Space-time allocation method for educational resources based on padis-int population prediction

Abstract

The application discloses a method for spatiotemporal allocation of educational resources based on Padis-Int population prediction, which comprises the following steps: obtaining and processing Padis-Int population prediction data, constructing an educational resource dynamic demand model, constructing an educational resource spatiotemporal allocation optimization model, solving a multi-objective optimization in a rolling time domain, and outputting and visualizing a scheme. The peak-valley characteristics of the school-age population of Padis-Int are directly mapped to the school life cycle, greatly reducing resource mismatch. At the same time, the coupled decision of 'when to build, where to build, and how big to build' is solved, avoiding the disadvantages of traditional methods that first determine the spatial layout and then passively deal with time fluctuations. The rolling time domain mechanism enables the plan to respond to the latest population situation, especially suitable for new urban areas and shrinking cities with rapid population changes. The Pareto frontier of cost and service level makes the decision-making process transparent and quantifiable.

Description

Technical Field

[0001] This invention relates to the field of educational resource planning and computer decision support technology, specifically a spatiotemporal allocation method for educational resources based on Padis-Int population prediction. Background Technology

[0002] "Padis-Int" is an international population forecasting software developed by the China Population and Development Research Center. It can predict the future population size of different regions, ages, and genders. Educational resources are not just schools and school buildings, but also include teachers, educational funding, teaching equipment, and other hardware and software. How to scientifically plan the number, location, and resource allocation of schools in advance based on future population changes, and avoid the waste or inadequacy of educational resources, is an important research topic.

[0003] Specifically, where should schools be built? Where should some be closed or merged, and where should new ones be built? When should construction begin, when should enrollment be expanded, and when should it be reduced? The goal is not to build everything at once, but rather to adjust in stages and dynamically. In the context of population changes, the aim is to maximize the efficiency and fairness of resource allocation. For example, ensuring all children can attend schools near their homes with minimal construction costs, while avoiding situations where schools are built but then left vacant. The aim is to achieve a balanced and efficient allocation of resources.

[0004] Current allocation of educational resources is largely based on static population censuses and linear trends, resulting in two major disconnects:

[0005] First, there is a disconnect between population forecasting and resource planning. Planning departments have not made full use of professional data such as Padis-Int, which are detailed down to age, urban / rural location, and annual rolling forecasts.

[0006] Second, there is a disconnect between time and space planning. School site selection and teacher recruitment often fail to accurately match the future population peaks and troughs in time and space migration, resulting in "schools being built but then left idle" or "a severe shortage of school places".

[0007] Therefore, there is an urgent need for a systematic method that can directly drive the spatiotemporal dynamic optimization of educational resources through high-precision population forecasting. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a spatiotemporal allocation method for educational resources based on Padis-Int population prediction, in order to achieve an optimal balance between cost and coverage, and to dynamically adjust the scheme as the prediction data is updated.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0010] The spatiotemporal allocation method for educational resources based on Padis-Int population projection includes the following steps:

[0011] S1. Acquiring and processing Padis-Int population projection data:

[0012] Obtain population projections for the target region over the next T years by spatial unit, gender, and single age from the Padis-Int system;

[0013] Based on the school segment division criteria, the population of school-age groups for each year and each spatial unit is extracted to form a spatiotemporal population matrix; spatial units are geocoded to establish a transportation network map required for educational resource accessibility analysis;

[0014] S2. Construct a dynamic demand model for educational resources:

[0015] Using a spatiotemporal population matrix, combined with policy parameters such as target enrollment rate, class size standard, and student-teacher ratio, the demand for school places, teachers, and school building area for each spatial unit in each time slice is calculated.

