be served within the latest specified time. This indicates the priority service status of demand point d. If demand point d is a priority service point, the value is 1; otherwise, it is 0. The latest service time for demand point d; The penalty cost per unit of timeout. The time for service demand point d.

[0058]

[0059] Constraint (2) is a truck loading volume capacity constraint, ensuring that the total volume of the drones and all goods to be delivered initially loaded on the truck does not exceed its capacity limit; where, The maximum loading volume of truck k; , These refer to the volumes of large and small drones, respectively. This indicates that if truck k has a service demand point d, and If the value is 1, then the value is 1; otherwise, the value is 0. Let d be the volume of demand at demand point d.

[0060]

[0061] Constraint (3) is the initial power constraint for the drones, which stipulates that all drones are fully charged when they leave the warehouse.

[0062]

[0063] Constraint (4) is a path origin and destination and uniqueness constraint, requiring each truck to start from the warehouse and eventually arrive at the virtual destination, and to execute only one delivery loop covering multiple hub points.

[0064]

[0065] Constraint (5) is a repeat access prohibition constraint to prevent trucks from repeatedly accessing the same hub point.

[0066]

[0067] Constraint (6) is a flow balance constraint to ensure the continuity of the truck path.

[0068]

[0069] Constraint (7) is a time continuity constraint, which establishes a recursive relationship between the arrival and departure times of trucks between hubs visited in succession.

[0070]

[0071] Constraint (8) is the power criterion for the service capability of UAVs, defining the necessary power condition for UAVs to serve demand points from hub points: the power they arrive with must be sufficient to cover the consumption of the round-trip flight and reserve a safe return margin. Among them, To ensure the safe battery level of the drone, guaranteeing its safe return trip; , Let u and v represent the conditions if drones u and v can serve demand point d from hub point i, and If the value is 1, then the value is 1; otherwise, the value is 0. This represents the penalty coefficient.

[0072]

[0073] Based on constraint (8), constraint (9) serves as a service-oriented access constraint, stipulating that trucks can only go to hubs that, upon their arrival, have at least one drone carrying the power condition of constraint (8) capable of serving the corresponding demand point.

[0074]

[0075] Constraint (10) is a requirement full coverage constraint, which requires that each requirement point must be served exactly once.

[0076]

[0077] Constraint (11) is a single-point service restriction for drones, which limits the same drone to serving at most one demand point at the same hub.

[0078]

[0079] Constraint (12) is the drone's payload constraint, ensuring that the delivery task does not exceed the drone's maximum payload capacity; among which, Let d be the weight of the quantity required at demand point d. , These represent the maximum payload of large and small drones, respectively.

[0080]

[0081] Constraint (13) is a feasibility constraint for task allocation, which clarifies that the UAV can only be allocated to serve the demand points that meet the power criterion of constraint (8).

[0082]

[0083] Constraint (14) is a vehicle-machine service coupling constraint that binds the service behavior of the drone to the physical arrival of the truck, meaning that the drone can only perform tasks at the hub where the truck actually stops.

[0084]

[0085] Constraint (15) is a service timeliness constraint, which defines the time for the drone to arrive at the demand point, providing a basis for evaluating service timeliness.

[0086]

[0087] Constraint (16) is a charging power update constraint during the journey, which describes the charging power update logic during the journey, that is, the truck can charge the drone while it is in motion.

[0088]

[0089] Constraint (17) is the departure power update constraint, and the comprehensive update formula for departure power is given to calculate the power of the UAV when it leaves the hub. This power comprehensively considers the power it arrives with, the power consumption of the mission execution, and the charging that may be carried out during the docking period.

[0090]

[0091] Constraint (18) is a minimum dwell time constraint for trucks, requiring that the dwell time of trucks at the hub point must at least satisfy the completion of the tasks (including flight and service time) of all UAVs assigned there, in order to ensure the synchronization of operations.

