A method of school district division considering spatial constraints

Abstract

The present invention discloses a school district division method considering spatial constraints. Firstly, the school enrollment plan number and the travel time and distance of school-age students are comprehensively considered, so as to determine the school district division plan under the condition of satisfying the uniform distribution of school places and the friendly travel time and distance of students; secondly, considering the inconvenience caused by the separation of urban main roads to students' travel, in the school district division, the constraint condition of the separation of urban main roads is set in advance, so as to make students' school travel more friendly; thirdly, the number of school-age students in the next three years and the number of students planned to be enrolled by the school are fully considered, so as to determine the final school district division plan that meets at least three years, and effectively solve the problem of a big change in school district division every year.

Description

Technical Field

[0001] The present invention relates to the field of geographic information system and space optimization technology, and in particular to a school district division method taking into account space constraint conditions. Background Art

[0002] my country's "Compulsory Education Law of the People's Republic of China", passed in 1986 and amended in 2018, and the "Implementation Rules of the Compulsory Education Law of the People's Republic of China" promulgated in 1992 clearly require the principle of primary and secondary school students to go to school nearby. In terms of specific implementation, the policy of nearby enrollment is limited by many factors such as urban spatial expansion caused by rapid urbanization and uneven spatial distribution of basic education resources. In fact, it has long been difficult and is prone to social controversy. Therefore, how to scientifically and reasonably divide school districts from both demand and supply aspects, while taking into account the efficiency of commuting to school (comprehensive balance of time, distance and safety, etc.) is a hot issue in the field of education. At present, the solution to the problem of school district division mainly takes into account constraints such as school saturation, student enrollment time and distance not exceeding a certain limit, and uses methods such as linear programming to obtain the optimal solution that meets the corresponding constraints. However, the result often results in imbalances such as the need to cross the main roads to go to school (affecting student commuting safety), and some schools are oversaturated but some schools have too few students. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] The present invention provides a school district division method taking into account spatial constraints to solve the above problems.

[0005] (II) Technical solution

[0006] To achieve the above object, the present invention provides the following technical solution: a method for dividing school districts considering spatial constraints, comprising the following steps:

[0007] Step S1: constructing a geospatial database, which includes latitude and longitude information, road network information and student information within a specified area;

[0008] Step S2: Divide the designated area into a plurality of minimum plot units enclosed by urban branch roads according to the road network information;

[0009] Step S3: Taking the minimum plot unit obtained in step S2 as a benchmark, combined with student information, calculate the number of school-age students in each minimum plot unit; select the center point of each minimum plot unit, calculate the road network distance and time distance between different minimum plot units, and construct a plot distance matrix;

[0010] Step S4: Determine the school district division criteria. To minimize the commuting time of students, the constraint conditions are determined by the number of school-age students in the minimum plot unit and the plot distance matrix. Under the school district division criteria, the constraint conditions are calculated to determine the estimated school district division plan.

[0011] Step S5: Repeat steps S1 to S4 to calculate the estimated school district division plans for the second and third years. Combining the estimated school district division plans for the three years, the final school district division plan is obtained. The final school district division plan can cover the enrollment needs of new students in the next three years.

[0012] Preferably, the geospatial database in step S1 specifically includes:

[0013] Longitude and latitude information: longitude and latitude information of different schools, longitude and latitude information of the smallest plot unit;

[0014] Road network information: road distribution information, road grade, number of intersections;

[0015] Student information: the school's planned enrollment number, the number of students in the school district in different grade levels, the number of students outside the school district, and the number of new births in the corresponding year.

[0016] Preferably, the process of constructing the minimum plot unit in step S2 is as follows:

[0017] Construct a road network G = (V, E) of urban branch roads or above in the specified area.

