Gpu flight dynamic scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse

Abstract

The application relates to a GPU flight dynamic scheduling method and system based on a tropical semiring algebra and tensor orthogonal collapse. In view of the problems of graph search combination explosion, physical resource allocation overlap and computing power bottleneck in air dispatching, a pure tensor ultrafast computing architecture is constructed. First, based on the space-time constraints of flights, a multi-dimensional space connectivity tensor is initialized to establish the network ground state. Second, the tropical semiring algebra is used to map the concurrent route search to tensor multiplication, and the global candidate flight string is extracted. Third, the path correlation matrix is constructed and self-point multiplication is performed to quickly complete global orthogonal conflict detection. Finally, the outer product penalty boundary is generated by using the conflict-free flight to reduce the dimension of the bottom tensor and realize the exclusive locking and cyclic derivation of the physical resources. The application converts the complex mutual exclusion scheduling into pure algebraic operation, realizes the millisecond-level and zero-overlap accurate scheduling, and greatly improves the air dynamic scheduling efficiency.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of air transport planning and high-performance computing, and more specifically, to a GPU-based dynamic flight scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse. Background Technology

[0002] Currently, the existing methods used in air transport planning mainly include the following three types: (1) Traditional graph search and network flow algorithm: The flight network is abstracted into a directed acyclic graph (DAG) or a spatiotemporal network graph, and the depth-first search (DFS), breadth-first search (BFS), Dijkstra or time-space network flow model is used to find legal flight connection paths. (2) Column generation and set partitioning model: The standard solution in the industry. This solution is divided into two stages: First, a large number of legal flight strings are generated through the rule engine to form a "candidate pool" (i.e., "column generation"), and then it is transformed into a large-scale 0-1 integer programming problem and input into a third-party commercial solver (such as Gurobi, CPLEX) to obtain the optimal solution that does not overlap (i.e., "set partitioning"). (3) Graph processing structure and business rule engine based on CPU scalar computation: In the existing flight and crew scheduling system, the storage and computation of the underlying data generally adopt the CPU scalar computation mode based on the traditional von Neumann architecture. Specifically, this manifests in the following ways: 1. Data Structure Level: Flight networks mostly use pointer-based adjacency lists or object-oriented (OOP) entity graph models for storage. Relationships between nodes and edges are established through memory pointers for association and navigation. 2. Computational Paradigm Level: Algorithm progression heavily relies on control flow instructions. Specifically, during pathfinding and conflict resolution, numerous if-else conditional branch statements, while loops, and complex business rule trees are used to systematically assess time constraints, capacity limitations, and overlapping conflicts. 3. Hardware Execution Level: Deeply reliant on the CPU's powerful branch predictor and multi-level caches (L1 / L2 / L3 cache) to handle complex serial logic.

[0003] The pain points of traditional search algorithms based on heuristic graph traversal (such as DFS, BFS, Dijkstra) are as follows: Aviation networks are high-density directed graphs, and traditional search algorithms suffer from a severe "state space explosion" problem when handling massive amounts of flights across time sequences. The branches of the search tree grow exponentially, resulting in huge memory overhead and highly redundant overlapping subproblems, failing to meet the real-time requirements of dynamic scheduling. The pain points of set partitioning models based on operations research are also significant: Industry often uses a two-stage method of "candidate column generation + exact coverage," which heavily relies on expensive third-party linear programming solvers. Furthermore, the "candidate column generation" stage typically still relies on a serial rule engine, failing to address the computational bottleneck at the underlying data structure level. Finally, there are the pain points related to underlying hardware architecture adaptation: Traditional graph search algorithms contain extremely high conditional branch complexity and irregular memory access patterns, which are inherently incompatible with the single-instruction multiple-dataflow architecture of modern GPUs, leading to severe idleness of hardware computing power with high-concurrency computing cores. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies such as graph search combinatorial explosion, overlapping physical resource allocation, and computing power bottlenecks in air scheduling. It provides a GPU-based dynamic flight scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse, which effectively reduces computational complexity and greatly improves the efficiency of dynamic air scheduling.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse is provided, including the following steps: S1. Spatiotemporal physical topology modeling and initialization: Obtain the departure and arrival spatiotemporal attribute characteristics of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints; S2. Tropical semi-ring tensor space derivation: In a GPU computing environment, the tropical semi-ring operator is used to execute the state transition equation and concurrently calculate the global shortest path weights, and generate the predecessor adjoint matrix within the same instruction cycle for path decoding. S3. Orthogonalization of the correlation matrix and conflict detection: Candidate paths are sampled from the target level tensor and a binary path-node correlation matrix is ​​constructed. Global orthogonality test is performed by calculating the Gram matrix of the path-node correlation matrix to filter out legal flight strings with no resource overlap at the physical level. S4. Outer product mask generation and tensor collapse: Extract the occupancy state feature vector of the legal flight string selected in step S3, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources. S5. State Convergence and Output: Determine the global element convergence state of the ground state connectivity matrix. If the preset convergence state has not been reached, repeat steps S2 to S5. If the preset convergence state has been reached, output the global conflict-free backbone scheduling plan and the set of independent and detached outliers.

