A method for path planning of the first k differential dynamic restricted search areas

Abstract

The present invention provides a method for planning paths of the top-k differential dynamic restricted search areas, comprising the following steps: 1) using a new calculation method for penalty coefficients; 2) setting different calculation methods for statistical parameters based on different penalty coefficients on the basis of step 1); 3) dynamically selecting different search areas according to different OD (Origin-Destination) Euclidean distances in the present invention. Among the top-k path solutions obtained by the present invention, on the premise that the similarity is not higher than the set maximum similarity, the time complexity of the method can be reduced by up to 64%.

Description

Technical Field

[0001] The present invention is designed for application fields such as logistics distribution, transportation, intelligent optimization, network analysis, etc., and particularly relates to a method for planning paths with the first k different dynamic restricted search areas. Background Art

[0002] In recent years, with the rapid popularization and development of technologies such as geographic information systems, global positioning systems, remote sensing, and wireless communication, path planning in urban road networks has become an essential requirement in people's daily lives. It can provide reference routes for people's driving and facilitate their daily travel. However, due to the rapid growth of the number of vehicles in recent years and the unreasonable urban traffic planning, the traffic efficiency of vehicles has been restricted. Therefore, how to plan multiple different paths that meet people's daily travel needs in urban road networks has become a hot issue of concern and research for many domestic and foreign scholars.

[0003] In a network, this corresponds to the problem of the first k shortest paths (top-k shortest path, KSP). In a directed network of any length, the KSP problem is an extension of the single-source shortest path problem, aiming to find the first k optimal paths from the starting node to the ending node. When k = 1, this method is the shortest path method. Although the k optimal paths obtained in the process of solving the KSP problem can effectively make up for the problem that a single shortest path cannot meet the user's needs, currently, the methods for solving the KSP problem generally have the problems of relatively high method complexity and too high similarity of the solutions of the first k optimal paths. By analyzing the KSP problem, it is found that the KSP problem can generally be divided into an acyclic KSP problem and a cyclic KSP problem. The former requires that all obtained paths must be simple paths and cannot contain loops; the latter has no restrictions on the paths. According to different KSP problems, the solving methods are also different. The method for solving the acyclic problem is called the restricted acyclic KSP method, mainly including the deviation path method and the improved Dijkstra method; the method for solving the cyclic problem is called the general KSP method, mainly including the labeling method, the path deletion method, the deviation path method, and the improved intelligent method.

[0004] Although traditional k - shortest path methods can find the first k shortest path solutions based on the start and end points in a given graph, providing multiple candidate paths for users to select according to their needs, the first k shortest paths returned by the methods are often highly similar, that is, there are a large number of overlapping edges among the obtained paths. This phenomenon is particularly obvious in large - scale road networks. Therefore, the method of the first k shortest paths based on diversity has received much attention from many scholars at home and abroad. Akgün et al. proposed that on the premise of generating a large number of candidate paths, by using a discrete model to select subsets, the minimum dissimilarity in the selected subsets can be maximized. Experimental results show that the calculation results of this method can find k paths with greater diversity. Wilton et al. studied the problem of the shortest dissimilarity path in wireless sensor network path planning. By removing the edges on the shortest path that has been calculated from the graph, the next shortest dissimilarity path is generated, and this path will not intersect with the previous shortest paths. Experimental results show that this method can achieve a reliable communication level. Caleb et al. studied the problem of the shortest dissimilarity path in robot path planning. The proposed method removes the edges adjacent to the shortest path that has been calculated from the graph to avoid obstacles. Experimental results show that under tolerable losses, this method can generate a more diverse set of paths faster. Liu et al. proposed a general framework in a bidirectional road network model to efficiently approximate the solution of the first k shortest path queries based on diversity, and designed the lower bound of the shortest path and the lower bound of the dissimilarity path. Experimental results show that the method proposed in the paper can efficiently filter a large number of unnecessary paths, thereby reducing the search space of the method and improving the search efficiency of the method. Zhou Zitao proposed a KSP method based on a penalty factor in a wireless network model. Experimental results show that although the results obtained by this method are not the shortest paths, the similarity of the first k path solutions obtained by this method is much lower than that of the first k shortest path solutions obtained by traditional KSP methods.