[0018] Where V = {v1,v2,…,v i},v i represents the ith intersection, V is the set of all intersections in the specified area; E = {e 12 ,e 23 ,…,e ij},e ij represents the road segment connecting intersection i and intersection j, and E is the set of all road segments in the specified area;

[0019] The road network and intersection enclosed area is identified as the minimum plot unit I, and the minimum plot unit is a surface area converted from the point and line enclosed area, where:

[0020] I={(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…),(e 12 ,e 25 ,e 26 ,…,v1,v2,v5,v6,…),…}.

[0021] Preferably, the process of calculating the number of school-age students in each minimum plot unit in step S3 is as follows:

[0022] Calculate the number of primary school age students:

[0023] First, based on the number of students in the school district and the number of students outside the school district who have enrolled in grades one to six, and combined with the number of newborns in the corresponding year, the ratio of the number of newborns in each grade to the number of students in the school district and the number of students outside the school district was obtained;

[0024] Based on the above ratio, combined with the number of newborns in the current year who have not yet entered school, the number of primary school-age students in the next few years can be inferred.

[0025] Calculate the number of junior high school-age students:

[0026] First, count the number of students in the school district and the number of students outside the school district in the first to third grade of junior high school in the past three years, as well as the number of students in the school district and the number of students outside the school district in the fourth to sixth grade of elementary school in the past, and determine their change ratio; thus, estimate the number of junior high school-age students in the next three years;

[0027] Divide the estimated number of school-age students into a number of minimum statistical units based on the road network information;

[0028] If the area of ​​the smallest statistical unit is larger than the area of ​​the smallest plot unit, the number of school-age students corresponding to the smallest statistical unit shall be divided into each smallest plot unit in proportion, and the number of school-age students in each smallest plot unit shall be obtained;

[0029] If the area of ​​the minimum statistical unit is smaller than the area of ​​the minimum plot unit, the number of school-age students corresponding to multiple minimum statistical units will be aggregated into the corresponding minimum plot unit, and then the number of school-age students in each minimum plot unit will be obtained.

[0030] Preferably, the process of constructing the plot distance matrix in step S3 is as follows:

[0031] For any minimum plot unit

[0032] I i =(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…),

[0033] Get the latitude and longitude information of the smallest plot unit, and get the time distance and road network distance between any smallest plot units during the school hours, and then get the time distance matrix T as follows:

[0034]

[0035] The road network distance matrix D is:

[0036]

[0037] Among them, the time distance matrix T and the road network distance matrix D constitute the plot distance matrix.

[0038] Preferably, the constraints in step S4 include:

[0039] The first constraint: school distance constraint

[0040]

[0041]

[0042] d ij ×L ij ≤D max (3)

[0043] Among them, N i represents the number of people in the smallest plot unit i; d ij represents the distance from the smallest plot unit plot i to school j; L ij Indicates whether the minimum plot unit i is assigned to school j, if yes, it is 1, otherwise it is 0; Equation (1) indicates that the total distance to school for all students is the minimum; Equation (2) indicates that each minimum plot unit can only be assigned to a unique school under the nearest enrollment; Equation (3) indicates the maximum school distance constraint;

[0044] Second constraint: school size constraint

[0045]

[0046] S j ≤C max (5)

[0047] S j ≥C min (6)

[0048] The third constraint: main road separation constraint

[0049] L ij ×L mj =0 (7)

[0050] Among them, the minimum plot unit i and the minimum plot unit m cannot be allocated to the same school j at the same time;

[0051] Finally, the linear programming method is used to calculate and solve the estimated school district division plan under the school district division criterion of minimizing students' commuting time.

