Multi-unmanned aerial vehicle time window constrained cooperative computing unloading method in space-air-ground network

Abstract

The invention discloses a multi-unmanned aerial vehicle time window constrained cooperative computing unloading method in an air-space-ground network, and belongs to the technical field of wireless communication and edge computing. According to the method, an unmanned aerial vehicle and high-altitude platform collaborative edge computing system model is constructed, and a mixed integer nonlinear programming problem is established with the purpose of minimizing the comprehensive cost of the unmanned aerial vehicle scheduling number and energy consumption; an outer layer adopts a covariance matrix adaptive evolutionary algorithm to adaptively search an optimal task unloading proportion, an inner layer solves a multi-unmanned aerial vehicle path planning sub-problem with a time window and energy constraint based on a branch pricing algorithm, and joint optimization is realized through iteration interaction of the inner layer and the outer layer. Simulation results show that the number of used unmanned aerial vehicles and system energy consumption can be remarkably reduced, and the resource utilization rate and task execution efficiency of an air-space cooperative computing system are effectively improved.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and edge computing technology, specifically to a collaborative computation offloading method for time window constraints of multiple UAVs in air-space-ground networks. Background Technology

[0002] With the increasing maturity of Space-Air-Ground Integrated Network (SAGIN) technology, utilizing aerial platforms to assist ground networks in task offloading has become a key technological approach to address the problem of limited computing resources in remote areas, oceans, and other scenarios with weak ground infrastructure. Unmanned aerial vehicles (UAVs), High Altitude Platforms (HAPs), and Low Earth Orbit (LEO) satellites, with their advantages of flexible deployment and wide coverage, serve as emerging aerial edge computing nodes, providing a feasible solution for building a ubiquitous computing environment with full coverage. Currently, academic research in this field has expanded from simple connectivity coverage to the spatial extension of computing power, focusing on improving the cost-effectiveness of system computation offloading and achieving dual performance optimization of energy consumption and latency through multi-dimensional resource scheduling and joint optimization of flight trajectories.

[0003] In the research on computation offloading and resource scheduling under the SAGIN architecture, existing work mainly focuses on addressing the optimization challenges brought about by the coupling of multi-dimensional resources such as communication, computing, and energy. For latency-sensitive tasks, Mao et al. proposed a hybrid cloud-edge computing framework that coordinates air and ground, minimizing the maximum computation latency of IoT nodes by jointly optimizing UAV deployment locations, computing and communication resource allocation. Zeng et al., in a wirelessly powered mobile edge computing system that collaborates with a central cloud, effectively shortened user task waiting time by utilizing regional scheduling and trajectory optimization algorithms. However, UAVs and IoT devices generally face energy-constrained bottlenecks, and energy consumption optimization has gradually become a research hotspot. Ding et al. proposed a joint precoding and task allocation scheme for satellite-HAP edge computing networks to minimize the system's weighted total energy consumption; Qin et al., for more complex air-ground integrated environments, adopted multi-agent deep reinforcement learning (MADDPG) to collaboratively optimize task offloading and trajectory planning, significantly reducing the system's long-term average energy consumption. Furthermore, researchers have conducted in-depth analyses of energy consumption issues related to computational offloading in typical scenarios such as low-Earth orbit satellite and UAV collaboration, stochastic computational task flows, fixed-wing UAV-assisted edge computing, and air-to-ground energy consumption tradeoffs. Regarding multi-UAV collaboration, Hao et al. introduced a task prioritization mechanism and employed deep reinforcement learning to maximize the long-term system benefits weighted by energy consumption and latency. Pervez et al., on the other hand, achieved the minimization of the comprehensive computational cost by integrating energy consumption and latency based on alternating optimization within a block coordinate descent framework.

[0004] While the aforementioned studies have made significant progress in performance optimization, their time-dimensional considerations are mostly limited to optimizing or constraining computational latency, failing to fully adapt to the more stringent timeliness requirements of real-world tasks. In typical application scenarios such as periodic environmental monitoring in remote areas, emergency rescue, and military reconnaissance, computational tasks typically have clear and strict time window constraints; that is, tasks must be started or completed within a specific time period, otherwise they will completely lose their timeliness value. Although Josilo et al. studied the offloading and scheduling problem of periodic tasks in a fixed edge server scenario, using game theory models to optimize task scheduling and link allocation, achieving the minimization of computational costs, they did not address UAV dynamic scheduling and trajectory planning. Samir et al. addressed data transmission requirements with hard deadlines by optimizing UAV trajectories to maximize the number of service nodes; Li et al. used reinforcement learning methods to solve the time window path planning problem in underwater sensor data acquisition; and Shen et al. explored path optimization under time window constraints in a multi-UAV collaborative scenario, aiming to minimize the number of UAVs used and the average task completion time, respectively. However, the aforementioned studies mainly focus on data acquisition or transmission processes, lacking a systematic exploration of the joint optimization of computational offloading and UAV scheduling under time window constraints. In particular, UAVs, as highly mobile and energy-constrained computing nodes, exhibit complex spatiotemporal coupling characteristics in their task offloading decisions, flight trajectory planning, scheduling quantity, and task time windows, making the problem extremely challenging to solve. Furthermore, the number of UAVs deployed and their operational energy consumption directly determine the system's computational service cost. How to construct an efficient computational mechanism for collaboration between UAVs and High Altitude Platforms (HAPs) while meeting strict time window constraints, and minimize the joint cost of UAV deployment quantity and energy consumption, remains a key issue that urgently needs to be addressed. Summary of the Invention

