Regional school site selection optimization method and system based on improved black plinuan search algorithm

Abstract

The invention discloses a regional school site selection optimization method and system based on an improved black plinuan search algorithm, and the method comprises the steps: building a regional school site selection optimization model through an XGBoost algorithm, and enabling the regional school site selection optimization model to achieve the optimization of a multi-target optimization function composed of school bearing pressure, student school accessibility and school service coverage rate as a target; according to the method, a regional school site selection optimization model is solved through an improved Black-South optimization algorithm, and the improved Black-South optimization algorithm is obtained through a Sine chaotic mapping initialization population, a golden sine search strategy and the search performance of a Gaussian disturbance improvement algorithm, so that the diversity of the population is increased, and the global search and local optimization capability of the algorithm is improved. According to the method, the regional school site selection optimization model can be established through the XGBoost algorithm, the optimization speed can be effectively improved, and the global search and local optimization capability of the algorithm can be effectively improved by improving the Black-Youlinuan optimization algorithm and increasing the diversity of populations.

Description

Technical Field

[0001] The present invention relates to a method for optimizing the location of regional schools, and in particular to a method and system for optimizing the location of regional schools based on an improved black kite search algorithm. Background Art

[0002] "Enrollment in the nearest school" is a major measure to ensure the balanced development of compulsory education. It not only reflects people's ardent hope for educational equality, but also highlights the government's concern for education. With the increase of urban population and the improvement of people's living standards, people are no longer satisfied with the basic requirement of "having a school to go to", but instead regard the school's teaching level and teaching resources as the first factor in choosing a school.

[0003] As a result, problems such as the increased distance for students to go to school during the compulsory education stage, insufficient school capacity, and cross-district schooling have become increasingly serious. How to effectively evaluate the implementation of the "nearby enrollment" policy in the region and improve the spatial layout of primary and secondary schools to shorten the distance for students to go to school has always been the focus of research by scholars in the field of education. GIS analysis and mathematical modeling are often used in existing technologies to optimize school site selection.

[0004] Although this method can minimize the sum of the squares of students' school distances and ensure that the partitions have a certain degree of clustering, it still has the following defects:

[0005] 1. Due to the large administrative area and large population density differences in my country, the number of students and schools per unit area is larger than that targeted by existing technologies. However, existing technologies do not pay too much attention to the initial point of school site selection and the convergence speed of heuristic algorithms, resulting in slow optimization speed.

[0006] 2. Traditional optimization methods cannot solve the problem that even if there are many schools in the area, the school service areas overlap, which increases students' school time.

[0007] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of the application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0008] The purpose of the present invention is to overcome the shortcoming of slow optimization speed in the prior art and to provide a regional school site selection optimization method and system based on an improved Black Kite search algorithm, which improves the optimization speed by seeking an approximate optimal solution with the shortest distance for internal students to go to school.

[0009] To achieve the above objectives, the technical solution of the present invention is:

[0010] A regional school location optimization method based on an improved black kite search algorithm, the optimization method comprising:

[0011] S1. Construct a regional school location optimization model, obtain data, and establish a regional school location optimization model based on the XGBoost algorithm. The regional school location optimization model aims to optimize the multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage;

[0012] S2. Improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm;

[0013] S3. Solve the regional school location optimization model. Solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

[0014] The S1 comprises the following steps:

[0015] S1.1. Obtain the student’s home address data H and the student’s school address data S, convert the student’s home address data H and the student’s school address data S into longitude and latitude data H′ and S′, and use H′ and S′ to calculate the student’s walking distance to school D = {d1, d2, d3, …d n} and walking time to school T = {t1, t2, t3, ... t n}, extract the location difference data E between home and school from data H′ and S′ = {e1, e2, e3, …e n}, E includes Haversine distance, reciprocal of Haversine distance, difference in longitude and latitude between school and student, and ratio of Haversine distance to difference in longitude and latitude;

[0016] S1.2. The regional school location optimization model includes:

[0017]

[0018] In the above formula, D′ i is the predicted school distance of the ith student, H′ i is the home longitude and latitude data of the i-th student, S′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used;

[0019] The overall error of the XGBoost model is determined by accumulating the difference between the actual distance D and the predicted distance D′. The overall error of the model is:

[0020]

[0021] In the above formula, X objRepresents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i , D′ i ) is the difference between the actual distance and the predicted distance;

[0022] The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for:

[0023]

[0024] In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, γ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

[0025] In S2, the population is initialized by Sine chaotic mapping, the golden sine search strategy and the Gaussian perturbation are used to improve the search performance of the algorithm, thereby obtaining an improved black kite optimization algorithm.