[0052] (III) Beneficial effects

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] Firstly, the planned enrollment of schools and the travel time and distance of school-age students are comprehensively considered, so as to determine the school district division plan while ensuring that the school places are evenly distributed and the students' travel time and distance are friendly. Secondly, considering the inconvenience caused by the separation of urban main roads to students' travel, the constraint condition of the separation of urban main roads is set in advance in the school district division, so as to make the students' school travel more friendly. Thirdly, the number of school-age students and the planned enrollment number of schools in the next three years are fully considered, so as to determine the final school district division plan that meets at least three years, and effectively solve the problem of major changes in school district division every year. In general, different from the traditional school district division plan that only considers nearby enrollment as a single condition, the present invention further reasonably divides school districts based on dynamic population and school capacity data to avoid the situation of oversaturation of school enrollment, and on this basis, further considers the spatial constraints such as the division of urban main roads, so as to ensure the safe commuting of primary and secondary school students. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0056] Figure 1 shows an overall flow chart of an embodiment of the present invention;

[0057] Figure 2 A schematic diagram showing the division of the minimum land plot unit according to an embodiment of the present invention is shown;

[0058] Figure 3 A schematic diagram of the final school district division scheme according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] See attached Figure 1 -Attached Figure 3 The present invention discloses a method for dividing school districts taking into account spatial constraints, comprising the following steps:

[0061] Step S1: constructing a geospatial database, which includes latitude and longitude information, road network information and student information within a specified area;

[0062] Step S2: Divide the designated area into a plurality of minimum plot units enclosed by urban branch roads according to the road network information;

[0063] Step S3: Taking the minimum plot unit obtained in step S2 as a benchmark, combined with student information, calculate the number of school-age students in each minimum plot unit; select the center point of each minimum plot unit, calculate the road network distance and time distance between different minimum plot units, and construct a plot distance matrix;

[0064] Step S4: Determine the school district division criteria. To minimize the commuting time of students, the constraint conditions are determined by the number of school-age students in the minimum plot unit and the plot distance matrix. Under the school district division criteria, the constraint conditions are calculated to determine the estimated school district division plan.

[0065] Step S5: Repeat steps S1 to S4 to calculate the estimated school district division plans for the second and third years. Combining the estimated school district division plans for the three years, the final school district division plan is obtained. The final school district division plan can cover the enrollment needs of new students in the next three years.

[0066] Furthermore, the geospatial database in step S1 specifically includes:

[0067] Longitude and latitude information: longitude and latitude information of different schools, longitude and latitude information of the smallest plot unit; specifically, WGS84 longitude and latitude can be used.

[0068] Road network information: road distribution information, road grade, number of intersections; specifically including expressways, urban expressways, national highways, provincial highways, urban trunk roads, county roads, urban secondary trunk roads, urban branch roads, rural roads, other accessible roads, and other inaccessible road grades.

[0069] Student information: the school's planned enrollment number, the number of students in the school district in different grade levels, the number of students outside the school district, and the number of new births in the corresponding year; specifically, it includes the school's planned enrollment number for the next three years and the actual enrollment number in the past three years.

[0070] Furthermore, the process of constructing the minimum plot unit in step S2 is as follows:

[0071] Construct a road network G = (V, E) of urban branch roads or above in the specified area.

[0072] Where V = {v1,v2,…,v i},v i represents the ith intersection, V is the set of all intersections in the specified area; E = {e 12 ,e 23 ,…,e ij},e ijrepresents the road segment connecting intersection i and intersection j, and E is the set of all road segments in the specified area;

[0073] The road network and intersection enclosed area is identified as the minimum plot unit I, and the minimum plot unit is a surface area converted from the point and line enclosed area, where:

[0074] I={(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…),(e 12 ,e 25 ,e 26 ,…,v1,v2,v5,v6,…),…}.

[0075] In actual operation, the road network data can be processed into shapefile format, and the line elements can be interrupted at the intersections of roads and nodes can be generated. The line-to-surface method can be used to convert the linear shapefile data into surface shapefile data. Each surface data I is the smallest plot unit.

[0076] Furthermore, the process of calculating the number of school-age students in each minimum plot unit in step S3 is as follows:

[0077] Calculate the number of primary school age students:

[0078] First, based on the number of students in the school district and the number of students outside the school district who have enrolled in grades one to six, and combined with the number of newborns in the corresponding year, the ratio of the number of newborns in each grade to the number of students in the school district and the number of students outside the school district was obtained;

[0079] Based on the above ratio, combined with the number of newborns in the current year who have not yet entered school, the number of primary school-age students in the next few years can be inferred.