[0092]

[0093] Finally, constraint (19) is defined as a service relationship and clarifies the service attribution relationship between each truck and the demand point in the form of an auxiliary variable.

[0094]

[0095] Constraints (20)–(22) specify the range of values ​​for the decision variables.

[0096] This constraint system, through top-down logical design, ensures the feasibility and synergy of the solution across multiple dimensions, including resources, paths, tasks, power consumption, and time.

[0097] (III) Randomized Greedy Algorithm

[0098] This embodiment addresses the truck-drone collaborative emergency logistics delivery problem by constructing a mixed-integer linear programming model that incorporates power constraints, time window constraints, and priority requirements. The model involves multiple trucks, large and small drones, multiple hub points, and demand points. Its decision variables include truck route planning, drone task allocation, dynamic power management, and service time scheduling, exhibiting complex characteristics of high dimensionality, nonlinearity, and strong constraints. Given the NP-hard nature of the problem and the challenge of solving large-scale instances, this embodiment designs a randomized greedy algorithm to generate high-quality feasible solutions within a reasonable timeframe.

[0099] The algorithm employs a fully dynamic construction framework, simultaneously deciding on truck routes and drone services during the iteration process, such as... Figure 3 As shown, its core process is as follows:

[0100] Step 1: Initialization and Parameter Setting. Load the problem instance data, initialize the random number seed, set the algorithm control parameters (such as whether to enable roulette wheel selection, whether to enable the repair mechanism, etc.), and create an empty solution structure.

[0101] Step 2: Drone Allocation. A randomization strategy is used to dynamically allocate drones to each truck, supporting one large drone and one small drone per truck, while preserving the diversity allocation mechanism of the population generation model.

[0102] Step 3: Categorize Requirements: Based on the priority attribute of the requirements ( They are divided into priority demand points and ordinary demand points. Meanwhile, high-priority demand points are further categorized according to their latest service time. An initial candidate list is constructed in ascending order to give it a higher baseline weight in the heuristic score calculation.

[0103] Step 4: Fully Dynamic Path Construction. The core of the algorithm uses a state-driven iterative approach to plan the path for each truck.

[0104] 1. Each truck departs from the warehouse, maintaining its current location, visited hubs, current time, drone battery level, and served service requests. Initialize each truck's status: current location is the warehouse, time is 0, battery is fully charged, and the service list is empty.

[0105] 2. In the current state, assess the possibility of all unvisited hub points as the next stop, considering factors including:

[0106] Route feasibility (road damage status) );

[0107] The drone's battery level after charging during the trip;

[0108] Uncovered demand points that can be served at this hub point;

[0109] Comprehensive heuristic score (including distance, priority, time urgency, cost and diversity, etc.).

[0110] 3. The next station is dynamically determined from candidate hubs through a roulette wheel selection mechanism, balancing the local optimality of greedy selection with the global search capability of random exploration.

[0111] 4. Update truck status, record service events, and calculate changes in charging and discharging capacity during the stopover period.

[0112] Step 5: Handling Unserved Demand Points. If there are still unserved demand points after the main iteration, the algorithm initiates a secondary allocation mechanism to attempt to insert them into the existing feasible paths of trucks, ensuring complete coverage of the solution.

[0113] Step Six: Variable Calculation and Correction. Based on the constructed paths and service relationships, calculate all decision variables and auxiliary variables, including time variables, electricity consumption variables, and service relationship variables. If the correction mechanism is enabled, the solution will be checked for feasibility and corrected.

[0114] Step 7: Convergence Recording and Analysis. In population generation mode, the algorithm automatically records convergence metrics such as the objective function value, optimal solution update status, mean, and standard deviation for each iteration, and generates corresponding convergence curves and statistical reports, providing a basis for algorithm performance evaluation.