[0005] The various methods of the first k path planning based on diversity proposed by the above - mentioned scholars fully consider the diversity among the paths obtained by the methods, and to a certain extent, meet the needs of users for multiple paths. However, the methods still have some limitations, which can be summarized as follows: 1) Most of the data models used in previous or current methods of the first k path planning based on diversity are bidirectional road network models or wireless network models, etc. However, the bidirectional road network model and the wireless network model cannot well

[0006] represent the actual road conditions in the real world; 2) Some methods of the first k path planning based on diversity only consider calculating dissimilar paths under different path similarity metrics, without considering the lengths of the obtained paths; 3) The existing methods of the first k path planning based on diversity do not consider the characteristic attributes of the spatial distribution of the road network, which affects the search efficiency of the methods to a certain extent.

[0007] Therefore, a method for planning paths in a dynamically restricted search area with the top k different paths is provided to solve the existing problems. Summary of the Invention

[0008] A method for planning paths in a dynamically restricted search area with the top k different paths provided by the present invention takes into account the spatial characteristics of the road network, solves the problems that the similarities of the top k paths obtained by the traditional k - shortest path method are too high and the total length is too long, reduces the spatial complexity of road network storage and the time complexity of method search, improves the execution efficiency of the method, and finally achieves the purpose of improving the real - time performance and accuracy of the planning method.

[0009] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0010] A method for planning paths in a dynamically restricted search area with the top k different paths includes the following steps:

[0011] Step 1. Given the vector data of the road network, the road network can be understood as a graph data structure, that is, the road network can be abstracted as a graph G. Determine the starting node and the ending node from the graph G to obtain a statistical parameter function and a penalty coefficient function;

[0012] Step 2. According to the starting node and the ending node given in Step 1, calculate the Euclidean distance between the starting node and the ending node to obtain the penalty coefficient and the statistical parameter value. The specific operations are as follows:

[0013] 2.1 Substitute the Euclidean distance α between the starting node and the ending node into the fitting functions R 95% and Sim 95% to obtain a ratio coefficient R and a penalty coefficient δ;

[0014] 2.2 Take the starting node and the ending node as the foci, and establish an elliptical restricted search area with Rα as the major - axis length. Obtain the statistical parameter value lower than a certain similarity through the Euclidean distance between the starting node and the ending node;

[0015] Step 3: When different path solutions are obtained through the operations of Step 1 and Step 2, they need to be processed to obtain different path solutions lower than a certain similarity. The specific process is as follows:

[0016] 3.1 When the first path solution S is obtained, mark all the solutions of the first path, that is, let S i ’·δ = 1, where S i ∈S, and multiply all the road - segment solutions by the penalty coefficient and put them into the graph G;

[0017] 3.2 When solving the second path, obtain the statistical parameter value according to the penalty coefficient δ and j. j is the j - th path obtained currently, and obtain the j - th path solution according to the traditional method;

[0018] When obtaining the solution of the j-th path, judge the path sub-solution. If the path sub-solution has been marked as S i ’·δ = 1, at this time, remove the path sub-solution from S', and divide the path sub-solution by the penalty coefficient δ and put it back into S';

[0019] 3.4 The path sub-solution is not marked, that is, S i ’·δ = 0, at this time, mark the path, that is, make S i ’·δ = 1, and multiply all the road segment solutions by the penalty coefficient and put them into the graph G;

[0020] Step 4: Repeat the above process until the k-th path is searched, and the method ends.

[0021] The penalty coefficient and statistical parameters obtained in the above step 2 are obtained by fitting the penalty coefficient function and statistical parameter function of the statistical parameters of different Euclidean distances.

[0022] The specific operations of the above step 1 are as follows:

[0023] 1.1 Systematically extract N nodes in the road network to construct the set G O , G D ; The Cartesian product G OD = G O × G D = {(O, D)|(O ∈ G O ) ∧ (D ∈ G D )}, Regarding each element in G OD as the starting and ending points of the shortest path to be solved, then G OD contains a total of M sample elements;

[0024] 1.2 Solve F OD , E OD , R OD , and Sim OD for each element in the set G OD respectively; F OD is the actual distance between the starting and ending points, E OD is the Euclidean distance, R OD is the ratio coefficient, and Sim OD is the similarity of different paths in the set;

[0025] 1.3 Sort the M sample elements in ascending order of Euclidean distance, and take every 100 sample elements as a group in order; sort each group in descending order of r and sim values, select the 5th number in each group to form two new sets respectively, and finally perform curve fitting on the sample elements in the two new sets;

[0026] 1.4 Curve fit the sample elements in different sets in step 1.3 to obtain the statistical parameter function R 95% and the penalty coefficient function δ 95% .

