CN111709593B - Space resource optimal allocation method based on weak space constraint - Google Patents
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Abstract
The invention discloses a space resource optimal allocation method based on weak space constraint, which comprises the following steps: reading in attributes and spatial information of a constraint target and a to-be-optimized distribution target, and calculating a distance matrix and an adjacent matrix; the second step is that: after the priority execution sequence of the constraint targets is dynamically judged according to calculation, a set which can meet the priority constraint targets is quickly judged through set increase and decrease and a series of matrix operations; the third step: after the set is obtained, updating a distance matrix, an adjacent matrix and a series of other related parameters through matrix operation; and finally, circularly executing the second step and the third step by adopting the updated parameters until no optional constraint target exists. The method overcomes the defects that the linear programming method cannot meet the requirement of space adjacency and the method for constructing the balance area has low optimization speed and low precision in large-scale data application, and has the advantages of high speed and high precision while ensuring high space adjacency.
Description
Technical Field
The invention relates to the field of space resource optimal allocation, in particular to a space resource optimal allocation method based on weak space constraint.
Background
The optimal allocation of space resources is an important foundation of social fairness. Taking educational resources as an example, the 'entering nearby' is one of the basic national policies for maintaining education equity and social fairness in China, and many scholars discuss how to enter nearby. At present, linear programming, genetic algorithms and the like are widely used for optimizing and distributing educational resources, however, the algorithms usually only consider the constraints among attributes such as the number of people to be learned, educational resource limits and the like, and ignore the spatial relationship (whether adjacent) of grids or residential points on the space; in addition, a method for constructing a balance area is also a common means for resource optimization allocation, but due to strong space constraint of the balance area, the calculation convergence speed is very slow and the result error is large in large-scale application.
Therefore, at present, a compromise mode is considered to be adopted, and reasonable allocation of resources is performed on the premise of weak space constraint, so that the effects of considering space continuity, maintaining high precision and performing quick calculation are achieved, and a new means is provided for solving similar problems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a space resource optimal allocation method based on weak space constraint aiming at the defects of low calculation convergence speed and large result error in the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a space resource optimal allocation method based on weak space constraint comprises the following steps:
s1, acquiring a constraint target set comprising a plurality of constraint targets and grid polygon data corresponding to each target to be optimized;
s2, calculating the space distance between the constraint target and the mesh polygon, and constructing a space distance matrix A; the attribute values of each target to be optimized are sequentially stored in a first list attr according to the unique grid serial number ID, and the attribute values of each constraint target are stored in a second list attrx according to the unique point serial number ID;
s3, recording the position coordinate point of each constraint target to a first recording data set geomxy; determining a mesh polygon map sheet based on all mesh polygon data, and recording a lower left corner coordinate point of the mesh polygon map sheet into a second recording data set ldxy;
s4, acquiring a point unique serial number ID of each constraint target, establishing a first serial number set, and converting the first serial number set into a first absolute mapping ID serial number list apid by adopting an absolute mapping method; acquiring a grid unique serial number ID of each target to be optimized, establishing a second serial number set, and converting the second serial number set into a second absolute mapping ID serial number list agid by adopting an absolute mapping method;
s5, based on the position coordinate points of each constraint target recorded in the first record data set geomxy, taking the constraint target closest to the coordinate point at the lower left corner of the grid polygon map as an initial constraint target, and recording a set formed by the initial constraint targets as pid;
s6, taking the spatial distance matrix A as an object, executing a minimum position matrix calculation method, obtaining a plurality of first to-be-optimized selection targets after matrix screening operation is carried out, and recording a set formed by the first to-be-optimized selection targets as gid;
s7, executing 'attrx [ apid [ pid ] ]', and acquiring an attribute value T corresponding to the initial constraint target from a second list attrx; executing 'attr [ agid [ gid ] ]', and acquiring an attribute value O corresponding to a first target to be optimized from a first list attr;
s8, updating the data objects included in the first to-be-optimized selection target set gid based on the size relationship between the attribute value O and the attribute value T;
s9, updating the first and second absolute mapping ID serial number lists based on the updated set gid, recalculating the spatial distance matrix A through the updated absolute mapping ID serial number lists, and updating the first record data set geomxy;
and S10, circularly executing the steps S5-S9 based on the updated result until the first absolute mapping ID serial number list apid is empty, and outputting a resource allocation result.
