A degree assignment method and device based on space constraints and reachability constraints and a medium

Abstract

The application provides a degree allocation method based on space constraint and accessibility constraint, comprising the following steps: S1, school district information collection and geographic registration; S2, according to the voluntary information, the student address and the geographic information of the school, the travel distance of the student to the school is calculated, and a student-school distance constraint matrix is constructed; S3, the utility score of the school is calculated; S4, according to the distance constraint matrix, the utility score of the school, the school capacity constraint, the voluntary information and the allocation target, the probability of the student entering the reported school is calculated; S5, according to the number of students admitted by the school and the probability of the student entering the school, the student is selected from high to low, and the degree is allocated. Through the experiment verification 1 of the application, the differentiated preference at the individual scale is considered, the expected utility standard deviation is minimized as the target, and the allocation imbalance caused by the space distance is compensated; through the experiment verification 2 of the application, the degree allocation balance and the student satisfaction are considered, and the allocation accuracy and speed are improved.

Description

Technical Field

[0001] This invention relates to the field of geospatial information and degree resource allocation technology, specifically to a degree allocation method, device, and medium based on spatial constraints and accessibility constraints. Background Technology

[0002] The current allocation of compulsory education places mainly takes two forms: enrollment based on proximity to school district and random assignment. Enrollment based on proximity to school district is usually determined by the correspondence between the student's residential address and the school's enrollment area; random assignment is usually determined by random methods such as drawing lots or lottery based on the student's preferences.

[0003] The aforementioned methods are relatively clear and easy to implement, meeting basic enrollment management needs. However, they are essentially based on fixed-zone rules or simple random rules for allocation, lacking objective spatial constraints and quantitative calculation support. Specifically, the neighborhood-based enrollment method easily leads to students' school places being directly affected by their residential location and school district boundaries. Because different schools differ in the quality of educational resources, enrollment capacity, and spatial distribution, simply allocating based on fixed zones makes it difficult to quantify and balance the differences in school places received by different students at an individual scale.

[0004] Randomized placement can break the bond between fixed residential location and specific schools to some extent, but some students may feel that the results of randomized placement are not as good as the original neighborhood-based placement, thus reducing their satisfaction with the allocation of school places. In addition, the current randomized placement method cannot dynamically allocate school places based on the school's remaining enrollment quota and the probability of students entering the school during multiple rounds of admissions.

[0005] It can be seen that existing technologies lack a degree allocation method that can simultaneously take into account allocation equilibrium, distance constraints, capacity constraints, student preference, and the acceptability of allocation results within a randomized admission framework. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the first aspect of this invention provides a degree allocation method based on spatial constraints and reachability constraints, specifically including:

[0007] S1. School District Information Collection and Geographic Registration;

[0008] S2. Based on the volunteer information, student address and school geographical information, calculate the travel distance from the student to the school and construct the student-school distance constraint matrix;

[0009] S3. Calculate the school's utility score;

[0010] S4. Based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the volunteer information, and the allocation target, calculate the probability that the student will be admitted to the school they applied for.

[0011] S5. Based on the school's enrollment quota and the probability of students entering the school, students are selected from high to low and degrees are allocated.

[0012] Furthermore, step S1 includes:

[0013] Obtain the address information of the enrollment areas of each school within the administrative region;

[0014] The address information is converted into latitude and longitude coordinates and imported into GIS software. Remote sensing layers are then overlaid to make all address information correspond to building units in the remote sensing image, thereby obtaining GIS point data of the address information.

[0015] Furthermore, in S2, the method for calculating the distance from students to school is as follows: using the GIS point data of the student's address and the school's address, the Baidu Maps API interface is called to calculate the distance to school.

[0016] Furthermore, in S3, the school's utility score is calculated as follows: a normalized education quality score is used as the utility score for parents to obtain for each school. The education quality score is calculated by comprehensively weighting the number of municipal-level subject leaders, municipal-level backbone teachers, district-level subject leaders, district-level core subject leaders, the number of district-level core subjects, and the number of district-level research leaders in the school.

[0017] Furthermore, in S4, the objective function is:

[0018]

[0019] The constraints are:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; This represents the average expected utility of all students obtaining a degree; For students For the school Utility rating For students At school The probability of admission; The variables are 0 and 1, when the student From residence to school The distance is within the maximum distance threshold The value is 1 if the time is within the specified range, and 0 otherwise. For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance;

[0027] The student was obtained by using the Gurobi optimizer. At school The probability of admission .

