CN117787662B - Space demand balance partitioning method, electronic equipment and storage medium - Google Patents
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Abstract
The invention provides a space demand balance partitioning method, which comprises the following steps: collecting information of each demand point and supply point in the area, dividing the space into a plurality of unit grids according to the set resolution when the number of the demand points is large, counting the demand values of all the demand points in each unit grid as the demand values of the grids, and setting two grids closest to each other as adjacent grids to construct an initial adjacent network; when the number of the demand points is small, each demand point in the space is used as a network node, and a Dirony triangulation algorithm is adopted to construct an initial adjacent network; the region is mutated to obtain a region dividing result; and calculating an area requirement balance index and an area division aggregation index of the area division result, calculating an area division integral index according to the two indexes, and iterating until the integral index is larger than a set index minimum value to obtain a final area division result.
Description
Technical Field
The invention belongs to the field of space partitioning, and particularly relates to a space demand balanced partitioning method, electronic equipment and a storage medium.
Background
In real life, demand points such as freight demands, security demands, fire extinguishing demands, etc. are often encountered to be scattered at various locations in space, but several fixed supply points in space such as freight centers, equipment repair shops, fire stations, etc. are required to meet these scattered demands. How to better distribute the corresponding relation between the demand points and the supply points, so that the supply and the demand can be well matched, the total amount supplied by each supply point is balanced, and the demand points can be timely satisfied by the supply points, thus being an urgent and significant problem to be solved.
Space partitioning is one of the effective means for solving the above problems, and by partitioning the demand points to the supply points, the correspondence between the demand points and the supply points is planned, and the problem of balanced planning of the demand is solved. However, in the prior art, space is partitioned mainly by hierarchical division of the space through clustering or calculation indexes, and the defects of strong subjectivity and difficulty in quantification exist. Therefore, there is a need for a balanced partitioning method that meets space requirements in real time.
Disclosure of Invention
The invention provides a space demand balanced partitioning method, which solves the problems of strong subjectivity and difficult quantization of the existing partitioning method.
In order to solve the technical problems, the invention provides a space demand balance partitioning method, which comprises the following steps:
Step S1: collecting information of each demand point and each supply point in the area, dividing the space into discrete spaces if the number of the demand points is greater than a set demand point number threshold value, and executing step S2; otherwise, dividing into continuous spaces, and executing the step S3;
Step S2: dividing the discrete space into a plurality of unit grids according to the set resolution, counting the demand values of all demand points in each unit grid, taking the demand values as the demand values of grids, setting two grids closest to each other as adjacent grids to construct an initial adjacent network, and executing the step S4;
Step S3: taking each demand point in the continuous space as a network node, and constructing an initial adjacent network by adopting a Dirony triangulation algorithm;
Step S4: for the discrete space, obtaining a region dividing result after the region is mutated by acquiring the neighbors of the demand points; for the continuous space, obtaining a region dividing result by obtaining the association points or the association edges of the demand points to mutate the region;
Step S5: calculating the regional demand balance and regional division aggregation evaluation indexes of the regional division result, calculating to obtain a regional division integral index according to the two indexes, comparing the integral index with a set index minimum value, and executing the step S4 when the integral index is smaller than the set index minimum value until the integral index is larger than the set index minimum value, so as to obtain the final regional division result.
Preferably, the constructing the initial adjacent network by using the triangulation algorithm in the step S3 includes the following steps:
Step S31: constructing an initial super triangle, and putting the initial super triangle into a triangle list, wherein the initial super triangle comprises all demand points;
step S32: sequentially inserting the required points in the point set, finding out triangles of the circumscribed circle containing the inserted points, marking the triangles as illegal triangles, and adding the illegal triangles into a to-be-deleted list;
step S33: forming an edge polygon according to the sides of all illegal triangles;
Step S34: deleting illegal triangles in the list to be deleted;
Step S35: constructing a new triangle according to the edge on the edge polygon and the current point, and adding the new triangle into a triangle list;
Step S36: triangles that have common vertices with the original supertriangle are deleted from the triangle list.
Preferably, the method for performing mutation on the region by acquiring the neighbors of the demand point in the discrete space in step S4 includes: calculating the number of ordinal numbers of the areas where the neighbors of each demand point are located, and adding the demand point into a list to be mutated when the number of ordinal numbers is larger than the set number of ordinal numbers; and randomly acquiring a to-be-mutated demand point, and randomly changing the region ordinal number corresponding to the point into any neighbor ordinal number different from the original ordinal number.
