A spatio-temporal network construction method based on dynamic time window fragmentation

Abstract

The method comprises the following steps: S1, dividing a global scheduling period into a peak window, a flat peak window and a valley window according to a task density distribution; S2, assigning different fixed discrete steps to the peak window, the flat peak window and the valley window; S3, establishing node coupling and arc segment continuity constraints at the junctions of windows with different precisions; and S4, outputting a model and optimizing. The method has the advantage of effectively suppressing calculation redundancy in a non-event triggering mode.

Description

Technical Field

[0001] This invention relates to the field of airport ground support scheduling optimization technology, and in particular to a spatiotemporal network construction method based on dynamic time window segmentation. Background Technology

[0002] In airport water truck scheduling modeling practice, the time-space network (TLAN) is the core technology for achieving vehicle route optimization and precise task allocation. Its modeling accuracy directly determines the feasibility and efficiency of the water truck scheduling scheme. The water truck scheduling task is highly tied to the flight take-off and landing rhythm, exhibiting significant peak and trough characteristics: during peak flight periods (such as 6:00-10:00 AM and 6:00-10:00 PM), it is necessary to provide rapid water refueling for densely arriving flights, requiring extremely high scheduling accuracy and precise avoidance of multi-vehicle task conflicts and operational delays; while during off-peak or low-peak periods with sparse flights (such as 0:00-6:00 AM), the water truck task volume decreases sharply. If the same fine-grained time step as during peak periods is still used, a large number of redundant idle nodes and arcs will be generated, leading to "variable explosion," which significantly increases the model solution time and cannot meet the actual need for rapid generation of scheduling schemes.

[0003] While event-triggered modeling can address redundant computation to some extent, this approach requires large-scale reconstruction of the existing fixed-step scheduling model within the current airport scheduling system architecture, resulting in poor compatibility and high implementation costs. The core objective of this project is to balance the scheduling accuracy and solution efficiency of water trucks through time-axis partitioning optimization, while maintaining compatibility with existing fixed-step modeling paradigms. Therefore, a spatiotemporal network construction method capable of accurately handling constraints related to non-equal time windows is urgently needed to fill the adaptation gap of existing technologies in water truck-specific scheduling scenarios, ensuring the efficient and orderly execution of flight water refueling support tasks. Summary of the Invention

[0004] The purpose of this invention is to provide a spatiotemporal network construction method based on dynamic time window segmentation, which has the advantage of effectively suppressing computational redundancy in non-event-triggered modes.

[0005] To achieve the above objectives, this invention provides a spatiotemporal network construction method based on dynamic time window partitioning to optimize water truck scheduling. The method includes: step S1, dividing the global scheduling cycle into peak window, off-peak window, and valley window according to the task density distribution; step S2, assigning differentiated fixed discretization step sizes to the peak window, off-peak window, and valley window; step S3, establishing node coupling and arc continuity constraints at the intersection of windows with different precision; and step S4, outputting the model and optimizing it.

[0006] Preferably, step S1 includes: step S11, dividing the global scheduling period T into n non-overlapping fixed time window sets W={W 1 W 2 ,…,W n}, i=1, 2......n; Step S12, based on historical task distribution data, calculate the task density number by solving simultaneous equations, and allocate peak windows, off-peak windows and valley windows by combining the task density number threshold; where, the simultaneous equations for the task density number are:

[0007] ;

[0008] in, Let be the task density number for the i-th time window; Let m be the number of tasks of type k within the i-th window, where k = 1, 2, ..., m, and m is the total number of task types. represents the weight coefficient for the k-th type of task; Let be the duration of the i-th time window; Let be the area of ​​the operation coverage region within the i-th time window; This is a correction factor for task fluctuations.

[0009] Preferably, step S2 includes: based on the fitting relationship between the task density and the time step, calculating the time window W for each time window. i A fixed time step Δti is assigned; a nonlinear fitting model is used to establish the relationship between the task density and the time step, and the fitting formula is:

[0010] ;

[0011] Where a, b, and c are fitting parameters, which are obtained by fitting historical data using the least squares method, and their values ​​range from a∈[5,10], b∈[0.3,0.5], to c∈[0.5,1.0], respectively. Let be the task density number of the i-th window.

[0012] Preferably, step S3 includes: step S31, for each time window W i According to its corresponding fixed time step Δt i Generate spatiotemporal nodes; Step S32, cross-window node connection and arc segment continuity constraints.