[0028] Furthermore, in S4, the objective function is:

[0029]

[0030]

[0031]

[0032]

[0033] The constraints are:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; It represents the expected utility of all students obtaining a degree; The variable is 0 or 1. It is set to 1 when the expected utility of the "random-nearby" school enrollment optimization model is less than the expected utility of the nearby school enrollment model, and 0 otherwise. For students For the school Utility rating For students At school The probability of admission; For variables of 0 and 1, when students From residence to school The distance is within the maximum distance threshold The value is 1 if the time is within the specified range, and 0 otherwise. For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance; It is based on For variables of 0 and 1 with a fixed size, when When less than 0 The value is 1, representing a student. Oppose random admission; otherwise, take 0. The expected utility obtained by the neighborhood-based school enrollment model.

[0041] Furthermore, the objective function is:

[0042]

[0043] yes The Utopian point, , It is a parameter representing the importance of the target. + =1.

[0044] Furthermore, in S5, admissions are based on the order of preference and the probability of entering the school, specifically including:

[0045] S51. For this round of applications, for each school, calculate the current enrollment quota and the number of applicants.

[0046] S52. If the number of applicants is less than or equal to the current enrollment quota, all applicants will be admitted. If the number of applicants is greater than the current enrollment quota, the students will be sorted by probability of admission from highest to lowest, and the top N students will be admitted (N = the remaining enrollment quota of the school).

[0047] S53. Unsuccessful applicants proceed to the next round, and S31 and S32 are repeated until all applications are processed.

[0048] According to a second aspect of the present invention, a degree allocation device comprises:

[0049] The school district information collection and geographic registration module is used to obtain the address information of each school within the administrative district and the house number address information of the enrollment area, and convert them into GIS point data; and establish a unified spatial benchmark.

[0050] The travel distance calculation module calculates the travel distance from students to schools based on volunteer information, student addresses, and school geographical information, and constructs a student-school distance constraint matrix.

[0051] The school utility rating module is used to calculate the school's utility rating.

[0052] The probability of admission calculation module calculates the probability of a student being admitted to the school they applied to, based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the student's application information, and the allocation target.

[0053] The degree allocation module is used to admit students based on their probability of admission to the school, from highest to lowest, for each round of applications, according to the school's current enrollment quota.

[0054] According to a third aspect of the present invention, a computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the degree allocation method as described in the first aspect above.

[0055] Compared with the prior art, the degree allocation method provided by the present invention has the following beneficial effects:

[0056] (1) This invention realizes the consideration of individual-scale differential preferences, with the goal of minimizing the standard deviation of expected utility, and compensates for the distribution imbalance caused by spatial distance.

[0057] (2) This invention takes into account both the balanced allocation of degrees and student satisfaction, and improves the accuracy and speed of allocation through particle swarm optimization algorithm.

[0058] (3) The method and system of the present invention can be widely applied to the random allocation of compulsory education places in cities across the country, providing quantitative basis and technical support for education administrative departments to formulate scientific and reasonable random enrollment policies. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating a degree allocation method according to an embodiment of the present invention;

[0060] Figure 2 This is a schematic diagram of the structure of a degree allocation system according to an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram of the allocation structure for Experimental Verification 1 of the present invention;

[0062] Figure 4 This is a schematic diagram of the spatial results of Experimental Verification 2 and the Nearby School Enrollment Model of the present invention;

[0063] Figure 5 This is a schematic diagram illustrating the changes in the opposition rate and the standard deviation of expected utility as a function of parameters in Experiment 2 of this invention.

[0064] Figure 6 This is a schematic diagram showing the change of the expected degree allocation line under different parameters in Experimental Verification 2 of the present invention. Detailed Implementation

[0065] 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.

[0066] Randomized admission has been piloted in some regions. This invention, based on the equity-oriented spatial optimization method in geography, proposes a degree allocation method at the individual scale that satisfies spatial and distance accessibility constraints. The system is based on student preferences and uses minimizing the standard deviation of the expected utility of all students' degree allocations as its objective function. It calculates the probability of each student entering their preferred school and allocates degrees to each student according to this probability, thus improving the accuracy and rationality of degree resource allocation in randomized admission.

[0067] S1. School District Information Collection and Geographic Registration;

[0068] S2. Based on the volunteer information, student address and school geographical information, calculate the travel distance from the student to the school and construct the student-school distance constraint matrix;

[0069] S3. Calculate the school's utility score;

[0070] S4. Based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the volunteer information, and the allocation target, calculate the probability that the student will be admitted to the school they applied for.

[0071] S5. Based on the school's enrollment quota and the probability of students entering the school, students are selected from high to low and degrees are allocated.

[0072] In step S1, the specific house numbers and building numbers of buildings within the enrollment areas of each school in the target administrative region are obtained and incorporated into the database. This information can be obtained from the school's official website's enrollment brochure for this year.