[0027] In step 1.2, the actual distance of the starting and ending points is F OD , and the Euclidean distance is E OD , then the ratio coefficient R = F OD / E OD ; for the extracted samples, a set of ratio coefficients R OD can be obtained;

[0028] The Euclidean distance between the starting and ending points is E OD , set different penalty coefficients, and the similarity of different paths is Sim OD , then the functional relationship between the Euclidean distance and the similarity under different penalty coefficients is obtained.

[0029] Advantages of the present invention: Compared with other methods, the first k path solutions obtained by the present invention have significantly improved time complexity on the premise of ensuring that the similarity is not higher than the set maximum similarity, solving the problem that the existing first k shortest path methods rarely consider the spatial position relationship between the starting node and the target node, and the paths obtained by the search have high repetition and too long total length. Description of the Drawings

[0030] Figure 1 Flow chart of the present invention. Detailed Embodiments

[0031] The embodiments of the present invention are described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0032] The embodiments of the present invention will be described in detail below with reference to the drawings.

[0033] A method for planning the first k different dynamic restricted search area paths includes the following steps:

[0034] Step 1: Given the vector data of the road network, the road network can be understood as a graph data structure, that is, the road network can be abstracted as a graph G. Determine the starting node and the ending node from the graph G to obtain the statistical parameter function and the penalty coefficient function; the specific process is as follows:

[0035] 1.1 Systematically extract N nodes in the road network to construct a set G O , G D; Cartesian product G OD = G O × G D = {(O, D) | (O ∈ G O ) ∧ (D ∈ G D )}, where each element in G OD is regarded as the start and end points of the shortest path to be found. Then G OD contains a total of 40,000 sample elements.

[0036] 1.2 Solve F OD , E OD , R OD , and Sim OD for each element in G OD respectively; F OD is the actual distance between the start and end points, E OD is the Euclidean distance, R OD is the ratio coefficient, and Sim OD is the similarity of different paths in the set.

[0037] 1.3 Sort the 40,000 sample elements in ascending order of Euclidean distance, and group every 100 sample elements in sequence. Sort each group in descending order of r and sim values, select the 5th number in each group to form two new sets respectively, and finally perform curve fitting on the sample elements in the two new sets.

[0038] 1.4 Perform curve fitting on the sample elements in different sets in Step 1.3 to obtain the statistical parameter function R 95% and the penalty coefficient function δ 95% :

[0039] Step 2 Given the start node and end node according to Step 1, and calculate the Euclidean distance between the start node and end node to obtain the penalty coefficient and statistical parameter values. The specific operations are as follows:.

[0040] 2.1 Substitute the Euclidean distance α between the start node and end node into the fitting functions R 95% and Sim 95% to obtain a ratio coefficient R and a penalty coefficient δ.

[0041] 2.2) Take the start node and end node as the foci, and establish an elliptical restricted search area with Rα as the major axis length, and obtain the statistical parameter values below a certain similarity through the Euclidean distance between the start node and end node.

[0042] Step 3 When obtaining different path solutions through the operations in Step 1 and Step 2, it is necessary to process them to obtain different path solutions below a certain similarity. The specific process is as follows:

[0043] 3.1 When the first path solution S is obtained, mark all the solutions of the first path, that is, let S i '·δ =1, where S i ∈S, and multiply all the road segment solutions by the penalty coefficient and put them into the graph G.

[0044] 3.2 When solving the second path, it is necessary to obtain the statistical parameter value based on the penalty coefficient δ and j (the jth path currently obtained), and obtain the jth path solution according to the traditional method.

[0045] 3.3 When the jth path solution is obtained, it is necessary to judge the path sub-solution. If the path sub-solution has been marked as S i '·δ =1, then the path sub-solution needs to be removed from S' and divided by the penalty coefficient δ to put the path sub-solution back into S'.