[0005] The purpose of this invention is to provide a collaborative computational offloading method for multiple UAVs under time window constraints in an integrated air-space-ground network. This method aims to solve the strong coupling problem between computational offloading and multi-UAV scheduling under time window constraints in an integrated air-space-ground network, overcome the solution difficulties caused by the non-convex coupling of discrete and continuous variables, and solve the technical problems of existing solutions not fully considering the number of UAVs to be scheduled and energy consumption, having excessively high task execution costs, and being unable to accurately meet strict timeliness requirements.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a collaborative computational offloading method for time window constraints of multiple UAVs in an air-space-ground network, comprising the following steps: S1. Constructing an aerospace collaborative computing system model: The system includes a high-altitude platform deployed in the stratosphere, several low-altitude UAVs, and ground sensing nodes distributed in the monitoring area; the high-altitude platform is equipped with an edge computing server, the UAVs fly at different altitudes in the troposphere, and the ground sensing nodes generate computing tasks with strict time window constraints; S2. Construct a mixed-integer nonlinear programming optimization problem: take the comprehensive cost objective function of minimizing the number of UAVs scheduled and the energy consumption of UAVs as the decision variables, and set constraints including time window constraints, UAV energy constraints, maximum operation time constraints, task unique service constraints, and flow conservation constraints. S3. A two-layer collaborative optimization strategy is adopted to solve the optimization problem: the outer layer optimization takes the task unloading ratio vector as an individual and adopts the covariance matrix adaptive evolution strategy to iteratively search for the optimal task unloading ratio in the continuous solution space; the inner layer optimization, under the given unloading ratio, aims to minimize the overall cost and adopts the branch pricing algorithm to solve the multi-UAV trajectory scheduling sub-problem that satisfies the constraints of time window, energy and path. S4. Iterative Interaction and Output: The optimal cost returned by the inner layer is used as the fitness value of the outer layer individuals. The population evolution is guided by updating the outer layer distribution parameters. The process is iterated alternately until the termination condition is met, and the optimal unloading ratio and the optimal UAV scheduling scheme are output.

[0007] Furthermore, in step S2, the time window constraint is applied jointly by the recursive relationship of the UAV's arrival time at the task node and the task completion time boundary: drones From node When flying to a node, arrive at the node The time requirement is met: In the formula, For drones, For a set of task nodes, For drones From node fly to node Decision variables, For the drone to reach the node Time, For drones at nodes Hovering wait time at the location For drones at nodes The execution time of the task is calculated. For drones from nodes Fly to the node Flight time; node The time window constraint for handling tasks is represented as follows: In the formula, For nodes Available start time for the task. This is the deadline for the time window corresponding to the node's task.

[0008] Furthermore, the total energy consumption of the drone includes local computing energy consumption, communication transmission energy consumption, flight energy consumption, and hovering energy consumption, among which flight energy consumption is calculated based on an aerodynamic model: in, For UAV at speed Flight power during cruise and These represent the blade profile power and induced power during UAV hovering. Let be the tip angular velocity of the blade. This represents the average induced velocity of the rotor during hovering. and These are the fuselage drag ratio and the rotor area to rotor area ratio, respectively. and These are air density and blade rotor area, respectively.

[0009] Furthermore, the iterative process of the covariance matrix adaptive evolution strategy includes: initializing the population distribution parameters, generating candidate unloading ratio vectors and performing boundary correction, evaluating fitness through an inner branch pricing algorithm, updating the distribution parameters based on fitness ranking, until the maximum number of iterations or the convergence threshold is met.

[0010] Furthermore, in step S3, the adaptive evolution strategy of the covariance matrix generates the candidate unloading proportion vector in the g-th iteration as follows: in, Let be the i-th candidate unloading ratio vector generated in the g-th iteration. It is the mean vector. Let g be the global step size for the g-th iteration. The covariance matrix of the g-th iteration To follow a pattern with a mean of 0 and a covariance matrix of... The multivariate normal distribution, The number of candidate solutions generated in each iteration.

[0011] Furthermore, in step S3, the branch pricing algorithm reconstructs the UAV scheduling problem through a set partitioning model, decomposes it into a main problem and a shortest path generation subproblem with resource constraints, and uses a label setting algorithm to solve the subproblem to dynamically generate the optimal path.

[0012] Furthermore, the main problem of the branch pricing algorithm is constructed using the following formula: in, For the set of all feasible UAV paths; Let r be the execution cost; The selection state of path r; Indicates whether the path serves a node. ; The maximum number of schedulable UAVs; constraint C9 ensures that each task is covered by only one UAV path. Its corresponding dual variable; constraint C10 limits the number of UAVs scheduled to not exceed , It is its corresponding dual variable.

[0013] Furthermore, when the branch pricing algorithm solves the shortest path subproblem with resource constraints, when the node... Along the path Extend to nodes At that time, new tags The resource status update method is as follows: in, To extend to nodes The arrival time after that, For nodes The left boundary of the time window corresponding to the task. To reach the node Time, For the node Service hours, For the node Fly to the node Flight time, To extend to nodes The cumulative energy consumption after that, To reach the node Cumulative energy consumption per hour From node Fly to the node Flight energy consumption, For the node The computational energy consumption for performing the task. For the node Energy consumption during hovering. To extend to nodes The cumulative implied costs thereafter To reach the node The cumulative implied cost at that time For the node arrive The actual incremental cost For nodes The corresponding dual variable, only when and This extension is valid at that time.

[0014] Furthermore, the branch pricing algorithm employs a branching strategy based on arc flow: after solving the linear relaxation of the restricted master problem, the cumulative flow on each arc is calculated according to the values ​​of the path selection variables; arcs with non-integer cumulative flow values ​​are selected as branch objects; branch constraints of forced passage and prohibited passage are applied to the selected arcs respectively, generating two sub-problems; the availability of arcs is updated in the network corresponding to each sub-problem, and the column generation algorithm is called again to solve the problem.

[0015] Furthermore, the termination condition of the two-layer collaborative optimization strategy is: the number of iterations of the outer layer reaches the preset maximum number of generations, or the change in the optimal fitness value of several consecutive generations is less than the preset convergence threshold; after the algorithm converges, the set of optimal paths output by the inner layer is converted into a UAV trajectory scheduling matrix, which, together with the optimal unloading ratio vector, is used as the final optimization result output.

[0016] The beneficial effects of the above scheme are as follows: 1. This invention achieves joint optimization of UAV deployment scale and operational energy consumption. The BCOS algorithm adaptively searches for the optimal task offloading ratio through the outer CMA-ES layer, while the inner branch pricing algorithm accurately solves for UAV paths that satisfy time windows and energy constraints, effectively overcoming the strong coupling problem between discrete scheduling and continuous offloading variables. Simulation results show that when the task scale is 60, BCOS only needs to schedule 13 UAVs to complete all tasks, reducing the number of UAVs used compared to the benchmark algorithm; at the same time, the total system energy consumption is reduced by 17% to 33%, significantly improving the cost-effectiveness of the air-space collaborative computing system.