[0026] The S2 comprises the following steps:

[0027] S2.1. Construct an original black kite search algorithm, wherein the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model. The original black kite attack behavior model is:

[0028]

[0029] In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size;

[0030] The mathematical model expression of the black kite migration behavior is as follows:

[0031]

[0032] In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F ri represents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other locations;

[0033] S2.2. Initialize the population through Sine chaotic mapping, where the Sine chaotic mapping is defined as:

[0034] Y i+1 =μsin(πY i );

[0035] In the above formula, Y i ∈[-1, 1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range;

[0036] S2.3. Improve the attack behavior through the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is:

[0037]

[0038] In the above formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r1 represents the distance of movement, and r2 represents the direction of movement. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include:

[0039]

[0040] In the above formula, τ is the golden section coefficient;

[0041] S2.4. Improve the search performance of the algorithm through Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is:

[0042]

[0043] In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference;

[0044] After the disturbance, the greedy rule is added, and by comparison and The fitness value of the position, which determines whether the position needs to be updated;

[0045] The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum accommodating number of people and the distance students go to school.

[0046] The S3 comprises the following steps:

[0047] S3.1. Generate a kernel density map of the distribution of students whose primary school distance exceeds 2.5 kilometers and whose secondary school distance exceeds 3.5 kilometers through kernel density analysis, which is used to determine the number of new schools and the initial longitude and latitude coordinates, and provide an initial plan for the subsequent new school layout optimization model;

[0048] S3.2, set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3;

[0049] S3.3. Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

[0050] A regional school location optimization method system based on an improved black kite search algorithm, the system comprising a model building module, an algorithm improvement module and a model solving module;

[0051] The model building module is used to establish a regional school location optimization model based on the XGBoost algorithm, wherein the regional school location optimization model aims to optimize a multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage;

[0052] The algorithm improvement module is used to improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm;

[0053] The model solving module is used to solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

[0054] The specific operation steps of the model building module are:

[0055] Obtain the student's home address data H and the student's school address data S, convert the student's home address data H and the student's school address data S into longitude and latitude to obtain data H' and S', and use H' and S' to calculate the student's walking distance to school D = {d1, d2, d3, ...d n} and walking time to school T = {t1, t2, t3, ... t n}, extract the location difference data E between home and school from data H′ and S′ = {e1, e2, e3, …e n}, E includes Haversine distance, reciprocal of Haversine distance, difference in longitude and latitude between school and student, and ratio of Haversine distance to difference in longitude and latitude;

[0056] The regional school location optimization model includes:

[0057]

[0058] In the above formula, D′ i is the predicted school distance of the ith student, H′ i is the home longitude and latitude data of the i-th student, S′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used;

[0059] The overall error of the XGBoost model is determined by accumulating the difference between the actual distance D and the predicted distance D′. The overall error of the model is:

[0060]

[0061] In the above formula, X obj Represents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i , D′ i ) is the difference between the actual distance and the predicted distance;

[0062] The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for:

[0063]

[0064] In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, γ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

[0065] The specific operation steps of the algorithm improvement module are as follows: the search performance of the algorithm is improved by using Sine chaotic mapping to initialize the population, golden sine search strategy and Gaussian perturbation to obtain an improved black kite optimization algorithm.

[0066] The algorithm improvement module comprises the following steps:

[0067] Construct an original black kite search algorithm, the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model, the original black kite attack behavior model is:

[0068]

[0069] In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size;

[0070] The mathematical model expression of the black kite migration behavior is as follows:

[0071]

[0072] In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F ri represents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other locations;

[0073] The population is initialized by a Sine chaotic map, which is defined as:

[0074] Y i+1 =μsin(πY i );

[0075] In the above formula, Y i ∈[-1, 1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range;

[0076] The attack behavior is improved by the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is:

[0077]

[0078] In the above formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r1 represents the distance of movement, and r2 represents the direction of movement. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include:

[0079]

[0080] In the above formula, τ is the golden section coefficient;

[0081] The search performance of the algorithm is improved by Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is:

[0082]

[0083] In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference;

[0084] After the disturbance, the greedy rule is added, and by comparison and The fitness value of the position, which determines whether the position needs to be updated;

[0085] The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum number of students and the distance to school.

[0086] The specific operation steps of the model solving module are:

[0087] The kernel density analysis method is used to generate a kernel density map of the distribution of students whose primary school distance is more than 2.5 kilometers and whose secondary school distance is more than 3.5 kilometers. This is used to determine the number of new schools and the initial longitude and latitude coordinates, and to provide an initial plan for the subsequent new school layout optimization model.