[0115] The key technologies of this algorithm are reflected in several aspects: First, it adopts a roulette wheel selection strategy to transform deterministic heuristic scores into probability distributions, thereby introducing controllable randomness in local optimization and avoiding premature entrapment in local optima; Second, it achieves fine coupling between power consumption and resupply processes and path decisions, accurately simulating two charging modes during movement and docking, ensuring that the drone always meets the safe power constraints; Third, it embeds a priority-driven and time-window sensitive mechanism, arranging priority demand points in ascending order of their latest service time. This design ensures that urgent demands closer to the latest service time are executed first, thereby avoiding service failure due to timeouts. This further responds to time constraints within the priority framework, ensuring that high-priority demands are met within the time window. At the same time, by giving urgent demands higher weight and deadline pressure in the evaluation function, i.e., by integrating heuristic scores (including distance, priority, time urgency, cost, and diversity), it ensures that the drone always meets the safe power constraints. The system assigns more points to hubs that can serve priority and urgent needs, increasing the probability of the roulette wheel selecting the hub, thereby guiding the path to prioritize serving key nodes; fourth, it integrates automatic repair and post-processing logic, which can detect and correct infeasible situations such as uncovered demand points, improving the success rate and robustness of the solution.

[0116] The main contribution of the greedy algorithm provided in this embodiment lies in proposing a state-driven, fully dynamic collaborative planning framework. Unlike the traditional two-stage method of path-first, task-later allocation, this approach enables simultaneous real-time decision-making for truck movement, drone dispatch, and energy management. Furthermore, the algorithm designs a heuristic evaluation function that integrates multiple objective factors and cleverly balances solution quality and population diversity through randomization. Crucially, the algorithm integrates a complete convergence recording and analysis module, capable of tracking the evolution of the objective function, the optimal solution update frequency, and population statistical characteristics in real time. This provides direct evidence for algorithm performance evaluation and parameter tuning. This module also generates detailed power change curves and service timelines, deepening the understanding of the solution's energy efficiency and time compliance. This randomized greedy algorithm can not only serve as an independent heuristic solver, obtaining satisfactory solutions within a finite time, but its generated diverse and high-quality feasible solution set can also serve as a high-quality initial population for advanced metaheuristic algorithms (such as genetic algorithms and simulated annealing), thus providing an effective and practical method for solving such complex collaborative logistics planning problems.

[0117] (iv) Numerical Experiments

[0118] This embodiment implements a randomized greedy algorithm on the Python platform. An experimental network containing 11 path nodes (1 warehouse, 9 hub points, and 1 virtual endpoint) and 28 demand points is used to analyze the model and algorithm and verify the model's effectiveness. The experimental network is configured with 4 trucks, 4 large drones, and 4 small drones. The spatial distribution and topology of the nodes and demand points are as follows: Figure 4 As shown.

[0119] Table 1 lists parameters such as the truck's and drone's flight speed, cost per unit distance, drone's endurance, waiting cost per unit time, and cost per unit time distance. These parameters were obtained by searching the official websites of the relevant equipment.

[0120] Table 1. Parameter values;

[0121]

[0122] 1. Algorithm convergence characteristics and optimal solution analysis

[0123] In a standard test case comprising 4 trucks, 8 drones, 9 hub points, and 28 demand points, the randomized greedy algorithm proposed in this embodiment demonstrated excellent convergence performance and solution quality after 400 iterations. Figure 5As shown, the algorithm continuously optimizes the objective function (total operating cost) during the iteration process, and finally obtains the optimal solution with a total cost of 1103.90 (yuan), which is 16.49% lower than the initial solution, fully demonstrating the effectiveness of the algorithm in solution space exploration and optimization.

