CN112800353A - Method for limiting shortest path of search area by dynamic ellipse based on virtual boundary - Google Patents
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Abstract
The invention provides a method for limiting the shortest path of a search area by a dynamic ellipse based on a virtual boundary, which comprises the following steps: 1) a new statistical parameter calculation mode is used, and different statistical parameters can be obtained according to different Euclidean distances of the starting node and the terminating node; 2) the dynamic restriction search area path planning method for constructing the virtual boundary by selecting a lower confidence level on the basis of the step 1) can effectively reduce the search scale. The invention constructs a smaller limited search area based on a lower confidence level, effectively reduces the search scale and the search time, and simultaneously ensures the shortest search path.
Description
Technical Field
The invention relates to the application fields of logistics distribution, transportation, intelligent optimization, network analysis and the like, in particular to a method for searching the shortest path of an area based on dynamic oval limitation of a virtual boundary.
Background
With the rapid development and wide application of technologies such as mobile Geographic Information System (GIS), Global Positioning System (GPS), wireless communication, and the like, more and more people will choose to travel by relying on a path provided by a navigation device. However, as the holding capacity of automobiles is continuously increased, the passing capacity of urban roads is insufficient to hinder the passing efficiency of vehicles. Therefore, how to select the optimal driving path in a complex urban road network becomes a hot problem for many scholars to take care of and research.
In a network, this corresponds to a shortest path problem. In a directed network of arbitrary length, The Shortest Path (TSP) problem is to find the shortest directed path from one source node to the other, and the TSP problem is one of the most fundamental problems in network optimization. Algorithms for solving the TSP problem are many, and commonly used shortest path algorithms include Dijkstra algorithm, a-x algorithm, ant colony algorithm, genetic algorithm, simulated annealing algorithm, and the like, wherein the Dijkstra algorithm is the most famous algorithm for solving the problem on the edge-weighted non-negative graph. The main idea of Dijkstra's algorithm is to diffuse around the starting node O until it surrounds the target node D. Although the Dijkstra algorithm can effectively search the shortest path between the OD pairs, the algorithm only considers the topological characteristics of the network in the design process and ignores the spatial distribution characteristics of the network, so that the path search has no directionality, and therefore, a large number of nodes irrelevant to the shortest path are introduced into the calculation, and the efficiency of the algorithm is influenced. Therefore, the application of the traditional Dijkstra algorithm in navigation software is hindered by the high resource overhead and the low search efficiency.
Since the time complexity of Dijkstra's algorithm is proportional to the square of the number of nodes, various optimization algorithms are developed around reducing the number of nodes. Assuming that the number of nodes is proportional to the area of the search area, reducing the area of the search area becomes one of the main methods for solving the problem. In the traffic network, after the starting point and the end point are determined, the trend of the path is reflected. Nordbeck provides a shortest path algorithm based on ellipse restriction according to the network characteristics, and the algorithm restricts a search node set within a certain search range, thereby greatly reducing the search scale of the shortest path algorithm. Lu et al propose a shortest path algorithm with a minimum rectangle containing an ellipse as a constraint area, and experimental results show that although the algorithm increases the search area compared with the shortest path algorithm based on ellipse constraint, the algorithm does not need to perform a large number of multiplication and evolution operations, and the algorithm is effective in searchingThe rate is improved. Fu et al propose that the line connecting OD pairs is taken as a rectangular diagonal line, and then a threshold value T is set1And expanding the original rectangle to form a larger rectangle R, and finally setting the two sides of the diagonal line of the rectangle R as a search area. The experimental result shows that compared with the Dijkstra algorithm, the search scale of the algorithm is obviously reduced, and the execution speed of the algorithm is effectively improved. Wang et al propose a parallelogram-constrained shortest path algorithm, which takes the smallest parallelogram containing an ellipse as a constrained search area, and experimental results show that the search time required by the algorithm is less than that required by unconstrained and elliptical constraint under various conditions. Bu and the like propose an improved algorithm for dynamically changing the search direction in a dynamic search region and limiting the search region according to the spatial characteristics of a road network, and compared with a Dijkstra algorithm, the algorithm reduces the time and space complexity of the algorithm and improves the efficiency of the algorithm. Wang et al propose an optimal path algorithm for restricting search area based on common characteristics of typical urban road networks, the algorithm searches shortest paths in two types of ellipses with different sizes aiming at different Euclidean distances of OD, and experimental results show that the time complexity of the algorithm can be reduced by 33% -47% compared with the ellipse restriction search area algorithm when the distance of OD to Euclidean is larger. Zhou et al propose a shortest path algorithm based on corner direction rectangles, which reduces the search area by cutting the corresponding corner point area based on the direction rectangles, and experimental results show that the algorithm can significantly improve the shortest path search efficiency without affecting the reliability.
