Unmanned aerial vehicle medical material distribution optimization method

Abstract

The invention discloses an unmanned aerial vehicle medical material distribution optimization method, which combines path planning and charging facility layout, adopts a mixed integer linear programming (MILP) model and a heuristic algorithm, and aims to realize efficient medical material distribution. Firstly, basic data is provided for unmanned aerial vehicle path planning and charging facility site selection by obtaining application scene information, such as customer requirements, unmanned aerial vehicle performance and candidate charging facility positions; then, on the basis of inherent characteristics of the charging facilities, by combining unmanned aerial vehicle path planning, site selection of the charging facilities is optimized, and an optimization model with the minimum total cost is constructed; by introducing a mathematical heuristic algorithm, a high-quality distribution path and charging facility layout scheme is given on the premise of meeting constraints such as electric quantity, load and timeliness. According to the method, the unmanned aerial vehicle medical material distribution efficiency can be effectively improved, the distribution task can be efficiently and reliably completed under the limiting conditions of the electric quantity, the time window, the load and the like, and the method has high practical application value.

Description

Technical Field

[0001] This invention belongs to the field of smart medical supply delivery, specifically involving an optimized method for drone-based medical supply delivery. Background Technology

[0002] The delivery and collection of urban medical supplies is a crucial component of the healthcare service system. Its operational efficiency not only affects the response speed and operating costs of medical services but also directly impacts the progress of smart healthcare system development and the improvement of public health security. Current medical supply delivery methods primarily rely on ground transportation, which is easily constrained by factors such as urban traffic congestion, resulting in low delivery efficiency, limited service coverage, and difficulty in meeting the demands for timely and reliable medical services.

[0003] Unmanned Aerial Vehicles (UAVs), unrestricted by ground transportation, offer advantages in speed, efficiency, and flexibility, demonstrating broad application prospects in smart medical logistics. Utilizing UAVs to deliver medical supplies is expected to significantly improve transportation efficiency and service coverage. However, current UAVs still face practical challenges such as limited flight endurance, limited payload capacity, and the need to meet customer time windows. Optimized route planning is crucial to improving service efficiency and reducing operating costs. While route optimization can improve delivery efficiency, limited endurance still makes it difficult to meet the service needs of all customers. Therefore, introducing charging infrastructure is an effective way to address the endurance bottleneck of UAVs. By strategically deploying charging facilities along service routes, UAVs can replenish their power mid-journey, significantly extending their service range and mission capabilities, thereby improving overall service levels. In this context, the location of charging facilities directly impacts UAV accessibility and system operational efficiency, becoming a critical factor in UAV route planning. The capacity limitations of charging facilities and the differences in charging time among UAVs are also significant factors affecting the feasibility of delivery solutions. Because drones arrive at charging facilities with varying remaining battery levels, their required charging times differ. Furthermore, if the number of drones planned for charging at a single facility exceeds its capacity limit, the service plan becomes infeasible. Therefore, the site selection and route optimization for charging facilities must comprehensively consider practical issues such as facility capacity constraints and charging time allocation.

[0004] For the complex multi-factor optimization problems mentioned above, designing efficient and stable solution algorithms is crucial. Currently, common algorithms in related research can be broadly categorized into two types: exact algorithms, which can find the optimal solution by combining acceleration strategies, although their computation time is relatively long; and heuristic algorithms, which are faster and suitable for quickly solving large-scale problems, but often fail to obtain the optimal solution. Therefore, achieving a balance between solution time and solution quality, and constructing efficient algorithms suitable for practical applications, has become a key technical issue in ensuring the efficiency of medical services and reducing operating costs. Summary of the Invention

[0005] This invention addresses the specific challenges faced by drone applications in medical supply delivery scenarios: the self-pickup and self-delivery model among medical institutions creates designated pick-up and delivery point pairs with strict time-sensitivity requirements. The delivery time constraints between these point pairs are significantly stricter than those of conventional single-point delivery. Simultaneously, the inherent range limitations and payload constraints of drones make path planning and endurance assurance core bottlenecks. To address these challenges, this invention provides an optimized method for drone-based medical supply delivery, designing an efficient collaborative scheduling mechanism for pick-up and delivery point pairs under time constraints. This ensures that pick-up and delivery points with strong time-sensitivity correlations complete collaborative delivery within strict time windows or the maximum allowable transfer time. This is achieved by accurately expressing and handling the time coupling constraints between point pairs in the model. Compared to battery swapping stations, deploying charging piles significantly reduces initial investment and operation / maintenance costs, better meeting the economic needs of large-scale practical applications. The charging-site selection problem requires optimizing the spatial layout of charging facilities to effectively support the endurance requirements of the drone network while minimizing total cost. Addressing the complex combinatorial optimization problem of drone-based medical supply delivery scenarios necessitates the use of high-performance solution strategies. Mathematical heuristic algorithms, which combine heuristics with mathematical models (MILP), effectively integrate precise models with heuristic rules. Compared to purely heuristic methods such as Adaptive Large Neighborhood Search (ALNS), they can provide higher quality (higher accuracy, closer to the optimal solution) feasible solutions within an acceptable computation time, ensuring the practical feasibility and superiority of the solution under multiple complex constraints such as load, range, time window, and charging.

[0006] To solve the technical problem, the technical solution of the present invention is as follows:

[0007] An optimized method for drone-based medical supply delivery, the method comprising:

[0008] Step 1: Input customer requirements, drone performance parameters and coordinates of candidate charging facilities, analyze and organize time constraints, focus on identifying pairing pick-up and delivery points and time window requirements, and output structured scenario data;

[0009] Step 2: Obtain charging facility information and drone battery consumption rate, analyze charging facility efficiency and access patterns, optimize facility layout to reduce downtime, and obtain charging facility layout plan;

[0010] Step 3: Charging site selection and path model establishment. Based on the scenario data obtained in Step S1 and the charging facility analysis results obtained in Step 2, a mixed integer linear programming model is established, and the objective function and constraints are set to obtain the mathematical optimization model.