[0088] Set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3;

[0089] Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] 1. In a regional school site selection optimization method based on an improved black kite search algorithm, the present invention establishes a regional school site selection optimization model through an XGBoost algorithm, and the regional school site selection optimization model takes the optimal multi-objective optimization function composed of school carrying pressure, student school accessibility, and school service coverage as the goal, and solves the regional school site selection optimization model through an improved black kite optimization algorithm to obtain a regional school site selection optimization scheme, and the XGBoost algorithm optimizes the objective function, combines the Taylor formula expansion and regularization method to speed up the training speed of the model and reduce the risk of overfitting, thereby improving the optimization speed. Therefore, this design can establish a regional school site selection optimization model through the XGBoost algorithm, effectively improving the optimization speed.

[0092] 2. In the regional school site selection optimization method based on the improved black kite search algorithm of the present invention, the student aggregation characteristics are analyzed by the kernel density analysis method in the solution step, the initial solution of the heuristic algorithm is determined, and the MBKA algorithm is used to optimize it, and the population is initialized by Sine chaotic mapping, so that the initial population can cover the entire search space to avoid falling into the local optimal solution, increase the population diversity, improve the global search of the algorithm, speed up the convergence speed of the model, and find the approximate optimal solution with the shortest distance for students to go to school in the region. Therefore, this design can randomly select the initial solution of the optimization scheme, effectively improving the optimization speed.

[0093] 3. In the regional school site selection optimization method based on the improved black kite search algorithm of the present invention, the search performance of the algorithm is improved by Sine chaotic mapping initialization population, golden sine search strategy and Gaussian perturbation to obtain an improved black kite optimization algorithm, thereby increasing the diversity of the population and improving the global search and local optimization capabilities of the algorithm. Therefore, this design can increase the diversity of the population by improving the black kite optimization algorithm, and effectively improve the global search and local optimization capabilities of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 is a flow chart of the method of the present invention.

[0095] Figure 2 It is a structural diagram of the system described in the present invention.

[0096] Figure 3 It is a schematic diagram of the school space optimization model in Example 1.

[0097] Figure 4 It is a structural diagram of the device described in Example 4.

[0098] Figure 5 This is a curve chart showing the decrease in distance to primary school students optimized by different algorithms in Example 1.

[0099] Figure 6This is the service blind spot distribution diagram after optimization in Example 1.

[0100] Figure 7 This is the optimized layout diagram of the new school in Example 1. DETAILED DESCRIPTION

[0101] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0102] Embodiment 1:

[0103] See also Figure 3 to Figure 4 In this embodiment, according to the Basic Standards for Running Compulsory Education Schools in a Certain Province, the number of students in primary and junior high schools shall not exceed 2,000. Taking into account the accessibility of students and the maximum carrying capacity of schools, students are reallocated to corresponding schools and a new school space optimization model is constructed. The new school space optimization model is shown in Figure 3 ;

[0104] For students in the blind spot of educational services, ArcGIS kernel density analysis method is used to determine the number of new schools, and the center of the gathering point is used as the initial school address. The MBKA algorithm proposed in Chapter 5 is used to optimize the site selection of new primary and secondary schools with the goal of minimizing the total distance for students to go to school and maximizing the school service range.

[0105] In this embodiment, in order to intuitively display the distribution of students and schools, the kernel density analysis method is used to generate a kernel density map of the distribution of students whose primary school distance exceeds 2.5 kilometers and whose secondary school distance exceeds 3.5 kilometers, which is used to determine the number of new schools and the initial longitude and latitude coordinates, and provide an initial plan for the subsequent new school layout optimization model;

[0106] According to the "Standards for Running Compulsory Education Schools in a Certain Province", the number of students in primary and secondary schools shall not exceed 2,000. This study takes 2,000 as the maximum capacity of the school to observe whether students will be unable to attend school nearby under this condition and to judge whether the number of schools in the region is sufficient. Based on the above issues, taking the primary school "home-school" data as an example, Table 1 and Table 2 are constructed:

[0107] Table 1, primary school table

[0108]

[0109] Table 2, Student Table

[0110]

[0111] The data is input into the regional school location optimization model, and the regional school location optimization solution is obtained by improving the Black Kite optimization algorithm;

[0112] The present invention takes the total distance of students to school in the region as the objective function, takes the school capacity not exceeding 2000 as the restriction condition, and optimizes the student matching school allocation plan and the layout of the newly built school to make the objective function approximately minimized. The objective function is as follows:

[0113]

[0114] Where N is the number of students in the region, xi, yi represent the longitude and latitude coordinates of the ith student, lng[i], lat[i] are the longitude and latitude coordinates of the school to which the ith student is assigned, H is the distance fitting model, Si represents the number of students in the ith school, L is a constant of 2000, and λ is the penalty factor for the number of students exceeding the limit, which is used to adjust the degree of exceeding the limit.