[0006] This invention presents a GPU-based dynamic flight scheduling method based on tropical semiring algebra and tensor orthogonal collapse. Based on flight spatiotemporal topological constraints, it constructs a ground-state connectivity matrix representing the initial state of the network. It introduces the "Tropical Semiring" system, mapping shortest path search to parallel tensor multiplication, and extracts predecessor node indices using the adjoint matrix within the same computation cycle. It constructs a path-node association matrix and calculates its Gram matrix. The method utilizes a matrix (self-dot product) to achieve global orthogonality verification and concurrent conflict detection. It generates an infinite penalty mask based on the dot product operation of the occupied state feature vector, performing orthogonal collapse and state updates on the ground state matrix to achieve exclusive locking and adaptive iteration of physical resources. This invention completely transforms the highly complex graph theory pathfinding and mutually exclusive scheduling into rule-based tensor addition, minimum value reduction, and matrix multiplication, perfectly adapting to high-concurrency GPU computing architectures and reducing scheduling time from hours to seconds or even milliseconds. Furthermore, it proposes an orthogonalization detection method for the association matrix, directly exposing node overlap conflicts through algebraic operations without traversal checks, ensuring that the generated flight sequences meet strict orthogonal constraints in physical fuselage allocation.

[0007] Furthermore, step S1 specifically includes: S11. Initialization input for the multidimensional connectivity tensor, including One flight, Each airport has its own departure and arrival airports, and the departure and arrival times for each flight are as follows: ; S12. Spatial Projection: Construction Starting Boolean matrix and The landing Boolean matrix Perform matrix multiplication. Obtain the spatial co-occurrence matrix; S13. Time Filtering: Based on the set minimum / maximum transit time thresholds, filter... Time difference calculation for effectively connected coordinates in the matrix , Indicates flight The actual takeoff time characteristics, Indicates flight The actual landing time characteristics; satisfying the threshold constraint. Assign to ground state connectivity matrix Non-connected or illegal nodes are assigned positive infinity. .

[0008] Furthermore, step S2 specifically includes: S21. Algebraic substitution for concurrent pathfinding based on tropical semi-rings: replace "multiplication and summation" in matrix multiplication with "addition and finding the minimum value"; S22. State Transition Equations: Concurrent Execution of State Transition Equations in the GPU The calculation depth is The global shortest path weight of the layer; where, State tensor The elements in the text represent the flight Connect to flight The minimum value of the path weight; State tensor China from flights To intermediate flights The minimum value of the path weight; Represents the ground state connectivity matrix China from intermediate flights To the flight The time cost of a single-step transfer; S23. Accompanying Index Extraction: Within the same instruction cycle for calculating the minimum value, record the intermediate nodes that yielded the minimum value. Generate the predecessor index matrix , used for deterministic decoding of paths.

[0009] Furthermore, step S3 specifically includes: S31. Path Reduction and Sampling: Using tensor reduction instructions, from the target-level state tensor... Extract the top with the smallest total weight Candidate paths, and through the adjoint matrix Reverse decoding yields a complete sequence of nodes; S32. Construction of the association matrix: The mapping generates a dimension of... Path-node association binary matrix ; S33. Orthogonality calculation: Perform matrix multiplication Solve for the Gram matrix; S34. Conflict-free set filtering: analytic matrix Extract the row vectors whose non-main diagonal elements are all 0, add the extracted row vectors to the confirmed flight schedule set, and obtain the valid flight string.