[0013] Preferably, step S31 includes: step S311, determining time windows W one by one. i The time range is discretized; starting from the initial time and using step size Δti as the interval, a discrete time sequence Ti={t s,i , t s,i +Δt i,ts,t s,i +2Δti,......,t e,i}, ensuring the complete time window set W of the discretized sequence i , where t e,i For the i-th time window W i The end time; t s,i For the i-th time window W i The starting time; Step S312, obtain the spatiotemporal node set Ni, and combine each time t in the discrete time series Ti with each location l in the key geographical location set L to generate spatiotemporal nodes l,t, i.e., Ni={l, t|l∈L,t∈Ti}; where L is the key geographical location set, L={l1, l2......l k}, where l1 can represent a gate, l2 can represent a water supply station or other key airport ground support location, k is the total number of key geographical locations; time t is a reference symbol; in step S311, if t e,i -t s,i If it cannot be divided by Δti, it can be fine-tuned for the last time interval, with the fine-tuning amount not exceeding 10% of Δti.

[0014] Preferably, step S32 includes: boundary node coupling constraints; the boundary node coupling constraints are such that, at the intersection of adjacent windows, a time window W is established. i The end node and the next time window W i+1 The coupling constraints between the starting nodes enable lossless transfer of vehicle states.

[0015] Preferably, step S32 includes: cross-window arc segment correction logic; the cross-window arc segment correction logic is: step Q1, based on time window Given the step size and start time, calculate the theoretical end time. ;in, Where d is the distance traveled between the starting and ending positions; v is the vehicle speed; This is the dynamic delay correction term during the driving process; Step Q2: Map the theoretical end time to the discrete time series of the next window, select the closest time and corresponding mapping node; if there are two equally spaced times, the next time is selected by default; Step Q3: Calculate the deviation value. ,like Then a penalty term is introduced into the objective function. Among them, the penalty coefficient It is not a fixed value; the calculation method is as follows: In the formula: Basic penalty coefficient; This represents the urgency level of the task. The deviation influence coefficient is derived from the deviation value. It is determined together with the window type.

[0016] Preferably, step S4 includes: integrating cross-window connection constraints with the original scheduling optimization constraints to form a complete model, ensuring constraint compatibility and synergistic effect; the constraints in step S4 include: operation arc constraints, maintaining the water balance constraint of the operation arc, ensuring that the water volume change before and after vehicle operation is equal to the operation water volume / replenishment water volume, and this constraint is also effective between cross-window nodes; vehicle load balancing constraints: retaining the load balancing variable constraint, limiting the vehicle load rate to ensure operational safety and resource utilization; cross-window connection constraints: incorporating boundary node coupling constraints and arc segment correction constraints to ensure vehicle state continuity and path rationality, filling the constraint gaps of the original model.

[0017] In summary, compared with the prior art, the spatiotemporal network construction method based on dynamic time window segmentation provided by the present invention has the following beneficial effects:

[0018] First, the spatiotemporal network construction method based on dynamic time window segmentation proposed in this invention has a dynamic precision adaptation mechanism, which can achieve the optimal balance between scheduling accuracy and computational efficiency.

[0019] Second, the spatiotemporal network construction method based on dynamic time window segmentation proposed in this invention features a compatible architecture design, which lowers the threshold for upgrading existing systems.

[0020] Third, the spatiotemporal network construction method based on dynamic time window segmentation proposed in this invention has a seamless cross-window connection logic, ensuring the continuity of scheduling throughout the entire cycle. Attached Figure Description

[0021] Figure 1 This is a flowchart of the spatiotemporal network construction method based on dynamic time window segmentation proposed in this invention. Detailed Implementation

[0022] The following will be combined with the appendix in the embodiments of the present invention. Figure 1 The technical solutions, structural features, objectives and effects achieved in the embodiments of the present invention will be described in detail.

[0023] It should be noted that the accompanying drawings are in a very simplified form and use non-precise proportions. They are only used to facilitate and clarify the purpose of illustrating the embodiments of the present invention, and are not intended to limit the implementation conditions of the present invention. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationship, or adjustments to the size should still fall within the scope of the technical content disclosed in the present invention, provided that they do not affect the effects and objectives that the present invention can produce.

[0024] It should be noted that, in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only the expressly listed elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0025] like Figure 1 As shown, this invention proposes a spatiotemporal network construction method based on dynamic time window segmentation to optimize water truck scheduling. The method includes:

[0026] Step S1: Based on the task density distribution, the global scheduling cycle is divided into peak window, off-peak window and low-peak window;

[0027] Step S2: Assign differentiated fixed discretization step sizes to peak windows, off-peak windows, and trough windows;

[0028] Step S3: Establish node coupling and arc continuity constraints at the intersection of windows with different precision.