[0017] 2. This invention significantly improves the spatiotemporal compactness of task processing and the single-machine service capability. The adaptive adjustment of the outer offloading ratio flexibly compresses task processing latency, precisely matching the dynamic arrival time of the UAV, thereby greatly reducing the invalid hovering waiting time of the UAV at task nodes. Under the same task scale, the total waiting time of BCOS is reduced by 20.1% compared to the branch pricing algorithm using a fixed offloading strategy, effectively improving the compactness of path planning and the utilization rate of UAV resources, allowing a single UAV to serially serve more task nodes.

[0018] 3. This invention possesses excellent adaptability to time constraints. As the task time window widens, BCOS can adaptively utilize the time margin to plan more efficient long-endurance flight trajectories for individual UAVs, further reducing UAV scale and energy consumption while meeting time requirements. Experiments show that as the time window widens, the number of UAVs scheduled by the system and the total energy consumption both exhibit a steady downward trend, verifying the robustness and generalization ability of the proposed method under task scenarios with varying degrees of urgency.

[0019] 4. This invention has significant performance advantages over existing methods. When the task size reaches 100, the system task execution cost of BCOS is reduced by 23%, 41%, and 48% respectively compared to the branch pricing algorithm, improved ant colony algorithm, and genetic algorithm that only optimize path scheduling. This fully demonstrates the necessity of joint optimization of unloading decision and path scheduling, as well as the advancement of the proposed two-layer collaborative framework in solving this type of complex coupled problem. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the space-air-ground collaborative computing network model of the present invention; Figure 2 This is a schematic diagram of the framework of the two-layer collaborative optimization strategy (BCOS) of the present invention; Figure 3 This is a convergence analysis curve of the BCOS algorithm of this invention; Figure 4 This is a schematic diagram of the UAV scheduling trajectory and calculated offloading ratio allocation generated by BCOS in this invention; Figure 5 A graph comparing the task execution costs of different algorithms; Figure 6 A bar chart comparing the number of UAVs scheduled and the energy consumption of UAVs for different algorithms; Figure 7 A bar chart comparing the total waiting time of UAVs using different algorithms; Figure 8 This is a graph showing the impact of the time window width on system performance. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0023] This invention presents an air-space collaborative computing architecture comprised of a High Altitude Platform (HAP) and multiple Unmanned Aerial Vehicles (UAVs) to handle time-sensitive computing tasks generated by ground sensing nodes within strict time windows. The system aims to minimize overall task execution costs by jointly optimizing computation offloading strategies and UAV scheduling schemes while meeting task time constraints.

[0024] I. Construction of the System Model 1. Network Model This invention considers a space-air collaborative computing network system under the SAGIN architecture, such as... Figure 1 As shown. The system consists of three parts: 1) A high-performance computing server-equipped HAP is stationarily deployed in the stratosphere, serving as an airborne edge computing center and macro base station within the system's coverage area, responsible for handling computationally intensive tasks offloaded from UAVs; 2) Several low-altitude UAVs are deployed in the troposphere, responsible for assisting in completing computational tasks within different time windows. The set of UAVs is denoted as . 3) Ground sensing nodes are randomly deployed within the monitoring area and are responsible for collaborating with UAVs to generate timely computing tasks within the coverage area. The node set is denoted as . .

[0025] To avoid mid-air collisions, the dispatched UAVs were distributed at different altitude levels with a vertical spacing of 1 meter. Each UAV departed from the starting point at a fixed altitude. and speed The UAV cruises within the area, sequentially visiting ground sensing nodes according to the plan. It hovers directly above each node, collaboratively generating computational tasks, and after completing each task, returns to the starting point within a specified time T. To describe the UAV's flight trajectory, an extended node set is defined as follows: Node 0 represents the UAV's take-off and landing point. Let node... The two-dimensional coordinates are Then the UAV at the node The hovering coordinates when performing a task above can be represented as: Furthermore, the flight trajectory of each UAV can be mathematically represented as an ordered three-dimensional coordinate sequence. ,in This represents the sequence of nodes actually visited by UAV-m. Define a trajectory scheduling binary variable. ,in UAV- From node fly to node ,otherwise, Define a binary variable for service allocation. ,in UAV- service node ,otherwise, Based on the above model, the total number of UAVs scheduled during each round of computation task execution can be calculated as follows: .

[0026] 2 Communication model Communication between the HAP and UAV operates in the Ka band allocated by the ITU. Since the HAP is located in the stratosphere and the UAV is at low altitude, there is no terrain obstruction between them; therefore, the communication channel is dominated by a line-of-sight (LoS) link. Let the total bandwidth of the space-air link be... The Euclidean distance between HAP and UAV is The carrier frequency is The total path loss of the space-air link is then modeled as follows: (1) in For free space path loss, , and These represent the additional losses caused by atmospheric absorption, rainfall attenuation, and beam pointing error, respectively, and can be calculated based on standard models such as ITU-R P.676 and P.838. The calculation is as follows: (2) Furthermore, the signal power received by the HAP for: (3) in, For UAV transmission power, and Antenna gains for UAV and HAP, respectively. Convert the received power to a linear value. Then the received signal-to-noise ratio (SNR) can be expressed as: (4) in Thermal noise power, Boltzmann's constant, The system noise temperature, For receiver noise figure, This represents the communication bandwidth between a single UAV and HAP. Considering coding overhead and protocol layer efficiency losses, a system efficiency factor is introduced. The actual achievable channel rate between the HAP and UAV is: (5) 3. Task latency and energy consumption model node The computational task generated at this point can be represented as a tuple. ,in For nodes The amount of data generated by collaborative sensing with UAVs The number of CPU cycles required to calculate a task. This is the time window for the task, meaning the task is only valid within this time interval and must be completed before the window ends. Assume a partial offloading strategy is used during the computation task execution, with the offloading ratio... Indicates task The portion of the computation is unloaded to the HAP for processing, while the remaining portion is processed locally in the UAV. Since the computation tasks are executed synchronously both locally in the UAV and remotely in the HAP, the execution time of each computation task is determined by both the local computation time and the task unloading time. The local computation time can be expressed as... ,in This refers to the calculation frequency of the UAV. The task offloading time includes both task transfer time and calculation time at the HAP. The task transfer time can be calculated as... The computation delay at HAP is ,in The computing resources allocated to a single UAV by HAP This represents the total computational frequency of HAP. Therefore, the task... The total computation time is .

