Multi-unmanned aerial vehicle emergency medical material dispatching path planning method for low-altitude economy

Abstract

The invention belongs to the field of low-altitude economy application, unmanned aerial vehicle application, emergency logistics management and intelligent optimization algorithms, and discloses a low-altitude economy-oriented multi-unmanned aerial vehicle emergency medical material dispatching path planning method, which comprises the following steps of: 1, determining known conditions of a model based on a real scene; step 2, constructing an unmanned aerial vehicle path planning model, wherein the unmanned aerial vehicle path planning model takes the main target as the minimum aging perception cost and takes the secondary target as the minimum economic cost; step 3, solving an unmanned aerial vehicle path planning model based on a knowledge-assisted two-stage coevolution NSGA-II algorithm; 4, taking a result based on the two-stage coevolution NSGA-II algorithm as a multi-unmanned aerial vehicle emergency medical material scheduling path; according to the method, dynamic balance of emergency medical material dispatching timeliness, fairness and economical efficiency is realized, scientificity and efficiency of multi-unmanned aerial vehicle dispatching path planning are remarkably improved, reliable technical support is provided for rapid, accurate and economical medical material distribution in an emergency scene, and the emergency response capability and the disaster victim guarantee level are promoted.

Description

Technical Field

[0001] This invention belongs to the fields of low-altitude economic applications, drone applications, emergency logistics management, and intelligent optimization algorithms, specifically involving a multi-drone emergency medical supplies scheduling path planning method for low-altitude economic applications. Background Technology

[0002] Emergencies are characterized by their high destructiveness and wide-ranging impact, posing significant challenges to the deployment of emergency medical supplies. The efficient deployment of these supplies after a disaster is directly related to the safety of affected populations. Unmanned aerial vehicles (UAVs), as a crucial carrier for contactless delivery, are suitable for various delivery scenarios, avoiding ground transportation disruptions and reducing the risk of injury or death to rescue personnel. They have become an important tool for emergency medical supply deployment. The low-altitude economy, as a new economic model, has its core advantages in the efficient utilization of low-altitude airspace resources and the large-scale application of UAVs and other low-altitude aircraft. UAVs, as the core delivery carrier of the low-altitude economy, are suitable for material delivery in various emergency scenarios. Leveraging the airspace planning and optimization characteristics of the low-altitude economy, they can avoid ground transportation disruptions and reduce the risk of injury or death to rescue personnel. They have become an important tool for emergency medical supply deployment.

[0003] Existing research largely focuses on the rational perspective of decision-makers, neglecting the subjective psychological feelings of disaster victims and lacking humanitarian fairness. It concentrates scheduling objectives on scheduling time and transportation costs, with only a few studies addressing the urgency of needs and allocation fairness, but none adequately considering the subjective psychological experience of disaster victims. In real-world scenarios, disaster victims compare their aid time and the priority of their needs with other needs delivered on the same flight, leading to a sense of "relative deprivation." Existing models fail to quantify this psychological feeling, making it difficult to truly achieve fairness in humanitarian aid and potentially exacerbating negative emotions among disaster victims. Furthermore, the Unmanned Aerial Vehicle Path Planning (UAVRP) problem is NP-hard. Traditional heuristic algorithms struggle to balance convergence and diversity when solving multi-constraint problems, easily getting trapped in local optima. Overemphasizing convergence can lead to overlapping Pareto front solutions and insufficient flexibility; overemphasizing diversity may result in infeasible solutions that fail to meet actual scheduling needs, especially in scenarios with large and complex distribution of needs, where algorithm performance degrades significantly.

[0004] Therefore, addressing the shortcomings of traditional emergency material dispatch models that primarily focus on efficiency and economy while neglecting the subjective feelings of disaster victims, this invention comprehensively considers realistic constraints such as drone payload, range, and demand time windows, and introduces the theory of relative deprivation to construct a multi-drone path planning model that better fits actual scenarios. Furthermore, addressing the difficulty of balancing convergence and solution diversity in solving complex, multi-constraint path planning problems using traditional algorithms, this paper proposes a knowledge-assisted two-stage co-evolutionary model (NSGA-II) to accelerate convergence and enhance the diversity of advantageous solutions through dual-population co-evolution and improve the diversity of advantageous solutions, thereby achieving efficient solutions to the aforementioned model. Summary of the Invention

[0005] Against the backdrop of rapid development of the low-altitude economy and the gradual opening of low-altitude airspace resources, in order to fully leverage the flexible scheduling advantages of low-altitude UAVs and address the imbalance between fairness and efficiency in existing emergency medical supply scheduling, this invention provides a multi-UAV emergency medical supply scheduling path planning method for the low-altitude economy to solve the problems in the existing technology. The technical solution adopted by this invention is as follows: A multi-UAV emergency medical supply dispatching path planning method for the low-altitude economy is characterized by the following steps: Step 1: Based on the real-world scenario, determine the known conditions of the model; Step 2: Construct a UAV path planning model. The UAV path planning model includes minimizing the timeliness perception cost as the primary objective and minimizing the economic cost as the secondary objective. Step 3: Solve the UAV path planning model using the knowledge-assisted two-stage co-evolutionary NSGA-Ⅱ algorithm; Step 4: The results of the knowledge-assisted two-stage co-evolutionary NSGA-II algorithm are used as the scheduling path for multi-UAV emergency medical supplies. Furthermore, in step 1, the known conditions include: the geographical locations of the demand points and the emergency distribution center are known; the emergency medical supplies demand at each demand point is known; the severity of each demand point is known; emergency medical supplies are sufficient; emergency medical supplies have been categorized and grouped; each demand point is visited by only one drone; the drone's flight speed is constant; emergency medical supplies are only dispatched from the emergency distribution center to the demand points; each demand point only reports a single demand quantity; and the drone's flight path is... Click Points and from Click The points have the same flight path.

