CN111612257B - Shortest path solving method based on space normalization - Google Patents
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Abstract
The invention aims to provide a space-normalization-based shortest path solving method, which comprises the following steps of: the road network is classified into a vector geographic space, and a starting place and a destination are obtained; constructing a first circle comprising a start point and a destination by taking the center of the connection line of the start point and the destination as a round point and taking the length of the connection line of the start point and the destination as a diameter; finding out all paths in a first circle, and carrying out topology construction on the paths; filtering again through the connection line of the starting place and the destination and the topology structure surface to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons; the merged polygons are split into different paths according to the starting place and the destination, and the first initial path is obtained by selecting the path with the shorter path. The invention solves the problem that the traditional A-algorithm valuation function is difficult to select, and solves the problem that the ant colony algorithm, the genetic algorithm, the neural network algorithm and the like can only solve the approximate solution and can not obtain the mathematical optimal solution.
Description
Technical Field
The invention relates to the fields of computer graphics, geographic information science and logic, in particular to a shortest path solving method based on space normalization.
Background
The shortest path problem is always a classical problem in computer science and geographic information science, and traditional similar problems are solved by adopting classical computer algorithms such as ant colony algorithm, A-algorithm, dijkstra algorithm and the like, wherein the Dijkstra algorithm can solve mathematical optimal solution but has low efficiency; other algorithms have high efficiency, but the mathematical optimal solution cannot be calculated, and the solutions of the various algorithms are different in thinking, so that the problems of optimization and accuracy are difficult to consider, and the research direction is divided into two main flow directions: the search efficiency optimization of the Dijkstra algorithm and the precision improvement of other algorithms are improved, namely, no learner can unify the search efficiency optimization and the precision improvement of the other algorithms until now, and the high efficiency of the other algorithms and the mathematic rigorous solution of the Dijkstra algorithm are solved and two are one.
The shortest path problem is solved in a plurality of disciplines such as computer graphics, mathematics, logics, geographic information science and the like for decades, the research and solving directions are different, the efficiency is difficult to consider, the accuracy is difficult to consider, and the efficiency is difficult to consider, so that the research in the field goes into the dead beard and the contradiction cannot be solved so far. The shortest path is necessarily existed as shown by simple mathematical analysis, and the shortest path is characterized in that the distance between any two points on the path is shortest, and the local solution and the whole solution are organically unified, so that natural differentiation is studied to ensure the local direction and the whole direction.
The existence and geometric characteristics of the shortest path strength can know that the problem is finally length comparison, the length comparison is essentially line problem solving, and the line is the boundary of the plane, so that the problem solved by other algorithms can be normalized to the geometric space, the reduction optimization of the sample space can be completed by geometric means, then the Dijkstra algorithm is utilized to solve the optimal solution, and finally, the unification of all the shortest path algorithms in the space field is realized, and the unification of the shortest path searching speed and quasi is achieved.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, in order to achieve the above-mentioned objects, the present invention provides a space-based shortest path solving method for constraining a divergent problem of a solution space when solving a shortest path, comprising the steps of:
s1, attributing a road network to a vector geographic space to obtain a starting place and a destination;
s2, constructing a first circle comprising a starting place and a destination by taking the center of the connecting line of the starting place and the destination as a round point and taking the length of the connecting line of the starting place and the destination as a diameter;
s3, finding out all paths in the first circle, and carrying out topology construction on the paths;
s4, filtering the topological structure surface obtained in the step S3 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons;
s5, dividing the polygon combined in the step S4 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained first initial path.
As an optional improvement technical scheme: the step S3 further includes: as long as the path is in the circle or has a cross with the circle, the topology structure surface is selected.
As an optional improvement technical scheme: and S6, constructing a second circle by taking the length of the first initial path as the diameter and taking the connecting line center of the starting place and the destination as a round point, carrying out topological structure on the paths filtered out in the range of the second circle to obtain a second initial path, comparing the second initial path with the first initial path, and checking the accuracy of the first initial path.