[0115] In order to further reflect the performance improvement of the MBKA algorithm of the present invention after the improved strategy, this section selects the black kite optimization algorithm BKA, the sparrow search algorithm SSA, the dung beetle optimization algorithm DBO and the gray wolf optimization algorithm GWO as comparison algorithms, and verifies the superiority of the MBKA algorithm by comparing the optimal solution (Best), average (Average) and variance (STD). The parameters of each algorithm are shown in Table 3:

[0116] Table 3. Algorithm parameter settings

[0117]

[0118] Among them, ρ represents the probability of selecting the attack strategy in the BKA algorithm, μ is used to control the chaos of the Sine map, when μ = -1, the random numbers are uniformly distributed between [-1, 1]; k is the deflection coefficient, α indicates whether the dung beetle deflects, when α = 1, no deflection occurs, when α = -1, deflection occurs, b, R are constant values; r1, r2 are used to increase the randomness of the generation of the gray wolf population.

[0119] See also Figure 5 The following are the decline curves of MBKA, BKA, SSA, DBO and GWO algorithms on the primary school data in Hanyang District. The x-axis represents the number of algorithm iterations, and the y-axis represents the total distance between students in the region. As can be seen from the figure, the improved MBKA algorithm has achieved comprehensive improvements in initial population selection, convergence speed and optimal solution compared to the basic BKA algorithm; compared with the DBO and GWO algorithms, MBKA also has better performance when facing high-dimensional data, but compared with the SSA algorithm, MBKA still has room for improvement in population initialization.

[0120] The optimal solutions, average values, and variances of each algorithm when optimizing the school distance of students in a certain district are shown in Table 4:

[0121] Table 4. Comparison of results

[0122] algorithm Optimal solution average value variance MBKA 139965.359 148905.951 4057.244 BKA 171563.297 173015.611 3453.551 DBO 140057.495 148905.951 9057.244 SSA 140057.495 139989.043 3320.530 GWO 193364.487 193364.487 2.910

[0123] It can be seen that the MBKA algorithm obtains the minimum total distance of students to school, which is 139965.359, and the mean and variance are 148905.951 and 4057.244 respectively, which is slightly inferior to the SSA algorithm, indicating that the improved BKA algorithm has improved its ability to optimize high-dimensional data;

[0124] After the optimization and adjustment of the corresponding schools, the optimization of primary school service capacity and accessibility is shown in Table 5:

[0125] Table 5. Comparison of service range and accessibility before and after optimization

[0126]

[0127] Through comparison, it was found that the MBKA algorithm achieved better results. After optimization, the service rate of primary schools within 500 meters increased from 18.20% to 38.51%, the proportion of covered students increased, the farthest distance for students to go to school did not change, and the average school distance for students in the administrative area was reduced from 3.01 kilometers to 2.85 kilometers. The number of students with a school distance of more than 2.5 km decreased by 14.97%. However, there are still 24.33% of students who have a long distance to school. In order to further realize the enrollment of students nearby, new schools will be built to increase the capacity of students in the administrative area.

[0128] See also Figure 6 ,The kernel density analysis diagram of students whose school distance is still more than 2.5 kilometers after optimization by MBKA algorithm. By observing the student aggregation characteristics, it can be seen that there are a large number of students with difficulty commuting to school in the central and southeastern parts of Hanyang District. In order to solve this problem, a new primary school will be built.

[0129] See also Figure 7 , schematic diagram of the site selection for the new school. Through ArcGIS analysis, 7 new primary schools are planned to be built. The school spatial layout is optimized through the MBKA heuristic algorithm. The new school is located in the center of the student gathering point where the distance to school is more than 2.5 km, which better meets the needs of nearby students to attend school nearby.

[0130] Table 6. Comparison of service rate and accessibility before and after the construction of new schools

[0131]

[0132] See Table 6 for a comparison of the service rate and accessibility of each optimization model before and after the construction of a new school. It was observed that the MBKA algorithm found a better location. After the construction of the new school, the service rate of schools within 500 meters in the area increased from 38.51% to 43.40%, the number of people who went to school more than 2.5 kilometers decreased by 3.37%, the average school distance decreased from 2.85 kilometers to 1.78 kilometers, and the standard deviation of the school distance also decreased, indicating that the differences in the school distances of students in the region have become smaller, and the farthest school distance has been shortened by 2.97 kilometers. The overall service rate and accessibility have been greatly improved compared to before.