[0010] Furthermore, step S4 specifically includes: S41. Occupancy Status Feature Extraction: Map the node indices involved in the successfully matched, conflict-free, and legitimate flight strings from step S3 to a dimension-... One-dimensional Boolean occupancy state vector ; S42. Global Orthogonal Constraint Mask Generation: Based on the formula Perform vector operations to generate a vector of dimension 1. An infinitely large penalty mask matrix; the mask matrix forces the row and column eigenvalues ​​corresponding to the already occupied flight nodes to positive infinity, forming a physical exclusivity constraint; among which, The dimension is The cross-shaped penalty mask matrix; The dimension is The whole Column vector; for transposed full Row vectors; S43. Ground-state network state collapse and iterative feedback: Performing tensor addition operations The spatial state collapse update of the ground state connectivity matrix is ​​performed using a mask matrix, where... This represents the result generated after the current round of mask overlay and spatial state collapse, used for the [number]th round. A new generation of ground-state connectivity matrix calculated through round-by-round iteration; express The current ground state connectivity matrix used in the round of iterative calculation.

[0011] Furthermore, step S5 specifically includes: S51. System state convergence and outlier node settlement: Re-input the updated collapsed ground state matrix into step S2 to trigger a new round of deduction; S52. Algorithm Convergence Criterion: When the ground state matrix... All global elements converge to positive infinity. When the network connectivity is completely exhausted, the iteration stops. S53. Scheduling Structure Output: Aggregate the valid flight strings output from each iteration round to generate a globally conflict-free backbone scheduling plan; retrieve the Boolean occupancy state vector. The index with a median value of 0 outputs a set of outlier flights for subsequent repositioning planning.

[0012] This invention also provides a GPU-based dynamic flight scheduling system based on tropical semi-ring algebra and tensor orthogonal collapse, comprising: Spatiotemporal physical topology modeling and initialization module: used to obtain the departure and arrival spatiotemporal attribute characteristics of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints; Tropical semi-ring tensor space derivation module: In a GPU computing environment, it uses the tropical semi-ring operator to execute the state transition equation and concurrently calculate the global shortest path weights, and generates the predecessor adjoint matrix for path decoding within the same instruction cycle; The orthogonalization and conflict detection module of the path-node association matrix is ​​used to sample candidate paths from the target level tensor and construct a binary path-node association matrix. It performs a global orthogonality test by calculating the Gram matrix of the path-node association matrix and filters out legal flight strings with no resource overlap at the physical level. The outer product mask generation and tensor collapse module is used to extract the occupancy state feature vector of the legal flight string selected in the correlation matrix orthogonalization and conflict detection module, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources. State Convergence and Output Module: Used to determine the global element convergence state of the ground state connectivity matrix, control the iteration loop of the deduction module; and when connectivity is completely exhausted, output the global conflict-free backbone scheduling plan and the set of independent and detached out-of-group flights.

[0013] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0014] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described above.

[0015] Compared with the prior art, the beneficial effects of the present invention are: 1. The present invention provides a GPU-based dynamic flight scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse, which completely transforms the highly complex graph theory pathfinding and mutually exclusive scheduling into regular tensor addition, minimum value reduction and matrix multiplication, perfectly adapting to the high-concurrency computing architecture of GPU, and compressing the scheduling time from several hours to seconds or even milliseconds.

[0016] 2. The present invention provides a GPU-based dynamic flight scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse. It proposes an "orthogonalization detection method of association matrix", which directly exposes node overlap and conflict through algebraic operations without the need for traversal and investigation, ensuring that the generated flight strings meet strict orthogonal constraints in physical fuselage allocation.

[0017] 3. The present invention provides a GPU flight dynamic scheduling method and system based on tropical semi-ring algebra and tensor orthogonal collapse. Relying on tensor block mechanism and asynchronous memory scheduling strategy, the time and space complexity of the algorithm grows sublinearly or gently linearly with the increase of flight scale, effectively avoiding memory overflow in high-dimensional combinatorial optimization. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse of the present invention. Figure 2 This is a schematic diagram of the GPU flight dynamic scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse in Example 1. Figure 3 This is a block diagram of the GPU-based dynamic flight scheduling system based on tropical semi-ring algebra and tensor orthogonal collapse in Example 3. Detailed Implementation

[0019] The present invention will be further described below with reference to specific embodiments. The accompanying drawings are for illustrative purposes only, representing schematic diagrams rather than actual physical objects, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0020] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0021] Symbol and variable descriptions To facilitate understanding of the tensor algebra derivation and network mapping logic involved in this embodiment, the core mathematical symbols and variables used in the specification are uniformly defined as follows.

[0022] 1. Basic Network and Spatiotemporal Constraint Characteristics The total number of physical flights participating in the scheduling calculation across the entire network.