[0006] Furthermore, in step 2: The primary objective is to minimize the perceived cost of timeliness, as shown in the formula: ; in, Indicates the number of demand points. This indicates the total number of drones invoked and the total number of sub-paths, where k represents the drone number. Indicates the demand point number; For demand points Non-ideal time costs; The secondary objective is to minimize economic costs, as shown in the formula: ; in, To reduce the cost of drone deployment, The cost of transporting drones.

[0007] Furthermore, demand points Non-ideal time cost sub-path demand points The non-ideal time cost is zero if delivered on time. For all The total cost of dissatisfaction is calculated using the following formula: ; in, To satisfy the child's dissatisfaction with the cost, t i For demand points The actual delivery time of emergency medical supplies, lw i Indicate demand points The original latest time for receiving supplies, j is the demand point number; Dissatisfied with costs sub-path demand points Relative to demand point The non-ideal time cost of point-to-point communication, i.e. For a single The cost of dissatisfaction is calculated using the following formula: ; in, Indicate demand points The actual delivery order within the sub-path Indicate demand points Delivery priority, lw i Indicate demand points The original latest time for receiving the supplies; To accept the cost, For the cost of double violation, To reluctantly accept the cost, Perceived costs of unfairness; Acceptance Cost For drones later than LW iThe cost of delivering on time but with lower priority requests on the same flight arriving later is calculated using the following formula: ; Double cost of violation For drones later than LW i The formula for calculating the cost of earlier delivery for lower-priority requests on the same flight, based on delivery time, is: ; Unable to accept the cost For drones later than LW i The cost of delivery times that are slower than priority, and for lower-priority requests on the same flight that arrive later, is calculated using the following formula: ; Perceived Cost of Injustice For drones later than LW i The cost of delivery time and order lagging behind priority, while lower priority requests on the same flight are delivered earlier, is calculated using the following formula: ; Furthermore, the cost of deploying drones The total dispatch cost of the called-up drones is calculated using the following formula: ; in Indicates drone The cost of deployment; Transportation costs of drones The product of the drone's flight distance and the cost per unit distance is given by the formula: ; in, For the unit transportation cost of drones, Indicate demand points Distance to demand point j Indicates drone Do the service points serve the needs in a sequential manner? and d 0i Indicates the distance from the distribution center to the demand point. distance, Indicate demand points Is it a drone? The first node of the service Indicate demand points Is it a drone? The last node of the service; Furthermore, the constraints of the UAV path planning model include: The sub-path number constraint means that the number of sub-paths cannot exceed the number of required points. The formula is: ; The drone closed-loop constraint means that if a drone is dispatched, it should depart from the emergency delivery center, complete the delivery task, and return to the emergency delivery center, i.e., a sub-path closed loop, as shown in the formula: ; Demand point service constraint means that a demand point can only be served by one drone, and the number of drones entering the demand point equals the number of drones leaving. In other words, a drone can only fly from one node to the current node, and can only leave the current node to fly to the next node. The formula is: ; The drone payload constraint states that the total demand of all demand points on a subpath cannot exceed the maximum payload of the drone serving that subpath. The formula is: ; Where ul k Indicates drone The maximum load, Indicate demand points The demand for emergency medical supplies, Indicate demand points Is it by drone? Serve; The drone endurance constraint means that the sum of the distances traveled by a drone on the service sub-paths does not exceed the drone's maximum range. The formula is: ; Mmile k Indicates drone Maximum mileage; The time window constraint means that the actual delivery time of a demand point is equal to the sum of the actual delivery time of the previous demand point, the unloading time, and the drone's flight time from the previous node to the current node. The formula is: ; in, Indicate demand points The unloading time, Indicates drone The speed of travel; The funding constraint means that the economic cost of the scheduling plan should be within a given funding limit. The formula is: ; Among them fund limit This represents the upper limit of funding for the allocation plan; The model-related decision variable constraints are given by the following formula: ; Furthermore, in step 3, the knowledge-assisted two-stage co-evolutionary NSGA-II algorithm includes two stages; wherein: Phase 1, Dual-Population Co-evolution: Design the encoding of the UAV path planning solution, which includes two parts: UAV combination and demand point sequence; construct a dual-population framework of main population and auxiliary population. The main population solves the constructed UAV path planning model, while the auxiliary population solves simplified auxiliary problems related to the main objective, UAV performance constraints, funding limitations, and demand point constraints; the main objective is to minimize the timeliness perception cost; the main population and auxiliary population evolve through discontinuous crossover and mutation update strategies. Phase Two: Discontinuous Multi-Mode Update Strategy. The main population output from Phase One is used as the input for Phase Two, dividing the main population output from Phase One into a dominant subpopulation and a subpopulation of inferior individuals. The dominant subpopulation is updated using the GA strategy. The inferior subpopulation is embedded in the QL algorithm framework, and the evolutionary mode is selected from the multi-mode update strategy based on the multi-state partitioning criterion. After each iteration, the subpopulations are re-divided, and the top n individuals evolved from the inferior subpopulation are assigned to the dominant subpopulation and continue to evolve.