[0027] In addition, definition For UAV arrival nodes If the UAV's time is earlier than the available time for the mission. Arrival before ( (), requires hovering and waiting, the waiting time can be expressed as The arrival time of the UAV after completing its task and flying to the next node l must satisfy the recursive relation: (6) in, For UAV slave nodes Fly to the node The flight time. To meet the time window constraints for mission execution, the node... The time logic relationship that needs to be satisfied is as follows: (7) In the framework of the aerospace collaborative computing task execution studied in this invention, the total energy consumption of the UAV consists of four parts: local computing, communication transmission, flight and hovering, with their respective energy consumption as follows: 1) Local calculation of energy consumption: ,in Energy consumption coefficient; 2) Communication energy consumption: ; 3) Flight energy consumption: Based on aerodynamic models, flight power It is speed The nonlinear function can be expressed as: (8) in, and The blade profile power and induced power are shown in the UAV hovering state. Let be the tip angular velocity of the blade. This represents the average induced velocity of the rotor during hovering. and These are the fuselage drag ratio and the rotor area to rotor area ratio, respectively. and Let these be the air density and the rotor blade area, respectively. Then the total flight energy consumption of the UAV is... (9) 4) Hovering energy consumption: ,in This refers to the hovering power of the UAV.

[0028] Therefore, the total energy consumption of the UAV can be calculated as follows: (10) 4. Optimize problem formulation Considering that HAP nodes are typically equipped with stable and sufficient computing resources and energy supply, enabling them to remain idle for extended periods and continuously provide computing services, this invention primarily focuses on the task execution cost overhead on the UAV side. Existing research mostly focuses only on UAV energy consumption optimization, without considering optimizing the number of UAVs scheduled. However, in practical applications, the scale of UAV scheduling is directly related to intrinsic costs such as airspace occupation and equipment wear and tear. Therefore, this invention constructs a comprehensive cost model that includes both the number of UAVs scheduled and UAV energy consumption. The research objective of this invention is to jointly optimize the task offloading ratio under the constraints of strict task time windows, UAV energy budgets, and maximum operating time. UAV trajectory scheduling matrix To minimize the execution cost of the computational task, a cost function is defined. in This is the cost factor for using a single UAV. Let be the unit energy cost coefficient. Then the optimization problem can be formalized as: (11) (11a) (11b) (11c) (11d) (11e) (11f) (11g) (11h) in, For the maximum energy reserve of each UAV, The maximum number of UAVs that can be scheduled. The time taken for UAV m to execute tasks in each round can be represented as: (12) The energy consumption of UAV m in each round of task execution is represented as: (13) Constraint C3 ensures that each task is served by exactly one UAV. C4 is a flow conservation constraint, ensuring the connectivity of each UAV path and its eventual return to the starting point. C5 constrains that the number of scheduled UAVs cannot exceed the maximum number of UAVs in reserve. C6 constrains that each scheduled UAV must return within time T and its energy consumption cannot exceed its own energy limit. C7 is a time window constraint for each computation task, and all computation tasks must be completed before the end of the time window. C8 is a time causal logic constraint for UAVs accessing two adjacent nodes along the way.

[0029] II. Problem Solving In the system model constructed in the previous section, the optimization problem P1 was formalized as a mixed-integer nonlinear programming (MINLP) problem. Solving this problem mainly faces two core challenges: 1) The problem involves discrete trajectory scheduling variables. With continuous task unloading ratio variable 1) The unloading ratio directly affects task processing latency and UAV energy consumption, and these quantities, in turn, serve as parameters constraining the schedulable scheme of the UAV. The two are closely related through nonlinear functions, exhibiting strong spatiotemporal coupling, which leads to a highly nonconvex feasible region, making it difficult for traditional methods to handle effectively. 2) UAV trajectory scheduling is essentially a variant of the Vehicle Path-to-Way (VRPTW) problem with time window constraints. Its solution space grows exponentially with the number of tasks K. Solving this problem requires finding the optimal planning scheme that satisfies various constraints within a huge set of feasible paths, and it has been proven to have NP-hard complexity. Directly using existing commercial solvers is unlikely to obtain the global optimum in polynomial time. To effectively solve this problem, this invention proposes a novel two-layer collaborative optimization strategy. This strategy decouples the original problem into two nested inner and outer sub-problems. Through iterative optimization of the inner and outer layers, the computational challenges caused by strong variable coupling and combinatorial explosion in joint optimization can be effectively alleviated.

[0030] 1. Problem Decoupling and Optimization Framework The objective function of the original optimization problem Simultaneously dependent on continuous variables with discrete variables Directly solving for these factors together is computationally infeasible. Note that once the unloading ratio... Fixed, for each task Processing latency Communication energy consumption, local computing energy consumption, and hovering energy consumption can all be accurately calculated. At this point, the inner problem is transformed into a multi-vehicle routing problem with time windows and energy constraints (MVRPTW-E) requiring time windows, energy limits, and path closure. Correspondingly, the outer problem is transformed into a problem within a hypercube... Search for the optimal in a K-dimensional continuous space This minimizes the task execution cost returned by the inner layer. Minimum.

[0031] Therefore, this invention employs a hybrid solution strategy combining evolutionary algorithms and exact combinatorial optimization, with the outer optimization task unloading ratio vector. To balance latency and energy consumption between local computing and remote offloading; the inner layer, given Under the given conditions, a drone scheduling scheme satisfying time window, energy, and path constraints is found. The overall algorithm achieves joint optimization through iterative interaction, thereby obtaining the final optimized unloading ratio. UAV scheduling strategy ,like Figure 2 As shown.

[0032] Regarding the outer layer problem, given that the objective function has relation to continuous high-dimensional variables... The gradient information is difficult to express analytically and has multiple local extrema. This invention employs the Covariance Matrix Adaptive Evolution Strategy (CMA-ES) to solve it. For the inner-layer problem, this invention models it as a Set Partitioning Problem (SPP) and uses the precise Branch-and-Price (B&P) algorithm to ensure the feasibility and near-optimal nature of the scheduling scheme.