[0073] Then, the house address information and school address information are converted into latitude and longitude coordinates and mapped to GIS software. Remote sensing layers are overlaid, and manual verification is performed to ensure that all address information corresponds to building units in the remote sensing image. After completing spatial correction, deduplication, and removal of address information that does not meet the requirements, such as obvious deviation points, a building-level GIS point dataset is generated to establish a unified spatial benchmark.

[0074] In one embodiment, GIS point data of the catchment areas corresponding to each primary school and school data are imported into remote sensing imagery. For each primary school, a face containing the buildings corresponding to all catchment area GIS points is defined as the school district data, thereby generating a school district map for the administrative region. The division process avoids non-residential areas such as parks and bodies of water.

[0075] In S2, the map service API is called to calculate the actual road distance from each student's GIS point to the GIS points of each school in the volunteer list, and a student-school distance constraint matrix is ​​constructed. A spatial accessibility constraint matrix can also be generated based on a preset maximum commuting distance threshold.

[0076] In S3, good schools bring good utility; therefore, a normalized education quality score is used as the utility score for each school. The education quality score can be obtained by comprehensively weighting the scores of municipal-level subject leaders, municipal-level backbone teachers, district-level subject leaders, district-level core subject leaders, the number of district-level core subjects, and the number of district-level research leaders in the school. Among them, the score of municipal-level science leaders > the score of municipal-level backbone teachers > the score of district-level subject leaders (core subjects) and the score of district-level research leaders > the score of district-level subject leaders (non-core subjects) > the separate bonus for district-level subject leaders covering all core subjects. For example, 10 points for municipal-level science leaders, 8 points for municipal-level backbone teachers, 7 points for district-level subject leaders (core subjects) and district-level research leaders, 5 points for district-level subject leaders (non-core subjects), and a separate bonus for district-level subject leaders covering all core subjects (e.g., 3 points). The total score is calculated, converted to a percentage, and then normalized.

[0077] In S4, in one embodiment, the distance constraint matrix, school utility score, school capacity constraint, maximum distance threshold, and the following objective function and constraints obtained from S2 and S3 can be used to calculate the student's... At the volunteer school The probability of admission :

[0078] Objective function:

[0079]

[0080]

[0081] Constraints:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; This represents the average expected utility of all students obtaining a degree; For students At school The probability of admission; The variables are 0 and 1, when the student From residence to school The distance is within the maximum distance threshold The value is 1 if it is within the spatial reachability constraint matrix (or 0 otherwise); For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance.

[0088] The objective function aims to minimize the standard deviation of the expected educational quality each student receives. The probability of a student entering their preferred school, calculated using this function, is then ranked according to student school preferences. A maximum school distance constraint is imposed to ensure students attend schools near their homes, and random allocation is guided by the principle of resource allocation equilibrium at the individual scale. By minimizing the standard deviation of the expected educational quality obtained from each residential community, this approach tends to compensate for the uneven resource allocation caused by the spatial distance between students' "residences" and schools, as well as the inaccurate distribution of educational resources under distance constraints, through differentiated probability allocation.

[0089] Equation (1) is the objective function, and the rest are constraints: Equation (2) calculates the student The expected utility of obtaining a degree is the sum of the product of the student's utility ratings for each school and the probability of admission; Equation (3) requires that everyone can be admitted; Equations (4) and (5) are used to limit the upper and lower limits of the capacity of each school, for example, setting the upper limit of the school to 20% of the current student population and the lower limit to 45 students; Equation (6) requires that the probability of the school assigning each student is between 0 and 1; Equation (7) is the maximum distance constraint to school. It can be set to 3km.

[0090] The student can be calculated using the Gurobi optimizer. At school The probability of admission .

[0091] In another embodiment, the distance constraint matrix, the school's utility score, the school capacity constraint, the maximum distance threshold, the opposition rate, and the following objective function and constraints can be obtained from S2 and S3 to calculate the student's score. At the volunteer school The probability of admission :

[0092] The objective function is:

[0093]

[0094]

[0095]

[0096]

[0097] The constraints are:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; It represents the expected utility of all students obtaining a degree; For variables of 0 and 1, when The value is 1 if it is less than the expected utility of the neighborhood school enrollment model, and 0 otherwise. For students For the school Utility rating For students At school The probability of admission; For variables of 0 and 1, when students From residence to school The distance is within the maximum distance threshold The value is 1 if it is within the spatial reachability constraint matrix (or 0 otherwise); For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance; It is based on For variables of 0 and 1 with a fixed size, when When less than 0 The value is 1, representing a student. Oppose random admission; otherwise, take 0. The expected utility obtained by the neighborhood-based school enrollment model.