[0008] Furthermore, in Phase 1, the main population and auxiliary populations evolve through discontinuous crossover, including: randomly shuffling the first part of the two parent chromosomes and selecting the same number of genes as the original chromosomes; if a gene duplication occurs in the first part of a reselected parent chromosome, it is deleted and reselected until all selected genes are unique; and clustering the demand points based on the number of sub-paths to generate new sub-paths in sequence, and performing constraint checks to retain sub-paths that satisfy all constraints.

[0009] Furthermore, in Phase Two, the evolutionary approach is selected from the multi-mode update strategy based on the multi-state partitioning criterion, which includes relative distance. Summation superiority ; relative distance Defined as the ratio of the difference between the best and worst values ​​of two subpopulations on the primary objective, the formula is: ; in and These represent the minimum values ​​of the primary objectives of the inferior and dominant subpopulations, respectively. and These represent the maximum values ​​of the primary objectives of the inferior and dominant subpopulations, respectively. Superiority Defined as the ratio of the number of particles in a weaker subpopulation whose primary objective is better than the overall mean to the number of particles whose primary objective is worse than the mean, the formula is: ; in and These represent the number of individuals in the inferior subpopulation whose value is less than or equal to the overall mean, and the number of individuals in the primary target subpopulation whose value is greater than the mean, respectively.

[0010] Furthermore, the multi-mode update strategies in Phase 2 include: the optimal insertion cost path crossing strategy, the internal worst sub-path crossing strategy, and the worst sub-path reorganization strategy.

[0011] This invention offers the following advantages: It enhances the timeliness, fairness, economy, and algorithmic efficiency of emergency medical supply dispatching from multiple dimensions. In terms of model construction, a dual-objective model is built, with minimizing perceived timeliness costs as the primary objective and economic costs as a secondary objective. The theory of relative deprivation is introduced, quantifying the subjective negative feelings of disaster victims through costs such as acceptance costs and double violation costs. This prioritizes the timely delivery of supplies to high-priority demand points while avoiding the lack of fairness caused by mismatches between priority and delivery order along the same path, effectively alleviating the perceived unfairness among disaster victims. Simultaneously, the model fully considers realistic constraints such as drone payload, drone range, and demand time windows, as well as known conditions such as the geographical location of demand points and the demand volume, ensuring the practical feasibility of the dispatching plan. Regarding the algorithm for solving the problem, the knowledge-assisted two-stage co-evolutionary NSGA-II algorithm, through the co-evolution of the main population and auxiliary populations, and the combination of the GA strategy for the dominant subpopulation and the QL algorithm framework for the inferior subpopulation, not only improves the convergence speed of the algorithm, but also ensures the diversity and quality of Pareto optimal solutions by using non-dominated sorting and crowding distance as quantitative judgment criteria, thus avoiding local optimum traps. Overall, this invention, based on the needs of low-altitude economic development, fully integrates the advantages of low-altitude airspace resource optimization and UAV collaborative scheduling, achieving a dynamic balance between the timeliness, fairness, and economy of emergency medical supply scheduling. It significantly improves the scientificity and efficiency of multi-UAV scheduling path planning, providing reliable technical support for rapid, accurate, and economical medical supply delivery in low-altitude economic scenarios, and helping to improve emergency response capabilities and the protection level of disaster-stricken people. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the algorithm flow of the present invention; Figure 2 This is a schematic diagram of the pseudocode for the algorithm of this invention; Figure 3 Example diagram of encoding; Figure 4 Example diagram of cross strategy; Figure 5 Here is an example of a mutation strategy; Figure 6 The optimal insertion cost path crossing strategy; Figure 7 The worst-case sub-path crossing strategy is used. Figure 8 This is the worst sub-path reorganization strategy. Detailed Implementation

[0013] The following will be based on embodiments of the present invention. Figures 1-8 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0014] A multi-UAV emergency medical supply dispatching path planning method for the low-altitude economy is characterized by the following steps: Step 1, Based on the real-world scenario, determine the known conditions of the model: To simplify the problem and ensure the solvability of the model, the following assumptions are made based on the real-world scenario: (1) The geographical locations of the demand points and emergency distribution centers are known.

[0015] (2) The demand for emergency medical supplies at each demand point is known.

[0016] (3) The severity (priority) of each demand point is known.

[0017] (4) Sufficient emergency medical supplies.

[0018] (5) In order to ensure the timely delivery of emergency medical supplies, emergency medical supplies have been classified and grouped. Therefore, the emergency medical supplies delivered are homogeneous, that is, only the dispatch of a single emergency medical supply is considered.

[0019] (6) The demand at each demand point is met by only a single drone, that is, a demand point is accessed by only one drone.

[0020] (7) The drone flies at a constant speed and hovers to avoid collisions with other drones.