[0033] 2. Outer Layer Optimization: Evolutionary Search for Task Unloading Ratio In the two-layer collaborative optimization strategy proposed in this invention, the outer layer is responsible for optimizing the task unloading ratio vector. Given that the objective function has respect to continuous high-dimensional variables... The gradient information is difficult to express analytically and has multiple local extrema. Therefore, this invention adopts the adaptive covariance matrix evolution strategy (CMA-ES)

[23] to solve the problem. CMA-ES is a derivative-free stochastic evolution algorithm for non-convex optimization problems in continuous domains. Its core mechanism is to maintain and iteratively update a multivariate normal distribution in the solution space. It automatically captures complex dependencies between decision variables and dynamically adjusts the search range, thereby efficiently approximating the optimal unloading strategy without gradient information. It is the mean vector. For global step size, Let be the covariance matrix. In outer-layer optimization, the objective function can be expressed as: (14) in Discrete decision variables for inner-layer optimization.

[0034] The specific process of outer layer optimization is as follows: First, initialize the population distribution parameters, including the unloading ratio. mean vector Covariance matrix and step length In the g-th iteration, the distribution is generated from the current Gaussian distribution. Candidate unloading ratio vectors: (15) Since the sampling space of the multivariate normal distribution is unbounded, the generated candidate solutions may exceed the domain of the unloading ratio. To ensure the feasibility of the solution, the sampling results need to be processed by boundary projection. The corrected candidate solution is then defined. Its k-th dimension component is calculated as follows: (16) Subsequently, the fitness of each corrected candidate solution is evaluated. Fitness function. Defined as the minimum task execution cost of the inner optimization problem under a given unloading strategy, that is... It is important to note that if a certain offloading strategy results in an unsolvable inner scheduling subproblem (for example, some tasks cannot meet the time window constraints due to an unreasonable offloading ratio), then that individual will be given a very large penalty value. This is done to eliminate infeasible solutions in subsequent evolutions. Then, based on the calculated fitness value... ,right Sort the candidate solutions in ascending order. Select the solution with the best fitness. Individuals ( The distribution parameters are updated through weighted reorganization to guide the population towards low-cost regions. The update formula for the mean vector is as follows: ,in, Let j represent the best individual ranked j in generation g. Normalized weight coefficients and Simultaneously, the global step size is adjusted using an evolutionary path mechanism. Covariance Matrix Updates are made to adaptively adjust the search step size and direction. This iterative process continues until a preset termination condition is met (such as reaching the maximum number of iterations). Or the change in fitness value is less than the threshold. After the algorithm converges, it outputs the optimal unloading ratio vector. Substituting this into the inner layer model yields the optimal scheduling scheme for the system.

[0035] 3. Inner Layer Optimization: Drone Scheduling Based on Branch Pricing In the dual-layer collaborative optimization strategy proposed in this invention, the inner layer is responsible for achieving a given unloading ratio. This invention addresses the multi-UAV trajectory planning problem under the premise that the computational latency and energy consumption of all tasks are constant. Since the original problem is an NP-hard variant of the Vehicle Routing Problem with Time Window (VRPTW), it is difficult to solve directly. This invention employs a branch-and-price (B&P) algorithm, which integrates column generation and branch-and-bound techniques, enabling efficient handling of large-scale combinatorial optimization problems.

[0036] First, the original problem model is reconstructed into a set partitioning model using Dantzig-Wolfe decomposition. Then, the problem is decomposed into a master problem (MP) based on path selection and a shortest path generation subproblem with resource constraints. Definition This is the set of all feasible UAV paths that satisfy the time window constraint, maximum endurance, and energy limit. For any path... Define its execution cost The sum of fixed start-up costs and variable energy costs is then... It can be calculated as ,in Let r be the total energy consumption of the UAV corresponding to path r. Introduce a binary variable. This indicates the selection status of path r. If path r is selected, then... ,otherwise Introducing parameters This indicates whether the path serves node k. The inner optimized MP can then be expressed as: (17) Among them, constraint C9 ensures that each task is covered by only one path. For its corresponding dual variable, constraint C10 restricts the number of UAVs scheduled to not exceed , It is its corresponding dual variable.

[0037] Due to the set of feasible paths The size of the problem grows exponentially with the number of nodes, and directly enumerating all paths to solve the MP problem suffers from the curse of dimensionality. Therefore, this invention introduces a column generation algorithm to dynamically generate paths by alternately solving the Restricted Master Problem (RMP) and the Pricing Subproblem. This method only needs to maintain a minimal subset of feasible paths. By continuously to Adding "high-quality paths" that can improve the objective function drives the solution of RMP to gradually approach the optimal solution of MP.

[0038] The process of finding a "high-quality path" is called column generation, which can be mathematically represented as finding a new path with a negative reduced cost. Join RMP. Define the impermissible cost of path r. for: (18) Therefore, the goal of the pricing sub-problem is to find an immutable cost. path Once found, add it to the RMP set. Then resolve RMP. If the above path cannot be found, it means that the current linear relaxation solution is optimal and the column generation process has converged.

[0039] This subproblem is essentially a Shortest Path Problem with Resource Constraints (SPPRC), with the goal of satisfying a time window. Maximum operating time T and maximum energy Under the premise of finding the starting point The path that starts and returns with the minimum negative reciprocal cost.

[0040] To solve the above subproblems, this invention employs a labeling algorithm. The label of node k is defined as follows: Let $k$, $k$, $k$, and $k$ represent the cumulative predetermined cost, arrival time, cumulative energy consumption, and the set of visited nodes (to ensure the path does not contain sub-loops), respectively. The algorithm starts from the source and expands sequentially backward. When node k is along the path... When expanding to node l, the new label The resource status has been updated as follows: (19) in Including waiting and service time, This represents the actual incremental cost of the jump. Only when... and When the expansion is effective, the search space is pruned, and if the tag... Superior to or equal to the label in all resource consumption (Right now , , and ), then the tag They are dominated and discarded. Finally, at the starting point 0, the path corresponding to the label with negative irreducible cost is selected and added to RMP.

[0041] It is important to note that the column generation algorithm yields a linearly relaxed solution to RMP, which may result in a fractional solution. To obtain the final integer solution, a branching mechanism needs to be introduced after the column generation algorithm converges. This invention adopts an arc-based branching strategy. First, the branching mechanism is calculated for each arc in the network. Cumulative traffic : (20) in, For indicator functions, if path r contains arcs ,but Otherwise, it is 0. This formula indicates that all selected paths are on the arc. The traffic overlay value. Select traffic. The arc closest to 0.5 Perform binary branching: (1) Forced branching: stipulate that the UAV must pass through the arc (Right now (2) Retain the arc in the pricing subproblem and remove all outgoing arcs except for l from node k, thereby eliminating paths that do not meet the constraints; (3) Prohibit branches: stipulate that UAVs are prohibited from passing through the arc. (Right now Remove the arc from the subproblem network.