Preferably, the method for obtaining the region division result after the mutation of the region by obtaining the association points or the association edges of the demand points in the continuous space in the step S4 includes: if the demand point in the area B is adjacent to the demand point in the area A, adding the point into a list to be mutated; if the demand point in the area B and the two demand points in the area A form a Dirony triangle, adding the demand point into a list to be mutated; and randomly acquiring the demand points in the list to be mutated, and changing the demand points into the points in the area A.
Preferably, the expression of the area demand balance index in step S5 is:
；
In the method, in the process of the invention, Is the number of feed points; /(I)For feed points/>Actually corresponds to the total demand of the demand points; /(I)For feed points/>Capability that can be provided;
The expression of the region division aggregation index is as follows:
；
In the method, in the process of the invention, Is the number of demand points; /(I)、/>For the requirement point/>Is the abscissa of (2); /(I)、/>For the requirement point/>An abscissa corresponding to the supply point; /(I)Is the weight of the aggregate index.
Preferably, in step S5, the overall index of region division is obtained by weighting two indexes:
；
In the method, in the process of the invention, The weight of the regional demand balance index.
The present invention also provides an electronic device including: a memory, a processor, and a computer program stored in the memory and configured to be executed by the processor to implement one of the space requirement balanced partitioning methods described above.
The present invention additionally provides a computer readable storage medium having a computer program stored therein, the computer program being executable by a processor to implement a space requirement balanced partitioning method as described above.
The invention has the advantages that at least comprises:
1. Adopting a concept of a cellular automaton and a Dirony triangulation algorithm to construct an adjacent relation between demand points in a discrete space and a continuous space, so that region division is more regular, and the problem of region division when demand and total supply amount are not matched or demand is not synchronous can be solved;
2. The region demand balance and region division aggregation of the division result are considered, so that the problem of multi-objective planning with optimal demand balance and distance can be solved;
3. The corresponding relation between the demand points and the supply points is planned through a heuristic cell growth rule, so that the balance planning problem of the demand is solved, the supply points can meet the demand of the demand points in time, and the area distribution result is more reasonable.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a network structure and initial partition construction for different spaces in an embodiment of the present invention;
FIG. 3 shows two growth rules in continuous space according to an embodiment of the present invention;
FIG. 4 is a graph showing the result of dividing a region by 300 demand points randomly generated in an embodiment of the present invention;
FIG. 5 is a diagram illustrating a change in the zone requirement balance index according to an embodiment of the present invention;
fig. 6 is a schematic diagram of change of the regional division aggregation level according to the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is evident that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by a person skilled in the art without any inventive effort, are intended to be within the scope of the present invention, based on the embodiments of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a space requirement balanced partitioning method, which includes the following steps:
Step S1: collecting information of each demand point and each supply point in the area, dividing the space into discrete spaces if the number of the demand points is greater than a set threshold value of the number of the demand points, and executing step S2; otherwise, dividing into continuous spaces, and executing step S3.
When the number of the required points in the space is large, the calculated amount of the Dirony triangulation algorithm is large, so that a discrete space method is selected.
Step S2: dividing the discrete space into N multiplied grids according to the set resolution, counting the demand values of all demand points in each unit grid, taking the demand values as the demand values of the grids, setting two grids closest to each other as adjacent grids to construct an initial adjacent network, and executing the step S4.
Step S3: and constructing an initial adjacent network by taking each demand point in the continuous space as a network node and adopting a Dirony triangulation algorithm.
Specifically, the method for constructing triangulation includes a dironi triangulation algorithm, a Bowyer-Watson algorithm, a region-limited dironi triangulation algorithm and the like, and the dironi triangulation algorithm adopted by the embodiment of the invention has the following advantages: the formed triangles are not overlapped with each other, the formed triangles can cover the whole plane, each point is not positioned in the circumcircle of the triangle which does not contain the point, the minimum angle in all the generated triangles is the largest, and the uniformity of the side lengths of all the triangles is the best.
The triangulation algorithm can ensure that the demand points are automatically adjacent when being close, and is better used for dividing subsequent areas, and comprises the following steps:
Step S31: an initial super triangle is constructed and put into a triangle list, the initial super triangle including all the demand points.