[0011] Step 4: Using the mathematical optimization model obtained in step S3, solve the model using a mathematical heuristic algorithm, and combine simulated annealing and local optimization techniques. Through iterative search of the equilibrium solution space, obtain the drone delivery route and charging facility location scheme.

[0012] Furthermore, in step S1, the customer information includes: the geographical coordinates of the paired pick-up and delivery point, the time window, and the material requirements; the drone performance parameters include: flight speed, maximum payload capacity, and battery capacity.

[0013] Furthermore, in step S3, the objective function includes minimizing the total cost, including the cost of purchasing the drone, the cost of constructing the charging facility, and the transportation cost. The constraints include: drone pickup and delivery path and facility location constraints, drone load limit constraints, drone power limit constraints, drone time constraints, and charging sequence constraints at the drone charging facility.

[0014] Furthermore, step S3 specifically includes:

[0015] S301: Input the scenario data from step 1 and the charging facility analysis data from step 2, classify customer needs, identify each customer node, ensure the timeliness requirements of customer point delivery tasks, organize the performance parameters of the drone, organize the locations of candidate charging facilities, confirm the charging efficiency and availability of each charging facility, and calculate each node, including the relative position and distance between the customer point and the charging facility, to provide a basis for subsequent route planning.

[0016] S302: Establish decision variables, define the decision variables in the problem, and ensure that the model can express the optimization objective and constraints; define a 0-1 decision variable to indicate whether the drone flies from one node to another; if it flies, the variable is 1, otherwise it is 0; define a 0-1 decision variable for each candidate charging facility node to indicate whether the charging facility is selected for construction; if selected, the variable is 1, otherwise it is 0; charging facility access variable: define a variable for each drone to indicate whether the drone needs to access the charging facility; if it does, the variable is 1, otherwise it is 0.

[0017] S303: Establish the objective function and five core constraints. These five constraints ensure the rationality and feasibility of the route planning and charging facility site selection scheme.

[0018] Constraint 1: Route and Facility Location Constraints

[0019] Ensure that each customer node is accessible by drone, and that each node can only be connected via one path. Pickup and delivery points must be paired, and the delivery point must be after the pickup point.

[0020] Constraint 2: Drone load limit constraint

[0021] Ensure that the load of each drone does not exceed its maximum carrying capacity. In each delivery mission, the drone's load must be consistent with the cargo requirements along the route and must not exceed the drone's maximum load.

[0022] Constraint 3: Drone power limit constraint

[0023] The drone's battery power needs to be limited to ensure that the drone has enough remaining power when flying on each route segment. If the drone's battery is low, it must go to a charging facility to replenish its power. The charging facility must be reasonably inserted into the route to ensure the feasibility of the route in terms of battery power.

[0024] Constraint 4: Time Window Constraint

[0025] The arrival time of each node must be within the specified time window. If there are strict time window requirements, it must be ensured that the delivery point is strictly after the pickup point and that the timeliness requirements are met.

[0026] Constraint 5: Charging sequence constraint at charging facilities

[0027] When a drone needs to be charged, the order in which charging facilities are accessed must follow certain rules. If a charging facility is selected, the drone must stay at the selected charging facility when it needs to be charged, and there must be no conflict in accessing the charging facilities to ensure that each charging can be carried out effectively and will not have an unreasonable impact on the path.

[0028] S304: Model Solving. The model is solved using mathematical optimization methods to obtain delivery routes and charging facility location schemes that satisfy all constraints, including the starting point, ending point, nodes on the route, and their access order for each drone. Based on the location results of the charging facilities, it is ensured that drones can be charged in time when their power is low, and that the layout of the charging facilities is economical.

[0029] S305: Model Validation and Adjustment. Validate the rationality of the model's solution results and adjust them according to actual conditions. Validate the solved path and charging facility layout scheme to ensure that the drones can complete all delivery tasks as planned. Evaluate the energy feasibility of the path, the time window satisfaction, and whether the load constraints are met. Adjust the model based on the validation results, correcting any deficiencies in path planning and charging facility location selection, and obtain an optimized charging facility location scheme and drone delivery path that meets the five core constraints. Output the final path plan, specifying the driving route, charging facility location, and access order for each drone.

[0030] Furthermore, step S4 specifically includes solving the mathematical optimization model established in step 3 using a heuristic algorithm, thereby obtaining a high-quality delivery route and charging facility site selection scheme that satisfies all constraints.

[0031] S401: Initial solution generation, constructing an initial solution as the starting point for optimization;

[0032] Starting from the warehouse, a greedy strategy is used to randomly select unassigned pickup points and insert them into the path; based on the pairing dependencies, the corresponding delivery points are inserted into the path in the order of the shortest path to ensure a closed loop, i.e., finally returning to the warehouse node; this process is iterated until all pickup and delivery points are assigned, generating a preliminary delivery path; a preliminary path planning scheme and charging facility layout are output.

[0033] S402: P / D node removal operator, which improves the path structure by removing certain P / D nodes;

[0034] Select a removal operator (including random removal operator, relevant removal operator, or worst-cost removal operator) to remove some P / D nodes. Pairing constraints apply: if a pickup point is removed, its corresponding delivery point must be removed simultaneously to ensure the consistency of the path structure. Exclude warehouse nodes; the removal operation cannot involve warehouse nodes. Output the path structure after node removal to prepare for the next insertion operation.

[0035] S403: P / D node insertion operator, which re-inserts removed P / D nodes into the path to optimize the path order;

[0036] Insertion operators (including random insertion, greedy insertion, or regret insertion operators) are used to re-insert P / D nodes into the current path. Priority is given to re-inserting removed pickup points, and their corresponding delivery points are also inserted accordingly, ensuring that pickup points precede delivery points. For nodes with strict time window requirements, delivery points are inserted immediately after their corresponding pickup points to meet timeliness constraints. The output is the adjusted path, ensuring that the path structure is reasonable and meets timeliness and order constraints.