The space resource optimal allocation method based on weak space constraint of the invention realizes the calculation and update of the dynamic shortest distance of the space target, and utilizes the dynamic distance (for example, the target to be optimized is an adjacent polygon, a connection matrix can be increased to serve as constraint) as the weak space constraint (because the distance constraint is adopted, the maximum service distance of the constraint target can be limited in application), and performs resource optimal allocation according to the attribute constraint, so that the position proximity relation of the target to be optimized allocated on the space can be maintained to the maximum extent, and the method has the characteristic of high response speed, and for about 5000 targets to be optimized and about 130 constraint targets, on a single-core cpu, after the data preparation is completed, the optimal allocation only needs about 1 minute.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method for optimal allocation of spatial resources based on weak spatial constraints according to the present invention;
FIG. 2 is a flowchart illustrating an operation of adding to-be-optimized target selection sets according to a spatial resource optimization allocation method based on weak spatial constraints;
FIG. 3 is a flowchart of an object removal operation based on an adjacency matrix under the method for optimal allocation of spatial resources based on weak spatial constraints according to the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Fig. 1 is a flowchart of a method for optimal allocation of spatial resources based on weak spatial constraints according to the present invention, which includes the following steps:
s1, obtaining a constraint target set comprising a plurality of constraint targets and grid polygon data corresponding to each target to be optimized.
Specifically, in this embodiment, the number of students entering the school is used as a constraint target, and the number of children of the correct age for the primary school entering the school is used as a target to be optimized. The decision allowance parameter percentage may be set to 0.05 to read in mesh polygon data with the number of children of the correct age of elementary school and elementary school point data including the number of students.
S2, calculating the space distance between the constraint target and the mesh polygon, and constructing a space distance matrix A; the attribute values of each target to be optimized are sequentially stored in a first list attr according to the unique grid serial number ID, and the attribute values of each constraint target are stored in a second list attrx according to the unique point serial number ID.
Specifically, when step S2 is implemented, as known to those skilled in the art, a spatial distance matrix corresponding to mesh polygons in the elementary school and an adjacency matrix between mesh polygons may be calculated through a spatial calculation method, and the number of children with suitable age for the elementary school (i.e., the attribute values of each object to be optimized) and the number of students entering the school (i.e., the attribute values of each constraint object) are recorded in the first list attr and the second list attrx according to mesh unique sequence numbers, respectively.
S3, recording the position coordinate point of each constraint target to a first recording data set geomxy; and determining a complete mesh polygon map sheet based on all the mesh polygon data, and recording the coordinate point at the lower left corner of the mesh polygon map sheet to a second record data set ldxy.
Specifically, when step S3 is implemented, coordinates of the primary school point location data (x, y) may be sequentially recorded in the first recording data set geomxy, and a lower left corner coordinate of the mesh polygon map may be obtained, and the lower left corner coordinate of the mesh polygon map may be recorded in the second recording data set ldxy.
S4, acquiring a point unique serial number ID of each constraint target, establishing a first serial number set, and converting the first serial number set into a first absolute mapping ID serial number list apid by adopting an absolute mapping method; and acquiring the unique grid serial number ID of each target to be optimized, establishing a second serial number set, and converting the second serial number set into a second absolute mapping ID serial number list agid by adopting an absolute mapping method.
S5, based on the position coordinate points of each constraint target recorded in the first record data set geomxy, taking the constraint target closest to the coordinate point at the lower left corner of the grid polygon map as an initial constraint target, and recording a set formed by the initial constraint targets as pid; wherein:
when the initial constraint target is determined, the position coordinate points of each constraint target are doubly ordered according to "[ x, y ] or [ y, x ], and the constraint target corresponding to the ordered first group of coordinate points is used as the initial constraint target.
S6, taking the spatial distance matrix A as an object, executing a minimum position matrix calculation method, obtaining a plurality of first to-be-optimized selection targets after matrix screening operation is carried out, and recording a set formed by the first to-be-optimized selection targets as a set gid; wherein:
when the target to be optimized is screened, the screening of the object can be further realized by setting the maximum service distance of the initial constraint target and executing the matrix selection operation. The maximum service distance is considered, that is, for some resource sites (such as schools), although the numerical condition is not met, the search range cannot be too large (the school cannot be too far away, for example, some regions have partial mountainous regions and are widely sparse).
S7, executing 'attrx [ apid [ pid ] ]', and acquiring an attribute value T corresponding to the initial constraint target from a second list attrx; executing 'attr [ agid [ gid ] ]', and acquiring an attribute value O corresponding to a first target to be optimized from a first list attr;
it should be noted that executing "apid [ pid ]" is the sequence number of the starting constraint target after obtaining the mapping; executing "attrx [ apid ] ]", namely obtaining the serial number of the initial constraint target, and then obtaining the attribute value corresponding to the initial constraint target from the second list attrx.