[0105] The neighborhood-based school enrollment model is an existing technology that uses deterministic allocation based on the commuting distance from the student's residence to the school, with each student being assigned to a school.

[0106] In this embodiment, the regional resource allocation equilibrium is measured by calculating the standard deviation of the expected utility obtained by each student participating in the degree allocation using formula (12). Based on students' satisfaction with the allocation of degrees to nearby schools, students participating in the allocation will object to the allocation mechanism if their expected quality of education obtained through random allocation is worse than that of nearby schooling. Whether a student objects can be represented by a binary variable in formula (13), where, It is based on For variables of 0 and 1 with a fixed size, when When less than 0 The value is 1, representing a student. Oppose random admission; otherwise, take 0. The expected utility obtained by the neighborhood-based school enrollment model is calculated based on the fact that enrollment in the neighborhood only guarantees a place at one specific school. The value is the reciprocal order of the school that awarded the degree in the applicant's preference list. The total number of objections is calculated using formula (14).

[0107] The objective of this embodiment is to simultaneously minimize the standard deviation of educational quality and the number of dissenters; therefore, the model objective is Equation (11).

[0108] In another embodiment, to balance the relationship between different objectives, the present invention transforms the objective function into a single-criterion form by linearly combining the objectives with their corresponding weights, as follows:

[0109]

[0110] Utopia Point The ideal optimal solution is obtained by minimizing each objective under constraints. An evaluation function is established by constructing the distance between the actual point and the utopian point. The optimal solution that satisfies the objective function can be obtained by optimizing it (the constraints are still the formulas (16)-(21)). For primary school students, considering their physical and psychological conditions, there are certain constraints on the distance to school and on the school capacity, ensuring that the number of students enrolled in the school is basically in line with reality.

[0111] , These are parameters representing the importance of the objective; the sum of the two parameters must be 1. Specifically, when this model... When the value is 0, the model is transformed into a single-objective "random-nearby" enrollment optimization model that minimizes the standard deviation of expected utility.

[0112] Equation (15) is the objective function, representing the minimum standard deviation of the expected utility of each student in obtaining the quality of education and the minimum number of students dissatisfied with the allocation results; the rest are constraints: Equation (16) calculates the students'... The expected utility of obtaining a degree is the sum of the product of the student's utility ratings for each school and the probability of admission; Equation (17) requires that everyone can be admitted; Equations (18) and (19) are used to limit the capacity and upper and lower limits of each school, for example, setting the upper limit of the school to 20% of the current student population and the lower limit to 45 students; Equation (20) requires that the probability of the school assigning each student is between 0 and 1; Equation (21) is the maximum distance constraint to school, in order to reflect the principle of "relative proximity", It can be set to 3km.

[0113] The Particle Swarm Optimization (PSO) algorithm can be used to solve multi-objective optimization problems, yielding the probability of each student being assigned to a school. If the number of students and schools within an administrative region is large, and there are many constraints, this becomes a large-scale computational problem. PSO is characterized by fast convergence and high accuracy in solving large-scale and complex planning problems, supporting high-concurrency data input and parallel optimization computation. This not only improves the accuracy of the assignment but also increases its speed, reducing the time students spend waiting for results.

[0114] In step S5, admissions are conducted according to the order of preferences and the probability of being admitted to the school. Specifically, this includes:

[0115] S51. For this round of applications, for each school, calculate the current enrollment quota and the number of applicants.

[0116] S52. If the number of applicants is less than or equal to the current enrollment quota, all applicants will be admitted. If the number of applicants is greater than the current enrollment quota, the students will be sorted by probability of admission from highest to lowest, and the top N students will be admitted (N = the remaining enrollment quota of the school).

[0117] S53. Unsuccessful applicants proceed to the next round (k+1 choices), and S51 and S52 are repeated until all choices have been processed.

[0118] According to a second aspect of the invention, a degree allocation device based on spatial constraints and accessibility constraints is proposed, such as... Figure 2 As shown, it includes:

[0119] The school district information collection and georeferencing module is used to acquire the address information of each school within the administrative district and the house number address information of the enrollment area, and convert them into GIS point data. It can convert house number address information and school address information into latitude and longitude coordinates and import them into GIS software. Remote sensing layers are overlaid, and manual verification ensures that all address information corresponds to building units in the remote sensing image. After removing obviously off-target points, duplicate points, and other non-compliant address information, GIS point data is obtained, thereby establishing a unified spatial benchmark.