[0023] The total number of airports (or destinations) involved in the entire network.

[0024] The first in the network A specific flight node (e.g.) ).

[0025] :flight The characteristics of actual takeoff (departure) time.

[0026] :flight The actual landing (arrival) time characteristics.

[0027] The waiting time cost for connecting flights is expressed by the equation: The calculation yielded the result.

[0028] / The algorithm sets the minimum allowed transit time (MCT) and the maximum transit time threshold.

[0029] 2. Physical topological projection and tensor derivation variables Dimensions are The Boolean attribute projection matrix of departure (departure).

[0030] Dimensions are The Boolean attribute projection matrix of arrival (arrival).

[0031] Dimensions are The spatial co-occurrence connectivity matrix, defined by the projection operator get.

[0032] Dimensions are The ground-state connectivity matrix represents the minimum time cost of all single-step legal connections in the initial state of the network.

[0033] State tensor China from flights To intermediate flights The minimum value of the path right.

[0034] Represents the ground state connectivity matrix China from intermediate flights To the flight The time cost of a single-step transfer.

[0035] The system deduction reached a depth of The global state transition matrix of the layer records the transitions across... The optimal total transfer waiting time for each flight node.

[0036] State tensor The elements in the text represent the flight Connect to flight The minimum value of the path right.

[0037] Dimensions are The predecessor adjoint matrix is ​​generated synchronously in the minimum reduction instruction, and records the transit bridge node index when the minimum right-of-way is obtained, which is used for the deterministic reverse decoding of the path.

[0038] 3. Orthogonal conflict detection and physical collapse variables The total number of top-quality candidate flight strings (paths) extracted in each iteration of the decoding phase.

[0039] Dimensions are The binary path-node correlation matrix represents the requisition of underlying physical fuselage resources by candidate flight sequences.

[0040] Dimensions are The conflict development matrix (i.e., the Gram matrix) ), used to verify the absolute orthogonality between candidate paths.

[0041] Dimensions are A one-dimensional Boolean occupancy state feature vector, where the element values ​​are... This indicates that the flight has been exclusively allocated, with a value of This indicates that the device is in a free or idle state.

[0042] Dimensions are The whole Column vector; Its transposed full Row vectors.

[0043] Dimensions are The cross-shaped penalty mask matrix is ​​obtained by outer product operation. It is generated instantly, representing the physical collision avoidance barrier of the entire network.

[0044] After tensor collapse and mask stacking operations ( The next generation of ground state connectivity matrix is ​​generated after the previous iteration and is used for the next round of iteration updates.

[0045] This represents the result generated after the current round of mask overlay and spatial state collapse, used for the [number]th round. A new generation of ground-state connectivity matrix calculated in round-by-round iterations.

[0046] express The current ground state connectivity matrix used in the round of iterative calculation.

[0047] : In a tropical semi-ring algebraic system, a positive infinite scalar physically represents a spatial disconnection, a temporal violation, or the physical annihilation (allocation lock) of the corresponding node.

[0048] Example 1 This embodiment is the first embodiment of a GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse, such as... Figure 1 and Figure 2 As shown, it includes the following steps: Step S1. Spatiotemporal physical topology modeling and initialization: Obtain the departure and arrival spatiotemporal attribute features of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints.

[0049] Specifically: S11. Initialization input for the multidimensional connectivity tensor, including One flight, Each airport has its own departure and arrival airports, and the departure and arrival times for each flight are as follows: ; S12. Spatial Projection: Construction Starting Boolean matrix and The landing Boolean matrix Perform matrix multiplication. Obtain the spatial co-occurrence matrix; S13. Time Filtering: Based on the set minimum / maximum transfer time thresholds (MinT / MaxT), filter... Time difference calculation for effectively connected coordinates in the matrix , Indicates flight The actual takeoff time characteristics, Indicates flight The actual landing time characteristics; satisfying the threshold constraint. Assign to ground state connectivity matrix Non-connected or illegal nodes are assigned positive infinity. .

[0050] Step S2. Tropical semi-ring tensor space derivation: In the GPU computing environment, the state transition equation is executed using the tropical semi-ring operator to concurrently calculate the global shortest path weights, and the predecessor adjoint matrix is ​​generated within the same instruction cycle for path decoding.

[0051] Specifically: S21. Algebraic substitution for concurrent pathfinding derivation based on tropical semi-rings: replacing "multiplication and summation" in traditional matrix multiplication with "addition and finding the minimum value"; traditional matrix multiplication refers to the standard matrix multiplication operation in classical linear algebra, that is, multiplying the elements first and then summing them.