[0016] The demand model incorporates population forecast uncertainty handling and uses the high, medium, and low schemes provided by Padis-Int to generate demand ranges;

[0017] S3. Constructing a spatiotemporal optimization model for educational resource allocation:

[0018] The optimization model utilizes Padis-Int's high, medium, and low-scheme data to model uncertainties and generate robust configuration schemes. The objective function is to minimize the total lifecycle cost, which includes:

[0019] Fixed investment and operating costs for the construction, expansion, and renovation of schools;

[0020] The asset disposal costs and social costs of closing and merging campuses;

[0021] The average annual comprehensive commuting cost for students;

[0022] Teacher allocation and training costs;

[0023] S4. Multi-objective optimization solution in the rolling time domain:

[0024] An improved non-dominated sorting genetic algorithm with an elitist strategy is used to solve the model;

[0025] The encoding method adopts a hybrid encoding.

[0026] During the forecast period T, rolling time-domain optimization is implemented: every 5 years, the model is rerun based on the latest Padis-Int forecast data to generate the next round of implementation plan, achieving closed-loop dynamic optimization of "forecast-planning-update".

[0027] The Pareto front solution set is output, and through an interactive decision-making interface, planners can select the optimal spatiotemporal configuration scheme based on cost preferences.

[0028] S5. Solution Output and Visualization:

[0029] The optimal solution output includes:

[0030] Spatial and temporal allocation of educational resources and GIS maps.

[0031] Preferably, the spatial unit includes streets, school districts, and grids.

[0032] Preferably, the overall commuting cost includes both distance and time costs.

[0033] Preferably, the constraints include:

[0034] The degree coverage rate of each spatial unit in each time period shall not be lower than the preset threshold;

[0035] The school's service radius shall not exceed the legal limit;

[0036] Class sizes and teacher workloads should not exceed the limits;

[0037] Smoothing constraints on changes in school size during its existence.

[0038] Preferably, the decision variables are the year each school is put into use, the year it is closed, its spatial location, its annual enrollment scale, its number of teachers, and the specific site coordinates of the newly built school.

[0039] Preferably, the spatial location is latitude and longitude.

[0040] Preferably, the integer encoding of the encoding method represents time, and the real number encoding represents spatial location.

[0041] Preferably, the spatiotemporal configuration table of educational resources includes the timeline and scale changes of each school, and the GIS map dynamically displays the coverage area of ​​the school's service area and the supply and demand gap at each period.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] (1) Precise matching: Padis-Int’s peak and valley characteristics of school-age population are directly mapped to the school life cycle, greatly reducing resource mismatch.

[0044] (2) Spatiotemporal coordination: It solves the coupled decision-making of "when to build, where to build, and how big to build" at the same time, avoiding the drawbacks of traditional methods that first determine the spatial layout and then passively deal with time fluctuations.

[0045] (3) Dynamic adaptation: The rolling time domain mechanism enables planning to respond to the latest population situation, which is especially suitable for new urban areas and shrinking urban areas with rapid population changes.

[0046] (4) Quantitative decision-making: Provide the Pareto frontier of cost and service level to make the decision-making process transparent and quantifiable. Attached Figure Description

[0047] Figure 1 This is the overall flowchart of the present invention. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] like Figure 1 As shown, this invention provides a technical solution: a spatiotemporal allocation method for educational resources based on Padis-Int population prediction, comprising the following steps:

[0050] S1. Acquiring and processing Padis-Int population projection data:

[0051] The Padis-Int system was used to obtain population projections for the target area for the next T years by spatial unit, gender, and single age. Spatial units include streets, school districts, and grids.

[0052] Based on the school segment division criteria, the population of school-age groups for each year and each spatial unit is extracted to form a spatiotemporal population matrix; spatial units are geocoded to establish a transportation network map required for educational resource accessibility analysis;

[0053] S2. Construct a dynamic demand model for educational resources:

[0054] Using a spatiotemporal population matrix, combined with policy parameters such as target enrollment rate, class size standard, and student-teacher ratio, the demand for school places, teachers, and school building area for each spatial unit in each time slice is calculated.