As an optional improvement technical scheme: step S6 further comprises the steps of:
s61, constructing a second circle by taking the length of the first initial path as the diameter and taking the center of the connecting line of the starting place and the destination as a round point;
s62, finding out all paths in the second circle, and carrying out topology surface construction on the paths;
s63, filtering the topological structure surface obtained in the step S62 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons;
s64, dividing the polygon combined in the step S63 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained second initial path;
s65, comparing the second initial path with the first initial path to check the accuracy of the first initial path.
As an optional improvement technical scheme: step E2 further includes: as long as the path is within the circle or intersects with the second circle, the topology construction surface is selected.
In particular, the reason for the circle construction process in the step S2 is analyzed as follows:
in step S2, a first circle with the length of the connection line between the origin and the destination as the diameter is constructed, the problem is expanded from a one-dimensional space with the distance length to a two-dimensional space, the space of a possible solution is constrained by the range concept of the two-dimensional space, and then an initial solution, namely a first initial path, is obtained.
The step S3 has the following implementation functions:
the solution space of the problem is expanded to the field of two-dimensional surfaces through the construction surface, and the purpose of merging polygons is to quickly find out the surface which can contain the starting place and the destination, so as to find out possible problem solutions, and simultaneously, provide theoretical description and initial values for the cycle optimization of the subsequent computer.
The implementation functions of the steps S4 and S5 are as follows:
by utilizing the concept that the two-dimensional surface is a closed line, the starting place, the destination, the surface and the line are combined together by combining polygons, and an initial solution is found by the closed line, so that convenience is brought to the subsequent compression of a solution space and the solution of a true value.
The step S6 has the implementation functions that:
the initial solution obtained by step S5 is an approximate solution, and the true value length is necessarily within the two-point line and the approximate solution. The range circle is built again through the approximate solution, and the geometric analysis can know that the range circle necessarily contains true values, so that the effective, quick and accurate solution of the true solution is constrained again and ensured.
The invention unifies shortest path solving in traditional computer graphics and logics into geographical space category, and limits paths participating in solving to a small range through related technologies such as geometry, space science and the like. The range is linearly related to the target point connection line and is irrelevant to the global sample number, so that the Dijkstra algorithm sample space optimization problem is solved. The length problem is a one-dimensional logic problem by means of the dimension-increasing and dimension-decreasing thinking, and the space analysis technology is a logic judgment technology of a two-dimensional space object, so that the space analysis technology is utilized to convert the whole problem solution into the local problem solution to obtain a final solution, the problem that other algorithms such as biological algorithms and intelligent algorithms only can solve the problem that the local optimal solution is difficult to solve the whole optimal solution is solved, and the method is a new attempt for using the space science thinking for unified shortest path solution in recent years.
The shortest path is a one-dimensional problem in a two-dimensional environment, and thus its solution complexity is not lower than the square of the number of samples. For a one-dimensional problem in a two-dimensional environment, there must be a one-dimensional and two-dimensional association, which is an implicit topological relationship of objects in the two-dimensional environment. The invention builds a range circle, namely a process of expanding a solution space of a distance from one dimension to two dimensions of constraint, so that the two-dimensional problem can be unidimensionally realized by taking the thinking of dimension increase and dimension decrease as guidance and by means of the association between the dimensions of topological relation, and further, the one-dimensional problem solution can be rapidly solved.
The invention solves the problem that the traditional A-algorithm valuation function is difficult to select, and solves the problem that the ant colony algorithm, the genetic algorithm, the neural network algorithm and the like can only solve the approximate solution and can not finish the mathematical optimal solution. Compared with the patent ZL201510790636.5, the invention is the front-end of the patent, changes the global two-dimension in the one-dimensional problem two-dimension process into the local two-dimension process, and has the advantages that a global sample does not need to be subjected to two-dimension topological structure, a large amount of storage space and calculation resources are saved, and technical support is provided for realizing real-time shortest path analysis.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is an illustration of the original route in the embodiment.
FIG. 3 is a schematic diagram of constructing a filter range circle with direct connection in an embodiment.
Fig. 4 is a schematic diagram of all path facets obtained by filtering in the example.