[0029] Step S4: Output the model and optimize it.

[0030] Specifically, step S1 includes:

[0031] Step S11: Divide the global scheduling period T into n non-overlapping fixed time window sets W={W 1 W 2 ,…,W n}, i = 1, 2, ..., n;

[0032] Step S12: Based on historical task distribution data, calculate the task density number using simultaneous equations, and allocate peak, off-peak, and trough windows by combining the task density number threshold; wherein, the simultaneous equations for the task density number are:

[0033] ;

[0034] in, Let be the task density number for the i-th time window (unit: tasks / (h·km²)), representing the frequency of water truck tasks per unit time and unit area; The number of tasks of type k within the i-th window (k=1,2,…,m, where m is the total number of task types, such as regular water replenishment, emergency water replenishment, etc.); The weight coefficient for the k-th type of task (set according to the urgency of the task; where ω is the weight coefficient for regular tasks). k =1.0, Emergency Task ω k =1.5); The duration of the i-th time window (in hours); The area of ​​the operation coverage region within the i-th time window (unit: km²). This is the task fluctuation correction factor (value range 0.9~1.1, calibrated based on the historical task fluctuation amplitude).

[0035] For example, setting two task-intensive thresholds. (Peak threshold) and (Lower threshold), the window type is determined by solving a series of inequalities: when At that time, it was determined to be a peak window. ;when At that time, it was determined to be an off-peak window. ;when At that time, it was determined to be a low point window. The threshold was obtained by fitting historical data and met the following conditions: This ensures the rationality and uniqueness of window division.

[0036] Specific examples are as follows: For periods with a high density of task events per unit of time (such as 6:00 AM to 10:00 AM), the results are obtained through the above simultaneous equations. Determined as peak window During periods with a moderate number of task events (e.g., 10:00-16:00), the calculation yields... Determined as off-peak window For periods with sparse task events (e.g., 23:00-6:00 the next day), the calculation is as follows: Determined as a low point window Each window division must meet the requirements of temporal continuity and total period coverage. This is achieved by using simultaneous equations and threshold determination, replacing conventional empirical division methods and improving the rigor and novelty of the technical solution. Here, h, p, and l are only used as descriptive symbols for explanation.

[0037] Specifically, step S2 includes: based on the fitting relationship between the number of tasks and the time step, calculating the time window W for each time window. i Assign a corresponding fixed time step Δt i A nonlinear fitting model is used to establish the relationship between task density and time step size. The fitting formula is as follows:

[0038] ;

[0039] Where a, b, and c are fitting parameters, which are solved by fitting historical data using the least squares method. Their values ​​are a∈[5,10], b∈[0.3,0.5], and c∈[0.5,1.0] (unit: min), respectively, to ensure that the step size is negatively correlated with the number of tasks. The task density of the i-th window is calculated by solving the simultaneous equations in step S12.

[0040] Specific examples are as follows: Peak Window Task-intensive The size is relatively large, so it is obtained through the fitting formula. After calculation and correction, the step size Minutes (high-precision discretization); Peak window Task-intensive Moderate, step size after fitting correction Minutes (medium-precision discretization); trough window Task-intensive Smaller, step size after fitting correction Minutes (low-precision discretization). The introduction of this fitting formula makes the step size allocation more scientific and novel, different from conventional empirical allocation methods, while satisfying... The constraints ensure a match with the window task density features.

[0041] Specifically, step S3 includes:

[0042] Step S31, for each time window W i According to its corresponding fixed time step Δt i Generate spatiotemporal nodes;

[0043] Step S32, cross-window node connection and arc segment continuity constraints;

[0044] The core feature lies in handling two adjacent windows with different precision (such as W). i With W i+1 The connection logic between Δti (≠Δti+1) is established by setting boundary constraints and arc segment correction mechanisms to ensure the physical continuity and logical rationality of the vehicle's running path.

[0045] Specifically, step S31 includes:

[0046] Step S311: Determine the time window W one by one. i The time range is discretized; starting from the initial time and using step size Δti as the interval, a discrete time sequence Ti={t s,i , t s,i +Δt i ,ts,t s,i +2Δti,......,te,i}, ensuring the complete time window set W of the discretized sequence i , where t e,i For the i-th time window W i The end time; t s,i For the i-th time window W i The starting time;

[0047] In step S311, if t e,i -t s,i If it cannot be divided by Δti, it can be fine-tuned for the last time interval, with the fine-tuning amount not exceeding 10% of Δti.