[0021] (8) Emergency medical supplies are dispatched only from the emergency distribution center to the point of need, and not between the points of need.

[0022] (9) Each demand point only reports the single demand quantity, and the sum of the maximum payload of the dispatched drones is sufficient to meet the single demand quantity of all demand points, that is, only the single delivery of drones is considered.

[0023] (10) The UAV’s flight path from point i to point j is the same as that from point j to point i.

[0024] Step 2 involves constructing a drone path planning model. This model prioritizes minimizing timeliness perception costs as the primary objective and minimizing economic costs as the secondary objective. This prioritization is based on the principle of weak economic efficiency in emergency medical supply dispatch. Step 2 specifically includes: Main objective: Minimize perceived timeliness cost C P .

[0025] Based on the theory of relative deprivation, the formula for quantifying the subjective negative feelings of disaster victims is as follows: ; in, Indicates the number of demand points. This indicates the total number of drones invoked and the total number of sub-paths, where k represents the drone number. Indicates the demand point number; For demand points The non-ideal time cost.

[0026] Secondary objective: Minimize economic cost C M .

[0027] ; in, To reduce the cost of drone deployment, The cost of transporting drones.

[0028] Demand points Non-ideal time cost sub-path demand points The non-ideal time cost is zero if delivered on time. For all The total cost of dissatisfaction is calculated using the following formula: ; in, To satisfy the child's dissatisfaction with the cost, t i For demand points The actual delivery time of emergency medical supplies, lw i Indicate demand points The original latest time for receiving supplies, where j is the demand point number. Dissatisfied with costs sub-path demand points Relative to demand point The non-ideal time cost of point-to-point communication, i.e. For a single The cost of dissatisfaction is calculated using the following formula: ; in, Indicate demand points The actual delivery order within the sub-path Indicate demand points Delivery priority, lw i Indicate demand points The original latest time for receiving the supplies; To accept the cost, For the cost of double violation, To reluctantly accept the cost, Perceived costs of unfairness; Acceptance Cost Drones are later than LW i The cost of delivering on time, but for lower-priority requests on the same flight that are delivered later.

[0029] ; Double cost of violation Drones are later than LW i Timely delivery and earlier delivery of low-priority requests on the same flight reduce costs.

[0030] ; Unable to accept the cost Drones are later than LW i Furthermore, the delivery order lags behind the priority, and the delivery to low-priority demand points on the same flight is delayed, resulting in higher costs.

[0031] ; Perceived Cost of Injustice Drones are later than LW i Furthermore, the delivery order lags behind the priority, and the lower priority demand points on the same flight are delivered earlier, which incurs costs.

[0032] ; Drone deployment costs Total dispatch costs of the called-up drones.

[0033] ; in Indicates drone The cost of deployment.

[0034] Transportation costs of drones The product of the drone's flight distance and the cost per unit distance.

[0035] ; in, For the unit transportation cost of drones, Indicate demand points Distance to demand point j Indicates drone Do the service points serve the needs in a sequential manner? and d 0i Indicates the distance from the distribution center to the demand point. distance, Indicate demand points Is it a drone? The first node of the service Indicate demand points Is it a drone? The last node of the service.

[0036] The constraints of the UAV path planning model include: The sub-path number constraint means that the number of sub-paths cannot exceed the number of required points. The formula is: ; The drone closed-loop constraint means that if a drone is dispatched, it should depart from the emergency delivery center, complete the delivery task, and return to the emergency delivery center, i.e., a sub-path closed loop, as shown in the formula: ; Demand point service constraint means that a demand point can only be served by one drone, and the number of drones entering the demand point equals the number of drones leaving. In other words, a drone can only fly from one node to the current node, and can only leave the current node to fly to the next node. The formula is: ; The drone payload constraint states that the total demand of all demand points on a subpath cannot exceed the maximum payload of the drone serving that subpath. The formula is: ; Where ul k Indicates drone The maximum load, Indicate demand points The demand for emergency medical supplies, Indicate demand points Is it by drone? Serve;.

[0037] The drone endurance constraint means that the sum of the distances traveled by a drone on the service sub-paths does not exceed the drone's maximum range. The formula is: ; Mmile k Indicates drone The maximum mileage.

[0038] The time window constraint means that the actual delivery time of a demand point is equal to the sum of the actual delivery time of the previous demand point, the unloading time, and the drone's flight time from the previous node to the current node. The formula is: ; in, Indicate demand points The unloading time, Indicates drone The driving speed.

[0039] The funding constraint means that the economic cost of the scheduling plan should be within a given funding limit. The formula is: ; Among them fund limit This represents the upper limit of funds for the allocation plan.

[0040] The model-related decision variable constraints are given by the following formula: ; ; ; ; Step 3: Solve the UAV path planning model using the knowledge-assisted two-stage co-evolutionary NSGA-II algorithm. Traditional algorithms struggle to balance convergence and solution diversity when solving complex, multi-constraint path planning problems. To address this issue, this invention designs a knowledge-assisted two-stage co-evolutionary NSGA-II algorithm (TSKAC-NSGA-II), the flowchart of which is shown below. Figure 1 The algorithm pseudocode is shown. Figure 2 As shown. The algorithm mainly consists of two stages. In the first stage, the algorithm focuses on improving the convergence of the main population. In the second stage, the algorithm focuses on improving the diversity of dominant solutions. The division between the two stages is defined as follows: ; in, The phase division factor is denoted by It, where It is the current iteration round, and MaxIt is the maximum iteration round. The number of individuals (chromosomes) in the population.