[0052] S22. State Transition Equations: Concurrent Execution of State Transition Equations in the GPU The calculation depth is The global shortest path weight of the layer; where, State tensor The elements in the text represent the flight Connect to flight The minimum value of the path weight; S23. Accompanying Index Extraction: Within the same instruction cycle for calculating the minimum value, record the intermediate nodes that yielded the minimum value. Generate the predecessor index matrix , used for deterministic decoding of paths.

[0053] Step S3. Orthogonalization of the association matrix and conflict detection: Sample candidate paths from the target level tensor and construct a binary path-node association matrix. Perform a global orthogonality test by calculating the Gram matrix of the path-node association matrix to filter out legal flight strings with no resource overlap at the physical level.

[0054] Specifically: S31. Path Reduction and Sampling: Using tensor reduction instructions, from the target-level state tensor... Extract the top with the smallest total weight Candidate paths, and through the adjoint matrix Reverse decoding yields a complete sequence of nodes; S32. Construction of the association matrix: The mapping generates a dimension of... Path-node association binary matrix ; S33. Orthogonality calculation: Perform matrix multiplication Solve for the Gram matrix; S34. Conflict-free set filtering: analytic matrix Extract the row vectors whose non-main diagonal elements are all 0. The corresponding flight strings have absolute orthogonality in the network topology (i.e. no node overlap). Add the extracted row vectors to the confirmed flight schedule set to obtain the valid flight strings.

[0055] Step S4. Outer product mask generation and tensor collapse: Extract the occupancy state feature vector of the legal flight string selected in step S3, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources.

[0056] Specifically: S41. Occupancy Status Feature Extraction: Map the node indices involved in the successfully matched, conflict-free flight strings from step S3 to a dimension-1. One-dimensional Boolean occupancy state vector ; S42. Global Orthogonal Constraint Mask Generation: Based on the formula Perform vector operations to generate a vector of dimension 1. An infinitely large penalty mask matrix; the mask matrix forces the row and column eigenvalues ​​corresponding to the already occupied flight nodes to positive infinity, forming a physical exclusivity constraint; among which, The dimension is The cross-shaped penalty mask matrix; The dimension is The whole Column vector; for transposed full Row vectors; S43. Ground-state network state collapse and iterative feedback: Performing tensor addition operations The spatial state of the ground-state connectivity matrix is ​​updated by using a mask matrix. This operation leverages the repulsive property of the tropical semi-ring algebraic minimization operation to adaptively mask the assigned nodes in subsequent iterations.

[0057] Step S5. State Convergence and Output: Determine the global element convergence state of the ground state connectivity matrix. If the preset convergence state has not been reached, repeat steps S2 to S5. If the preset convergence state has been reached, output the global conflict-free backbone scheduling plan and the set of independent and detached outliers.

[0058] Specifically: S51. System state convergence and outlier node settlement: Re-input the updated collapsed ground state matrix into step S2 to trigger a new round of deduction; S52. Algorithm Convergence Criterion: When the ground state matrix... All global elements converge to positive infinity. When the network connectivity is completely exhausted, the iteration stops. S53. Scheduling Structure Output: Aggregate the valid flight strings output from each iteration round to generate a globally conflict-free backbone scheduling plan; retrieve the Boolean occupancy state vector. The index with a median value of 0 outputs a set of outlier flights for subsequent repositioning planning.

[0059] Test comparison: Total number of flights involved in the calculation: 2569; Number of airports: 351; Test equipment: GPU: RTX 5090, CPU: R7 9800X3D Perform a simulation (the sequence includes flight numbers k=2 to 8); Total CPU time: 13806.23 seconds, total GPU time: 31.02 seconds. The GPU's tensor concurrent computation speed is approximately 445.1 times that of the CPU (both the CPU and GPU execute the same tropical semi-ring algebra and tensor chain multiplication derivation instructions).

[0060] This embodiment presents a GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse. Addressing the challenges of combinatorial explosion in map search, overlapping physical resource allocation, and computational bottlenecks in air traffic control, this embodiment constructs a pure tensor-based high-speed computation architecture. First, a multi-dimensional spatial connectivity tensor is initialized based on flight spatiotemporal constraints to establish the network ground state. Second, concurrent pathfinding is mapped to tensor multiplication using tropical semi-ring algebra to extract global candidate flight strings. Third, a path association matrix is ​​constructed, and global orthogonal conflict detection is quickly achieved through self-dot multiplication. Finally, an outer product penalty bound is generated using conflict-free flights to perform dimensionality reduction and collapse on the underlying tensor, achieving exclusive locking and iterative deduction of physical resources. The method provided in this embodiment transforms complex mutually exclusive scheduling into pure algebraic operations, achieving millisecond-level, zero-overlap precise scheduling, significantly improving the efficiency of dynamic air traffic control.