[0124] Through in-depth analysis of the convergence process, the performance characteristics of the algorithm in three key stages can be observed:

[0125] (1) Initial rapid optimization stage: The algorithm achieved significant performance improvement in the first 12 iterations, with the objective function value rapidly decreasing from 1321.82 (yuan) to 1150.45 (yuan), a reduction of 13%. The efficient convergence in this stage is due to the algorithm's fully dynamic construction framework, which can quickly explore multiple feasible regions in the solution space and avoid getting trapped in local optima too early through a randomized selection mechanism. This feature enables the algorithm to quickly locate high-quality solution regions in the early stages of the solution process, laying the foundation for subsequent fine optimization.

[0126] (2) Progressive Improvement Stage: During iterations 12 to 118, the algorithm gradually improved the quality of the solution through six key improvements, with an average improvement interval of 23.4 iterations. This stage demonstrated the algorithm's fine-tuning capabilities, enabling coordinated optimization of path planning, task allocation, and power management while maintaining solution feasibility. Notably, the optimal solution obtained by the algorithm in iteration 118 achieved zero timeout penalty, fully satisfying the time window constraints of all priority requirements, demonstrating its superiority in handling complex time constraints.

[0127] (3) Stable convergence phase: After obtaining the optimal solution, the algorithm maintains the stability of the solution quality in the subsequent 282 iterations, proving the robustness of the obtained solution. This convergence characteristic shows that the algorithm can not only efficiently search for high-quality solutions, but also ensure the stability of the solutions, providing a reliable guarantee for practical applications.

[0128] Cost structure analysis of the optimal solution further verifies the economic rationality of the algorithm. Of the total cost of 1103.90 yuan, truck operating costs account for 42.4% (468.40 yuan), drone flight costs account for 35.0% (386.48 yuan), and charging costs account for 22.6% (249.02 yuan). This proportion reflects that in a collaborative logistics system, transportation and direct services are the main cost components, while charging costs remain at a reasonable level, indicating that the algorithm effectively balances the synergistic relationship between energy replenishment and task execution during the planning process.

[0129] 2. In-depth analysis of collaborative operation mechanisms and resource allocation

[0130] To further verify the algorithm's collaborative optimization capability under complex constraints, this embodiment conducts a micro-analysis of the resource allocation and operation mechanism of the optimal solution. Table 2 shows the detailed operation plan of the four trucks, including the path sequence, drone task allocation, and cost composition. Figure 6 The algorithm visualizes the dynamic changes in the battery levels of eight drones, revealing its innovative energy management strategies.

[0131] Table 2. Optimal Solution Collaborative Operation Scheme Configuration Details;

[0132]

[0133] As shown in Table 2, the collaborative network constructed by the algorithm exhibits dual characteristics of differentiated load balancing and spatial resource optimization. The task allocation of the four trucks is dynamically adjusted based on the spatial distribution of demand points and weight constraints: Truck 2's large drone serves four demand points, while Truck 3 serves only two. This asymmetric allocation is not a simple equilibrium but an intelligent optimization based on the serviceability (weight constraint) of each demand point and its spatiotemporal matching with the path. In terms of path planning, each truck forms an efficient service loop, avoiding unnecessary intersections and repeated visits, and strictly adheres to the constraint that "the same truck does not repeatedly visit the same hub point," demonstrating the algorithm's accuracy in path optimization.

[0134] Figure 6 The power consumption curves shown provide empirical support for the algorithm's energy collaborative management capabilities. The horizontal axis, representing the event sequence, indicates the step number of the drone's task execution; it has no physical unit and is only used to identify the order of events. The power consumption curves of all eight drones exhibit an intelligent charging and discharging mode: replenishing power reserves through mobile charging during operation, rationally consuming energy during service execution, and recharging during docking based on remaining power and subsequent task requirements. Of particular note is that the power consumption of all drones was consistently maintained above a safe threshold, ensuring the continuity and safety of operations. The power consumption management modes of different drones demonstrate the algorithm's adaptive characteristics: for task-intensive drones (such as the small drone 1 serving 5 demand points), the algorithm optimizes the order in which they access hub points, ensuring sufficient charging opportunities before critical tasks; while for drones with lighter tasks, it rationally schedules charging times to avoid resource idleness. This differentiated energy management strategy allows the system to maximize energy efficiency and reduce overall operating costs while ensuring safe operation.