FIG. 5 is a schematic diagram of a polygon connected with a starting point by a connection filtering in an embodiment.
Fig. 6 is a vectorization diagram of the embodiment after merging polygons after finding a face and importing the merged polygons into a space coordinate system.
Fig. 7 is a schematic view of a road area covered by a second round cover in an embodiment.
Fig. 8 is a schematic diagram of an optimal solution of the second circle in the embodiment.
Fig. 9 is a schematic diagram of restricting a search range by a peripheral circle of an ellipse in the embodiment.
Fig. 10 to 12 are schematic views of restricting a search range by an ellipse.
Fig. 13 is a schematic diagram of restricting a search range by a circle.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
Example 1
Referring to fig. 1, the shortest path solving method based on space planning in this embodiment has an operating platform that is a Windows 7 operating system on a PC, and a geographic information system platform that is a 5.3.3 version of beijing hypergraph geographic information platform software, and includes the following steps:
s1, the road network is normalized to a vector geographic space, and an origin and a destination are obtained, as shown in fig. 2.
S2, taking the center of a connecting line of the starting place and the destination as a round point, and taking the length of the connecting line of the starting place and the destination as a diameter to construct a first circle comprising the starting place and the destination; as in fig. 3.
S3, finding out all paths in the first circle, and carrying out topological structure on the paths, as shown in FIG. 4; as long as the path is within the circle or intersects the first circle, the topology construction surface is selected.
S4, filtering the topological structure surface obtained in the step S3 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons, as shown in FIG. 5;
s5, dividing the polygon combined in the step S4 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained first initial path, as shown in FIG. 6. As the polygon is a closed line, two points on any polygon can be connected by two paths, and the short point is the initial value.
The shortest path selection may be performed by using the prior art to obtain the final shortest path.
According to the scheme, a better path can be obtained by means of quick solving, the whole process comprises vectorizing a geographic space, screening out a one-dimensional path by utilizing the characteristic of easiness in construction of a circle and the advantage of a two-dimensional plane of the circle, carrying out topological structure surface and dimension lifting on the one-dimensional path to form a two-dimensional closed path block, and then carrying out superposition and filtering on a connecting line of a one-dimensional starting place and a destination and the two-dimensional closed path block to select the shortest path so as to solve an initial path; the solving process does not depend on the updating and changing of the map, and only the path is needed to be screened out; and the process of screening the path is also convenient, so that the solving efficiency is improved.
Example two
The present embodiment is a preferable mode of the first embodiment; the solution scheme provided in the first embodiment is a necessary technical scheme, and the present embodiment provides a sufficient technical scheme based on the necessary technical scheme as a preference.
S61, in the first embodiment, the length of the first initial path has been solved, and a second circle is constructed with this length as a diameter and the center of the origin and destination connection as a dot, as shown in fig. 7.
S62, finding out all paths in the second circle, and carrying out topological structure on the paths, as shown in FIG. 7; as long as the path is within the circle or intersects with the second circle, the topology construction surface is selected.
S63, filtering the topological structure surface obtained in the step S62 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons;
s64, dividing the polygon combined in the step S63 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained second initial path. Since the polygon is a closed line, two points on any polygon can have two paths connected, and the short point is the initial value, as shown in fig. 8.
S65, comparing the second initial path with the first initial path to check the accuracy of the first initial path.
The result obtained in the first embodiment can be verified by the recalculation of the present embodiment, and the result of the calculation of the first embodiment can be confirmed without any error, so that the present embodiment is a sufficient verification process.
In this embodiment, the calculation is performed by using the length of the first initial path calculated in the first embodiment, and thus the second circle formed may be larger than or equal to the first circle, which is a sufficient verification for the first embodiment.
Meanwhile, a certain superposition path exists between the second circle and the first circle, so that the calculation result of the first circle can be stored and retrieved for use when the second circle is calculated.
In the first and second embodiments, the calculation of the shortest path may be performed by using the prior art to obtain the final shortest path, as shown in fig. 8, where the dotted line in fig. 8 is a straight line path between the start point and the destination, and the thick solid line is the calculated shortest path. The prior art adopted may be the patent number ZL201510790636.5, which is certainly not limited to this set of technical solution, as long as the shortest path acquisition technique can be completed.