[0120] The travel distance calculation module calculates the travel distance from students to schools based on volunteer information, student addresses, and school geographical information, and constructs a student-school distance constraint matrix.

[0121] The school utility rating module is used to calculate the school's utility rating.

[0122] The probability of admission calculation module calculates the probability of a student being admitted to the school they applied to, based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the student's application information, and the allocation target.

[0123] The degree allocation module is used to admit students based on their probability of admission to the school, from highest to lowest, for each round of applications, according to the school's current enrollment quota.

[0124] It should be noted that the degree allocation device provided in this embodiment of the invention is used to execute all the processes and steps of the degree allocation method in the above embodiment. The working principles and effects of the two are one-to-one, and will not be elaborated further here.

[0125] A third aspect of the present invention provides a computer-readable storage medium comprising a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform the degree allocation method provided in the above embodiments. The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard disk, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0126] Experimental verification 1:

[0127] This invention uses the allocation of primary school places in Xicheng District, Beijing as an example to illustrate the first embodiment in S4 of this invention. Xicheng District is one of the central urban districts of Beijing, with a large number of primary schools. The quality and spatial distribution of school educational resources vary, and the district has already implemented multi-school zoning and random admission practices. The example study involved 62 primary schools and 19,938 school-age students in Xicheng District (the same as Experimental Verification 2). This experiment uses the probability of a student entering each school as the decision variable. Based on information such as student preference, school capacity, commuting distance from the student's residence to the school, and school educational quality, the probability of a student entering different schools is calculated. The goal is to minimize the standard deviation of expected utility for all students obtaining a school place, thereby improving the resource balance and accuracy of the school place allocation results. The implementation process of this experiment includes the following steps.

[0128] Step 1: Obtain basic data. Obtain the residential addresses of students participating in the school allocation within the administrative region, the addresses of each school, the enrollment capacity of each school, the educational quality evaluation information of each school, and the students' application information. Specifically, the student's residential address is used to determine the student's spatial location, the school address is used to determine the school's spatial location, the school's enrollment capacity is used to set constraints on the number of students a school can accept, the school's educational quality evaluation information is used to calculate the student's utility score for the school, and the student's application information is used to determine the order of students' preferences for different schools.

[0129] Step 2: Construct a spatial database. Convert student residential addresses and school addresses into geospatial point data and unify them to the same coordinate system. Calculate the commuting distance from each student's residence to each school based on the road network or map service interface. Student-school combinations where the distance from the student's residence to the school exceeds the maximum distance threshold are marked as unassignable combinations; student-school combinations where the distance does not exceed the maximum distance threshold are marked as assignable combinations. In this embodiment, the maximum commuting distance threshold is set to 3km to ensure that the random enrollment results still meet the principle of relatively nearby enrollment.

[0130] Step 3: Calculate student utility ratings for schools. A normalized education quality score is used as the student utility rating for each school. The education quality score is obtained by weighting the scores of city-level subject leaders, city-level backbone teachers, district-level subject leaders, district-level core subject leaders, the number of district-level core subjects, and the number of district-level research leaders in the school. The order is: city-level science leader score > city-level backbone teacher score > district-level subject leader (core subject) score and district-level research leader score > district-level subject leader (non-core subject) score > additional points for full coverage of core subjects by district-level subject leaders. Specifically, city-level science leaders receive 10 points, city-level backbone teachers receive 8 points, district-level subject leaders (core subjects) and district-level research leaders receive 7 points, district-level subject leaders (non-core subjects) receive 5 points, and district-level subject leaders with full coverage of core subjects receive an additional point (e.g., 3 points). The total score is calculated, converted to a percentage, and then normalized.

[0131] Step 4: Calculate and obtain the student's information based on the objective and constraints. At school The probability of admission. (Set subscript) Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; This represents the average expected utility of all students obtaining a degree; For students For the school Utility rating For students At school The probability of admission; For students to school The distance. The objective function is to minimize the standard deviation of the expected utility of students obtaining a degree. The expected utility is obtained by weighted summing of the probability of a student entering each school and the corresponding utility score. Constraints include: the sum of the probabilities of each student entering each available school is 1; the total probability of students assigned to each school satisfies the upper and lower limits of school capacity; the probability of a student entering a school is between 0 and 1; student-school combinations exceeding the maximum distance threshold cannot be assigned.

[0132] Based on data such as the student-school utility rating matrix, the student-school commuting distance matrix, the upper and lower limits of school capacity, and the maximum commuting distance threshold, the probability matrix of students entering each school is obtained by using the Gurobi optimizer.