[0135] Further analysis of the collaborative mechanism reveals that the algorithm achieves multi-dimensional optimization through spatiotemporal task coupling and dynamic decision feedback. In the time dimension, the algorithm prioritizes services for priority needs with strict time windows, ensuring the timely delivery of emergency supplies. In the spatial dimension, it minimizes the overall travel distance by rationally planning truck routes. In the resource dimension, it dynamically adjusts the charging strategy based on real-time battery status, achieving precise energy replenishment. This multi-dimensional collaborative optimization mechanism enables the algorithm to generate operational solutions that meet both timeliness requirements and economic feasibility under complex constraints.

[0136] In summary, the randomized greedy algorithm proposed in this embodiment demonstrates excellent convergence performance and collaborative optimization capabilities when solving the truck-drone collaborative emergency logistics delivery problem. The algorithm not only efficiently generates high-quality feasible solutions but also achieves collaborative optimization under multi-dimensional constraints through intelligent task allocation, path planning, and energy management, providing an effective solution for the intelligent scheduling of complex logistics systems.

[0137] Against the backdrop of frequent major emergencies and the severe challenges of "rapid response and precise coverage" in emergency logistics, this embodiment focuses on the collaborative optimization problem of truck-drone collaborative delivery systems. From the perspectives of path planning, task allocation, and dynamic power management, it proposes an emergency dispatch decision framework for dynamic and uncertain environments. By constructing a mixed-integer linear programming model integrating time windows and priority constraints, and designing a state-driven randomized greedy algorithm for efficient solution, simulation experiments based on an experimental network containing 28 demand points yield the following conclusions:

[0138] (1) The optimization of the truck-drone collaborative system requires a comprehensive consideration of transportation costs, energy efficiency, and service timeliness. Minimizing costs alone or simply pursuing service speed will not achieve optimal overall system performance. This embodiment verifies that by integrating a collaborative optimization model with dynamic power management and time window constraints, it is possible to achieve on-time service for all priority demand points while reducing the total cost by 16.49%, indicating that the system has achieved an effective balance between the dual objectives of cost and timeliness.

[0139] (2) Dynamic power management and the dual-mode charging mechanism of charging during and after the trip significantly improve energy utilization and mission sustainability. By precisely coupling truck driving, UAV missions and battery charging and discharging processes, the system can adjust the energy allocation strategy in real time to avoid service interruptions caused by insufficient power and ensure that the power of all UAVs is always above the safety threshold. Experiments show that this mechanism keeps the charging cost ratio at a reasonable level of 22.6%, reflecting the synergistic advantages of "mobile charging replenishment and docked charging optimization".

[0140] (3) The state-driven fully dynamic programming framework is a key enabler for improving the system's response flexibility and collaborative efficiency. This framework breaks through the limitations of the traditional two-stage optimization of "path first, task later" and realizes synchronous decision-making for truck movement, drone dispatch, and power updates. This not only enhances the system's adaptability to dynamic road networks and real-time demands, but also provides a mechanism for quickly adjusting scheduling schemes in case of emergencies.

[0141] (4) The randomized greedy algorithm demonstrates good convergence and solution quality in solving high-dimensional complex constrained problems. The algorithm balances local optimization and global exploration through a roulette wheel selection mechanism, and stably converges to a high-quality solution within 400 iterations. The obtained solution also shows robustness in terms of path feasibility, time window satisfaction, and energy security. This algorithm can be used independently as a rapid decision-making tool in emergency scenarios, and can also provide a high-quality initial population for subsequent metaheuristic algorithms, demonstrating strong practicality and scalability.