[0037] S404: Charging facility insertion operator ensures that the path meets the power feasibility requirements and solves the problem of insufficient power by inserting charging facilities;

[0038] A subset of charging facility nodes are selected from the candidate set of charging facilities and inserted into paths where power supply is infeasible, based on the principle of minimizing the construction cost and path allocation cost of the charging facilities. The degree of improvement in power supply before and after the insertion of the charging facilities is evaluated, and locations that can eliminate power supply gaps or optimize power supply distribution are prioritized. If the selected charging facility location is unreachable, the solution is marked as infeasible and a penalty is imposed to prevent it from entering the final solution. The location and power supply status of the charging facilities in the output path are optimized to ensure that each path can meet the power supply requirements.

[0039] S405: Simulated annealing and penalty objective function to avoid heuristic algorithms getting stuck in local optima and enhance global exploration capabilities;

[0040] Based on the quality of the current best solution and the new solution, a decision is made on whether to accept the new solution. If the new solution is better, it is accepted directly; if the new solution is worse, it is accepted with a certain probability, which gradually decreases as the temperature decreases, i.e., the simulated annealing process. A penalty objective function is introduced to penalize infeasible solutions, such as those exceeding the power limit or time window conflicts, to guide the algorithm to avoid infeasible solutions. The output improves the global solution-finding ability while expanding the solution space through the simulated annealing mechanism.

[0041] S406: Operator weight update, dynamically adjust the weight of each operator to further optimize the quality of the solution;

[0042] The bias of operators is dynamically controlled using a roulette wheel selection mechanism. In each iteration, the selection probability of an operator is adjusted based on its historical performance. The performance of an operator in each cycle is determined by the quality of the generated solution. If an operator generates a solution that is better than the current solution, the operator is assigned a higher weight to increase its selection probability in subsequent iterations. The operator weights are updated, and the algorithm is adaptively optimized to improve the quality of the solution.

[0043] S407: Refined search based on local branches improves the quality of the solution through local optimization and avoids the algorithm from converging to a suboptimal solution too early;

[0044] Local branching is introduced to optimize the current optimal solution during the iteration process. By defining a neighborhood solution space, the neighboring regions of the solution are explored to enhance the diversity of solutions. Perturbation is performed in the neighborhood, and a mixed integer programming model is used to optimize the solution after each perturbation. If no improved solution is found, the search range of the neighborhood is gradually increased until a better integer feasible solution is found. The output is the solution that optimizes the current solution through local search, improves the quality of the solution, and ensures that the solution satisfies all constraints.

[0045] Compared with the prior art, the advantages of the present invention are as follows:

[0046] For medical supply delivery scenarios, this invention innovatively integrates drone charging facility site selection and route planning into a collaborative decision-making model, fully considering the mutual influence of the two decisions. Compared to battery swapping station models, charging facilities significantly reduce operating costs and improve the economic efficiency of logistics tasks. Under the premise of strictly meeting customer service time windows, this model can achieve efficient, accurate, and diversified supply delivery services, effectively improving customer satisfaction and promoting the diversification and quality upgrade of logistics services. Furthermore, the mathematical heuristic developed in this invention introduces a MILP-based mathematical model for solving the problem, enabling the acquisition of higher-quality integrated site selection-route solutions. Attached Figure Description

[0047] Figure 1 A technical flowchart of an optimized method for drone-based medical supply delivery according to the present invention. Detailed Implementation

[0048] The specific implementation of the present invention is described below with reference to embodiments:

[0049] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0050] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0051] Example 1:

[0052] This invention constructs a composite optimization method for drone delivery routes and charging facility site selection in medical scenarios based on mathematical heuristic algorithms. It integrates route planning and charging facility site selection decisions, employing mathematical heuristics to efficiently and effectively generate drone delivery routes and charging facility site selection schemes that satisfy complex constraints in medical settings. The technical solution of this invention is as follows:

[0053] S1: Obtain application scenario information. This information includes customer needs, time windows and coordinates, coordinates of candidate charging facilities, and drone flight speed, maximum payload capacity, and battery capacity. The section on matching pickup and delivery points, which has strict time window requirements for delivery tasks, highlights one of the characteristics of medical delivery application scenarios.

[0054] S2: Analysis of the Operating Characteristics of Charging Facilities. To improve the working efficiency and delivery range of drones while also considering economic benefits, this invention employs charging facilities to replenish the power of drones. This invention studies in detail the operating characteristics of charging facilities, including parameters such as charging efficiency and access modes, to ensure the quality of the site selection and planning scheme for drone charging facilities;

[0055] S3: Charging location selection - path model establishment. Based on the information obtained from S1 and S2, a mixed-integer linear programming model is established:

[0056] (1) Define the set, parameters, and decision variables;

[0057] (2) Establish a total cost minimization objective function, including the cost of purchasing drones, the cost of building charging facilities, and the cost of transporting drones;

[0058] (3) Construct constraint equations for 5 modules: UAV pick-up and delivery path and facility location constraints; UAV load limit constraints; UAV power limit constraints; UAV time constraints; and UAV charging sequence constraints at charging facilities.

[0059] S4: Based on a mathematical heuristic algorithm, the model established in S3 is solved to obtain a set of routes that enable all drones to provide services to customers and return to the warehouse while meeting load and power capacity requirements. This mathematical heuristic algorithm utilizes the MILP model introduced during the iterative solution process of ALNS to further optimize the solutions generated during the optimization iteration. That is, during the process of judging and updating solutions, when a new solution becomes the new global optimum, the solver is called to solve the MILP model, thereby further optimizing the solution. Mathematical Heuristic Algorithm Framework Figure 1 As shown.