[0133] Step 5: Allocate places based on probability results. For each round of applications, calculate the current number of applicants and the remaining enrollment quota for each school. If the number of applicants is less than or equal to the remaining enrollment quota, all applicants are admitted. If the number of applicants exceeds the remaining enrollment quota, students are ranked according to their probability of admission to the school from highest to lowest, and admissions are made sequentially until the school's enrollment quota is filled. Unadmitted students proceed to the next round of applications, and the above process is repeated until all places are allocated.

[0134] In this experiment, the following can be calculated: the student-school enrollment probability matrix, and the expected utility of each student (i.e., The expected commuting distance (obtained by summing the product of the student's commuting distance to each school and the corresponding admission probability) and the standard deviation of the student's expected utility are also considered. The standard deviation of expected utility is used to evaluate the degree allocation equilibrium; a smaller value indicates a smaller difference in degree attainment among different students. The expected commuting distance is used to evaluate the commuting burden under random admission outcomes.

[0135] The example calculation results show that the average expected utility of students is 0.0706, the expected commuting distance is 2.119 km, and the standard deviation of expected utility is 0.0009. This result indicates that, under the constraints of maximum commuting distance and school capacity, a probabilistic grading allocation can be formed that is tailored to individual students, while keeping the differences in expected utility among students at a low level.

[0136] From the perspective of the distribution structure, such as Figure 3As shown, instead of assigning students from the same area or community to a single school, the system allocates probabilities of students entering multiple schools based on their preferences, school capacity, and commuting distance. For students with relatively insufficient educational resources or unfavorable spatial locations, the probability of them entering more efficient schools can be increased to compensate for resource allocation disparities caused by residential location and spatial distribution of educational resources. For students in areas with relatively concentrated educational resources, probability adjustment prevents them from excessively occupying opportunities in high-quality schools, thereby achieving equalization of overall resource allocation.

[0137] In summary, this experiment, while satisfying school capacity constraints and maximum commuting distance constraints, integrates student preference, school education quality, and student spatial location into the degree allocation calculation process, outputs the probability of students entering each school, and forms a calculable, verifiable, and executable degree allocation scheme based on this.

[0138] Experimental verification 2:

[0139] This invention uses the allocation of primary school places in Xicheng District, Beijing as an example to verify the school place allocation method of the second embodiment in S4 of this invention. Xicheng District is one of the central urban districts of Beijing, with a large number of primary schools, differences in the quality and spatial distribution of school educational resources, and the district has already implemented multi-school zoning and random admission practices. Therefore, it is suitable as a verification area for the method of this invention.

[0140] In this experiment, the experimental data included student residential location data, school spatial location data, school education quality evaluation data, student application simulation data, and road network data. Specifically, student residential location data was used to determine the spatial location of students participating in the allocation; school spatial location data was used to determine the location of each school; school education quality evaluation data was used to calculate students' utility ratings for different schools; student application simulation data was used to reflect students' school preferences; and road network data was used to calculate the commuting distance between students' residences and schools. The example study involved 62 primary schools and 19,938 school-age students in Xicheng District. The specific implementation steps are as follows:

[0141] Step 1: Construct the basic database. This involves acquiring data on the residential locations of students participating in the school allocation process, school spatial location data, school education quality evaluation data, student application data, and road network data. Specifically, student residential location data is used to determine students' spatial locations; school spatial location data is used to determine the geographical coordinates of each school; school education quality evaluation data is used to calculate students' utility ratings of different schools; student application data reflects students' preference order for schools; and road network data is used to calculate the commuting distance between students' residences and schools. This example involves 62 primary schools and 19,938 school-age students in Xicheng District.

[0142] Step 2: Spatial data processing. Student residential addresses and school addresses are converted into spatial point data and unified to the same geographic coordinate system. Based on road network data, the shortest distance to school for each student is calculated. Student-school combinations exceeding the maximum commuting distance threshold are set as unassignable combinations in the model. In this embodiment, the maximum commuting distance threshold is set to 3km to ensure that random enrollment still adheres to the principle of relative proximity.

[0143] Step 3: Construct student utility ratings of the school. Same as the previous experiment.

[0144] Step 4: Using the probability of a student entering each school as the decision variable, and under the premise of satisfying school capacity constraints, maximum commuting distance constraints, and student enrollment probability constraints, while simultaneously considering the resource allocation equilibrium objective and the objection rate minimization objective, calculate the probability of a student entering each school. This embodiment uses the particle swarm optimization algorithm to solve this problem. The input includes the student utility rating matrix, the student-to-school commuting distance matrix, school capacity upper and lower limits, the maximum commuting distance threshold, and the weight parameters for the fairness objective and the objection rate objective; the output is the probability matrix of students entering each school. For each student, the sum of their probabilities of entering all available schools is 1; for each school, the total probability allocated to students satisfies the school capacity constraint.