[0142] This specific embodiment addresses the optimization problem of truck-drone collaborative delivery systems in emergency logistics. It constructs a mixed-integer linear programming model integrating route planning, drone task allocation, dynamic power management, and time window constraints, aiming to minimize total operating costs while ensuring the timeliness of priority demand points. The model rigorously characterizes key real-world constraints such as charging en route, recharging at stops, power safety thresholds, and service uniqueness, providing a complete mathematical description for the system's collaborative operation. Based on this, a randomized greedy algorithm is designed to efficiently solve the model, and numerical experiments verify the effectiveness of the model and method. This provides decision support with both rigorous modeling and practical solution for truck-drone collaborative delivery in dynamic and uncertain emergency logistics scenarios, effectively ensuring the scientific formulation and efficient implementation of collaborative delivery solutions.

[0143] Example 2

[0144] This embodiment provides a truck-drone collaborative dynamic scheduling system for emergency logistics, including:

[0145] The network construction module is configured to build a truck-drone collaborative delivery network, in which each truck is equipped with a collaborative unit including large and small drones; the network includes warehouses, hubs, and demand points.

[0146] The planning model construction module is configured to establish a mixed integer programming model with the goal of minimizing total operating costs and constraints of power management, service allocation, time windows, and collaborative feasibility; the total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs;

[0147] The solution module is configured to solve the model using a randomized greedy algorithm, simultaneously deciding on truck routes and drone tasks in a single iteration to obtain truck route schemes, drone service allocation schemes, and dynamic power scheduling schemes.

[0148] Example 3

[0149] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a truck-drone collaborative dynamic scheduling method in emergency logistics as described in Embodiment 1 above.

[0150] Example 4

[0151] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the truck-drone collaborative dynamic scheduling method for emergency logistics as described in Embodiment 1 above.