S8, updating the data objects included in the first to-be-optimized selection target set gid based on the size relationship between the attribute value O and the attribute value T; wherein:
(1) when O < (1-percent) × T, performing an adding operation on the target selection set to be optimized determined based on the set gid, specifically (refer to fig. 2, which is a flowchart of performing an adding operation on the target selection set to be optimized):
s81, taking the target to be optimized which is not recorded in the set gid as a second target to be optimized, and recording a set formed by the second target to be optimized as a set acid;
s82, calculating the distance between the constraint target and the grid corresponding to the second target to be optimized according to the constraint target and the second target to be optimized data recorded in the set ogid and the set pid, and the spatial distance matrix A;
specifically, if the primary school coordinate points are used as constraint targets, the primary school coordinate points may be obtained from the set pid according to the set gid, the set pid and the spatial distance matrix a, and after the corresponding grid is determined from the set gid, the distances between the primary school and the grid are sequentially calculated to obtain multiple distance values.
S83, after ascending sorting is carried out on the set ogid based on the obtained multiple distance values, whether a second target to be optimized and selected in the sorted set ogid is moved into the set gid is judged; wherein:
in the current step, the second to-be-optimized selection target is firstly moved into the set gid, and the corresponding attribute and the attribute O are calculated based on the attribute values of all the objects in the set gid1By comparing the attribute with O1And (1+ percentage) T and (1-percentage) T, and judging whether to carry out the immigration operation of the object.
Specifically, if the attribute value O exists, the attribute value O1If the value is larger than (1+ percent) T, skipping the current object and continuing the moving-in judgment of the next moving-in object; if the attribute value O exists1If the current target object to be optimized is less than (1-percent) T, determining to move the current second target object to be optimized into the set gid, and continuing to judge the movement of the next object to be moved;
and continuing to execute the step S9 after recording the set gid to the dictionary result after traversing all the objects in the set ogid.
S84, traversing the candidate set until the stopping condition is met or the set ogid is empty, and executing the step S9; it should be noted that the current stop condition may be:
when T × (1+ percentage) > = O > = T × (1-percentage), then the traversal of the candidate set is stopped and the target selection set to be optimized, determined based on the set gid, is recorded into the dictionary result.
(2) In another aspect of the present embodiment, when the moving-in object determination is performed when the adjacency matrix B can be calculated by using mesh polygons based on the adjacency relationship, the foregoing step S81 is replaced with:
based on the grid objects recorded in the set gid, determining an adjacent grid corresponding to each grid object according to the adjacency matrix B, determining a third selection target to be optimized based on the adjacent grids, and recording a set formed by the third selection target to be optimized as a set ogid;
step S82-step S84 are executed.
The above is the object addition operation performed when the adjacency matrix B is obtained. Considering the tie matrix, when the target to be optimized is a polygon or a point, the adjacent matrix is used for judging the immigrated object, so that the execution efficiency of the algorithm can be effectively improved.
In this embodiment, when updating the data objects included in the first to-be-optimized selection target set gid, in consideration of the spatial distance matrix a and the adjacency matrix B, object addition operation is performed based on the distance from each coordinate point of the primary school to the corresponding grid in the set ogid. The resource optimization allocation is carried out according to the attribute limitation, so that the spatial position proximity relation of the allocation target to be optimized can be kept to the maximum extent, and the method has the characteristic of high response speed.
(3) When O > (1+ percentage) × T, adopting the increasing operation mode of the set objects executed in the steps S81-S84 to remove the target selection set to be optimized determined based on the set gid, but specifically performing object recombination according to a descending sorting mode when sorting the set ogids based on the obtained multiple distance values;
and when judging whether to move the second target to be optimized included in the sorted set ogid out of the set gid, based on the following rules:
if the attribute value O1If the current second target object to be optimized is greater than (1+ percent) T, removing the current second target object to be optimized from the set gid; if the attribute value O1And if the value is less than (1-percent) T, skipping the current object and continuing to judge the removal of the next moved-in object.
(4) When the mesh polygon based on the adjacency relation can be calculated to obtain the adjacency matrix B, and O > (1+ percentage) × T, the object removal operation is performed (refer to fig. 3 for a specific flowchart):
s810, establishing an undirected graph according to the set gid and the adjacent matrix B;
s820, determining a first adjacent grid of each grid object of the set gid through the adjacency matrix B, determining a second adjacent grid adjacent to the first adjacent grid again on the basis of the first adjacent grid, and forming a candidate grid set by the second adjacent grid; taking the intersecting part of the set gid and the candidate grid set as a candidate grid sequence;
s830, combining the descending ordering result of the set ogid, after descending ordering of the candidate grid sequences, carrying out grid object removal judgment based on the ordered candidate grid sequences, wherein when the removal judgment is carried out, the method comprises the following steps:
removing the selected grid object from the set gid, judging whether the number of undirected graph subgraphs is increased or not, if so, skipping the current object, continuing the removal judgment of the next moved-in object, and if not, removing the current second target object to be optimized from the set gid.