[0042] The two subproblems generated by the above branching operation constitute two child nodes of the branch-and-bound tree. For each child node, the column generation algorithm is called again on the updated network topology to solve for a new linear relaxation solution. This process is performed recursively in the tree structure until all decision variables converge to integers, which signifies that the branch-and-bound search is complete, thus obtaining the given solution. The optimal scheduling scheme under the given conditions.

[0043] 4. Solution Analysis To systematically elucidate the execution logic of the Bi-level Collaborative Optimization Strategy (BCOS), Algorithm 1 details the iterative interaction process between the outer CMA-ES evolutionary search and the inner branch pricing exact solution. Within this framework, the outer algorithm performs global optimization in a continuously unloading proportional space, while the inner algorithm acts as an embedded "fitness evaluator" to minimize costs. The two algorithms execute alternately until convergence.

[0044] Algorithm 1: Two-Level Cooperative Optimization Strategy (BCOS) As can be seen from the execution flow of Algorithm 1, the computational complexity of the BCOS proposed in this invention is mainly determined by the number of outer evolution iterations. Population size The complexity of CMA-ES is determined by both the cost of the inner-layer fitness evaluation and the cost of a single fitness evaluation. In the outer-layer optimization, the core computational cost comes from the eigenvalue decomposition of the covariance matrix, and its complexity is related to the dimensionality of the decision variables. (i.e., the number of task nodes) is presented Relationship. However, the main computational bottleneck of the system lies in the invocation of the inner branch pricing algorithm. For each individual in the population, it is necessary to call the branch-bound tree. Column generation is performed on each node, and the efficiency of column generation depends on solving the pricing subproblem (ESPPRC). Although ESPPRC is theoretically an NP-hard problem, by employing a label setting algorithm to handle strict time windows and energy constraints, the growth of non-dominated labels is significantly suppressed. Let the number of network edges be... The average number of non-dominated labels is The complexity of a single inner-layer solution is approximately: ,in The average number of iterations generated for each column. In summary, the overall computational complexity of BCOS can be expressed as: Although the expression contains exponential terms, the algorithm maintains good computational feasibility when dealing with medium-sized problems thanks to the efficient pruning of the search space by column generation.

[0045] III. Simulation Analysis Numerical simulations will be used to verify the effectiveness and performance advantages of BCOS in practical applications. Assumptions Each task node is randomly deployed. Within the monitoring area, the UAV starting point is located at the center of the monitoring area. The amount of computational task data generated by each node in a single round is set to [amount missing]. The task computation density is HAP is deployed in In the stratosphere, the communication frequency band between the HAP and UAV uses a dedicated Ka band, and the total available bandwidth of the system is [missing information]. UAV transmission power is fixed at The link budget comprehensively considers free-space path loss, atmospheric attenuation, rain attenuation, and beam pointing error. Regarding the computational and energy consumption models, the CPU computation frequencies for HAP and UAV are set to [specific values ​​to be inserted here]. , UAV chip effective capacitance coefficient The UAV's dynamic energy consumption follows a quadcopter flight power model, set at a fixed altitude. by cruising speed, tip speed The parameters and power coefficient of the UAV in hovering and flight states are set with reference to the standard rotor parameters

[24] . In terms of algorithm parameter settings, the number of UAVs and the cost coefficient of energy consumption are set as follows: , The maximum number of iterations is set to Population size of the outer CMA-ES algorithm Initial search step size The maximum number of evaluations is 100. For the inner branch pricing algorithm, the Gurobi algorithm is used to solve the linear relaxation of the restricted main problem, the pricing subproblem is solved using the label setting algorithm, and the strong dominance rule is applied for pruning to accelerate convergence. The branching strategy is the highest fractional branch based on arc flow.

[0046] Figure 3 Displays the number of task nodes At that time, the convergence trajectory of the BCOS iterative optimization is shown. Because the outer CMA-ES algorithm uses multivariate normal distribution sampling for population iteration, its search process experiences exploratory fluctuations. Therefore, the curves in the figure record the changes in the historical global optimal solution up to the current stage during the iteration process. Figure 3 As can be seen, the system task execution cost gradually decreases with the number of iterations, reaching convergence and stability around the 100th iteration, thus verifying the convergence effectiveness of the algorithm. It is noteworthy that the task cost convergence curve exhibits a step-like decreasing trend during the optimization process. This is because the number of UAVs is a discrete variable, while UAV energy consumption is a continuous variable. If the number of UAVs decreases during iteration, a step-like change appears in the cost curve. This, combined with the continuous energy consumption curve, results in a step-like decreasing trend. The above experimental phenomena demonstrate the effectiveness of the proposed two-layer collaborative mechanism in searching within a mixed discrete and continuous solution space. By adaptively fine-tuning the continuous unloading ratio in the outer layer, the reconstruction of the discrete paths in the inner layer is effectively guided, thus successfully achieving the joint optimization of reducing the UAV fleet size and lowering operational energy consumption.

[0047] To visually demonstrate the combined optimization effect of BCOS in UAV scheduling, trajectory planning, and computational resource allocation, Figure 4 Showing the scale of the mission The topology of 11 UAV flight trajectories generated by BCOS and the calculated thermal distribution of the unloading ratio. Figure 4 In (a), each path starts from the take-off and landing points and returns, and all paths cover all task nodes. Figure 4 In (b), the task color mapping determines its optimal unloading ratio. Darker colors (close to 0) indicate tasks are primarily processed locally, while lighter colors (close to 1) indicate tasks heavily reliant on HAP offloading. The experimental results demonstrate that the BCOS algorithm proposed in this invention can adaptively adjust the offloading ratio based on the remaining execution time and energy budget of each task. The system seeks to find the optimal trade-off between transmission and computing power consumption. This spatiotemporal coupling mechanism of "path-computing" collaboration ensures that the system achieves global minimization of task execution cost while meeting strict battery capacity and time window constraints, verifying the adaptive decision-making capability of the proposed strategy in real-world application scenarios.