[0041] Phase 1, Co-evolution of Two Populations: First, considering the characteristics of heterogeneous UAV resources, an encoding method for UAV path planning solutions is designed. The solution consists of two parts: the first part is the UAV combination, and the second part is the sequence of demand points, such as... Figure 3As shown. Then, based on the idea of ​​CCMO co-evolution, a framework with two populations is constructed: a main population and an auxiliary population. The main population directly solves the original problem of the UAV path planning model, while the auxiliary population focuses on a simplified version of the auxiliary problem, which only contains part of the objective and constraints.

[0042] A single-objective model was designed for the auxiliary problem of UAV path planning. This model includes the main objective of minimizing the time-sensitive cost, as well as constraints related to UAV performance, funding, and demand points. Through a mechanism of sharing offspring information between the two populations, the larger feasible region of the auxiliary population helps the main population escape local optima, thus promoting rapid convergence of the main population within a smaller feasible region. In the first stage, the main and auxiliary populations evolve through a discontinuous crossover and mutation update strategy. Specifically: (1) Non-continuous crossover: The first part of the two parent chromosomes is randomly shuffled, and the same number of genes as the original chromosomes are selected. If a gene duplication occurs in the first part of a newly selected parent chromosome, it is deleted and a new selection is made until all selected genes are unique. Since the first-stage crossover operation may cause changes in the maximum payload or maximum range of the UAV in each scheme, it is necessary to cluster the demand points based on the number of sub-paths, generate new sub-paths in sequence, and perform constraint checks. Only sub-paths that meet all constraints will be retained. The specific operation method is as follows: Figure 4 As shown.

[0043] (2) Mutation strategy: Under the premise of satisfying the constraints, cross any two demand points in the sub-paths that satisfy the constraints. The specific operation method is as follows: Figure 5 As shown.

[0044] Phase Two, Non-continuous Multi-modal Update Strategy: The main population output from Phase 1 serves as the input for Phase 2. The main population is further divided into dominant and subordinate subpopulations. During iteration, the dominant subpopulation is updated using a GA (General Aspect-Oriented) strategy. The subordinate subpopulation is embedded within the framework of the QL (Quick Level) algorithm, selecting the most suitable evolutionary approach from multiple update strategies based on a multi-state partitioning criterion. After each iteration, the subpopulations are re-divided, and individuals that perform well after evolution from the subordinate subpopulation are moved to the dominant subpopulation, continuing to evolve in the same manner.

[0045] The design for the evolution of inferior subpopulations includes multi-state partitioning criteria and multi-mode update strategies, as detailed below: (1) Relative distance Relative distance is defined as the ratio of the difference between the best and worst values ​​of two subpopulations on the primary objective. The definition of relative distance is as follows: ; in and These represent the minimum values ​​of the primary objectives of the inferior and dominant subpopulations, respectively. and These represent the maximum values ​​of the primary objectives of the inferior and dominant subpopulations, respectively.

[0046] (2) Collective superiority Set superiority is defined as the ratio of the number of particles in a subpopulation whose primary objective is better than the overall mean to the number of particles whose primary objective is worse than the mean. The definition of set superiority is as follows: ; in and These represent the number of individuals in the inferior subpopulation whose primary objective is less than or equal to the overall mean, and the number of individuals whose primary objective is greater than the mean, respectively.

[0047] (3) Optimal Insertion Cost Path Crossing Strategy: For vehicle routing problems with time windows, OMBUKI et al. designed the BCRC (Best Correspondence Curve). The operation involves randomly selecting one sub-path from each of the two parent paths, removing the demand points from the other's sub-paths, and then, without violating constraints, re-inserting these demand points into the chromosome in the lowest-cost manner. If inserting a demand point into any sub-path would violate the constraints, a new sub-path is started to accommodate the demand point. This process continues until all demand points are properly inserted. The specific operation of this strategy is as follows: Figure 6 As shown.

[0048] (4) Internal worst-case sub-path crossing strategy: For an individual containing two or more sub-paths, first identify the two sub-paths with the highest time-perceived cost, then select a demand point for each sub-path and remove it from the corresponding sub-path, inserting it into the first feasible position that satisfies the constraints. This process ensures that the exchange of demand points between sub-paths adheres to the problem constraints while enhancing the randomness of the search and the diversity of solutions, thereby increasing the likelihood of discovering high-quality solutions. The specific operation of this strategy is as follows: Figure 7 As shown.

[0049] (5) Worst-case sub-path reorganization strategy: To address the problem of inefficiency in some sub-paths in existing solutions, this study designs a worst-case sub-path reorganization strategy. This strategy only applies to the least efficient sub-path, aiming to improve the possibility of improvement of the least efficient sub-path without destroying the solution structure. First, a relative timeliness perception index is defined. This metric is used to evaluate the efficiency of each sub-path. It quantifies the average delivery delay at each demand point by comparing the sub-path's non-ideal time cost with the number of demand points. Based on this metric, it identifies the shortcomings in the original solution. The subpath with the highest value is defined as the "worst subpath". Then, from this subpath, the demand point whose actual delivery order lags most behind its priority order is selected and re-inserted before any actual delivery order that satisfies the constraints. The specific operation of this method is as follows: Figure 8 As shown. The definition is as follows: ; in, Indicates subpath Non-ideal time cost, Indicates subpath The total number of demand points.