Step S32: and sequentially inserting the required points in the point set, finding out triangles of the circumscribed circle, which contain the inserted points, marking the triangles as illegal triangles, and adding the illegal triangles into the list to be deleted.
Step S33: an edge polygon is formed from the edges of all illegal triangles.
Step S34: and deleting illegal triangles in the list to be deleted.
Step S35: a new triangle is constructed from the edges on the edge polygon and the current point and added to the triangle list.
Step S36: triangles that have common vertices with the original supertriangle are deleted from the triangle list.
FIG. 2 is a diagram showing the results of generating a network structure and constructing an initial partition in different spaces according to an embodiment of the present invention.
Step S4: for the discrete space, obtaining a region dividing result after the region is mutated by acquiring the neighbors of the demand points; and for the continuous space, obtaining a region dividing result by obtaining the association points or the association edges of the demand points and carrying out mutation on the region.
For discrete space, the concept of cellular automaton is adopted, and region division is optimized by simulating the growth of regions. The concrete operation is to expand or contract the boundary of the area by adopting a heuristic search method on the boundary of the area so as to balance the requirements of different areas and consider the aggregation of the distribution of the required points.
Specifically, the number of ordinal numbers of the areas where the neighbors of each demand point are located is calculated, and when the number of ordinal numbers is larger than the set number of ordinal numbers, the demand point is added into a list to be mutated; and randomly acquiring a to-be-mutated demand point, and randomly changing the region ordinal number corresponding to the point into any neighbor ordinal number different from the original ordinal number.
As shown in fig. 3, there are two growth modes that can be varied in the continuous space.
1) And (3) dot growth: if a point in region B is adjacent to region a, the point can evolve into a point in region a.
2) Edge growth: if the point in the area B and two points in the area A form a Dirony triangle, the point can only evolve into the point in the area A, and the evolution of the area can be more balanced by using the method, so that the tendency that a single point continuously extends outwards can not occur.
And when each region grows, the algorithm acquires all the demand points which can generate variation, randomly selects one demand point and changes the partition of the demand point according to the rule.
Step S5: calculating the regional demand balance and regional division aggregation evaluation indexes of the regional division result, calculating to obtain a regional division integral index according to the two indexes, comparing the integral index with a set index minimum value, and executing the step S4 when the integral index is smaller than the set index minimum value until the integral index is larger than the set index minimum value, so as to obtain the final regional division result.
Specifically, the evaluation index of the area division is designed to consider the combination of the area demand balance and the area division aggregation. Wherein, regional demand balance index is:
；
In the method, in the process of the invention, Is the number of feed points; /(I)For feed points/>Actually corresponds to the total demand of the demand points; /(I)For feed points/>Capability may be provided.
The expression of the regional division aggregation evaluation index is:
；
In the method, in the process of the invention, Is the number of demand points; /(I)、/>For the requirement point/>Is the abscissa of (2); /(I)、/>For the requirement point/>An abscissa corresponding to the supply point; /(I)Is the weight of the aggregate index.
The regional division overall index can be obtained by weighting two indexes:
；
In the method, in the process of the invention, The weight of the regional demand balance index can be adjusted according to the designed balance requirement and aggregation requirement.
The regional division overall index can also be obtained by using a method of solving the pareto solution set through double-target planning.
After the evolution algorithm stabilizes the division of the region, a decision maker can manually adjust the division result of the region after evolution. When clicking a cell or a demand point, the cell or demand point will become a region corresponding to a random neighbor, and then the algorithm will further optimize the result according to the above rule with the initial value.
Using 300 randomly generated demand points and random demands, 5 supply point information is shown in table 1:
Table 1 randomly generated supply point information
The region division result obtained by the method is shown in fig. 4, and the change of the region demand balance index and the region division aggregation index in the iterative process is shown in fig. 5 and 6.
The present invention also provides an electronic device including: a memory, a processor, and a computer program stored in the memory and configured to be executed by the processor to implement one of the space requirement balanced partitioning methods described above.
The present invention additionally provides a computer readable storage medium having a computer program stored therein, the computer program being executable by a processor to implement a space requirement balanced partitioning method as described above.
The foregoing embodiments may be combined in any way, and all possible combinations of the features of the foregoing embodiments are not described for brevity, but only the preferred embodiments of the invention are described in detail, which should not be construed as limiting the scope of the invention. The scope of the present specification should be considered as long as there is no contradiction between the combinations of these technical features.