[0133] Embodiment 2:

[0134] See also Figure 1 , a regional school location optimization method based on an improved black kite search algorithm, the optimization method comprising:

[0135] S1. Construct a regional school location optimization model, obtain data, and establish a regional school location optimization model based on the XGBoost algorithm. The regional school location optimization model aims to optimize the multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage;

[0136] S2. Improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm;

[0137] S3. Solve the regional school location optimization model. Solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

[0138] The S1 comprises the following steps:

[0139] S1.1. Obtain the student’s home address data H and the student’s school address data S, convert the student’s home address data H and the student’s school address data S into longitude and latitude data H′ and S′, and use H′ and S′ to calculate the student’s walking distance to school D = {d1, d2, d3, …d n} and walking time to school T = {t1, t2, t3, ... t n}, extract the location difference data E between home and school from data H′ and S′ = {e1, e2, e3, …e n}, E includes Haversine distance, reciprocal of Haversine distance, difference in longitude and latitude between school and student, and ratio of Haversine distance to difference in longitude and latitude;

[0140] S1.2. The regional school location optimization model includes:

[0141]

[0142] In the above formula, D′ i is the predicted school distance of the ith student, H′ i is the home longitude and latitude data of the i-th student, S′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used;

[0143] The overall error of the XGBoost model is determined by accumulating the difference between the actual distance D and the predicted distance D′. The overall error of the model is:

[0144]

[0145] In the above formula, X obj Represents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i , D′ i ) is the difference between the actual distance and the predicted distance;

[0146] The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for:

[0147]

[0148] In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, γ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

[0149] In S2, the population is initialized by Sine chaotic mapping, the golden sine search strategy and the Gaussian perturbation are used to improve the search performance of the algorithm, thereby obtaining an improved black kite optimization algorithm.

[0150] The S2 comprises the following steps:

[0151] S2.1. Construct an original black kite search algorithm, wherein the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model. The original black kite attack behavior model is:

[0152]

[0153] In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size;

[0154] The mathematical model expression of the black kite migration behavior is as follows:

[0155]

[0156] In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F ri represents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other locations;

[0157] Similar to traditional optimization algorithms, the BKA algorithm randomly initializes the positions of the population in the search space. This method has the following three common disadvantages: (1) uneven coverage of the search range; (2) insufficient initialization diversity; and (3) difficulty in controlling the search strategy.

[0158] In order to increase the diversity of the initial population, this paper chooses the Sine chaotic mapping method to initialize the population:

[0159] S2.2. Initialize the population through Sine chaotic mapping, where the Sine chaotic mapping is defined as:

[0160] Y i+1 =μsin(πY i );

[0161] In the above formula, Y i ∈[-1, 1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range;

[0162] The Sine map is highly chaotic, and its chaos is affected by parameters. When u approaches 1 or -1, the chaotic performance is better, and it can be evenly distributed between [-1, 11. When μ = -1, the Sine sequence is completely in a chaotic state, so μ is taken as -1 in subsequent experiments.

[0163] The distribution diagram of the Sine chaotic sequence when μ=-1. The uniformly distributed initial population can cover the entire search space, which helps to avoid the algorithm from falling into the local optimal solution, increase the diversity of the population, and improve the convergence speed of the algorithm. Therefore, this study uses Sine chaotic mapping to optimize the initial population of the BKA algorithm and improve the shortcomings of the original BKA algorithm.

[0164] S2.3. Improve the attack behavior through the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is:

[0165]

[0166] In the above formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r1 represents the distance of movement, and r2 represents the direction of movement. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include:

[0167]

[0168] In the above formula, τ is the golden section coefficient;

[0169] Golden sine search strategy This algorithm combines the sine function and the golden section coefficient to search for the best solution within the search range, which narrows the search range, speeds up the convergence speed, and can also balance the global search and local search capabilities to find the optimal solution.

[0170] The r1 and r2 parameters in the GSA algorithm are used to divide the search space, guiding the black kite to quickly find the optimal attack position and reduce the possibility of falling into the local optimum.

[0171] S2.4. Improve the search performance of the algorithm through Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is:

[0172]

[0173] In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference;

[0174] In the migration behavior of the basic BKA algorithm, due to the existence of the leader strategy, the black kite will migrate towards the current optimal direction to find the approximate optimal solution. Therefore, if the current search direction is not the global optimal direction and the Cauchy mutation strategy cannot be effectively adjusted, the black kite population will continue to migrate towards the local optimal solution, resulting in a search stagnation. To solve this problem, this study uses mutation perturbation operations to interfere with the optimal individuals after the Cauchy mutation again to increase the possibility of the algorithm jumping out of the local optimal solution. Cauchy mutation and Gaussian mutation are both commonly used mutation operators in optimization algorithms, and both operators have their own advantages and disadvantages. Compared with Gaussian mutation, Cauchy mutation has a larger search range and can explore more solution spaces, but its excessive search range may also lead to jumping away from the optimal value and producing worse offspring; on the contrary, Gaussian mutation has better search ability within a small range. Therefore, this study continues to use Gaussian mutation for perturbation on the basis of BKA using Cauchy mutation to make up for the disadvantage of the large search range of Cauchy mutation and increase the possibility of finding the global optimal solution.