[0050] Step 4: Based on the results of the two-stage co-evolutionary NSGA-Ⅱ algorithm, a multi-UAV emergency medical supplies scheduling path is established.

[0051] like Figure 2 The NSGA-II algorithm, based on knowledge-assisted two-stage co-evolution, is used to solve the UAV path planning model. The specific algorithm flow is as follows: Input: Maximum number of iterations in stage 1 (MaxIt1), maximum number of iterations in stage 2 (MaxIt2), population size (population), crossover probability (crp), mutation probability (...) Phase division factor k, initial learning rate p1, final learning rate p2, number of demand points 1, number of drones called K', maximum drone payload Q, maximum range Unit transportation cost (m), latest delivery time Demand Priority Required point coordinates (x, y, z) Initialization: It1=0, It2=0, K=0.03, p1=p2=0.5, QL algorithm Q-table, decision variables ; Phase 1: ; 1. Crossover and mutation operations; 2. Merge the offspring of the main population and the offspring of the auxiliary population, and select the best individuals to update the main population and the auxiliary population; 3. If It1 = It1 + 1, and It1 = MaxIt1, then end phase one and output the population as input for phase two. Phase Two: ; 1. Subpopulation division: Divide the main population output in Phase 1 into a dominant subpopulation and a subpopulation with a disadvantage; 2. Dominant subpopulation update: Execute the GA update strategy; 3. Replacement of inferior subpopulations: Calculate relative distance Summation superiority ;Select update strategy based on relative distance and set superiority; 4. Update Q table: Update state-action value based on the evolutionary gains of the inferior subpopulation; 5. Population recombination: Individuals that perform better in a weaker subpopulation are moved to a stronger subpopulation; 6. If It2 = It2 + 1, and It2 = MaxIt2, then the loop ends. Output: Pareto front of the dominant subpopulation.

[0052] The experimental part of this invention consists of two parts: parameter experiments and calculation example experiments.

[0053] This section mainly introduces the dataset used in the simulation experiment, the experimental environment, and the running environment: an AMD Ryzen 7 5800H with Radeon Graphics 3.20GHz processor and 16GB of memory. MATLAB 2020b was used for programming, with a population size of 80, a crossover probability of crp of 0.8, and a mutation probability of mutp = 1 / num. var , where num var The number of decision variables.

[0054] The parameter experiments were conducted on an improved version of the Solomon C101-100 dataset. To reflect carrier heterogeneity, the carrier information in the original dataset was modified accordingly: the maximum load of a carrier in C101 is 200, and the minimum demand at each demand point is 50. Based on this, 10 additional carriers with maximum loads between 50 and 100, distributed in an arithmetic sequence, were configured to replace 10 of the original 25 carriers. Specifically, the maximum load of carrier 1 is 50, carrier 3 is 65, carrier 5 is 80, carrier 7 is 95, carrier 9 is 110, carrier 11 is 125, carrier 13 is 140, carrier 15 is 155, carrier 17 is 170, and carrier 19 is 185. The dispatch cost of a carrier is proportional to its maximum load. Ten independent experiments were conducted for each of the nine parameter combinations. The Kruskal-Wallis test was used to examine whether different parameter combinations significantly affected the algorithm's solution performance. The optimal parameter combination was obtained from nine possible combinations, laying the foundation for experimental examples.

[0055] The example experiments selected six subsets from the VRPTW standard dataset set by Solomon in 1987. [5]Improvements were made to align with the research questions in this paper, and simulation experiments were conducted based on these improvements. The Solomon dataset contains three sub-problems: C-class (C1, C2), R-class (R1, R2), and RC-class (RC1, RC2). In the C-class problems, demand points are clustered geographically or within time windows, with C1 and C2 containing 9 and 8 instances, respectively. In the R-class problems, demand points exhibit a uniform distribution, with R1 and R2 containing 12 and 11 instances, respectively. The RC-class problems combine features of both C-class and R-class problems, with RC1 and RC2 each containing 8 instances. The time windows for demand points are relatively narrow in C1, R1, and RC1 problems, while they are relatively wide in C2, R2, and RC2 problems. The number of demand points per instance varies, with three scales: 25, 50, and 100.

[0056] To test the adaptability of TSKAC-NSGA-II to different performance vehicles, different scales of demand points, and different levels of time constraints, and to enhance the matching degree between the instance and real-world scenarios, this invention improves the dataset with three scales of demand points in subsets C101, C201, R101, R201, RC101, and RC201. Specifically, in each instance, 10 additional vehicles with different performance characteristics are selected to replace the original 10 vehicles. The replacement criterion is that the maximum load of the new vehicle is set to a value within an arithmetic progression between the minimum demand amount of the demand point and the maximum load of the original vehicle. Correspondingly, the maximum mileage of the replaced vehicle is determined by multiplying the ratio of the maximum load of the replaced vehicle to the original maximum load by the maximum mileage of the original vehicle. Furthermore, the latest time limit for each demand point is sorted in ascending order as the delivery priority.