[0060] Furthermore, the specific processes for each step include:

[0061] S1. Obtain application scenario information;

[0062] Planning drones for medical supply delivery scenarios requires acquiring and processing a large amount of information. Of particular note is that customer needs are typically presented in the form of paired pick-up and delivery points; that is, a task includes one pick-up point and one strictly associated delivery point. This pairing model is one of the core characteristics of the medical scenario. The strict time windows for these paired pick-up and delivery points reflect the high time sensitivity of medical delivery; exceeding the time window may lead to task failure or loss of medical value.

[0063] Other information, such as drone performance parameters, defines the key performance indicators of drones performing delivery tasks and directly affects path planning; infrastructure information provides the geographical coordinates of candidate charging facilities in the network that can be used for drones to replenish their power mid-journey, which relates to the layout and availability of charging facilities and is crucial for planning complex delivery tasks.

[0064] S2. Analysis of the working characteristics of charging facilities;

[0065] The key challenge in deploying drone charging infrastructure for medical delivery lies in ensuring both endurance and mission continuity under strict drone power constraints, while also balancing economic efficiency. Relatively stable demand among medical institutions provides favorable conditions for efficient infrastructure planning and utilization. However, the time-sensitive delivery of medical supplies requires drones to precisely meet time windows at each stage, placing stringent demands on the timeliness of charging facility site selection. Furthermore, most technologies typically assume that a drone only accesses the same charging facility once, leading to resource waste. Therefore, optimizing charging equipment access patterns is crucial to improving efficiency and ensuring mission timeliness.

[0066] S3. Charging location selection-path model establishment;

[0067] To ensure the model's rationality, the following assumptions are made based on actual needs:

[0068] a. This model sets the drone logistics system with a single warehouse as the origin and destination of all tasks;

[0069] b. All drone models and performance parameters are completely identical and maintain a constant flight speed;

[0070] c. Each charging facility is equipped with only one charging device, which is exclusive, meaning that it can only provide energy replenishment services to a single drone at any given time.

[0071] d. The energy consumption of the drone is strictly linearly related to the flight distance, excluding energy loss during pick-up and delivery operations, charging wait times, and other non-flight phases;

[0072] e. All drones depart from the warehouse with a full charge and are fully charged to their rated capacity each time they arrive at the charging facility.

[0073] f. The modeling scenario ignores the potential impact of external environmental variables such as weather and wind speed on the drone's flight.

[0074] (1) Define the set, parameters, and decision variables;

[0075] The symbol definitions required in this application are shown in Table 1.

[0076] Table 1

[0077]

[0078]

[0079] (2) Establish the objective function that minimizes total cost;

[0080] This model aims to minimize total cost, which comprises three components: drone equipment configuration cost, charging infrastructure construction cost, and drone operating cost. Equipment configuration cost is the initial fixed investment required to perform logistics services; construction cost corresponds to the expenditure on deploying the charging network to ensure drone range; and operating cost, quantified, covers the expenses incurred during mission execution. The objective function is expressed as:

[0081]

[0082] K represents the collection of drones, C d For the purchase cost of a single drone, d ij Let x be the distance between point i and point j, S be the set of candidate charging facilities, and V be the set of all points, where V = P∪D∪S∪{o}∪{o′}, where nodes {o} and {o′} both represent the same drone warehouse. To distinguish the different roles of the warehouse in the model, {o} represents the departure node, and {o′} represents the return node; ijk The variable is 0-1. If drone k flies from point i to point j, the value is 1; otherwise, it is 0, j∈V\{o′}\{o}, i≠j, C t The cost per unit distance traveled by the drone; y i x is a 0-1 variable; if a charging facility is chosen to be built at point i, it is 1; otherwise, it is 0, i∈S; ojk This indicates that drone k flies from point o to point j;

[0083] (3) Construct constraint equations for the five modules;

[0084] a. Constraints on drone delivery routes and facility location;

[0085] Constraints (2) and (3) together ensure that all customer nodes are accessed by the drone only once, and the pickup point is prohibited from being the final node except for returning to the warehouse, to ensure that the corresponding delivery must be completed after pickup. For technical terminology purposes, the entire customer node group will henceforth be referred to as the P / D node.

[0086]

[0087] P represents the set of medical institutions that only have the task of retrieving supplies;

[0088]

[0089] D represents a group of medical institutions that only have material delivery tasks.

[0090] Constraint (4) restricts the drone to access only the coordinates of the selected charging facility.

[0091]

[0092] S is the set of candidate charging facilities, and M is a large number;

[0093] Network flow balance is achieved through constraint (5), which requires that the in-degree of intermediate nodes be the same as the out-degree to maintain the consistency of the flow direction of the path, i.e., path continuity.

[0094]

[0095] K represents the drone k, and constraint (6) forces the drone to depart from the warehouse and return after completing the task, ensuring a closed loop of the task.

[0096]

[0097] x jo′k Let U mean that UAV k flies from point j to point o′. Constraint (7) limits each UAV to a maximum of a single mission trip.

[0098]

[0099] Constraint (8) prohibits drones from accessing multiple charging facilities consecutively to improve mission efficiency and ensure the rationality of the application.

[0100]

[0101] Constraint (9) requires that the same UAV must serve the paired P / D node to ensure mission continuity.

[0102]

[0103] x i′jk Let UAV k fly from point i′ to 6j. Constraints (10), (11) and (12) monitor the UAV’s trajectory before and after the charging facility through the path tracking mechanism in order to optimize the utilization of charging resources and ensure the effectiveness of path planning.

[0104]

[0105]

[0106] β ijkThe variables are 0-1. If the drone k passes through point i to reach the charging facility and then flies to point j, the value is 1; otherwise, it is 0. i,j∈V\S, and constraints (13), (14), (15), and (16) are expressed using x. ijk y i Use variables to express intermediate variable z ik w ik The value is used to update the location and access status of charging facilities and equipment.