[0175] Although adding Gaussian perturbations can enhance the global search and local optimization capabilities of the algorithm, there is no guarantee that the position after Gaussian perturbation is better than the original position. Therefore, a greedy rule is added after the perturbation, that is, by comparing the fitness values ​​of the new and old positions, it is determined whether the position needs to be updated.

[0176] The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum number of students and the distance to school.

[0177] The S3 comprises the following steps:

[0178] S3.1. Generate a kernel density map of the distribution of students whose primary school distance exceeds 2.5 kilometers and whose secondary school distance exceeds 3.5 kilometers through kernel density analysis, which is used to determine the number of new schools and the initial longitude and latitude coordinates, and provide an initial plan for the subsequent new school layout optimization model;

[0179] S3.2, set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3;

[0180] S3.3. Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

[0181] Embodiment 3:

[0182] See also Figure 2, a regional school location optimization method system based on an improved black kite search algorithm, the system comprising a model building module, an algorithm improvement module and a model solving module;

[0183] The model building module is used to establish a regional school location optimization model based on the XGBoost algorithm, wherein the regional school location optimization model aims to optimize a multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage;

[0184] The algorithm improvement module is used to improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm;

[0185] The model solving module is used to solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

[0186] The specific operation steps of the model building module are:

[0187] Obtain the student's home address data H and the student's school address data S, convert the student's home address data H and the student's school address data S into longitude and latitude to obtain data H' and S', and use H' and S' to calculate the student's walking distance to school D = {d1, d2, d3, ...d n} and walking time to school T = {t1, t2, t3, ... t n}, extract the location difference data E between home and school from data H′ and S′ = {e1, e2, e3, …e n}, E includes Haversine distance, reciprocal of Haversine distance, difference in longitude and latitude between school and student, and ratio of Haversine distance to difference in longitude and latitude;

[0188] The regional school location optimization model includes:

[0189]

[0190] In the above formula, D′ i is the predicted school distance of the ith student, H′ i is the home longitude and latitude data of the i-th student, S′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used;

[0191] The overall error of the XGBoost model is determined by accumulating the difference between the actual distance D and the predicted distance D′. The overall error of the model is:

[0192]

[0193] In the above formula, X obj Represents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i , D′ i ) is the difference between the actual distance and the predicted distance;

[0194] The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for:

[0195]

[0196] In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, γ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

[0197] The specific operation steps of the algorithm improvement module are as follows: the search performance of the algorithm is improved by using Sine chaotic mapping to initialize the population, golden sine search strategy and Gaussian perturbation to obtain an improved black kite optimization algorithm.

[0198] The algorithm improvement module comprises the following steps:

[0199] Construct an original black kite search algorithm, the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model, the original black kite attack behavior model is:

[0200]

[0201] In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size;

[0202] The mathematical model expression of the black kite migration behavior is as follows:

[0203]

[0204] In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F rirepresents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other locations;

[0205] The population is initialized by a Sine chaotic map, which is defined as:

[0206] Y i+1 =μsin(πY i );

[0207] In the above formula, Y i ∈[-1, 1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range;

[0208] The attack behavior is improved by the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is:

[0209]

[0210] In the above formula, r1 is a random number between [0, 2π], r2 is a random number between [0, π], r1 represents the distance of movement, and r2 represents the direction of movement. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include:

[0211]

[0212] In the above formula, τ is the golden section coefficient;

[0213] The search performance of the algorithm is improved by Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is:

[0214]

[0215] In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference;

[0216] After the disturbance, the greedy rule is added, and by comparison and The fitness value of the position, which determines whether the position needs to be updated;

[0217] The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum number of students and the distance to school.

[0218] The specific operation steps of the model solving module are:

[0219] S3.1. Generate a kernel density map of the distribution of students whose primary school distance exceeds 2.5 kilometers and whose secondary school distance exceeds 3.5 kilometers through kernel density analysis, which is used to determine the number of new schools and the initial longitude and latitude coordinates, and provide an initial plan for the subsequent new school layout optimization model;

[0220] S3.2, set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3;

[0221] S3.3. Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

[0222] Embodiment 4:

[0223] See also Figure 5 , a regional school location optimization device based on an improved black kite search algorithm, the device comprising a processor and a memory;

[0224] The memory is used to store computer program code and transmit the computer program code to the processor;

[0225] The processor is used to execute the regional school location optimization method based on the improved black kite search algorithm described in Example 1 according to the instructions in the computer program code.