[0145] Step 5: Admit students according to their application order and the remaining enrollment quota of each school. Specifically, for each round of applications, the number of applicants and the remaining enrollment quota of each school are tallied. If the number of applicants is less than or equal to the remaining enrollment quota, all applicants are admitted. If the number of applicants exceeds the remaining enrollment quota, students are ranked according to their probability of admission to that school from highest to lowest, and admissions are conducted sequentially until the enrollment quota is filled. Students who are not admitted proceed to the next round of applications, and the above process is repeated until all students have been allocated places.

[0146] Step 6: Evaluate the allocation results. This experiment uses the nearest-neighborhood schooling model as a comparison model. This embodiment evaluates the allocation results from four aspects: average expected utility of students, standard deviation of expected utility, expected commuting distance, and opposition rate. Average expected utility of students reflects overall allocation satisfaction; standard deviation of expected utility reflects the degree of difference in obtaining a degree among different students, with a smaller value indicating a more balanced allocation of opportunities; expected commuting distance reflects the distance burden of students attending school; and opposition rate reflects the proportion of students whose expected utility decreased compared to the nearest-neighborhood schooling model.

[0147] Assuming that fairness and minimizing opposition are equally important, the results of this experiment and the nearest-enrollment (NE) model are shown in Table 1, while the spatial results are as follows. Figure 4 As shown.

[0148] Table 1 Comparison between the neighborhood-based school enrollment model and the allocation results of this experiment

[0149] As shown in the table, the average expected utility of students obtained in this experiment was 0.117, higher than 0.102 in the proximity-based enrollment model, an increase of approximately 14.7%. The standard deviation of expected utility decreased from 0.206 to 0.087, decreasing to approximately 42.5% of that in the proximity-based enrollment model, indicating that this experiment can significantly reduce the differences in degree attainment among different students and improve the resource balance of degree allocation. Meanwhile, the expected commuting distance in this experiment was 1.813 km, higher than 0.470 km in the proximity-based enrollment model, indicating that random enrollment, while improving the equality of opportunity, increases commuting distance to some extent. However, because this experiment included a maximum commuting distance constraint, the allocation results remained within a controllable range relative to proximity-based enrollment.

[0150] Further examining the individual student level, this experiment resulted in approximately 73.179% of students achieving higher expected utility compared to the neighborhood-based schooling model, with an average increase of 0.084; while approximately 26.821% of students experienced a decrease in expected utility compared to the neighborhood-based schooling model, with an average decrease of 0.2198. These results indicate that this experiment can improve allocation satisfaction for most students, but the randomized schooling mechanism may also negatively impact the outcomes for some students compared to the original neighborhood-based schooling model. Therefore, introducing an objection rate target is necessary.

[0151] To verify the effectiveness of the opposition rate target, this experiment further adjusted the weights of the fairness target and the opposition rate target. Let the weight of the fairness target be... The target weight for the opposition rate is ,and + =1. The results under different weight combinations are shown in Table 2.

[0152] Table 2 Sensitivity Analysis of Target Weights

[0153]

[0154] As can be seen from the table, when the target weight of the opposition rate As the target weights were gradually increased from 0 to 1, the opposition rate decreased from 34.331% to 19.471%, indicating that this experiment could reduce the degree of opposition that might arise from randomized admission allocation by adjusting the target weights. Simultaneously, the standard deviation of expected utility increased from 0.083 to 0.095, indicating that while reducing the opposition rate, the degree of equal opportunity also decreased. Specifically, when... When the standard deviation of expected utility is taken to be 0.8, the increase in the standard deviation of expected utility is relatively small, while the opposition rate decreases significantly, which is the allocation method most likely to be adopted in actual regional decision-making (e.g., Figure 5 (As shown).

[0155] Figure 6 This demonstrates the changes in the expected line of school enrollment opportunities under different parameters. With... The decrease and With the increase in the expected rate, the expected lines in the northeastern and southwestern parts of Xicheng District thicken, indicating that students in these areas receive increased utility compensation as their focus on the opposition rate target deepens. Conversely, the expected lines in the central and eastern parts become sparser. Considering the unique characteristic of Xicheng District—a higher average educational quality in the northeast and a lower average in the southwest—when the model's consideration of the opposition rate increases, it tends to reduce opposition to random admissions by adjusting areas with high allocation satisfaction and compensating for areas with low allocation satisfaction. =1、 When = 0, the model becomes a fairness-oriented stochastic-proximity enrollment optimization model, at which point the expectation line is almost entirely composed of uniform and chaotic thin lines, while when =0、 When the value is 1, the spatial differentiation of allocation is most obvious when the sole objective is to improve access to nearby schools.