[0107]

[0108] b. Drone load limitations;

[0109] Constraints (17), (18), (19), and (20) jointly track the real-time load status of the drone at the P / D node. Among them, constraints (19) and (20) specifically monitor the load changes of nodes adjacent to the charging facility, since the charging operation does not involve the storage or retrieval of materials, and its load remains unchanged. For clear quantitative representation, the demand of the pickup node is defined as a positive value, and the demand of the delivery node is defined as a negative value.

[0110]

[0111]

[0112]

[0113] q ki Let q represent the payload of drone k at point i, where i∈V\S,q ko =0, U is the maximum payload of the drone, u i Let i represent the amount of goods picked up or delivered. Constraint (21) requires that the load of the drone at all nodes must not exceed its maximum carrying capacity, thereby ensuring that the load limit is always met during operation.

[0114]

[0115] c. Drone power consumption limitations;

[0116] Constraints (22), (23), and (24) are used to monitor and update the real-time battery status of the drone at the P / D node. Among them, constraint (24) requires that the drone has a non-negative battery level when it arrives at the charging facility, ensuring that the drone has a minimum battery redundancy during flight to reach the charging facility.

[0117]

[0118]

[0119] Let $\frac{ ... Let ε be the battery level of the UAV k when it reaches point i, i∈V\{o′}, and ε be the battery consumption rate. Constraint (25) limits the battery level at the task node to remain constant, and clarifies that energy consumption only occurs during the flight segment.

[0120]

[0121] Constraint (26) ensures that the battery level of the drone is strictly greater than zero when it arrives at all service nodes and returns to the warehouse.

[0122]

[0123] The initial state is defined by constraint (27) as starting with a full charge, while constraint (28) stipulates that the drone will be fully charged at the charging facility, fundamentally eliminating the risk of subsequent missions being interrupted due to insufficient power.

[0124]

[0125]

[0126] d. Drone time constraints;

[0127] Constraints (29), (30) and (31) are used to track the arrival time of the drone at each P / D node and charging facility.

[0128]

[0129]

[0130] t ij t represents the transportation time between point i and point j. ki This represents the time when drone k arrives at point i, where i∈P∪D∪{o′};

[0131] Constraint (32) represents the queuing time at the charging facility, providing a flexible buffer for charging operations.

[0132]

[0133] s ki Let i represent the time when the drone k-path point i starts charging at the charging facility, i∈P∪D∪{o}. Constraint (33) records the time when the drone arrives at the first pickup or delivery point after leaving the charging facility, ensuring the timeliness of subsequent tasks.

[0134]

[0135] The critical sequential logic is enforced by constraint (34): when Rij When =1, the arrival time of pickup point i must be strictly earlier than that of delivery point j.

[0136]

[0137] Constraint (35) To ensure that time-sensitive medical supplies can be delivered within the specified time limit, point-to-point time control of medical supplies shall be implemented.

[0138]

[0139] T d E represents the time requirements for picking up and delivering time-sensitive medicines; E represents the set of medical institutions that deliver supplies with high time requirements for picking up and delivering them, E∈D, s i The service time for point i;

[0140] Constraint (36) forces all service nodes to arrive within a preset time window. This hard time window constraint ensures the precise synchronization of medical supplies handover and personnel work plans, guaranteeing the synergy of the medical process.

[0141]

[0142] [e i ,l i ] represents the time window of point i;

[0143] Ultimately, constraints (37)-(39) precisely quantify the charging time at the charging facilities, achieving strict management of the time dimension.

[0144]

[0145] Q indicates the maximum battery capacity of the drone;

[0146] e. Charging sequence constraints at drone charging facilities;

[0147] Constraints (40) and (41) avoid facility usage conflicts by rationally arranging the charging sequence of drones. This is achieved through a binary decision variable α. kk′i To plan the charging sequence of drones: when decision variable α kk′i When α = 1, it means that drone k′ has priority over drone k in using the charging facility; otherwise, when α = 1, it means that drone k′ has priority over drone k in using the charging facility. kk′i If the result is 0, the order of use will be swapped.

[0148]

[0149]

[0150] α kk′jLet S represent a 0-1 variable. If drone k is charged at charging facility i before drone k′, then the value is 1; otherwise, the value is 0, where i∈S.

[0151] This mechanism coordinates the start time and sequence of charging for each drone, ensuring conflict-free charging operations under limited facility resources, fundamentally guaranteeing the continuity and time reliability of the task chain, while maximizing the utilization efficiency of charging facilities.

[0152] S4. Based on the mathematical heuristic algorithm, the model established in S3 is solved to obtain a set of routes that enable all drones to provide services to customers and return to the warehouse while meeting the load capacity and power capacity requirements.

[0153] 1. Dynamically construct the initial solution by minimizing node spacing: First, generate a new path starting from the warehouse, and randomly select unassigned pickup points to insert into the path based on a greedy strategy; for the already inserted pickup points, insert their corresponding delivery points in order according to the principle of minimizing the path based on the pairing dependencies; the path ends at the warehouse node. Iterate through this process until all P / D nodes are assigned, thus forming the initial solution.

[0154] To ensure the integrity of the path scheme, charging facilities need to be inserted into the generated initial solution.

[0155] 2. P / D Node Removal Operator. Select a destruction operator to remove a specified number of P / D nodes from the current solution. Removal operators include random removal operators, correlated removal operators, and worst-cost removal operators, etc., which are all typical removal operators and will not be described in detail.

[0156] Under the constraint of a strict correspondence between P / D nodes, the materials required by the delivery point must be obtained through the associated pickup point. Therefore, it is essential to ensure that paired nodes are on the same path. Based on this constraint, removing a pickup point requires forcibly removing its associated delivery point to maintain the structural consistency of the solution; while removing a delivery point only requires deleting the node without affecting the path structure. It should be noted that all removal operations exclude warehouse nodes.

[0157] 3. P / D Node Insertion Operator. Select an insertion operator to re-insert the removed P / D nodes into the current solution according to a specified method, thereby generating a new customer access order. Insertion operators include random insertion operators, greedy insertion operators, and regret insertion operators, all of which are widely used classic insertion operators.