[0226] A computer medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for optimizing the location of regional schools based on an improved black kite search algorithm described in Example 1 is implemented.

[0227] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A regional school location optimization method based on an improved black kite search algorithm, characterized in that: The optimization method comprises: S1. Construct a regional school location optimization model, obtain data, and establish a regional school location optimization model based on the XGBoost algorithm. The regional school location optimization model aims to optimize the multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage; S2. Improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm; S3. Solve the regional school location optimization model. Solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

2. The regional school site selection optimization method based on the improved black kite search algorithm according to claim 1 is characterized in that: The S1 comprises the following steps: S1.

1. Obtain the student's home address data H and the student's school address data S, and convert the student's home address data H and the student's school address data S into longitude and latitude to obtain data H ′ and S ′ , using H ′ and S ′ Calculate the distance students walk to school D = {d1, d2, d3, ... d n } and walking time to school T = {t1, t2, t3, ... t n }, from data H ′ and S ′ Extract the location difference data between home and school E = {e1, e2, e3, ...e n }, E includes Haversine distance, reciprocal of Haversine distance, longitude and latitude difference between school and student, and ratio of Haversine distance to longitude and latitude difference; S1.

2. The regional school location optimization model includes: In the above formula, D ′ i is the predicted school distance of the ith student, H ′ i is the home latitude and longitude data of the i-th student, S ′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used; By accumulating the actual distance D and the predicted distance D ′ The difference between them determines the overall error of the XGBoost model, and the overall error of the model is: In the above formula, X obj Represents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i ,D ′ i ) is the difference between the actual distance and the predicted distance; The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for: In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, Υ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

3. The regional school site selection optimization method based on the improved black kite search algorithm according to claim 2 is characterized in that: In S2, the population is initialized by Sine chaotic mapping, the golden sine search strategy and the Gaussian perturbation are used to improve the search performance of the algorithm, thereby obtaining an improved black kite optimization algorithm.

4. The regional school site selection optimization method based on the improved black kite search algorithm according to claim 3 is characterized in that: The S2 comprises the following steps: S2.

1. Construct an original black kite search algorithm, wherein the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model. The original black kite attack behavior model is: In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size; The mathematical model expression of the black kite migration behavior is as follows: In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F ri represents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other locations; S2.

2. Initialize the population through Sine chaotic mapping, where the Sine chaotic mapping is defined as: Y i+1 =μsin(πY i ); In the above formula, Y i ∈[-1,1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range; S2.

3. Improve the attack behavior through the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is: In the above formula, r1 is a random number between [0,2π], r2 is a random number between [0,π], r1 represents the moving distance, and r2 represents the moving direction. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include: x-π+(1-τ)2π x1=-π+τ*2π In the above formula, τ is the golden section coefficient; S2.

4. Improve the search performance of the algorithm through Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is: In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference; After the disturbance, the greedy rule is added, and by comparison and The fitness value of the position, which determines whether the position needs to be updated; The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum number of students and the distance to school.

5. The regional school site selection optimization method based on the improved black kite search algorithm according to claim 4 is characterized in that: The S3 comprises the following steps: S3.

1. Generate a kernel density map of the distribution of students whose primary school distance exceeds 2.5 kilometers and whose secondary school distance exceeds 3.5 kilometers through kernel density analysis, which is used to determine the number of new schools and the initial longitude and latitude coordinates, and provide an initial plan for the subsequent new school layout optimization model; S3.2, set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3; S3.

3. Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

6. A regional school location optimization method system based on an improved black kite search algorithm, characterized in that: The system includes a model building module, an algorithm improvement module and a model solving module; The model building module is used to establish a regional school location optimization model based on the XGBoost algorithm, wherein the regional school location optimization model aims to optimize a multi-objective optimization function consisting of school carrying pressure, student accessibility, and school service coverage; The algorithm improvement module is used to improve the Black Kite Optimization Algorithm to obtain an improved Black Kite Optimization Algorithm; The model solving module is used to solve the regional school location optimization model by improving the Black Kite search algorithm to obtain the regional school location optimization plan.