[0057] In the experimental examples of this invention, four algorithms were selected as comparison algorithms: TS-NSGA-Ⅱ, NSGA-Ⅱ, OR-OPT-NSGA-Ⅱ, and CCMO. Each experiment was run independently 10 times, with a maximum of 800 evaluations per run.

[0058] Four indicators are used to systematically measure the comprehensive optimization capability of the algorithm: the perceived cost of timeliness in terms of quantifying the subjective sense of fairness among disaster-stricken people (C). P The economic cost of measuring the sustainability of allocated funds (C) M The success rate (i.e., C) reflects the feasibility of a solution satisfying the time window constraint. P The percentage of experiments with a value of 0 and the standard deviation of the stability of the algorithm output results.

[0059] Experimental results: The experimental results of the parameters show that κ, ρ 1 and ρ 2The value of ρ significantly affects the solution performance of TSKAC-NSGA-Ⅱ. 1 =ρ 2 When κ,ρ = 0.5, TSKAC-NSGA-Ⅱ achieves the lowest overall level of perceived cost value for the optimal solution in each experiment, and also has the lowest mean. Therefore, (κ,ρ) 1 ,ρ 2 The parameter combination (0.03, 0.5, 0.5) was selected as the basis for solving the UAV path planning model.

[0060] The experimental results show that the TSKAC-NSGA-Ⅱ algorithm proposed in this invention outputs the optimal solution in 16 out of 18 instances, excluding C101-25 and C201-25. In the case of a small number of demand points (25), the success rate of each algorithm is 100%, but TSKAC-NSGA-Ⅱ's C... M The average (1109.90) is lower than CCMO (1281.29) and NSGA-II (1494.92). In a medium-sized demand scenario (50 locations), OR-OPT-NSGA-II achieved a 0% success rate, while TSKAC-NSGA-II maintained 100%. M The mean (3079.44) is lower than CCMO (3993.86). In the case of a large number of demand points (100), the success rate of all algorithms is 0%, but TSKAC-NSGA-Ⅱ's C... P The mean (12.88) is much lower than that of NSGA-Ⅱ (65.29) and TS-NSGA-Ⅱ (83.41), indicating the best stability. TSKAC-NSGA-Ⅱ performs best on C, R, and RC datasets, and its advantages are more significant in large-scale and complex distribution scenarios.

[0061] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A multi-UAV emergency medical material dispatch path planning method for low-altitude economy, characterized in that, The method comprises the following steps: Step 1, determining known conditions of the model based on a real scene; Step 2, constructing a UAV path planning model, wherein the main target is to minimize time-sensitive cost, and the secondary target is to minimize economic cost; Step 3, solving the UAV path planning model based on a knowledge-assisted two-stage co-evolution NSGA-II algorithm; Step 4, taking the result of the knowledge-assisted two-stage co-evolution NSGA-II algorithm as the multi-UAV emergency medical material scheduling path.

2. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to claim 1, characterized in that, In step 1, known conditions include: the geographic locations of demand points and emergency distribution centers are known, the emergency medical material demand of each demand point is known, the severity of each demand point is known, the emergency medical material is sufficient, the emergency medical material has been classified and combined, one demand point is only accessed by one UAV, the flight speed of the UAV is constant, the emergency medical material is only dispatched from the emergency distribution center to the demand point, each demand point only reports a single demand, the UAV flight path from the demand point to the demand point and from the demand point to the demand point is the same. ​​​​ 3. The low-altitude economy-oriented multi-UAV emergency medical material dispatch path planning method according to claim 1, characterized in that, In step 2: The main target is to minimize time-sensitive cost, and the formula is: ； wherein, denotes the number of demand points, denotes the total number of called drones, the total number of sub-paths, k denotes the drone number, denotes the demand point number; is the non-ideal time cost for the demand point . The secondary target is to minimize economic cost, and the formula is: ； wherein, is the cost of dispatching the drone, is the cost of transporting the drone.

4. The method according to claim 3, characterized in that, demand point non-ideal time cost for sub-path upper demand point non-ideal time cost, 0 if on time, i.e. for all total dissatisfaction cost, formula: ； Wherein, t is the cost of the child i is the demand point the actual delivery time of emergency medical supplies, lw i denotes the demand point the latest time for the originally scheduled acceptance of supplies, j is the demand point number; Child not satisfied with cost For child path Upper demand point Relative to demand point Non-ideal time cost of point-to-point, that is Not satisfied with the cost of a single Child, the formula is: ； wherein, denotes a demand point the actual delivery order in the sub-path, denotes a demand point the delivery priority of the demand point, lw i denotes a demand point the latest time of the originally intended recipient of the goods; is the acceptance cost, is the double violation cost, is the helpless acceptance cost, is the unfairness perception cost; acceptance cost cost for late delivery of drones later than lw i cost for late delivery of drones later than lw cost for late delivery of drones later than lw ； Double violation cost For drone later than lw i Time delivery and same machine low priority demand point delivery earlier cost, formula: ； Cost of accepting For UAVs later than Lw i Time and delivery sequence fall behind priority, same machine low priority demand point delivery later cost, formula: ； Unfairness perceived cost For drones later than Lw i Time and delivery order behind priority, same aircraft low priority demand point delivery earlier cost, formula: 。 5. The method according to claim 3, characterized in that, Cost of drone dispatch The total cost of dispatching the called drones is the sum of the costs of the individual drones, which is given by ； wherein represents the deployment cost of the UAV ; Transportation cost of the UAV The product of the UAV flight distance and the unit distance cost, the formula is: ； in, For the unit transportation cost of drones, Indicate demand points Distance to demand point j Indicates drone Do the service points serve the needs in a sequential manner? and d 0i Indicates the distance from the distribution center to the demand point. distance, Indicate demand points Is it a drone? The first node of the service Indicate demand points Is it a drone? The last node of the service.

6. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to claim 5, characterized in that, The constraint conditions of the UAV path planning model comprise: A sub-path quantity constraint, which indicates that the number of sub-paths is not more than the number of demand points, and the formula is: ； A UAV closed-loop constraint, which indicates that if a UAV is dispatched, it should start from the emergency distribution center, complete the distribution task and return to the emergency distribution center, that is, the sub-path is closed-loop, and the formula is: ； A demand point service constraint, which indicates that a demand point can be served by only one UAV, and the number of UAVs entering the demand point is equal to the number of UAVs leaving the demand point, that is, a UAV can only fly from a node to the current node and can only leave the current node and fly to the next node, and the formula is: ； A UAV load constraint, which indicates that the total demand of all demand points on a sub-path is not more than the maximum load of the UAV serving the sub-path, and the formula is: ； wherein ul k represents a maximum load of a UAV , represents an emergency medical material demand of a demand point , represents whether a demand point is served by a UAV ; A UAV endurance constraint, which indicates that the sum of the distances traveled by a UAV on the sub-paths it serves is not more than the maximum range of the UAV, and the formula is: ； where Mmile k represents the maximum range of the UAV ; A time window constraint, which indicates that the actual delivery time of a demand point is equal to the sum of the actual delivery time of the previous demand point, the unloading time and the flight time of the UAV from the previous node to the current node, and the formula is: ； wherein, represents a demand point of unloading time, represents a flight speed of the unmanned aerial vehicle ​ A fund limit constraint, which indicates that the value of the economic cost of the scheduling scheme should be within the range of the given fund limit, and the formula is: ； Where fund limit is the upper limit of the fund for the dispatching scheme; A model-related decision variable constraint, and the formula is: 。 7. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to any one of claims 1-5, characterized in that, In step 3, the knowledge-assisted two-stage co-evolution NSGA-II algorithm comprises two stages; wherein: Stage one, double-population co-evolution: designing the coding of the UAV path planning solution, the solution comprising two parts of UAV combination and demand point sequence; constructing a double-population framework of the main population and the auxiliary population, the main population solving the constructed UAV path planning model, and the auxiliary population solving a simplified auxiliary problem of the main target, UAV performance constraint, fund limit and demand point-related constraint; the main target is to minimize time-sensitive cost; the main population and the auxiliary population evolve through non-continuous crossover, mutation update strategy; In the second stage, the main population output from the first stage is input into the second stage, and the main population output from the first stage is divided into a dominant sub-population and a disadvantaged sub-population; the dominant sub-population is updated by using a GA strategy; the disadvantaged sub-population is embedded in a QL algorithm framework, and an evolution mode is selected from a multi-mode update strategy based on a multi-state division criterion; after each iteration, the sub-population is re-divided, and the first n individuals in the disadvantaged sub-population after evolution are divided into the dominant sub-population and continue to evolve.

8. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to claim 7, characterized in that, In the first stage, the main population and the auxiliary population evolve through non-continuous crossover, including: randomly shuffling the first part of two parent chromosomes, and selecting the same number of genes from the shuffled first part of the parent chromosomes; if the first part of a parent chromosome after re-selection contains repeated genes, the repeated genes are deleted and re-selected until all selected genes are unique; and the demand points are clustered based on the number of sub-paths, new sub-paths are generated in turn, and constraint checking is performed, and the sub-paths that meet all constraint conditions are retained.

9. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to claim 7, characterized in that, The multi-state partition criterion in the second stage selects the evolutionary mode from the multi-mode update strategy, and the multi-state partition criterion includes relative distance and set optimality ; relative distance : defined as the ratio of the difference between the best and worst values of two subpopulations on the main objective, formula: ； wherein and minimizing the primary objective of the inferior subpopulation, and maximizing the primary objective of the superior subpopulation; collective optimality : defined as the ratio of the number of particles whose main objective is better than the average of the whole population and the number of particles whose main objective is worse than the average, the formula is: ； wherein and are the number of individuals in the inferior subpopulation that are less than or equal to the overall mean and the number of individuals in the primary target that are greater than the mean, respectively.

10. The low-altitude economy-oriented multi-UAV emergency medical material dispatching path planning method according to claim 9, characterized in that, The multi-mode update strategy in the second stage includes: an optimal insertion cost path crossover strategy, an internal worst sub-path crossover strategy, and a worst sub-path recombination strategy.

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