Referring to fig. 9 to 13, the search range may be constrained by an ellipse, which includes an elliptical range, or by a peripheral circle of the ellipse, directly from the first initial path length. The invention adopts a circle for constraint, and the main reasons are as follows:
1. the model is simple: the initial path length is only required to be related to the starting destination, the center of the circle is the center of the starting destination connecting line, and the radius is half of the initial path length, so that the target constrained by the distance and the starting point is met;
2. the mathematical solution is convenient: the ellipse not only needs to solve the long and short axes and the focus, but also is complex to solve when the coordinate system is converted, especially when the rotation calculation is performed, and the circle only needs to know the circle center, so that the graph rotation influence is not generated.
3. Searching is accurate: the original simplest graph can be converted without loss at any stage, while for ellipses, a loss of precision must occur when converting between different stages, as shown in fig. 11 and 12. .
The accuracy of the space search is greatly affected, and the possibility of search omission easily occurs, and as shown in fig. 11-12 below, the left line will be omitted when searching for a new platform. The method for establishing the ellipse to find the shortest path can refer to the Chinese patent application with the application number of CN 201910314226.1.
Referring to fig. 13, aob is a diameter, O is the center, and the diameter length is the multidimensional initial path:
AB<CA+CB
CA<AO+CO
CB<BO+CO
AO+CO<DO+CO＝L1
BO+CO<EO+CO＝L1
so CA+CB <2 x L1
From the properties of the circles, ca+cb=ca+af > L1;
that is, the distance from any point on the circle to the starting destination is not more than 2×l1 and not less than L1, i.e. the distance from any point on the circle to the starting destination is [ L1,2×l1), the lower limit of the solution space is L1, that is, the distance outside the circle must exceed the value, which means that the optimal solution must be within the circle. The original solution space is reduced from [ L0, + ] to [ L0,2 x L1] through the initial solution and the circle, the interval [ L0, L1] is the connection line between two points and the initial value, and the path solution in the range only needs to be carried out in the later stage, so that the optimal solution is necessarily included.
The present invention is not described in detail in the present application, and is well known to those skilled in the art.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (3)
1. The shortest path solving method based on space normalization is characterized by comprising the following steps of:
s1, attributing a road network to a vector geographic space to obtain a starting place and a destination;
s2, constructing a first circle comprising a starting place and a destination by taking the center of the connecting line of the starting place and the destination as a round point and taking the length of the connecting line of the starting place and the destination as a diameter;
s3, finding out all paths in the first circle, and carrying out topology construction on the paths;
s4, filtering the topological structure surface obtained in the step S3 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons;
s5, dividing the polygon combined in the step S4 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained first initial path;
s6, constructing a second circle by taking the length of the first initial path as the diameter and taking the center of a connecting line of the starting place and the destination as a round point, carrying out topological structure on the filtered path in the range of the second circle to obtain a second initial path, comparing the second initial path with the first initial path, and checking the accuracy of the first initial path;
step S6 further comprises the steps of:
s61, constructing a second circle by taking the length of the first initial path as the diameter and taking the center of the connecting line of the starting place and the destination as a round point;
s62, finding out all paths in the second circle, and carrying out topology surface construction on the paths;
s63, filtering the topological structure surface obtained in the step S62 through the connection between the starting place and the destination again to obtain a plurality of polygons for connecting the starting place and the destination, and merging the polygons;
s64, dividing the polygon combined in the step S63 into different paths according to the starting place and the destination, and selecting the path with the shorter path as the obtained second initial path;
s65, comparing the second initial path with the first initial path to check the accuracy of the first initial path.
2. The shortest path solving method according to claim 1, characterized in that step S3 further includes: as long as the path is in the circle or has a cross with the circle, the topology structure surface is selected.
3. The shortest path solving method according to claim 1, characterized in that step S62 further includes: as long as the path is within the circle or intersects with the second circle, the topology construction surface is selected.
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