[0055] The demand model incorporates population forecast uncertainty handling and uses the high, medium, and low schemes provided by Padis-Int to generate demand ranges;

[0056] S3. Constructing a spatiotemporal optimization model for educational resource allocation:

[0057] The optimization model utilizes Padis-Int's high, medium, and low-situation data for uncertainty modeling to generate robust configuration schemes. The objective function is to minimize the total lifecycle cost, which includes:

[0058] Fixed investment and operating costs for the construction, expansion, and renovation of schools;

[0059] The asset disposal costs and social costs of closing and merging campuses;

[0060] The average annual comprehensive commuting cost for students, which includes both distance and time costs;

[0061] Teacher allocation and training costs;

[0062] The constraints include:

[0063] The degree coverage rate of each spatial unit in each time period shall not be lower than the preset threshold;

[0064] The school's service radius shall not exceed the legal limit;

[0065] Class sizes and teacher workloads should not exceed the limits;

[0066] Smoothing constraints on changes in school size during its existence;

[0067] The decision variables are the year each school was opened, the year it was closed, its spatial location, its annual enrollment size, and its number of teachers. The spatial location is its latitude and longitude, as well as the specific site coordinates of the new school.

[0068] S4. Multi-objective optimization solution in the rolling time domain:

[0069] An improved non-dominated sorting genetic algorithm with an elitist strategy (NSGA-II) is used to solve the model;

[0070] The encoding method adopts a hybrid encoding, where the integer code represents time and the real number code represents spatial location;

[0071] During the forecast period T, rolling time-domain optimization is implemented: every 5 years, the model is rerun based on the latest Padis-Int forecast data to generate the next round of implementation plan, achieving closed-loop dynamic optimization of "forecast-planning-update".

[0072] The Pareto front solution set is output, and through an interactive decision-making interface, planners can select the optimal spatiotemporal configuration scheme based on cost preferences.

[0073] S5. Solution Output and Visualization:

[0074] The optimal solution output includes:

[0075] The spatiotemporal allocation of educational resources and GIS maps include a timeline and scale changes for each school, and a dynamic display of the service area coverage and supply-demand gap of schools at different times. This scheme can be directly used as the basis for special planning of educational facility layout.

[0076] The following example illustrates the allocation of primary school education resources in a certain city from 2030 to 2040:

[0077] Data Acquisition: Using the Padis-Int system, with 2025 as the base year, we obtained the high, medium, and low population projections for children aged 6-11 years in 50 school districts of the city from 2026 to 2045.

[0078] The following is the original prediction data table for Padis-Int:

[0079] years Spatial Unit age gender Population projections (medium-scale scenario) 2026 School District A 6 male 512 2026 School District A 6 female 498 2026 School District A 7 male 489 …… …… …… …… …… 2026 School District B 6 male 623 …… …… …… …… ……

[0080] The following is a schematic table of spatiotemporal population matrix:

[0081] Spatial Unit 2026 2027 2028 …… 2040 School District A 3210 3356 3512 …… 2891 School District B 4120 4233 4401 …… 3756 School District C 1876 1932 2001 …… 1654 …… …… …… …… …… ……

[0082] Demand Calculation: Based on the population of the medium-scale plan, a 99% enrollment rate, 45 students per class, and a student-teacher ratio of 1:19, calculate the annual demand for school places, class sizes, and teachers for each school district.

[0083] Model Construction: In the objective function, the average cost of building a new school is 30 million yuan, the average cost of operating a student is 10,000 yuan / year, and the commuting cost is calculated at 1.2 yuan per kilometer; in the constraints, the degree coverage rate must be ≥95%, and the maximum walking / driving service radius is set according to national standards.

[0084] Optimization Solution: Implement the improved NSGA-II algorithm using Python, setting the population size to 200 and the iteration to 500 generations; in chromosome encoding, time genes are represented by integers with year offset enabled, and spatial genes are represented by real number pairs to represent coordinates; every 5 years is a rolling cycle, and the latest Padis-Int predictions are substituted into the re-optimization;

[0085] Results output: The optimal solution shows that two new primary schools need to be built in the northeastern new area between 2032 and 2035, while the three primary schools in the old city will be gradually reduced in size and merged into one after 2038. This solution saves about 18% of the total cost over the entire cycle compared to traditional static planning and eliminates the shortage of school places.