[0152] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0153] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamic scheduling of trucks and drones in emergency logistics, characterized in that, include: Build a truck-drone collaborative delivery network, with each truck equipped with a collaborative unit containing both large and small drones; The network includes warehouses, hubs, and demand points; With the goal of minimizing total operating costs, and constrained by power management, service allocation, time windows, and collaborative feasibility, a mixed integer programming model is established; the total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs. The model is solved using a randomized greedy algorithm, which simultaneously makes decisions on truck routes and drone tasks in a single iteration to obtain truck route schemes, drone service allocation schemes, and dynamic power scheduling schemes. Establish a mixed-integer programming model with the following objective function: The objective function of the mixed-integer programming model aims to minimize the total operating cost of the system, which consists of four parts: The first part is the cost of truck travel, which is proportional to the total distance the truck travels in the route network; Let k be the cost per unit distance traveled by truck. , For the set of all available trucks; Let i be the set of truck path nodes; i and j are truck path nodes; Let i be the distance traveled between truck path nodes i and j; This means that if truck k travels from truck path node i to truck node j, and If the value is 1, then the value is 1; otherwise, the value is 0. The second part is the energy consumption cost of drone flight, which is determined by the amount of battery discharge when the drone flies back and forth to perform delivery tasks; For the set of demand points, For the set of hub points, For large drone collections, ; , These respectively indicate that if drones u and v are assigned to truck k, and If the value is 1, then the value is 1; otherwise, the value is 0. These represent the unit discharge cost for large and small drones, respectively. , ; , These represent the conditions if drones u and v are at hub point i serving demand point d, and If the value is 1, then the value is 1; otherwise, the value is 0. Let i be the flight distance between hub point i and demand point d. ; , The discharge rates are for large and small drones, respectively. The third part is the cost of charging drones, which covers the costs of all charging activities, including charging the truck while it is in motion, charging the standby drones while it is parked, and replenishing the power of the returning drones during mission breaks. , These are the charging cost coefficients for large drones and small drones, respectively. A collection of small drones, ; , The charging rates for large and small drones are respectively. For trucks The speed of travel; , These are the maximum battery capacities for large and small drones, respectively. , These represent the battery levels of drones u and v when they leave hub point i; , These represent the conditions if drones u and v are assigned to truck k, and If the value is 1, then the value is 1; otherwise, the value is 0. The time when the truck leaves hub point i; Let k be the time it takes for truck k to reach hub point i; , The flight speeds of large and small drones are respectively. , These represent the battery levels of drones u and v when they reach hub point i; The fourth part is the timeout penalty cost, which imposes a linear delay penalty on high-priority requests that fail to be served within the latest specified time. This indicates the priority service status of demand point d. If demand point d is a priority service point, the value is 1; otherwise, it is 0. The latest service time for demand point d; The penalty cost per unit of timeout. The time for service demand point d; Truck loading volume and capacity constraints ensure that the total volume of the drones and all goods to be delivered initially loaded onto the truck does not exceed its capacity limit, as follows: in, The maximum loading volume of truck k; , These refer to the volumes of large and small drones, respectively. This indicates that if truck k has a service demand point d, and If the value is 1, then the value is 1; otherwise, the value is 0. Let d be the volume of demand at demand point d. Initial battery power constraint for drones: All drones must be fully charged when they depart from the warehouse, as follows: The route origin and destination, as well as uniqueness constraints, require that each truck departs from the warehouse and ultimately arrives at a virtual destination, and executes only one delivery loop covering multiple hub points, as follows: The "Do Not Repeat" constraint prevents trucks from repeatedly visiting the same hub point. The constraint is as follows: Flow balance constraints, ensuring the continuity of truck paths, are as follows: The temporal continuity constraint establishes a recursive relationship between the arrival and departure times of trucks between consecutively visited hub points, as follows: The power consumption criterion for drone service capability defines that the power consumption of the drone arriving at the service demand point from the hub point must be sufficient to cover the consumption of the round-trip flight and reserve a safe return margin, with the following constraints: in, To ensure the safe battery level of the drone, guaranteeing its safe return trip; , Let u and v represent the conditions if drones u and v can serve demand point d from hub point i, and If the value is 1, then the value is 1; otherwise, the value is 0. Indicates the penalty coefficient; As a service-oriented access constraint, based on the drone service capability power criterion constraint, it is stipulated that trucks can only go to hub points where, upon arrival, at least one drone carrying a drone satisfies the power condition of the drone service capability power criterion constraint and is able to serve the corresponding demand point. The constraints are as follows: The requirement full coverage constraint requires that each requirement must be served exactly once, as follows: The single-point service limitation for drones restricts the same drone to serving at most one demand point at the same hub point, as follows: Drone payload constraints ensure that delivery tasks do not exceed the drone's maximum payload capacity, as follows: in, Let d be the weight of the quantity required at demand point d. , These represent the maximum payload of large and small drones, respectively. The feasibility constraints for task allocation clearly stipulate that drones can only be assigned to services that meet the power criterion requirements for drone service capabilities. The constraints are as follows: The vehicle-machine service coupling constraint defines that the drone can only perform tasks at the hub where the truck is actually parked, as follows: Service timeliness constraints define the time required for the drone to arrive at the demand point, providing a basis for evaluating service timeliness. The constraints are as follows: The en route charging power update constraint describes the logic for updating the charging power of the drone while the truck is en route. The constraint is as follows: The following constraints are provided for the departure battery update: A comprehensive formula for updating the departure battery is given to calculate the battery level of the drone when it leaves the hub. This battery level takes into account the arrival battery level, the power consumption during mission execution, and the charging that may occur during the docking period. The constraints are as follows: The minimum truck dwell time constraint requires that the truck's dwell time at the hub point must be sufficient to allow all drones assigned there to complete their tasks, including flight and service time, to ensure operational synchronization. The constraint is as follows: The service relationship definition, in the form of auxiliary variables, clarifies the service attribution relationship between each truck and the demand point, with the following constraints: The range of values ​​for the decision variables is as follows:

2. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The large drones and small drones differ in battery capacity, flight speed, payload capacity, and charging / discharging performance.

3. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The warehouse serves as both the starting point and virtual destination for all trucks. The hub point is an intermediate station where trucks can safely park and drones can be released; The demand point is the final material receiving point. The demand point is associated with a specific hub point and has priority attributes and a latest service time. The service of the demand point is completed by drones that take off from the specific hub point.

4. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The constraints, including power management, service allocation, time windows, and collaborative feasibility, specifically include: The power management constraints are used to ensure that the drone has sufficient power to complete the round-trip flight and reserve a safety margin before serving any demand point; the charging behavior of the drone during the truck's journey and during its stop at hub points is modeled and managed. The service allocation constraints are used to ensure that each demand point is served exactly once, and that the same drone serves at most one demand point at the same hub point. The time window constraint is used to set the latest service time for high-priority demand points and to impose penalties on their delayed service. The collaborative feasibility constraint is used to couple the service behavior of the drone with the physical access of the truck, stipulating that the drone can only be dispatched to perform tasks from the hub point actually arrived at by the truck, and the truck can only go to the hub point on which its drone can serve at least one related demand point at the current moment.

5. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The truck operating cost is proportional to the total distance the truck travels in the route network; The energy consumption cost of the drone flight is determined by the amount of battery discharge during the drone's round-trip flight to perform delivery tasks; The cost of charging the drone includes the cost of charging the drone while the truck is in motion, charging the standby drone while it is parked, and replenishing the power of the returning drone during mission breaks. The timeout penalty cost is a linear delay penalty imposed on high-priority requests that fail to be served within the latest specified time.

6. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The randomized greedy algorithm specifically includes: Requirements are categorized and sorted based on priority and time window. For each truck, dynamic maintenance status information is provided, including location, time, battery level, and serviced demand points; At each decision step, candidate hub points are evaluated based on the current state, and a heuristic score is calculated that includes distance, time urgency, and priority weights. The next hub point to visit is determined by a roulette wheel selection mechanism, and its status and battery level are updated. If there are any uncovered demand points, a secondary allocation and repair mechanism is executed to obtain a feasible solution that covers all demand points.

7. The truck-drone collaborative dynamic scheduling method in emergency logistics as described in claim 1, characterized in that, The truck routing scheme, drone service allocation scheme, and dynamic power dispatching scheme specifically include: The truck routing scheme is used to determine the order in which each truck departs from the warehouse and visits each hub point, as well as the arrival and departure times of each hub point; The drone service allocation scheme is used to determine which drone will serve which associated demand point at each visited hub point, and the corresponding service completion time. The dynamic power scheduling scheme is used to determine the real-time power status of each drone when it leaves the warehouse, arrives at and leaves each hub point, as well as the process of charging and recharging during the journey.

8. A truck-drone collaborative dynamic scheduling system for emergency logistics, employing the truck-drone collaborative dynamic scheduling method for emergency logistics as described in any one of claims 1-7, characterized in that, include: The network building module is configured to build a truck-drone collaborative delivery network, with each truck equipped with a collaborative unit that includes both large and small drones; The network includes warehouses, hubs, and demand points; The planning model construction module is configured to establish a mixed integer programming model with the goal of minimizing total operating costs and constraints of power management, service allocation, time windows, and collaborative feasibility; the total operating costs include truck driving costs, drone flight energy consumption costs, drone charging costs, and overtime penalty costs; The solution module is configured to solve the model using a randomized greedy algorithm, simultaneously deciding on truck routes and drone tasks in a single iteration to obtain truck route schemes, drone service allocation schemes, and dynamic power scheduling schemes.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the truck-drone collaborative dynamic scheduling method for emergency logistics as described in any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the truck-drone collaborative dynamic scheduling method for emergency logistics as described in any one of claims 1-7.

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