The above-mentioned scholars propose various algorithms for limiting shortest path of search area, which fully consider the feature attributes of road network spatial distribution, including the position relationship and distance relationship between the start node and the end node. The algorithm improves the efficiency of searching the shortest path by reducing the search area and reduces the data redundancy. However, the search area limited algorithm proposed by the above scholars is improved on the basis of the ellipse search area limited algorithm, so that a 95% confidence level is adopted in the process of calculating statistical parameters to ensure that most of the obtained path solutions are optimal, but the higher confidence level has the problem of larger search area.
Disclosure of Invention
The method for limiting the shortest path of the search area by the dynamic ellipse based on the virtual boundary solves the problems that the search time is increased and the memory is calculated due to the fact that the search area is too large under the confidence level of 95% adopted in the traditional method for limiting the shortest path of the search area, reduces the space complexity of road network storage and the time complexity of algorithm search, improves the algorithm execution efficiency, and finally achieves the purpose of improving the real-time performance and the accuracy of the planning method.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for limiting shortest path of search area based on dynamic ellipse of virtual boundary includes following steps:
1) providing vector data of a road network, defining an edge position b _ Ellipse and an Ellipse boundary array i _ Boundarray;
a certain representative number of nodes are systematically extracted from the traffic network node set to construct two node sets GOAnd GDThen its Cartesian product GOD=GO×GD={(O,D)|(O∈GO)∧(D∈GD)}，GODEach element in (1) can be regarded as an initial node and a final node of the shortest path to be solved;
let F be the actual distance of the starting and ending pointODThe Euclidean distance is EODThen, the ratio coefficient R = F can be obtainedOD/EOD(ii) a For the extracted samples, a set of ratio coefficients R is obtainedOD；
To RODThe element(s) in (b) is subjected to statistical analysis fitting under a certain confidence level to obtain a certain fitting function f (x), so that RODThe total number of (a) is elements that meet a certain confidence level, the value of which is not greater than f (x);
2) giving a starting node and a terminating node, and calculating the Euclidean distance between the two nodes;
substituting the Euclidean distance alpha between the two points into a fitting function to obtain a ratio coefficient R;
establishing an ellipse restriction search area by taking the initial node and the termination node as focuses and taking R alpha as a major axis length;
traversing all edges, if the starting point and the end point of the edge are both within the Ellipse, i _ Ellipse = 1; if there is one and only one edge starting or ending in the Ellipse, i _ Ellipse =2, and the edge is placed in i _ Boundarray; if the start and end points of the edge are outside the Ellipse, i _ Ellipse = 3;
arranging elements in the i _ boundarylarray in a counterclockwise order;
the nodes of the edges far away from the center of the ellipse are connected by straight lines in sequence,
the Euclidean distance between two points, the edge is set to be bidirectional,
=3；
finding the shortest path S' within the elliptical region (including the elliptical boundary);
if all the edge positions b _ Ellipse =1 of the shortest path, S = S', outputting a path S, and finishing the algorithm; otherwise, the virtual boundary is constructed to be used as a virtual solutionVS= (vs i， … ， vs j ) Replacing solutions outside the elliptical area to obtain a virtually complete solution within the elliptical areaS’= (s 1， s 2， … ， vs i ， … ， vs j ， … ， s n )；
Respectively searching for an optimal complete solution OS =(s) outside the ellipse for each continuous virtual solution according to a starting point and an end pointi, … , sj)；
Replacing the virtual solution in S' with the solution in OS can obtain the complete solution S = (S) of the optimal path1, s2, … , si, … , sj , … , sn) And ending the algorithm;
calculating statistical parameter functions under different confidence levels;
3) randomly selecting a certain number of sample elements in the road network, and calculating the probability of obtaining the optimal solution of the path under different confidence levels by all the sample elements.
And 3) selecting a statistical parameter function with the maximum optimal solution probability under a lower confidence level as a final statistical parameter function of the road network.
The invention has the beneficial effects that: the dynamic ellipse based on the virtual boundary limits the shortest path algorithm of the search area, which is provided by the invention, can obtain different statistical parameters according to OD to different Euclidean distances, and ensure that a road network obtains an optimal path under the condition of reducing the confidence level by constructing the virtual boundary. The main contribution of the algorithm is that a new statistical parameter calculation mode is provided based on a one-way road network model, and the accuracy of the algorithm is guaranteed by constructing a virtual boundary.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Specifically, the method for limiting the shortest path of the search area by the dynamic ellipse based on the virtual boundary comprises the following steps:
1) providing vector data of a road network, and determining a starting node and a terminating node, wherein the specific process comprises the following steps:
1.1) systematically extracting 400 nodes in the road network, and constructing a set GO，GD. Then G isODThe total number of 40000 sample elements.
1.2) to GODEach element in the solution is respectively solved for FOD，EODAnd ROD。
1.3) sorting 40000 sample elements from small to large according to the Euclidean distance, and forming a group by every 100 sample elements in sequence. And sorting each group according to the r value from large to small, selecting the 5 th number in each group to form a new set SE, and finally performing curve fitting on sample elements in the new set.