[0080] Specifically, it is known that the number of students in the school district from grade one to grade six in 2021 is

[0081] n 2015l 、n 2014l ,...,n 2010l ;

[0082] The number of non-district students in grades 1 to 6 in 2021 is

[0083] n 2015m 、n 2014m ,...,n 2010m ;

[0084] And the number of new births in 2021 for students in grades 1 to 6 in the corresponding years of birth is

[0085] N 2015 、N 2016 ,...,N 2010 ;

[0086] From this, we can conclude that the ratio of the number of new births in the corresponding years (2015-2010) from the first to the sixth grade in 2021 to the current number of students in the school district is:

[0087]

[0088] The ratio of the number of new births in the corresponding years (2015-2010) for grades 1 to 6 in 2021 to the current number of non-school district students is:

[0089]

[0090] It is known that the number of newborns in 2016 is N 2016 , the estimated number of school-age students in 2022 (school district students) is:

[0091]

[0092] The number of school-age students in 2022 (non-school district students) is:

[0093]

[0094] Calculate the number of junior high school-age students:

[0095] First, count the number of students in the school district and the number of students outside the school district in the first to third grade of junior high school in the past three years, as well as the number of students in the school district and the number of students outside the school district in the fourth to sixth grade of elementary school in the past, and determine their change ratio; thus, estimate the number of junior high school-age students in the next three years;

[0096] Specifically, the number of students in the school districts for the first to third grades of junior high school in 2021 is known to be:

[0097] p 2021l 、p 2020l 、n 2019l ;

[0098] The number of non-school district students from Grade 1 to Grade 9 are:

[0099] p 2021m 、p 2020m 、p 2019m ;

[0100] And the number of students in the first to third grade of junior high school in 2021 corresponding to the number of students in the fourth to sixth grade of primary school in 2018 are:

[0101] n 2009l 、n 2008l 、n 2007l ;

[0102] The number of non-district students in grades 4 to 6 of primary school in 2018 corresponding to the students in grades 1 to 3 of junior high school in 2021 are:

[0103] n 2009l 、n 2008l 、n 2007l ;

[0104] From this, the change ratio of students in the first to third grade of junior high school in 2021 to students in the fourth to sixth grade of elementary school in 2018 can be calculated as follows:

[0105]

[0106] The change ratio of non-school district students in the first to third grade of junior high school in 2021 to the non-school district students in the fourth to sixth grade of primary school in 2018 is:

[0107]

[0108] The estimated number of first-grade students of school age from 2022 to 2024 (school district students) is:

[0109] p 2022l =n 2010n *mean(S (2021，2009)l +S (2020，2008)l +S (2019，2007)l )

[0110]

[0111]

[0112] The number of students of the first grade of junior high school (non-school district students) from 2022 to 2024 are:

[0113] p 2022l =n 2010n *mean(S (2021，2009)l +S (2020，2008)l +S (2019，2007)l )

[0114]

[0115]

[0116] Divide the estimated number of school-age students into a number of minimum statistical units based on the road network information;

[0117] If the area of ​​the minimum statistical unit is larger than the area of ​​the minimum plot unit, the number of school-age students corresponding to the minimum statistical unit will be divided into each minimum plot unit in proportion, and the number of school-age students in each minimum plot unit will be obtained; specifically, when the minimum statistical unit is a residential area, the area of ​​the minimum statistical unit will be larger than the area of ​​the minimum plot unit.

[0118] If the area of ​​the minimum statistical unit is smaller than the area of ​​the minimum plot unit, the number of school-age students corresponding to multiple minimum statistical units will be aggregated into the corresponding minimum plot unit, and then the number of school-age students in each minimum plot unit will be obtained; specifically, when the minimum statistical unit is a residential building, the area of ​​the minimum statistical unit will be smaller than the area of ​​the minimum plot unit.