[0048] To verify the performance advantages of the proposed BCOS, this invention selects three benchmark algorithms for comparison. Since existing studies have not addressed the joint optimization of the calculation of the unloading ratio, all three benchmark algorithms use a fixed unloading ratio. The only difference lies in the UAV scheduling strategy: MACO Algorithm: The modified ant colony optimization (MACO) algorithm is used to construct a multi-UAV scheduling strategy that satisfies constraints through distributed ant agents.

[0049] GA Algorithm: It uses the classic genetic algorithm to encode and evolve the task allocation and access order. It performs iterative search in the solution space through selection, crossover and mutation operators to achieve scheduling and trajectory optimization of multiple UAVs.

[0050] The B&P algorithm employs the same branch-and-price exact solution algorithm as the inner layer of this invention, but ignores the outer layer optimization stage. This method is used to quantitatively analyze the additional performance gain brought by the "joint optimization strategy" compared to "optimizing path scheduling only".

[0051] The improved ant colony algorithm in this embodiment is derived from the literature: Shen S, Yang K, Wang K, et al. Number and operation time minimization for multi-UAV-enabled datacollection system with time windows[J]. IEEE Internet of Things Journal,2021, 9(12): 10149-10161. Figure 5The study presents the trend of task execution cost variation with task size K under different algorithms. As the number of tasks increases, the cost of all algorithms rises, but BCOS consistently outperforms other benchmark methods in terms of task execution cost, and this cost advantage becomes more significant with increasing task size. At K=100, BCOS's cost is approximately 23%, 41%, and 48% lower than B&P, MACO, and GA, respectively. This result demonstrates that BCOS effectively reduces system resource consumption by jointly optimizing the offloading ratio and UAV scheduling. BCOS's performance advantage is mainly attributed to: 1) the adaptive offloading strategy dynamically compresses task processing latency, improving the task throughput of a single UAV; and 2) precise path planning further reduces flight energy consumption and the number of UAVs used. In contrast, B&P's fixed offloading strategy is limited by a preset computational model, making it difficult to adapt to task heterogeneity, leading to decreased scheduling efficiency. While the heuristic methods of MACO and GA possess the ability to explore the solution space, they lack in-depth utilization of the problem structure, easily getting trapped in local optima, resulting in faster cost growth.

[0052] To delve into the details of the composition of task execution costs, Figure 6 Selecting a typical task scale scenario of K=60, we compared in detail the number of UAVs required for scheduling and the total energy consumption of different algorithms. Experimental results show that BCOS only requires the deployment of 13 UAVs to meet the timeliness constraints of all tasks, and its scheduling scale is significantly better than B&P, MACO, and GA mechanisms. In terms of energy consumption, BCOS also demonstrates superior energy-saving characteristics, with its total energy consumption reduced by 17%, 28%, and 33% compared to the three benchmark algorithms mentioned above, respectively. These results indicate that BCOS can effectively achieve synergistic optimization of UAV fleet size and operational energy consumption under complex spatiotemporal constraints, thus verifying its advantages in fine-grained resource allocation.

[0053] Figure 7Further comparison of the total UAV waiting time of different algorithms under a task size K=60 intuitively reflects the compactness of system scheduling. As shown in the figure, the BCOS and B&P algorithms based on precise branch-pricing scheduling significantly outperform the heuristic algorithms MACO and GA in UAV scheduling efficiency. Furthermore, under the premise of using the same inner scheduling mechanism, BCOS still shows a significant 20.1% reduction in total waiting time compared to B&P. This performance gain indicates that the outer CMA-ES algorithm, through adaptive and coordinated adjustment of the offloading ratio, can flexibly adjust the task processing time to accurately match the dynamic arrival time of the UAV, thereby reducing the invalid hovering waiting time of the UAV at the node and improving path compactness. This mechanism effectively achieves spatiotemporal joint optimization of task service time and UAV flight trajectory, improving the system's resource allocation efficiency. The simulation results show that an efficient computational offloading strategy not only optimizes computational energy consumption but also provides better spatiotemporal conditions for path scheduling, thereby reducing redundant time in the system and verifying the necessity of collaborative optimization based on offloading and scheduling in improving system service efficiency.

[0054] To verify the robustness of BCOS under different timeliness requirements, this invention designed three sets of task time windows with different widths: narrow, medium, and wide, corresponding to high-urgency task processing scenarios, routine monitoring task scenarios, and time-insensitive inspection task scenarios, respectively. Time window width Defined as average task processing time Multiples of, i.e. The multipliers for narrow, medium, and wide time windows are set as follows: , , . Figure 8 The system performance under different time window widths is demonstrated when the number of task nodes K=60. As the time window widens, the number of scheduled UAVs and UAV energy consumption gradually decrease. Specifically, in the narrow time window scenario, strict timeliness constraints limit the service capacity of a single UAV, forcing the algorithm to schedule more UAVs to process tasks in parallel to avoid task execution timeouts, while also increasing UAV energy consumption and system task execution costs. In contrast, in the wide time window, the relaxed timeliness constraints give the algorithm greater optimization freedom, allowing it to make full use of time margins, plan more efficient long-endurance flight trajectories for a single UAV, serially serve more task nodes, and thus reduce the number of UAVs and overall UAV energy consumption. The above results demonstrate that the time window width has a key impact on system resource scheduling and further verify the effectiveness of the proposed BCOS algorithm in dynamically adapting to timeliness constraints.

[0055] IV. Conclusion This invention addresses the time-sensitive computational task processing requirements in SAGIN by investigating the joint optimization problem of computational offloading and trajectory scheduling collaboratively performed by unmanned aerial vehicles (UAVs) and high-altitude platforms (HAPs) under time window constraints. Considering the complex spatiotemporal coupling between the deployment number, flight energy consumption, task processing latency, and time window of UAVs as highly maneuverable, energy-constrained mobile computing nodes, this invention constructs a mixed-integer nonlinear programming problem with the objective of minimizing the total task execution cost, and for the first time incorporates computational offloading ratio and multi-UAV path planning into a unified optimization framework. Addressing the non-convex nature of the original problem, this invention designs a two-layer collaborative optimization strategy to achieve hierarchical collaborative optimization of continuous offloading decision-making and discrete path planning. Through the dynamic coupling of outer-layer parameter search and inner-layer precise scheduling, the computational task allocation and UAV flight scheduling process are reasonably matched in the spatiotemporal dimensions. Simulation results demonstrate that the proposed collaborative optimization mechanism effectively improves system resource utilization efficiency and verifies its performance advantages in application. This invention provides theoretical support and practical pathways for future low-cost, high-timeliness aerospace collaborative task execution. Future work will explore online decision-making scenarios under dynamic task arrival and uncertainty environments.