[0061] Example 2 This embodiment is a second embodiment of a GPU flight dynamic scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse. This embodiment is similar to the first embodiment, except that, in this embodiment, based on the method of the first embodiment, a full-process simulation of tensor scheduling based on a 6-node miniaturized aviation network is provided.

[0062] Step 1: Scene Setup and Physical Topology Modeling. Set up a miniature aviation network, including 6 physical flights operating between four airports A, B, C, and D. to The physical takeoff and landing times (in 24-hour format) and spatial topology definitions for each flight are as follows: First Segment (Hydrone A) Hub B): Departure at 06:00, arrival at B at 08:00. Departure at 07:00, arrival at B at 09:00; Second leg (B hub) C Hub): Depart from B at 10:00 and arrive at C at 12:00. Depart from B at 11:00 and arrive at C at 13:00; Third Segment (C Hub) D Hub): Departure from C at 15:00, arrival at D at 17:00. Depart from C at 16:00 and arrive at D at 18:00; Extract the spatiotemporal connectivity attributes of each flight and calculate the waiting time for a valid connection in hours. Based on this, the initial construction dimension is... ground state connectivity matrix Matrix elements The transit time cost between flights, and the illegal borders where space is blocked or time is reversed, are uniformly set to positive infinity. .

[0063]

[0064] Note: For example Arrive at 08:00, connecting to the 10:00 departure. Waiting costs Hours; connecting to the 11:00 departure Waiting costs Hour.

[0065] Step 2. The tensor multiplication derivation system based on tropical semi-ring algebra performs tropical semi-ring tensor multiplication calculations in the GPU to find the optimal long-haul route spanning 3 flights.

[0066] Calculate the state transition matrix The algebraic rules are: .

[0067] get:

[0068] Note: For example Hours. It represents from fly to The minimum total waiting time is 4.

[0069] The system synchronously generates the predecessor adjoint matrix:

[0070] Note: The symbol "-" indicates that there is no valid connected path. It precisely indicates from arrive To achieve the optimal travel time of 4 hours, it is necessary to go through flights. As a transit point, the set of two candidate flight strings with the lowest total transit time across the entire network is decoded. Candidate string A ( ): (Transfer time: 4 hours) Candidate string B ( ): (Transfer time: (5 hours).

[0071] Decoding output: System direct retrieval matrix The minimum element in the matrix, and combined with the matrix indexing Inverse decoding with low complexity. The system successfully extracted the set of two candidate flight strings with the lowest total transfer time across the entire network. : Candidate string A ( ):extract ,pass Decode path (Transfer time: 4 hours); Candidate string B ( ):extract ,pass Decode path (Transfer time: 5 hours).

[0072] Step 3. Correlation Matrix Construction and Orthogonal Conflict Detection for Candidate Sets The system directly maps it to a dimension of Path-node association binary matrix :

[0073] For matrix Perform Gram matrix multiplication ( ), generating dimension is Conflict imaging matrix :

[0074] Effect Analysis: The main diagonal element 3 represents that each string contains 3 physical flight nodes; the secondary diagonal element 2 indicates that there are 2 physically overlapping nodes between the two strings. and Based on this, the system determines that the set is not orthogonal, indicating a physical competition for the allocation of fuselage resources.

[0075] Step 4. Prioritize allocation and outer product mask tensor collapse system: Based on the overall time optimality principle, confirm the admission candidate string A; and generate a one-dimensional Boolean occupancy state feature vector for this string. :

[0076] The system performs vector outer product operations. Generate an infinitely large penalty mask for the entire network. Perform tensor addition on this mask and the ground state matrix. Complete the requisition of flights ( The physical annihilation of the state. The new ground state matrix after collapse is as follows:

[0077] Step 5. The loop feedback and global scheduling convergence system will collapse and update the system. The data is then fed back into the GPU tropical semi-circular deduction module. At this point, the overlapping paths have been physically severed, and the underlying min operation automatically searches for a path in the remaining network, outputting the unique and valid supplementary path: candidate string C. ): (Transfer time: (6 hours) Map the candidate string C to feature vectors and generate a new mask. After performing the second tensor collapse, all global elements of the ground state matrix converge to infinity. The algorithm halted, and the system ultimately output a perfectly covered and absolutely orthogonal shift schedule: Shift 1: Shift 2: .