S9, updating the first and second absolute mapping ID sequence lists based on the updated set gid, and further realizing updating of the space distance matrix A and the first record data set geomxy based on the updated absolute mapping ID sequence lists;
specifically, updating the first and second absolute mapping ID sequence lists removes the grids that have been allocated from the corresponding sets. Specifically, the spatial distance matrix a is updated, that is, the columns corresponding to the set gid are removed from the spatial distance matrix a based on the updated set gid. Specifically, updating the first record dataset geomxy removes the row corresponding to the pid from the geomxy dataset.
And S10, circularly executing the steps S5-S9 based on the updated result until the first absolute mapping ID serial number list apid is empty, and outputting a resource allocation result.
It should be noted that the space resource optimal allocation algorithm disclosed in the present invention can support not only a polygon target, but also a point or a discrete polygon (the difference is that when there is no adjacency matrix, no adjacency judgment is made).
The space resource optimal allocation method based on weak space constraint realizes calculation and update of the dynamic shortest distance of a space target, utilizes the dynamic distance (for example, the target to be optimized is an adjacent polygon, a connection matrix can be increased to serve as constraint) as weak space limitation (the maximum service distance of the constraint target can be limited in application due to distance limitation), performs resource optimal allocation according to attribute limitation, can maintain the position proximity relation of the target to be optimized on the space to the maximum extent, has the characteristic of high response speed, and only needs about 1 minute for about 5000 targets to be optimized and about 130 constraint targets to be optimized on a single-core cpu after data preparation is completed.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (9)
1. A space resource optimal allocation method based on weak space constraint is characterized by comprising the following steps:
s1, acquiring a constraint target set comprising a plurality of constraint targets and grid polygon data corresponding to each target to be optimized;
s2, calculating the space distance between the constraint target and the mesh polygon, and constructing a space distance matrix A; the attribute values of each target to be optimized are sequentially stored in a first list attr according to the unique grid serial number ID, and the attribute values of each constraint target are stored in a second list attrx according to the unique point serial number ID;
s3, recording the position coordinate point of each constraint target to a first recording data set geomxy; determining a complete mesh polygon map sheet based on all mesh polygon data, and recording a lower left corner coordinate point of the mesh polygon map sheet into a second recording data set ldxy;
s4, acquiring a point unique serial number ID of each constraint target, establishing a first serial number set, and converting the first serial number set into a first absolute mapping ID serial number list apid by adopting an absolute mapping method; acquiring a grid unique serial number ID of each target to be optimized, establishing a second serial number set, and converting the second serial number set into a second absolute mapping ID serial number list agid by adopting an absolute mapping method;
s5, based on the position coordinate points of each constraint target recorded in the first record data set geomxy, taking the constraint target closest to the coordinate point at the lower left corner of the grid polygon map as an initial constraint target, and recording a set formed by the initial constraint targets as pid;
s6, taking the spatial distance matrix A as an object, executing a minimum position matrix calculation method, obtaining a plurality of first to-be-optimized selection targets after matrix screening operation is carried out, and recording a set formed by the first to-be-optimized selection targets as gid;
s7, executing 'attrx [ apid [ pid ] ]', and acquiring an attribute value T corresponding to the initial constraint target from a second list attrx; executing 'attr [ agid [ gid ] ]', and acquiring an attribute value O corresponding to a first target to be optimized from a first list attr;
s8, updating the data objects included in the first to-be-optimized selection target set gid based on the size relationship between the attribute value O and the attribute value T;
s9, updating the first and second absolute mapping ID sequence lists based on the updated set gid, and further executing the updating of the spatial distance matrix A and the first record data set geomxy through the updated absolute mapping ID sequence lists;
and S10, circularly executing the steps S5-S9 based on the updated result until the first absolute mapping ID serial number list apid is empty, and outputting a resource allocation result.
2. The method for optimal allocation of spatial resources based on weak spatial constraints as claimed in claim 1, wherein in step S5, when determining the initial constraint target, the constraint target corresponding to the first set of ordered coordinate points can be further used as the initial constraint target by double-sorting the position coordinate points of each constraint target by "[ x, y ] or [ y, x ].