7. The regional school location optimization system based on the improved black kite search algorithm according to claim 6 is characterized by: The specific operation steps of the model building module are: Obtain the student's home address data H and the student's school address data S, and convert the student's home address data H and the student's school address data S into longitude and latitude to obtain data H ′ and S ′ , using H ′ and S ′ Calculate the distance students walk to school D = {d1, d2, d3, ... d n } and walking time to school T = {t1, t2, t3, ... t n }, from data H ′ and S ′ Extract the location difference data between home and school E = {e1, e2, e3, ...e n }, E includes Haversine distance, reciprocal of Haversine distance, longitude and latitude difference between school and student, and ratio of Haversine distance to longitude and latitude difference; The regional school location optimization model includes: In the above formula, D ′ i is the predicted school distance of the ith student, H ′ i is the home latitude and longitude data of the i-th student, S ′ i The address data of the school attended by the students, E i is the location difference data between the home and school of the i-th student, K is the XGBoost model hyperparameter representing the total number of weak learners used; By accumulating the actual distance D and the predicted distance D ′ The difference between them determines the overall error of the XGBoost model, and the overall error of the model is: In the above formula, X obj Represents the overall model error, Ω(f k ) is the regularization term, n is the number of students, l(D i ,D ′ i ) is the difference between the actual distance and the predicted distance; The regularization term Ω(f k ) is used to control the complexity of the model and prevent the model from overfitting. The regularization term Ω(f k )for: In the above formula, the model hyperparameter t is the number of leaf nodes, ω j is the score of the jth leaf node, γ is the penalty coefficient used to control the depth of the leaf node, and λ is the regularization penalty coefficient.

8. The regional school site selection optimization system based on the improved black kite search algorithm according to claim 7 is characterized by: The specific operation steps of the algorithm improvement module are as follows: the search performance of the algorithm is improved by using Sine chaotic mapping to initialize the population, golden sine search strategy and Gaussian perturbation to obtain an improved black kite optimization algorithm.

9. The regional school location optimization system based on the improved black kite search algorithm according to claim 8 is characterized by: The algorithm improvement module comprises the following steps: Construct an original black kite search algorithm, the original black kite search algorithm includes a black kite attack behavior model and a black kite migration behavior model, the original black kite attack behavior model is: In the above formula, and denote the specific latitude and longitude addresses of the school selected by the i-th student in the j-th allocation scheme in the t-th and t+1-th iteration steps, r is a random number ranging from 0 to 1, p is a constant value of 0.9, T is the total number of iterations, t is the current number of iterations, and η is the iteration attenuation coefficient used to adjust the individual position update step size; The mathematical model expression of the black kite migration behavior is as follows: In the above formula, Indicates the latitude and longitude address of the school closest to home assigned in the t iterations so far, F i represents the school distance of student i in this allocation plan, F ri represents the shortest distance to school for i in the past t iterations, and m is a scaling factor used to adjust the attraction or repulsion of the solution toward the optimal solution or other positions; The population is initialized by a Sine chaotic map, which is defined as: Y i+1 =μsin(πY i ); In the above formula, Y i ∈[-1,1] is the chaotic sequence, μ is the control parameter, U d With L d Respectively represent the upper and lower limits of the d-dimensional search range; The attack behavior is improved by the golden sine search strategy. In the golden sine search strategy, the golden sine search strategy is introduced as a local search strategy into the position update formula of the attack behavior, and the GSA algorithm is used to divide the search space. The improved position update formula is: In the above formula, r1 is a random number between [0,2π], r2 is a random number between [0,π], r1 represents the moving distance, and r2 represents the moving direction. represents the latitude and longitude address of the school closest to home in the t iteration, x1 and x2 are coefficients obtained after introducing the golden section number, and the coefficients x1 and x2 include: In the above formula, τ is the golden section coefficient; The search performance of the algorithm is improved by Gaussian perturbation. In the Gaussian perturbation, Gaussian mutation is continued to be used for perturbation on the basis of Cauchy mutation. The improved position update expression is: In the above formula, is the latitude and longitude address of the selected school after update. The longitude and latitude addresses of the schools that are selected again after the interference; The input values ​​of the improved Black Kite optimization algorithm are the student address, school address, maximum number of students and the distance to school.

10. The regional school location optimization system based on the improved black kite search algorithm according to claim 9 is characterized in that: The specific operation steps of the model solving module are: The kernel density analysis method is used to generate a kernel density map of the distribution of students whose primary school distance is more than 2.5 kilometers and whose secondary school distance is more than 3.5 kilometers. This is used to determine the number of new schools and the initial longitude and latitude coordinates, and to provide an initial plan for the subsequent new school layout optimization model. Set the current number of students and whether there is an oversubscription in the regional school location optimization model to 0, select the random allocation plan of the student's corresponding school from the distribution kernel density map as the initial solution, use the improved Black Kite optimization algorithm to optimize the school allocation plan, and enter S3.3; Check whether the selected schools in the optimization result are oversubscribed. If so, return to S3.2 to reselect the initial solution. If not, output the current school allocation plan as the final optimization result.

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