[0119] Specifically, the minimum statistical unit is generally a residential community or a residential building. In actual operation, the number of school-age students in each minimum statistical unit (residential community) in the past three years is counted. For example, if the primary school districts are divided in 2021, 2022, and 2023, the number of people born in the three years of 2014.09.01-2015.08.31, 2015.09.01-2016.08.31, and 2016.09.01-2017.08.31 needs to be obtained. The smaller the spatial scale of the number of newborns, the more obvious the reliability of subsequent school district division. For example, if the number of newborns in each residential community or even each residential building can be obtained, the quality of the newborns obtained will be better than that obtained at the community scale.

[0120] Furthermore, the process of constructing the plot distance matrix in step S3 is as follows:

[0121] For any minimum plot unit

[0122] I i =(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…),

[0123] Get the latitude and longitude information of the smallest plot unit, and get the time distance and road network distance between any smallest plot units during the school hours. Specifically, you can call the existing mainstream map API to get it, and then get the time distance matrix T as follows:

[0124]

[0125] The road network distance matrix D is:

[0126]

[0127] Among them, the time distance matrix T and the road network distance matrix D constitute the plot distance matrix.

[0128] Preferably, the constraints in step S4 include:

[0129] The first constraint: school distance constraint

[0130]

[0131]

[0132] d ij ×L ij ≤D max (3)

[0133] Among them, N i represents the number of people in the smallest plot unit i; d ij represents the distance from the smallest plot unit plot i to school j; L ij Indicates whether the minimum plot unit i is assigned to school j, if yes, it is 1, otherwise it is 0; Equation (1) indicates that the total distance to school for all students is the minimum; Equation (2) indicates that each minimum plot unit can only be assigned to a unique school under the nearest enrollment; Equation (3) indicates the maximum school distance constraint;

[0134] Second constraint: school size constraint

[0135]

[0136] S j ≤C max (5)

[0137] S j ≥C min (6)

[0138] The third constraint: main road separation constraint

[0139] L ij ×L mj =0 (7)

[0140] Among them, the minimum plot unit i and the minimum plot unit m cannot be allocated to the same school j at the same time;

[0141] Finally, the linear programming method is used to calculate and solve the estimated school district division plan under the school district division criterion of minimizing students' commuting time.

[0142] The above method is used to calculate the estimated school district division plans for the second and third years. The three-year estimated school district division plans are combined, and the final school district division plan is determined based on local actual policies. The final school district division plan can cover the enrollment needs of new students in the next three years. The three-year period mainly considers the population size and structure, as well as the relative stability of administrative divisions and educational resource structures.

[0143] The final school district division plan can ensure that students' commuting does not exceed the designed distance / time, does not cross the main urban roads, and the saturation of each school can meet the actual situation of the school. Different from the traditional school district division plan that only considers nearby enrollment as a single condition, the present invention is based on dynamic population and school capacity data to further reasonably divide school districts to avoid the situation of over-saturation of school enrollment. On this basis, it further considers spatial constraints such as the division of urban main roads, thereby ensuring the safe commuting of primary and secondary school students.