[0078] Example 3 This embodiment is an example of a GPU-based dynamic flight scheduling system based on tropical semi-cyclic algebra and tensor orthogonal collapse. The system provided in this embodiment is based on the same inventive concept as the method in Embodiment 1, and the system corresponds to the aforementioned scheduling method. Figure 3 As shown, the system specifically includes: Spatiotemporal physical topology modeling and initialization module: used to obtain the departure and arrival spatiotemporal attribute characteristics of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints; Tropical semi-ring tensor space derivation module: In a GPU computing environment, it uses the tropical semi-ring operator to execute the state transition equation and concurrently calculate the global shortest path weights, and generates the predecessor adjoint matrix for path decoding within the same instruction cycle; The orthogonalization and conflict detection module of the path-node association matrix is ​​used to sample candidate paths from the target level tensor and construct a binary path-node association matrix. It performs a global orthogonality test by calculating the Gram matrix of the path-node association matrix and filters out legal flight strings with no resource overlap at the physical level. The outer product mask generation and tensor collapse module is used to extract the occupancy state feature vector of the legal flight string selected in the correlation matrix orthogonalization and conflict detection module, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources. State Convergence and Output Module: Used to determine the global element convergence state of the ground state connectivity matrix, control the iteration loop of the deduction module; and when connectivity is completely exhausted, output the global conflict-free backbone scheduling plan and the set of independent and detached out-of-group flights.

[0079] The various modules in the system provided in this embodiment are executed in a similar manner to the methods provided in the embodiments, and will not be described again here.

[0080] In the specific implementation of the above embodiments, the technical features can be combined in any non-contradictory way. For the sake of brevity, not all possible combinations of the above technical features are described. However, as long as the combination of these technical features is not contradictory, it should be considered to be within the scope of this specification.

[0081] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse, characterized in that, Includes the following steps: S1. Spatiotemporal physical topology modeling and initialization: Obtain the departure and arrival spatiotemporal attribute characteristics of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints; S2. Tropical semi-ring tensor space derivation: In a GPU computing environment, the tropical semi-ring operator is used to execute the state transition equation and concurrently calculate the global shortest path weights, and generate the predecessor adjoint matrix within the same instruction cycle for path decoding. S3. Orthogonalization of the correlation matrix and conflict detection: Candidate paths are sampled from the target level tensor and a binary path-node correlation matrix is ​​constructed. Global orthogonality test is performed by calculating the Gram matrix of the path-node correlation matrix to filter out legal flight strings with no resource overlap at the physical level. S4. Outer product mask generation and tensor collapse: Extract the occupancy state feature vector of the legal flight string selected in step S3, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources. S5. State Convergence and Output: Determine the global element convergence state of the ground state connectivity matrix. If the preset convergence state has not been reached, repeat steps S2 to S5. If the preset convergence state has been reached, output the global conflict-free backbone scheduling plan and the set of independent and detached outliers.

2. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 1, characterized in that, Step S1 specifically includes: S11. Initialization input for the multidimensional connectivity tensor, including One flight, Each airport has its own departure and arrival airports, and the departure and arrival times for each flight are as follows: ; S12. Spatial Projection: Construction Starting Boolean matrix and The landing Boolean matrix Perform matrix multiplication. Obtain the spatial co-occurrence matrix; S13. Time Filtering: Based on the set minimum / maximum transit time thresholds, filter... Time difference calculation for effectively connected coordinates in the matrix , Indicates flight The actual takeoff time characteristics, Indicates flight The actual landing time characteristics; satisfying the threshold constraint. Assign to ground state connectivity matrix Non-connected or illegal nodes are assigned positive infinity. .

3. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 2, is characterized in that... Step S2 specifically includes: S21. Algebraic substitution for concurrent pathfinding based on tropical semi-rings: replace "multiplication and summation" in matrix multiplication with "addition and finding the minimum value"; S22. State Transition Equations: Concurrent Execution of State Transition Equations in the GPU The calculation depth is The global shortest path weight of the layer; where, State tensor The elements in the text represent the flight Connect to flight The minimum path weight; State tensor China from flights To intermediate flights The minimum path weight; Represents the ground state connected matrix China from intermediate flights To the flight The time cost of a single-step transfer; S23. Accompanying Index Extraction: Within the same instruction cycle for calculating the minimum value, record the intermediate nodes that yielded the minimum value. Generate the predecessor index matrix , used for deterministic decoding of paths.

4. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 3, is characterized in that... Step S3 specifically includes: S31. Path Reduction and Sampling: Using tensor reduction instructions, from the target-level state tensor... Extract the top with the smallest total weight Candidate paths, and through the adjoint matrix Reverse decoding yields a complete sequence of nodes; S32. Construction of the association matrix: The mapping generates a dimension of... Path-node association binary matrix ; S33. Orthogonality calculation: Perform matrix multiplication Solve for the Gram matrix; S34. Conflict-free set filtering: analytic matrix Extract the row vectors whose non-main diagonal elements are all 0, add the extracted row vectors to the confirmed flight schedule set, and obtain the valid flight string.

5. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 4, characterized in that, Step S4 specifically includes: S41. Occupancy Status Feature Extraction: Map the node indices involved in the successfully matched, conflict-free, and legitimate flight strings from step S3 to a dimension-... One-dimensional Boolean occupancy state vector ; S42. Global Orthogonal Constraint Mask Generation: Based on the formula Perform vector operations to generate a vector of dimension 1. An infinitely large penalty mask matrix; the mask matrix forces the row and column eigenvalues ​​corresponding to the already occupied flight nodes to positive infinity, forming a physical exclusivity constraint; among which, The dimension is The cross-shaped penalty mask matrix; The dimension is The whole Column vector; for transposed full Row vectors; S43. Ground-state network state collapse and iterative feedback: Performing tensor addition operations The spatial state collapse update of the ground state connectivity matrix is ​​performed using a mask matrix, where... This represents the result generated after the current round of mask overlay and spatial state collapse, used for the [number]th round. A new generation of ground-state connectivity matrix calculated through round-by-round iteration; express The current ground state connectivity matrix used in the round of iterative calculation.

6. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 5, is characterized in that... The mask matrix forces the row and column feature values ​​corresponding to the occupied flight nodes to be positive infinity, forming a physical exclusivity constraint.

7. The GPU-based dynamic flight scheduling method based on tropical semi-ring algebra and tensor orthogonal collapse as described in claim 5, is characterized in that... Step S5 specifically includes: S51. System state convergence and outlier node settlement: Re-input the updated collapsed ground state matrix into step S2 to trigger a new round of deduction; S52. Algorithm Convergence Criterion: When the ground state matrix... All global elements converge to positive infinity. When the network connectivity is completely exhausted, the iteration stops. S53. Scheduling Structure Output: Aggregate the valid flight strings output from each iteration round to generate a globally conflict-free backbone scheduling plan; retrieve the Boolean occupancy state vector. The index with a median value of 0 outputs a set of outlier flights for subsequent repositioning planning.

8. A GPU-based dynamic flight scheduling system based on tropical semi-ring algebra and tensor orthogonal collapse, characterized in that, include: Spatiotemporal physical topology modeling and initialization module: used to obtain the departure and arrival spatiotemporal attribute characteristics of all flight nodes in the network, construct a spatial co-occurrence matrix, and generate a ground state connectivity matrix representing the initial state of the network by combining temporal threshold constraints; Tropical semi-ring tensor space derivation module: In a GPU computing environment, it uses the tropical semi-ring operator to execute the state transition equation and concurrently calculate the global shortest path weights, and generates the predecessor adjoint matrix for path decoding within the same instruction cycle; The orthogonalization and conflict detection module of the path-node association matrix is ​​used to sample candidate paths from the target level tensor and construct a binary path-node association matrix. It performs a global orthogonality test by calculating the Gram matrix of the path-node association matrix and filters out legal flight strings with no resource overlap at the physical level. The outer product mask generation and tensor collapse module is used to extract the occupancy state feature vector of the legal flight string selected in the correlation matrix orthogonalization and conflict detection module, perform vector outer product operation to instantly generate an infinitely large penalty mask matrix, and use the mask matrix to perform orthogonal collapse and state update on the ground state connected matrix to achieve exclusive locking of physical resources. State Convergence and Output Module: Used to determine the global element convergence state of the ground state connectivity matrix, control the iteration loop of the deduction module; and when connectivity is completely exhausted, output the global conflict-free backbone scheduling plan and the set of independent and detached out-of-group flights.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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