3. The method for optimal allocation of spatial resources based on weak spatial constraints as claimed in claim 1, wherein in step S6, when performing the object to be optimized screening, the object screening can be further achieved by performing a matrix selection operation by setting a maximum service distance of a starting constraint object.
4. The method according to claim 1, wherein in step S8, a bias parameter percentage is set, and when O < (1-percentage) > T, an adding operation is performed on the target selection set to be optimized, which is determined based on the set gid, specifically:
s81, taking the target to be optimized which is not recorded in the set gid as a second target to be optimized, and recording a set formed by the second target to be optimized as a set acid;
s82, calculating the distance between the constraint target and the grid corresponding to the second target to be optimized according to the constraint target and the second target to be optimized data recorded in the set ogid and the set pid, and the spatial distance matrix A;
s83, performing ascending sorting on the set ogid based on the obtained multiple distance values, and judging whether a second target to be optimized and selected in the sorted set ogid is moved into the set gid or not;
s84, traversing the candidate set until the stopping condition is met or the set ogid is empty, and executing the step S9; the stopping condition includes T × (1+ percent) > = O > = T × (1-percent); the candidate set is a set ogid.
5. The method for optimal allocation of spatial resources based on weak spatial constraints as claimed in claim 4, wherein in step S83, after moving the second selection object to be optimized into the set gid, the sum O of the attributes of the objects in the set gid is used as the basis1Judging whether to carry out the moving-in operation of the object according to the size relation between (1-percent) T and (1+ percent) T; wherein:
if there is a sum of attributes O1If the value is larger than (1+ percent) T, skipping the current object and continuing the moving-in judgment of the next moving-in object; if there is a sum of attributes O1Is less than (1-percent) T, moving the current second target object to be optimized into the set gid, and continuing the moving judgment of the next object to be moved;
until all objects in the set ogid have been traversed, execution continues with step S9.
6. The method for optimal allocation of spatial resources based on weak spatial constraints as claimed in claim 4, wherein when the adjacency matrix B is obtained by computing a mesh polygon based on adjacency relations, step S81 is replaced with a mesh object based on records in the set gid, an adjacent mesh corresponding to each mesh object is determined according to the adjacency matrix B, a third selection target to be optimized is determined based on the adjacent mesh, and a set formed by the third selection target to be optimized is recorded as a set ogid;
step S82-step S84 are executed.
7. The method according to claim 1, wherein in step S8, a bias parameter percentage is set, and when T × (1+ percentage) > = O > = T × (1-percentage), the target selection set to be optimized determined based on the set gid is stored, specifically:
the data objects in the set gid are recorded into the dictionary result.
8. The method for optimal allocation of spatial resources based on weak spatial constraints as claimed in claim 5, wherein in step S8, when O > (1+ percentage) × T, the aggregate object addition operation performed in steps S81-S84 is used to remove the target selection set to be optimized determined based on the aggregate gid, but when the aggregate ogid is sorted based on the obtained multiple distance values, the object reorganization is performed in a descending order;
and when judging whether the second target to be optimized and selected included in the sorted set ogid is considered to be moved out of the set gid or not, when the sum of the attributes O1If it is greater than (1+ percent) T, removing the current second target object to be optimized from the set gid(ii) a If the sum of the attributes O1And if the value is less than (1-percent) T, skipping the current object and continuing to judge the removal of the next moved-in object.
9. The method according to claim 4, wherein in step S8, when O > (1+ percentage) × T and the adjacency matrix B is obtained by computing a mesh polygon based on the adjacency relationship, the removing operation performed on the target selection set to be optimized determined based on the set gid specifically includes:
s810, establishing an undirected graph according to the set gid and the adjacent matrix B;
s820, determining a first adjacent grid corresponding to each grid object in the set gid through the adjacency matrix B, determining a second adjacent grid adjacent to the first adjacent grid again on the basis of the first adjacent grid, and forming a candidate grid set by the second adjacent grid; taking the intersecting part of the set gid and the candidate grid set as a candidate grid sequence;
and S830, combining the descending ordering result of the set ogid, after descending ordering of the candidate grid sequence, carrying out grid object removal judgment based on the ordered candidate grid sequence, wherein when the removal judgment is carried out, the method comprises the step of judging whether the number of undirected graph subgraphs is increased or not after the corresponding grid object is removed from the set gid, if so, skipping the current object, continuing the removal judgment of the next moved-in object, and if not, removing the current second target object to be optimized from the set gid.
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| CN105354782A (en) * | 2015-11-06 | 2016-02-24 | 东南大学 | Adaptation method for intensive layout of park green land based on space correlation quantification model |
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