[0056] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A collaborative computational unloading method for multiple UAVs under time window constraints in an air-space-ground network, characterized in that, Includes the following steps: S1. Constructing an aerospace collaborative computing system model: The system includes a high-altitude platform deployed in the stratosphere, several low-altitude UAVs, and ground sensing nodes distributed in the monitoring area; the high-altitude platform is equipped with an edge computing server, the UAVs fly at different altitudes in the troposphere, and the ground sensing nodes generate computing tasks with strict time window constraints; S2. Construct a mixed-integer nonlinear programming optimization problem: take the comprehensive cost objective function of minimizing the number of UAVs scheduled and the energy consumption of UAVs as the decision variables, and set constraints including time window constraints, UAV energy constraints, maximum operation time constraints, task unique service constraints, and flow conservation constraints. S3. A two-layer collaborative optimization strategy is adopted to solve the optimization problem: the outer layer optimization takes the task unloading ratio vector as an individual and adopts the covariance matrix adaptive evolution strategy to iteratively search for the optimal task unloading ratio in the continuous solution space; the inner layer optimization, under the given unloading ratio, aims to minimize the overall cost and adopts the branch pricing algorithm to solve the multi-UAV trajectory scheduling sub-problem that satisfies the constraints of time window, energy and path. S4. Iterative Interaction and Output: The optimal cost returned by the inner layer is used as the fitness value of the outer layer individuals. The population evolution is guided by updating the outer layer distribution parameters. The process is iterated alternately until the termination condition is met, and the optimal unloading ratio and the optimal UAV scheduling scheme are output.

2. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, In step S2, the time window constraint is applied jointly by the recursive relationship of the UAV's arrival time at the task node and the task completion time boundary: drones From node When flying to a node, arrive at the node The time requirement is met: In the formula, For drones, For a set of task nodes, For drones From node fly to node Decision variables, For the drone to reach the node Time, For drones at nodes Hovering wait time at the location For drones at nodes The execution time of the task is calculated. For drones from nodes Fly to the node Flight time; node The time window constraint for handling tasks is represented as follows: In the formula, For nodes Available start time for the task. This is the deadline for the time window corresponding to the node's task.

3. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, The total energy consumption of a drone includes local computing energy consumption, communication transmission energy consumption, flight energy consumption, and hovering energy consumption, among which flight energy consumption is calculated based on an aerodynamic model: in, For UAV at speed Flight power during cruise and These represent the blade profile power and induced power during UAV hovering. Let be the tip angular velocity of the blade. This represents the average induced velocity of the rotor during hovering. and These are the fuselage drag ratio and the rotor area to rotor area ratio, respectively. and These are air density and blade rotor area, respectively.

4. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, The iterative process of the covariance matrix adaptive evolution strategy includes: initializing the population distribution parameters, generating candidate unloading ratio vectors and performing boundary correction, evaluating fitness through the inner branch pricing algorithm, updating the distribution parameters based on fitness ranking, until the maximum number of iterations or the convergence threshold is met.

5. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, In step S3, the adaptive evolution strategy for the covariance matrix generates the candidate unloading proportion vector in the g-th iteration as follows: in, Let be the i-th candidate unloading ratio vector generated in the g-th iteration. It is the mean vector. Let g be the global step size for the g-th iteration. The covariance matrix of the g-th iteration To follow a pattern with a mean of 0 and a covariance matrix of... The multivariate normal distribution, The number of candidate solutions generated in each iteration.

6. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, In step S3, the branch pricing algorithm reconstructs the UAV scheduling problem through a set partitioning model, decomposing it into a main problem and a shortest path generation subproblem with resource constraints. The label setting algorithm is used to solve the subproblem to dynamically generate the optimal path.

7. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 6, characterized in that, In step S3, the main problem of the branch pricing algorithm is constructed using the following formula: in, For the set of all feasible UAV paths; Let r be the execution cost; The selection state of path r; Indicates whether path r serves a node. ; The maximum number of schedulable UAVs; constraint C9 ensures that each task is covered by only one UAV path. Its corresponding dual variable; constraint C10 limits the number of UAVs scheduled to not exceed , It is its corresponding dual variable.

8. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 6, characterized in that, In step S3, when the branch pricing algorithm solves the shortest path subproblem with resource constraints, when the node... Along the path Extend to nodes At that time, new tags The resource status update method is as follows: in, To extend to nodes The arrival time after that, For nodes The left boundary of the time window corresponding to the task. To reach the node Time, For the node Service hours, For the node Fly to the node Flight time, To extend to nodes The cumulative energy consumption after that, To reach the node Cumulative energy consumption per hour From node Fly to the node Flight energy consumption, For the node The computational energy consumption for performing the task. For the node Energy consumption during hovering. To extend to nodes The cumulative implied costs thereafter To reach the node The cumulative implied cost at that time For the node arrive The actual incremental cost For nodes The corresponding dual variable, only when and This extension is valid at that time.

9. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, The branch pricing algorithm employs a branching strategy based on arc flow: After solving the linear relaxation of the restricted master problem, the cumulative flow on each arc is calculated based on the values ​​of the path selection variables. Select arcs with cumulative flow values ​​that are not integers as branch objects; Apply branch constraints of forced passage and prohibited passage to the selected arc respectively to generate two subproblems; Update the availability of arcs in the network corresponding to each subproblem, and call the column generation algorithm again to solve the problem.

10. The collaborative computational unloading method for multiple UAVs with time window constraints in an air-space-ground network according to claim 1, characterized in that, The termination condition of the two-layer collaborative optimization strategy is: the number of iterations of the outer layer reaches the preset maximum number of generations, or the change in the optimal fitness value of several consecutive generations is less than the preset convergence threshold; after the algorithm converges, the set of optimal paths output by the inner layer is converted into a UAV trajectory scheduling matrix, which, together with the optimal unloading ratio vector, is used as the final optimization result output.

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