[0086] The following is the pseudocode for the core algorithm:

[0087] Algorithm: Time-Domain Optimization of Educational Resources Based on Padis-Int Prediction

[0088] enter:

[0089] Padis population projection data (pop_{i,t}), GIS data (dist, candidate coordinates, etc.).

[0090] Scroll window length L, total number of years planned T_max, sliding step size step

[0091] Output:

[0092] A complete spatiotemporal configuration plan (year of activation / deactivation, coordinates, and annual capacity for each school).

[0093] 1. t_current ← 1 / / Current starting year of the scrolling window

[0094] 2. existing_schools ← List of existing schools and their fixed attributes

[0095] 3. history_plan ← Empty list

[0096] 4. WHILE t_current + L <= T_max DO

[0097] 5. / / Extract population demand within the current window

[0098] 6. window_T ← [t_current, min(t_current + L, T_max)]

[0099] 7. Extract pop_{i,t} from Padis-Int to generate requirements d_{i,t}, where t ∈ window_T 8.

[0101] 9. / / Candidate facility set: existing schools + potential new school sites

[0102] 10. J ← existing_schools ∪ candidate_new_sites 11.

[0104] 12. / / Initialize the population (NSGA-II)

[0105] 13. P ← Initialize the population (N individuals)

[0106] 14. Individual coding: For each school j ∈ J:

[0107] 15. Enable year offset t_start_offset (relative to t_current)

[0108] 16. Disable year offset t_end_offset (can be a large number to indicate that the window will not be closed)

[0109] 17. Spatial coordinates (lon, lat) / / Fixed for existing schools, can be optimized for newly built schools

[0110] 18. Capacity sequence [cap_{j, t_current}, cap_{j, t_current+1}, ...,cap_{j, window_end}] 19.

[0112] 20. FOR gen = 1 TO MaxGenerations DO

[0113] 21. / / Decode and evaluate fitness

[0114] 22. FOR each individual p IN P DO

[0115] 23. Decode to obtain the z_{j,t} and cap_{j,t} coordinates of all schools.

[0116] 24. Run the student assignment sub-model:

[0117] 25. Assign students from each unit to schools based on distance and capacity.

[0118] 26. (Use a transportation problem algorithm or greedy allocation to satisfy the service radius constraint)

[0119] 27. Calculate the target value:

[0120] 28. F1 = Total Lifecycle Costs (Fixed + Operating + Commuting)

[0121] 29. F2 = Degree Satisfaction Rate

[0122] 30. Calculate the degree of constraint violation:

[0123] 31. CV = Penalty for insufficient degree coverage + Penalty for exceeding capacity limits + Penalty for violating radius rules

[0124] 32. Store the fitness vector (F1, F2, CV)

[0125] 33. END FOR 34.

[0127] 35. / / Non-dominated sorting, while considering constraint violations.

[0128] 36. Perform a constraint-non-dominated sort on P (prioritize feasible solutions, then sort by dominance relations).

[0129] 37. Calculate congestion level 38.

[0131] 39. / / Generate offspring

[0132] 40. Q ← Empty set

[0133] 41. WHILE |Q| < N DO

[0134] 42. Parent Generation 1, Parent Generation 2 ← Binary Tournament Choice (P)

[0135] 43. Child 1, Child 2 ← Cross (Parent 1, Parent 2)

[0136] 44. Offspring 1 ← Mutation (Offspring 1)

[0137] 45. Offspring 2 ← Mutation (Offspring 2)

[0138] 46. ​​Add child 1 and child 2 to Q.

[0139] 47. End When 48.

[0141] 49. / / Merge and select the next generation

[0142] 50. R ← P ∪ Q

[0143] 51. P ← Environment Selection (R, N) / / Based on non-dominated sorting and crowding

[0144] 52. END FOR 53.