It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (6)
1. A space demand balancing partitioning method, comprising the steps of:
Step S1: collecting information of each demand point and supply points in an area, wherein the supply points are freight centers or equipment repair factories or fire stations, and if the number of the demand points is greater than a set demand point number threshold value, dividing the space into discrete spaces, and executing step S2; otherwise, dividing into continuous spaces, and executing the step S3;
Step S2: dividing the discrete space into a plurality of unit grids according to the set resolution, counting the demand values of all demand points in each unit grid, taking the demand values as the demand values of grids, setting two grids closest to each other as adjacent grids to construct an initial adjacent network, and executing the step S4;
Step S3: taking each demand point in the continuous space as a network node, and constructing an initial adjacent network by adopting a Dirony triangulation algorithm;
step S4: for the discrete space, the region is mutated by acquiring the neighbors of the demand points to obtain a region dividing result:
Calculating the number of ordinal numbers of the areas where the neighbors of each demand point are located, and adding the demand point into a list to be mutated when the number of ordinal numbers is larger than the set number of ordinal numbers; randomly acquiring a to-be-mutated demand point, and randomly changing a region ordinal number corresponding to the to-be-mutated demand point into any neighbor ordinal number different from the original ordinal number;
For the continuous space, the region dividing result is obtained by obtaining the association points or association edges of the demand points to mutate the region:
if the demand point in the area B is adjacent to the demand point in the area A, adding the demand point in the area B into a list to be mutated; if the demand point in the area B and the two demand points in the area A form a Dirony triangle, adding the demand point in the area B into a list to be mutated; randomly acquiring a demand point in a list to be mutated, and changing the demand point into a point in an area A;
Step S5: and (3) calculating the region demand balance index and the region division aggregation index of the region division result, calculating to obtain a region division integral index according to the two indexes, comparing the integral index with a set index minimum value, and executing the step (S4) when the integral index is smaller than the set index minimum value until the integral index is larger than the set index minimum value, so as to obtain a final region division result.
2. A space requirement balanced partitioning method according to claim 1, wherein: the constructing the initial adjacent network by using the dironi triangulation algorithm in the step S3 includes the following steps:
Step S31: constructing an initial super triangle, and putting the initial super triangle into a triangle list, wherein the initial super triangle comprises all demand points;
step S32: sequentially inserting the required points in the point set, finding out triangles of the circumscribed circle containing the inserted points, marking the triangles as illegal triangles, and adding the illegal triangles into a to-be-deleted list;
step S33: forming an edge polygon according to the sides of all illegal triangles;
Step S34: deleting illegal triangles in the list to be deleted;
Step S35: constructing a new triangle according to the edge on the edge polygon and the current point, and adding the new triangle into a triangle list;
Step S36: triangles that have common vertices with the original supertriangle are deleted from the triangle list.
3. A space requirement balanced partitioning method according to claim 1, wherein: the expression of the area requirement balance index in step S5 is:
Wherein n is the number of supply points; s i is the total demand of the actual corresponding demand point of the supply point i; s i is the supply capacity of the supply point i;
the expression of the regional division aggregation evaluation index is as follows:
wherein m is the number of demand points; x i、yi is the abscissa of the demand point i; x Gi、yGi is the abscissa of the supply point corresponding to the demand point i; e is the weight of the aggregate index.
4. A space requirement balanced partitioning method according to claim 1, wherein: in step S5, the two indexes are weighted to obtain an overall index of regional division:
θ＝σ×θ1+(1-σ)×θ2；
Where σ is the weight of the regional demand balance index.
5. An electronic device, comprising: memory, processor and computer program characterized by: the computer program is stored in the memory and configured to be executed by the processor to implement a space requirement balanced partitioning method as claimed in any one of claims 1 to 4.
6. A computer-readable storage medium, characterized by: the computer readable storage medium has stored therein a computer program that is executed by a processor to implement a space requirement balanced partitioning method as set forth in any one of claims 1 to 4.
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| 等值线绘制中的多重网格剖分快速搜索算法;王鹏;周茂林;姚兴苗;张帆;邹文;;计算机应用研究;20110615(06);全文 * |
| 面聚类网格简化新算法;严京旗, 施鹏飞;电子学报;20020125(01);全文 * |
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