[0158] If a pickup point is removed in the previous step, the pickup point is re-inserted first, followed by the insertion of its corresponding delivery point. To ensure pickup and delivery timing constraints, all delivery points must be strictly placed after the associated pickup point; when there are strict time window requirements, delivery points must be inserted directly after the corresponding pickup point to meet timeliness constraints.

[0159] 4. Based on an iterative greedy algorithm framework, the charging facility insertion operator selects charging facility points from the candidate set, inserting them into infeasible paths based on minimizing the sum of construction and allocation costs, ultimately ensuring that all paths meet the power feasibility requirements. The allocation cost is evaluated by quantifying the improvement in the remaining power state before and after charging facility insertion. The core strategy prioritizes selecting nodes that maximize the elimination of path breakpoints, i.e., nodes where the drone's power is insufficient to support reaching the target or nodes that optimize power distribution. If the selected charging facility itself is inaccessible, the solution is directly marked as infeasible and penalized, thus excluding it from the final solution.

[0160] 5. The simulated annealing algorithm is combined with the penalty objective function to accept and update the solution.

[0161] To avoid the risk of heuristic algorithms getting trapped in local optima due to blindly accepting solutions, this invention uses simulated annealing as the solution acceptance criterion and introduces a penalized objective function to allow for the existence of some infeasible solutions. This design strategically relaxes constraints such as battery life, time window, and drone payload, guiding the algorithm to efficiently explore within an expanded solution space through a penalty mechanism, significantly enhancing global optimization capabilities and effectively suppressing local convergence trends. The specific form of the penalty objective function is as follows:

[0162] Z penalty =Z+c penalty +t penalty +b penalty (42)

[0164]

[0165] Among them, b penalty It's a penalty for exceeding the drone's battery limit.

[0166] The simulated degradation acceptance criterion can be understood as follows: when the temporary solution s′ is better than the current solution s or the globally optimal solution s′, the degradation acceptance criterion is met. best If so, then the temporary solution s′ will be accepted; otherwise, it will be accepted with probability. Accept, where T>0 represents temperature. Temperature from T start Initially, the temperature decreases after each iteration, and the expression for the temperature change is: T = cT, where c ∈ (0, 1) is the cooling rate.

[0167] 6. Update the weights of each operator.

[0168] The algorithm employs a roulette wheel selection mechanism to dynamically control the bias in selecting neighborhood search operators. This mechanism continuously tracks the historical performance of each operator and selects a pair of removal-insertion operators based on probability distribution at the beginning of each iteration. The algorithm divides the total iteration process into several equal-length periods, where the performance of each operator i in period j is characterized by its weight, cumulative score, and number of calls. At the beginning of each period, all operator weights are uniformly initialized to 1 / 3 to ensure equal probability selection; simultaneously, the scores are reset to 0. After each iteration within a period, the operator's score is updated based on the quality of the solution generated: if the new solution is better than the global optimum, the score increases by 50; if it is better than the current solution, it increases by 20; if the new solution is worse than the current solution but is accepted, it increases by 10. This score update mechanism drives the operator weights to dynamically adjust with performance, achieving adaptive optimization.

[0169] 7. Solve the mixed-integer linear programming model based on local branches, and further optimize the current optimal solution.

[0170] To avoid the algorithm getting stuck in local optima and improve the quality of solutions, a mixed-integer linear programming model based on local branching is introduced in the ALNS solution process. This method improves the solutions generated iteratively by exploring the neighborhood solution space to enhance solution diversity and prevent the algorithm from prematurely converging to suboptimal solutions. This strategy expands the global search range while dynamically balancing global exploration and local development capabilities, significantly optimizing the solution performance. The local branching technique, proposed by Fischetti and Lodi, is used in mathematical heuristics for local search in 0-1 mixed-integer programming: a Hamming distance neighborhood is defined with the current best solution as the base point, and a simplified optimization model is constructed by constraining the number of binary variable flips (the maximum Hamming distance parameter p). When there is no improved solution in the neighborhood, the value of p is systematically increased to expand the search radius, and this process is repeated until a better integer feasible solution is obtained or the value of p is reached. It is particularly important to emphasize that the setting of the parameter p has a decisive impact on the algorithm's performance—its value must strike a balance between computational efficiency and search potential, ensuring that the neighborhood size is small enough to achieve fast solution while also ensuring that the neighborhood covers the space of potentially better solutions.

[0171]

[0172] In constraint (45), R represents the feasible solution obtained by ALNS, and constraint (45) restricts the current solution. With reference solution x ijkThe deviation in Hamming distance does not exceed the parameter p, which controls the number of variable flips (from 0 to 1 or from 1 to 0) between the reference solution and the current solution. During iterative optimization, it is necessary not only to implement local perturbations in the variable neighborhood search but also to strictly adhere to the model's core constraints, including flow balance constraints, load constraints, energy constraints, and time constraints (see S3 for details). These constraints are necessary conditions for solution feasibility; any feasible solution must simultaneously satisfy all fundamental constraints. The objective function performs global optimization based on this feasible solution space to minimize the total cost.

[0173] Example 2:

[0174] In solving the model for step S3, the corresponding code was written in C# and a commercial solver was called to verify the effectiveness of the model of this invention. To facilitate understanding of the technical solution of this invention, numerical examples are used for illustration below.

[0175] The simulation design strictly adheres to the actual characteristics of urban medical supply distribution scenarios: a central medical node is used as the core, with medical institution nodes evenly distributed around it; candidate charging facility points are based on drone warehouse positioning, with concentric circles set with radii of 50% and 100% of the maximum flight range, respectively, and points are distributed at equal intervals along the circles, with the number dynamically adjusted according to node density. The simulation model also integrates core elements such as load constraints, power constraints, and time window constraints.