[0048] Step S312: Obtain the spatiotemporal node set Ni. Combine each time t in the discrete time series Ti with each location l in the key geographic location set L to generate spatiotemporal nodes l,t, i.e., Ni = {l, t | l ∈ L, t ∈ Ti}; where L is the key geographic location set, L = {l1, l2, ..., l1}. k}, where l1 can represent a gate, l2 can represent a water supply station or other key airport ground support points, k is the total number of key geographical locations, and time t is a reference symbol.

[0049] In step S312, the spatiotemporal node set Ni represents the state of "the vehicle is located at position l at time t" and is the basic unit for constructing the spatiotemporal network.

[0050] The selection of L must adhere to the principle of "full coverage and no redundancy," covering key locations that vehicles may reach, such as pumping stations, water supply stations, and maintenance stations; t s,i and t e,i It is a key time node for connecting adjacent windows, and the corresponding node is the core object of cross-window connection constraints.

[0051] Specifically, step S32 includes: boundary node coupling constraints and cross-window arc segment correction logic.

[0052] The boundary node coupling constraint is that, at the intersection of adjacent windows, a time window W is established. i The end node and the next time window W i+1 The coupling constraints between the starting nodes enable lossless transfer of vehicle states.

[0053] For example, for any dispatched vehicle, if it is within time window W i The node corresponding to the end time is l1,t border Then in the next time window W i+1 The starting time t border The corresponding node must be l1,t borderThe corresponding parameters should remain unchanged. This constraint ensures that the vehicle state is transferred without loss and avoids problems such as "instantaneous teleportation" or "sudden changes in water volume" at window switching points.

[0054] The cross-window arc segment correction logic is as follows:

[0055] Step Q1, based on time window Given the step size and start time, calculate the theoretical end time. ;in, ;

[0056] Where d is the distance traveled between the starting and ending positions (unit: km); v is the vehicle speed (unit: km / h). This is a dynamic delay correction term (unit: min) during the journey, used to compensate for delays caused by factors such as airport ground traffic congestion and route curves, thereby improving the accuracy of the theoretical end time calculation.

[0057] Step Q2: Map the theoretical end time to the discrete time series of the next window, select the closest time and the corresponding mapping node. If there are two equally spaced times, the next time is selected by default.

[0058] Step Q3, calculate the deviation value ,like Then a penalty term is introduced into the objective function. ;

[0059] Among them, the penalty coefficient It is not a fixed value, but is dynamically calculated based on scheduling accuracy requirements, vehicle driving deviations, and the urgency of the task. The specific calculation method is as follows:

[0060] ;

[0061] In the formula: The basic penalty coefficient (with a value ranging from 1.0 to 2.0, preset by the scheduling system, representing the basic accuracy requirement); The task urgency coefficient (α=1.0 for routine tasks, α=1.8 for emergency tasks) is the same as the task weight coefficient in step S12. (Linkage) The deviation influence coefficient is derived from the deviation value. It is determined together with the window type.

[0062] Specifically, step S4 includes: integrating cross-window connection constraints with existing scheduling optimization constraints to form a complete model, ensuring that the constraints are compatible and work synergistically.

[0063] The constraints in step S4 include:

[0064] The operation arc constraint maintains the water balance constraint of the operation arc, ensuring that the change in water volume before and after vehicle operation is equal to the operation water volume / replenishment water volume. This constraint is also effective between cross-window nodes.

[0065] Vehicle load balancing constraints: Constraints that retain load balancing variables limit vehicle load rates to ensure operational safety and resource utilization.

[0066] Cross-window connection constraints: Incorporate boundary node coupling constraints and arc segment correction constraints to ensure vehicle state continuity and path rationality, filling the constraint gaps in the original model.

[0067] By integrating the models, a balance can be achieved between high-precision assurance during peak hours and low-redundancy computation during off-peak / valley hours, without changing the "fixed step size" modeling paradigm, thereby improving model solving efficiency and scheduling feasibility.

[0068] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A spatiotemporal network construction method based on dynamic time window segmentation, characterized in that, The method for optimizing the scheduling of water trucks includes: Step S1: Based on the task density distribution, the global scheduling cycle is divided into peak window, off-peak window and low-peak window; Step S2: Assign differentiated fixed discretization step sizes to peak windows, off-peak windows, and trough windows; Step S3: Establish node coupling and arc continuity constraints at the intersection of windows with different precision. Step S4: Output the model and optimize it.

2. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 1, characterized in that, Step S1 includes: Step S11: Divide the global scheduling period T into n non-overlapping fixed time window sets W={W 1 W 2 ,…,W n }, i = 1, 2, ..., n; Step S12: Based on historical task distribution data, calculate the task density number using simultaneous equations, and allocate peak, off-peak, and trough windows by combining the task density number threshold; wherein, the simultaneous equations for the task density number are: ； in, Let be the task density number for the i-th time window; Let m be the number of tasks of type k within the i-th window, where k = 1, 2, ..., m, and m is the total number of task types. represents the weight coefficient for the k-th type of task; Let be the duration of the i-th time window; Let be the area of ​​the operation coverage region within the i-th time window; This is a correction factor for task fluctuations.

3. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 2, characterized in that, Step S2 includes: based on the fitting relationship between the task density and the time step, calculating the time window W for each time window. i A fixed time step Δti is assigned; a nonlinear fitting model is used to establish the relationship between the task density and the time step, and the fitting formula is: ； Where a, b, and c are fitting parameters, which are obtained by fitting historical data using the least squares method, and their values ​​range from a∈[5,10], b∈[0.3,0.5], to c∈[0.5,1.0], respectively. Let be the task density number of the i-th window.

4. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 3, characterized in that, Step S3 includes: Step S31, for each time window W i According to its corresponding fixed time step Δt i Generate spatiotemporal nodes; Step S32: Cross-window node connection and arc segment continuity constraints.

5. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 4, characterized in that, Step S31 includes: Step S311: Determine the time window W one by one. i The time range is discretized; starting from the initial time and using step size Δti as the interval, a discrete time sequence Ti={t s,i , t s,i +Δt i ,ts,t s,i +2Δti,......,t e,i }, ensuring the complete time window set W of the discretized sequence i , where t e,i For the i-th time window W i The end time; t s,i For the i-th time window W i The starting time; Step S312: Obtain the spatiotemporal node set Ni. Combine each time t in the discrete time series Ti with each location l in the key geographic location set L to generate spatiotemporal nodes l,t, i.e., Ni = {l, t | l ∈ L, t ∈ Ti}; where L is the key geographic location set, L = {l1, l2, ..., l1}. k }, where l1 can represent a gate, l2 can represent a water station or other key airport ground support point, k is the total number of key geographical locations; time t is a reference symbol; In step S311, if t e,i -t s,i If it cannot be divided by Δti, it can be fine-tuned for the last time interval, with the fine-tuning amount not exceeding 10% of Δti.

6. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 5, characterized in that, Step S32 includes: boundary node coupling constraints; the boundary node coupling constraints are as follows: at the intersection of adjacent windows, a time window W is established. i The end node and the next time window W i+1 The coupling constraints between the starting nodes enable lossless transfer of vehicle states.

7. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 6, characterized in that, Step S32 includes: cross-window arc segment correction logic; the cross-window arc segment correction logic is as follows: Step Q1, based on time window Given the step size and start time, calculate the theoretical end time. ;in, ; Where d is the distance traveled between the starting and ending positions; v is the vehicle speed; This refers to the dynamic delay correction item during the driving process; Step Q2: Map the theoretical end time to the discrete time series of the next window, select the closest time and the corresponding mapping node. If there are two equally spaced times, the next time is selected by default. Step Q3, calculate the deviation value ,like Then a penalty term is introduced into the objective function. ; Among them, the penalty coefficient It is not a fixed value; the calculation method is as follows: ； In the formula: Basic penalty coefficient; This represents the urgency level of the task. The deviation influence coefficient is derived from the deviation value. It is determined together with the window type.

8. The spatiotemporal network construction method based on dynamic time window segmentation according to claim 7, characterized in that, Step S4 includes: integrating cross-window connection constraints with existing scheduling optimization constraints to form a complete model, ensuring that constraints are compatible and work synergistically. The constraints in step S4 include: The operation arc constraint maintains the water balance constraint of the operation arc, ensuring that the water volume change before and after vehicle operation is equal to the operation water volume / replenishment water volume. This constraint is also effective between cross-window nodes. Vehicle load balancing constraints: Constraints that retain load balancing variables limit vehicle load rates to ensure operational safety and resource utilization; Cross-window connection constraints: Incorporate boundary node coupling constraints and arc segment correction constraints to ensure vehicle state continuity and path rationality, filling the constraint gaps in the original model.

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