1.4) Curve fitting of sample elements in SE to obtain a Curve formula R at 95% confidence level95%：
R95% = -2.065*x(0.06163)+5.406。
2) Giving a starting node and a terminating node, and calculating the Euclidean distance between the two nodes, wherein the specific process is as follows:
2.1) substituting the Euclidean distance alpha between two points into the fitting function R95%To obtain a ratio coefficient R.
2.2) establishing an ellipse limit search area by taking the starting node and the ending node as focuses and taking R alpha as a long axis length.
2.3) traverse all edges, if the start and end points of the edge are within the Ellipse, i _ Ellipse = 1; if there is one and only one edge starting or ending in the Ellipse, i _ Ellipse =2, and the edge is placed in i _ Boundarray; if the start and end points of the edge are outside the Ellipse, i _ Ellipse = 3.
2.4) arrange the elements in the i _ Boundarray in a counterclockwise order.
2.5) connecting nodes of edges far away from the center of the ellipse by straight lines in sequence,
the Euclidean distance between two points, the edge is set to be bidirectional,
=3。
2.6) find the shortest path S' within the elliptical area (including the elliptical boundary).
2.7) if all edge positions b _ Ellipse =1 of the shortest path, S = S', the path S is output, and the algorithm ends. Otherwise go to 2.8).
2.8) respectively searching for the optimal complete solution OS =(s) outside the ellipse according to the starting point and the end point for each continuous virtual solutioni, … , sj)。
2.9) solution in OSReplacing the virtual solution in S' can obtain the complete solution S = (S) of the optimal path1, s2, … , si, … , sj , … , sn) And the algorithm ends.
2.10) calculate the statistical parameter function at 90%, 85%, 80%, 75% and 70% confidence levels.
3) Randomly selecting 100 sample elements in a road network, and calculating the optimal path solution of the 100 sample elements under six confidence levels, wherein the specific process is as follows:
and selecting a statistical parameter function with the maximum optimal solution probability under a lower confidence level as a final statistical parameter function of the road network, and selecting the 85% confidence level to be optimal by comprehensively considering the accuracy and the time complexity of the algorithm.
The above examples are only for describing the preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims (2)
1. A method for limiting shortest path of search area by dynamic ellipse based on virtual boundary is characterized by comprising the following steps:
1) providing vector data of a road network, systematically extracting a certain representative number of nodes from a traffic network node set, constructing two node sets, and solving a Cartesian product of the two node sets, wherein each element in the Cartesian product can be regarded as a starting node and a final node of a shortest path to be solved;
let F be the actual distance of the starting and ending pointODThe Euclidean distance is EODThen, the ratio coefficient R = F can be obtainedOD/EOD. For the extracted samples, a set of ratio coefficients R is obtainedOD(ii) a To RODThe element(s) in (b) is subjected to statistical analysis fitting under a certain confidence level to obtain a certain fitting function f (x), so that RODThe total number of (a) is elements that meet a certain confidence level, the value of which is not greater than f (x);
2) giving a starting node and a terminating node, and calculating the Euclidean distance between the two nodes; substituting the Euclidean distance alpha between the two points into a fitting function to obtain a ratio coefficient R; establishing an ellipse restriction search area by taking the initial node and the termination node as focuses and taking R alpha as a major axis length;
when OD (origin-destination) pair cannot obtain a complete solution S of an optimal path in an ellipse search area, a virtual boundary is constructed to be used as a virtual solution VS = (VS)i,…,vsj) Replacing the solution outside the elliptical area, resulting in a virtually complete solution S' = (S) within the elliptical area1,s2,…,vsi,…,vsj,…,sn) (ii) a Then respectively searching for an optimal complete solution OS =(s) outside the ellipse for each continuous virtual solution according to a starting point and an end pointi,…,sj) (ii) a And finally, replacing the virtual solution in the S' with the solution in the OS to obtain a complete solution S = (S) of the optimal path1,s2,…,si,…,sj,…,sn)；
3) Randomly selecting a certain number of sample elements in a road network, and calculating the probability of obtaining the optimal solution of the path under different confidence levels of all the sample elements; and selecting the statistical parameter function with the maximum optimal solution probability under the lower confidence level as the final statistical parameter function of the road network.
2. The method of claim 1, wherein the method comprises the following steps: the statistical parameters obtained in the step 3 are statistical parameter functions obtained by fitting ratio coefficient points under a certain confidence level.
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| WO2007061264A1 (en) * | 2005-11-28 | 2007-05-31 | Yeong-Geun Ryu | Reducing method of shortest path searching area and calculating method of minimal expecting load and method of searching shortest path |
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| CN105929843A (en) * | 2016-04-22 | 2016-09-07 | 天津城建大学 | Robot path planning method based on improved ant colony algorithm |
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