[0176] The example number format is Sa-bc, where a represents the example number, b represents the total number of customer points, and c represents the number of candidate charging facility coordinates. Based on the Xunyi TR9 transport drone, which is widely used in domestic medical scenarios, baseline parameters were set. Core performance indicators and key model parameters are detailed in Table 2.

[0177] Table 2

[0178]

[0179] Table 3 presents a comparison of the solution results from two sets of 15 examples, including the objective function value, solution time, and the differences between the mathematical heuristic algorithm and the direct solution obtained by CPLEX. The columns are as follows: example number, objective function value obtained by CPLEX and its solution time (# indicates no feasible solution found), objective function value obtained by the mathematical heuristic algorithm and its solution time, and the relative deviation between the two results. The maximum running time of CPLEX is fixed at 7200 seconds, and the number of iterations for the mathematical heuristic algorithm is set to 3000.

[0180] Table 3

[0181]

[0182]

[0183] Experimental results show that for small-scale examples (S1-S5, 5 medical nodes), both CPLEX and the mathematical heuristic algorithm can obtain high-quality solutions within 10 seconds, with the latter taking less time. When the scale increases to 10 medical nodes (S6-S10), CPLEX can still obtain a feasible solution within 7200 seconds. However, when the scale expands to 15 medical nodes (S11-S15), CPLEX cannot obtain a feasible solution within the time limit, while the mathematical heuristic algorithm maintains stable solution-solving ability and obtains solutions that are consistent with or better than CPLEX solutions in a shorter time. These results verify the effectiveness of the model and demonstrate that the mathematical heuristic algorithm has significant advantages in computational performance and solution quality, and is particularly suitable for solving large-scale complex problems.

[0184] It is understood that the core of this invention lies in constructing a highly timely and reliable collaborative optimization model for charging facility location and route selection in medical drone logistics services. This model deeply integrates the timeliness requirements of medical logistics, particularly covering point-to-point pickup and delivery services for time-sensitive medical supplies, as well as facility location and route selection issues. It designs a complex delivery system that includes direct delivery from pickup points to delivery points and delivery via charging facilities. The core objective is to overcome the limitations of drone range by jointly optimizing the spatial layout of charging facilities and delivery routes to achieve precise delivery of medical resources under strict spatiotemporal constraints. This model simultaneously makes decisions on charging facility location selection, complex route planning, and drone scheduling, ensuring that the entire delivery network achieves spatiotemporal coordination under multiple constraints, providing systematic decision support for medical supply delivery.

[0185] It is understood that this invention introduces a mathematical model based on local branches to solve the problem, building upon the adaptive large-domain search heuristic algorithm. After obtaining a solution in the traditional heuristic part, MILP is used to obtain a better solution that satisfies all constraints. This combines the efficiency of heuristics with the high quality of accurate solutions, improving the reliability and economy of the obtained location-path scheme.

[0186] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0187] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. An optimized method for drone-based medical supply delivery, characterized in that, The method includes: Step 1: Input customer requirements, drone performance parameters and coordinates of candidate charging facilities, analyze and organize time constraints, focus on identifying pairing pick-up and delivery points and time window requirements, and output structured scenario data; Step 2: Obtain charging facility information and drone battery consumption rate, analyze charging facility efficiency and access patterns, optimize facility layout to reduce downtime, and obtain charging facility layout plan; Step 3: Charging site selection and path model establishment. Based on the scenario data obtained in Step S1 and the charging facility analysis results obtained in Step 2, a mixed integer linear programming model is established, and the objective function and constraints are set to obtain the mathematical optimization model. Step 4: Using the mathematical optimization model obtained in step S3, solve the model using a mathematical heuristic algorithm, and combine simulated annealing and local optimization techniques. Through iterative search of the equilibrium solution space, obtain the drone delivery route and charging facility location scheme.

2. The method for optimizing the delivery of medical supplies by unmanned aerial vehicles according to claim 1, characterized in that, In step S1, the customer information includes: the geographical coordinates of the paired pick-up and delivery point, the time window, and the material requirements; the drone performance parameters include: flight speed, maximum payload capacity, and battery capacity.

3. The method for optimizing the delivery of medical supplies by unmanned aerial vehicles according to claim 1, characterized in that, In step S3, the objective function includes minimizing the total cost, including the cost of purchasing drones, the cost of building charging facilities, and the cost of transportation. The constraints include: drone pickup and delivery path and facility location constraints, drone load limit constraints, drone power limit constraints, drone time constraints, and charging sequence constraints at drone charging facilities.