[0156] 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 degree allocation method based on spatial constraints and reachability constraints, characterized in that, include: S1. School District Information Collection and Geographic Registration; S2. Based on the volunteer information, student address and school geographical information, calculate the travel distance from the student to the school and construct the student-school distance constraint matrix; S3. Calculate the school's utility score; S4. Based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the volunteer information, and the allocation target, calculate the probability that the student will be admitted to the school they applied for. S5. Based on the school's enrollment quota and the probability of students entering the school, students are selected from high to low and degrees are allocated.

2. The degree allocation method according to claim 1, characterized in that, Step S1 includes: Obtain the address information of the enrollment areas of each school within the administrative region; The address information is converted into latitude and longitude coordinates and imported into GIS software. Remote sensing layers are then overlaid to make all address information correspond to building units in the remote sensing image, thereby obtaining GIS point data of the address information.

3. The degree allocation method according to claim 1, characterized in that, In S2, the method for calculating the distance from students to school is as follows: using GIS point data of students' residences and school addresses, the distance to school is calculated by calling the Baidu Maps API interface.

4. The degree allocation method according to claim 1, characterized in that, In S3, the school's utility score is calculated as follows: a normalized education quality score is used as the utility score for parents to obtain for each school. The education quality score is calculated by comprehensively weighting the number of municipal-level subject leaders, municipal-level backbone teachers, district-level subject leaders, district-level core subject leaders, the number of district-level core subjects, and the number of district-level research leaders in the school.

5. The degree allocation method according to claim 1, characterized in that, In S4, the objective function is: The constraints are: Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; This represents the average expected utility of all students obtaining a degree; For students For the school Utility rating For students At school The probability of admission; The variables are 0 and 1, when the student From residence to school The distance is within the maximum distance threshold The value is 1 if the time is within the specified range, and 0 otherwise. For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance; The student was obtained by using the Gurobi optimizer. At school The probability of admission .

6. The degree allocation method according to claim 1, characterized in that, In S4, the objective function is: The constraints are: Where: subscript Represents students, with a total number of students. ; Subscript This represents schools; the total number of schools is [number missing]. ; Students The expected utility of obtaining a degree; It represents the expected utility of all students obtaining a degree; The variable is 0 or 1. It is set to 1 when the expected utility of the "random-nearby" school enrollment optimization model is less than the expected utility of the nearby school enrollment model, and 0 otherwise. For students For the school Utility rating For students At school The probability of admission; For variables of 0 and 1, when students From residence to school The distance is within the maximum distance threshold The value is 1 if the time is within the specified range, and 0 otherwise. For the school The distribution yields the sum of the probabilities of admission for all students. , These are the upper and lower limits of the school's capacity. For students to school The distance; It is based on For variables of 0 and 1 with a fixed size, when When less than 0 The value is 1, representing a student. Oppose random admission; otherwise, take 0. The expected utility obtained by the neighborhood-based school enrollment model.

7. The degree allocation method according to claim 6, characterized in that, The objective function is: yes The Utopian point, , It is a parameter representing the importance of the target. + =1.

8. The degree allocation method according to claim 1, characterized in that, In S5, admissions are based on the order of preference and the probability of being admitted to the school, specifically including: S51. For this round of applications, for each school, calculate the current enrollment quota and the number of applicants. S52. If the number of applicants is less than or equal to the current enrollment quota, all applicants will be admitted. If the number of applicants is greater than the current enrollment quota, the students will be sorted by probability of admission from highest to lowest, and the top N students will be admitted (N = the remaining enrollment quota of the school). S53. Unsuccessful applicants proceed to the next round, and S31 and S32 are repeated until all applications are processed.

9. A degree allocation device, characterized in that, include: The school district information collection and geographic registration module is used to obtain the address information of each school within the administrative district and the house number address information of the enrollment area, and convert them into GIS point data; and establish a unified spatial benchmark. The travel distance calculation module calculates the travel distance from students to schools based on volunteer information, student addresses, and school geographical information, and constructs a student-school distance constraint matrix. The school utility rating module is used to calculate the school's utility rating. The probability of admission calculation module calculates the probability of a student being admitted to the school they applied to, based on the distance constraint matrix, the school's utility score, the school's capacity constraint, the student's application information, and the allocation target. The degree allocation module is used to admit students based on their probability of admission to the school, from highest to lowest, for each round of applications, according to the school's current enrollment quota.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the degree allocation method as described in any one of claims 1 to 8.

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