[0144] It should be noted that although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for dividing school districts considering spatial constraints, characterized in that: The following steps are involved: Step S1: constructing a geospatial database, which includes latitude and longitude information, road network information and student information within a specified area; Step S2: Divide the designated area into a plurality of minimum plot units enclosed by urban branch roads according to the road network information; Step S3: Taking the minimum plot unit obtained in step S2 as a benchmark, combined with student information, calculate the number of school-age students in each minimum plot unit; select the center point of each minimum plot unit, calculate the road network distance and time distance between different minimum plot units, and construct a plot distance matrix; Step S4: Determine the school district division criteria. To minimize the commuting time of students, the constraint conditions are determined by the number of school-age students in the minimum plot unit and the plot distance matrix. Under the school district division criteria, the constraint conditions are calculated to determine the estimated school district division plan. Step S5: Repeat steps S1 to S4 to calculate the estimated school district division plans for the second and third years, and combine the estimated school district division plans for the three years to obtain the final school district division plan, which can cover the enrollment needs of new students in the next three years; The process of constructing the minimum plot unit in step S2 is as follows: Construct a road network G = (V, E) of urban branch roads or above in the specified area. Where V = {v1,v2,…,v i },v i represents the ith intersection, V is the set of all intersections in the specified area; E = {e 12 ,e 23 ,…,e ij },e ij represents the road segment connecting intersection i and intersection j, and E is the set of all road segments in the specified area; The road network and intersection enclosed area is identified as the minimum plot unit I, and the minimum plot unit is a surface area converted from the point and line enclosed area, where: I={(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…),(e 12 ,e 25 ,e 26 ,…,v1,v2,v5,v6,…),…}; The process of constructing the plot distance matrix in step S3 is as follows: For any minimum plot unit I i =(e 12 ,e 23 ,e 34 ,…,v1,v2,v3,v4,…), Get the latitude and longitude information of the smallest plot unit, and get the time distance and road network distance between any smallest plot units during the school hours, and then get the time distance matrix T as follows: The road network distance matrix D is: Among them, the time distance matrix T and the road network distance matrix D constitute the plot distance matrix; The constraints in step S4 include: The first constraint: school distance constraint d ij ×L ij ≤C max (3) Among them, N i represents the number of people in the smallest plot unit i; d ij represents the distance from the smallest plot unit plot i to school j; L ij Indicates whether the minimum plot unit i is assigned to school j, if yes, it is 1, otherwise it is 0; Equation (1) indicates that the total distance to school for all students is the minimum; Equation (2) indicates that each minimum plot unit can only be assigned to a unique school under the nearest enrollment; Equation (3) indicates the maximum school distance constraint; Second constraint: school size constraint S j ≤C max (5) S j ≥C min (6) The third constraint: main road separation constraint L ij ×L mj =0 (7) Among them, the minimum plot unit i and the minimum plot unit m cannot be allocated to the same school j at the same time; Finally, the linear programming method is used to calculate and solve the estimated school district division plan under the school district division criterion of minimizing students' commuting time.

2. A method for dividing school districts considering spatial constraints according to claim 1, characterized in that: The geospatial database in step S1 specifically includes: Longitude and latitude information: longitude and latitude information of different schools, longitude and latitude information of the smallest plot unit; Road network information: road distribution information, road grade, number of intersections; Student information: the school's planned enrollment number, the number of students in the school district in different grade levels, the number of students outside the school district, and the number of new births in the corresponding year.

3. The method for dividing school districts considering spatial constraints according to claim 1, characterized in that: The process of calculating the number of school-age students in each minimum plot unit in step S3 is as follows: Calculate the number of primary school age students: First, based on the number of students in the school district and the number of students outside the school district who have enrolled in grades one to six, and combined with the number of newborns in the corresponding year, the ratio of the number of newborns in each grade to the number of students in the school district and the number of students outside the school district was obtained; Based on the above ratio, combined with the number of newborns in the current year who have not yet entered school, the number of primary school-age students in the next few years can be inferred. Calculate the number of junior high school-age students: First, count the number of students in the school district and the number of students outside the school district in the first to third grade of junior high school in the past three years, as well as the number of students in the school district and the number of students outside the school district in the fourth to sixth grade of elementary school in the past, and determine their change ratio; thus, estimate the number of junior high school-age students in the next three years; Divide the estimated number of school-age students into a number of minimum statistical units based on the road network information; If the area of ​​the smallest statistical unit is larger than the area of ​​the smallest plot unit, the number of school-age students corresponding to the smallest statistical unit shall be divided into each smallest plot unit in proportion, and the number of school-age students in each smallest plot unit shall be obtained; If the area of ​​the minimum statistical unit is smaller than the area of ​​the minimum plot unit, the number of school-age students corresponding to multiple minimum statistical units will be aggregated into the corresponding minimum plot unit, and then the number of school-age students in each minimum plot unit will be obtained.

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