4. The method for optimizing the delivery of medical supplies by unmanned aerial vehicles according to claim 1, characterized in that, Step S3 specifically includes: S301: Input the scenario data from step 1 and the charging facility analysis data from step 2, classify customer needs, identify each customer node, ensure the timeliness requirements of customer point delivery tasks, organize the performance parameters of the drone, organize the locations of candidate charging facilities, confirm the charging efficiency and availability of each charging facility, and calculate each node, including the relative position and distance between the customer point and the charging facility, to provide a basis for subsequent route planning. S302: Establish decision variables, define the decision variables in the problem, and ensure that the model can express the optimization objective and constraints; define a 0-1 decision variable to indicate whether the drone flies from one node to another; if it flies, the variable is 1, otherwise it is 0; define a 0-1 decision variable for each candidate charging facility node to indicate whether the charging facility is selected for construction; if selected, the variable is 1, otherwise it is 0; charging facility access variable: define a variable for each drone to indicate whether the drone needs to access the charging facility; if it does, the variable is 1, otherwise it is 0. S303: Establish the objective function and five core constraints. These five constraints ensure the rationality and feasibility of the route planning and charging facility site selection scheme. Constraint 1: Route and Facility Location Constraints Ensure that each customer node is accessible by drone, and that each node can only be connected via one path. Pickup and delivery points must be paired, and the delivery point must be after the pickup point. Constraint 2: Drone load limit constraint Ensure that the load of each drone does not exceed its maximum carrying capacity. In each delivery mission, the drone's load must be consistent with the cargo requirements along the route and must not exceed the drone's maximum load. Constraint 3: Drone power limit constraint The drone's battery power needs to be limited to ensure that the drone has enough remaining power when flying on each route segment. If the drone's battery is low, it must go to a charging facility to replenish its power. The charging facility must be reasonably inserted into the route to ensure the feasibility of the route in terms of battery power. Constraint 4: Time Window Constraint The arrival time of each node must be within the specified time window. If there are strict time window requirements, it must be ensured that the delivery point is strictly after the pickup point and that the timeliness requirements are met. Constraint 5: Charging sequence constraint at charging facilities When a drone needs to be charged, the order in which charging facilities are accessed must follow certain rules. If a charging facility is selected, the drone must stay at the selected charging facility when it needs to be charged, and there must be no conflict in accessing the charging facilities to ensure that each charging can be carried out effectively and will not have an unreasonable impact on the path. S304: Model Solving. The model is solved using mathematical optimization methods to obtain delivery routes and charging facility location schemes that satisfy all constraints, including the starting point, ending point, nodes on the route, and their access order for each drone. Based on the location results of the charging facilities, it is ensured that drones can be charged in time when their power is low, and that the layout of the charging facilities is economical. S305: Model Validation and Adjustment. Validate the rationality of the model's solution results and adjust them according to actual conditions. Validate the solved path and charging facility layout scheme to ensure that the drones can complete all delivery tasks as planned. Evaluate the energy feasibility of the path, the time window satisfaction, and whether the load constraints are met. Adjust the model based on the validation results, correcting any deficiencies in path planning and charging facility location selection, and obtain an optimized charging facility location scheme and drone delivery path that meets the five core constraints. Output the final path plan, specifying the driving route, charging facility location, and access order for each drone.

5. The method for optimizing the delivery of medical supplies by unmanned aerial vehicles according to claim 1, characterized in that, Step S4 specifically includes solving the mathematical optimization model established in step 3 using a heuristic algorithm to obtain a high-quality delivery route and charging facility site selection scheme that satisfies all constraints. S401: Initial solution generation, constructing an initial solution as the starting point for optimization; Starting from the warehouse, a greedy strategy is used to randomly select unassigned pickup points and insert them into the path; based on the pairing dependencies, the corresponding delivery points are inserted into the path in the order of the shortest path to ensure a closed loop, i.e., finally returning to the warehouse node; this process is iterated until all pickup and delivery points are assigned, generating a preliminary delivery path; a preliminary path planning scheme and charging facility layout are output. S402: P / D node removal operator, which improves the path structure by removing certain P / D nodes; Select a removal operator (including random removal operator, related removal operator, or worst-cost removal operator) to remove some P / D nodes. Pairing constraints: if a pickup point is removed, its corresponding delivery point must be removed at the same time to ensure the consistency of the path structure. Exclude repository nodes; removal operations cannot involve repository nodes. Output the path structure after removing the node to prepare for the next insertion operation; S403: P / D node insertion operator, which re-inserts removed P / D nodes into the path to optimize the path order; Insertion operators (including random insertion, greedy insertion, or regret insertion operators) are used to re-insert P / D nodes into the current path. Priority is given to re-inserting removed pickup points, and their corresponding delivery points are also inserted accordingly, ensuring that pickup points precede delivery points. For nodes with strict time window requirements, delivery points are inserted immediately after their corresponding pickup points to meet timeliness constraints. The output is the adjusted path, ensuring that the path structure is reasonable and meets timeliness and order constraints. S404: Charging facility insertion operator ensures that the path meets the power feasibility requirements and solves the problem of insufficient power by inserting charging facilities; A subset of charging facility nodes are selected from the candidate set of charging facilities and inserted into paths where power supply is infeasible, based on the principle of minimizing the construction cost and path allocation cost of the charging facilities. The degree of improvement in power supply before and after the insertion of the charging facilities is evaluated, and locations that can eliminate power supply gaps or optimize power supply distribution are prioritized. If the selected charging facility location is unreachable, the solution is marked as infeasible and a penalty is imposed to prevent it from entering the final solution. The location and power supply status of the charging facilities in the output path are optimized to ensure that each path can meet the power supply requirements. S405: Simulated annealing and penalty objective function to avoid heuristic algorithms getting stuck in local optima and enhance global exploration capabilities; Based on the quality of the current best solution and the new solution, a decision is made on whether to accept the new solution. If the new solution is better, it is accepted directly; if the new solution is worse, it is accepted with a certain probability, which gradually decreases as the temperature decreases, i.e., the simulated annealing process. A penalty objective function is introduced to penalize infeasible solutions, such as those exceeding the power limit or time window conflicts, to guide the algorithm to avoid infeasible solutions. The output improves the global solution-finding ability while expanding the solution space through the simulated annealing mechanism. S406: Operator weight update, dynamically adjust the weight of each operator to further optimize the quality of the solution; The bias of the operator is dynamically controlled by using a roulette wheel selection mechanism, and its selection probability is adjusted according to the historical performance of the operator in each iteration. The performance of an operator in each cycle is determined by the quality of the generated solution. If an operator generates a solution that is better than the current solution, the operator is assigned a higher weight to increase its selection probability in subsequent iterations. The operator weight is updated, the algorithm is adaptively optimized, and the quality of the solution is improved. S407: Refined search based on local branches improves the quality of the solution through local optimization and avoids the algorithm from converging to a suboptimal solution too early; Local branching is introduced to optimize the current optimal solution during the iteration process. By defining a neighborhood solution space, the neighboring regions of the solution are explored to enhance the diversity of solutions. Perturbation is performed in the neighborhood, and a mixed integer programming model is used to optimize the solution after each perturbation. If no improved solution is found, the search range of the neighborhood is gradually increased until a better integer feasible solution is found. The output is the solution that optimizes the current solution through local search, improves the quality of the solution, and ensures that the solution satisfies all constraints.

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