[0146] 54. / / Choosing an implementation plan from the Pareto front

[0147] 55. pareto_front ← Gets the set of feasible Pareto optimal solutions in P.

[0148] 56. selected_plan ← Decision-maker selection (pareto_front) / / If using TOPSIS or human interaction 57.

[0150] 58. / / Execute the decision made in the current window and scroll.

[0151] 59. Extract build / shutdown instructions from selected_plan within the time period [t_current, t_current + step - 1].

[0152] 60. Update existing_schools:

[0153] 61. Newly built schools become existing schools, with fixed coordinates.

[0154] 62. Closed schools are removed from existing_schools.

[0155] 63. Record the defined configuration segments to history_plan 64.

[0157] 65. t_current ← t_current + step

[0158] 66. End When 67.

[0160] 68. Output history_plan as a complete spatiotemporal configuration scheme.

[0161] It should be noted that, in this document, terms such as “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 those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0162] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A spatiotemporal allocation method for educational resources based on Padis-Int population prediction, characterized by: Includes the following steps: S1. Acquiring and processing Padis-Int population projection data: Obtain population projections for the target region over the next T years by spatial unit, gender, and single age from the Padis-Int system; Based on the school segment division criteria, the population of school-age groups for each year and each spatial unit is extracted to form a spatiotemporal population matrix; spatial units are geocoded to establish a transportation network map required for educational resource accessibility analysis; S2. Construct a dynamic demand model for educational resources: Using a spatiotemporal population matrix, combined with policy parameters such as target enrollment rate, class size standard, and student-teacher ratio, the demand for school places, teachers, and school building area for each spatial unit in each time slice is calculated. The demand model incorporates population forecast uncertainty handling and uses the high, medium, and low schemes provided by Padis-Int to generate demand ranges; S3. Constructing a spatiotemporal optimization model for educational resource allocation: The optimization model utilizes Padis-Int's high, medium, and low-situation data to model uncertainties and generate robust configuration schemes. The objective function is to minimize the total lifecycle cost, which includes: Fixed investment and operating costs for the construction, expansion, and renovation of schools; The asset disposal costs and social costs of closing and merging campuses; The average annual comprehensive commuting cost for students; Teacher allocation and training costs; S4. Multi-objective optimization solution in the rolling time domain: An improved non-dominated sorting genetic algorithm with an elitist strategy is used to solve the model; The encoding method adopts a hybrid encoding. During the forecast period T, rolling time-domain optimization is implemented: every 5 years, the model is rerun based on the latest Padis-Int forecast data to generate the next round of implementation plan, realizing closed-loop dynamic optimization of "forecast-planning-update"; The Pareto front solution set is output, and through an interactive decision-making interface, planners can select the optimal spatiotemporal configuration scheme based on cost preferences. S5. Solution Output and Visualization: The optimal solution output includes: Spatial and temporal allocation of educational resources and GIS maps.

2. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The spatial units include streets, school districts, and grids.

3. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The overall commuting cost includes both distance and time costs.

4. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The constraints include: The degree coverage rate of each spatial unit in each time period shall not be lower than the preset threshold; The school's service radius shall not exceed the legal limit; Class sizes and teacher workloads should not exceed the limits; Smoothing constraints on changes in school size during its existence.

5. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The decision variables are the year each school was opened, the year it was closed, its location, its annual enrollment size, its number of teachers, and the specific location coordinates of any new school.

6. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 5, characterized in that: The spatial location is in latitude and longitude.

7. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The integer encoding of the encoding method represents time, and the real number encoding represents spatial location.

8. The spatiotemporal allocation method for educational resources based on Padis-Int population prediction according to claim 1, characterized in that: The spatiotemporal allocation table of educational resources includes the timeline and scale changes of each school, and the GIS map dynamically displays the coverage area of ​​the school's service area and the supply and demand gap at each period.

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