[0046] 3.4 If the path subsolution is not marked, that is, S i '·δ =0, then the path needs to be marked, that is, let S i '·δ=1, and multiply all the segment solutions by the penalty coefficient and put them into graph G.

[0047] Step 4 Repeat the above process until the kth path is found and the method ends.

[0048] Through simulation experiments and applications, it is shown that the time complexity of the method can be reduced by 64% for the first k path solutions obtained by the present invention, under the premise of ensuring that the similarity is not higher than the set maximum similarity.

[0049] The above embodiments are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary engineering and technical personnel in the field should fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for path planning of the top-k differential dynamic restricted search areas, characterized in that: It includes the following steps: Step 1. Provide the vector data of the road network, understand the road network as a graph data structure, that is, abstract the road network as a graph G, and determine the starting node and the ending node from the graph G to obtain the statistical parameter function and the penalty coefficient function; The specific operations are as follows: 1.1 Systematically extract N nodes from the road network to construct a set G O , G D ; The Cartesian product G OD = G O × G D = {(O, D)|(O ∈ G O ) ∧ (D ∈ G D )}, Regarding each element in G OD as the starting and ending points of the shortest path to be solved, then G OD contains a total of M sample elements; 1.2 Solve F, E, R, and Sim for each element in set G OD respectively; OD F OD is the actual distance between the starting and ending points, E OD is the Euclidean distance, R OD is the ratio coefficient, and Sim OD is the similarity of different paths in the set; the actual distance between the starting and ending points is F OD , the Euclidean distance is E OD , then the ratio coefficient R = F OD / E OD can be obtained; for the extracted samples, the set of ratio coefficients R OD can be obtained; OD OD OD ​​​ The Euclidean distance from the starting point to the ending point is E OD , different penalty coefficients are set, and the similarity of different paths is Sim OD , and then the functional relationship between the Euclidean distance and the similarity under different penalty coefficients is obtained; 1.3 Sort the M sample elements in ascending order of Euclidean distance, and take every 100 sample elements as a group in sequence; sort each group in descending order of r and sim values, select the 5th number in each group to form two new sets respectively, and finally perform curve fitting on the sample elements in the two new sets; 1.4 Curve fitting is performed on the sample elements in different sets in step 1.3 to obtain the statistical parameter function R 95% and the penalty coefficient function δ 95%； Step 2. According to the starting node and the ending node given in Step 1, calculate the Euclidean distance between the starting node and the ending node to obtain the penalty coefficient and the statistical parameter value. The specific operations are as follows: 2.1 Substitute the Euclidean distance α between the starting node and the ending node into the fitting functions R 95% and Sim 95% to obtain a ratio coefficient R and a penalty coefficient δ; 2.2 Take the starting node and the ending node as the foci, and establish an elliptical restricted search area with Rα as the major axis length, and obtain the statistical parameter value lower than a certain similarity through the Euclidean distance between the starting node and the ending node; Step 3: When different path solutions are obtained through the operations in Step 1 and Step 2, they need to be processed to obtain different path solutions lower than a certain similarity. The specific process is as follows: 3.1 When obtaining the solution S of the first path, mark all the solutions of the first path, that is, let S i ’·δ = 1, where S i ∈S, and multiply all the section solutions by the penalty coefficient and put them into the graph G; 3.2 When solving the second path, obtain the statistical parameter value according to the penalty coefficient δ and j, where j is the jth path obtained currently, and obtain the jth path solution according to the traditional method; 3.3 When obtaining the solution of the j-th path, judge the path sub-solution. If the path sub-solution has been marked as S i ’·δ = 1, at this time, remove the path sub-solution from S' and divide the path sub-solution by the penalty coefficient δ and put it back into S' again; 3.4 The path sub-solution is not marked, i.e., S i ’·δ = 0. At this time, the path is marked, i.e., let S i ’·δ = 1, and multiply all the road segment solutions by the penalty coefficient and put them into graph G; Step 4: Repeat the above process until the kth path is searched, and the method ends.

2. The method for path planning of the top-k differential dynamic restricted search areas according to claim 1, wherein: The penalty coefficient and the statistical parameter in Step 2 are obtained from the penalty coefficient function and the statistical parameter function fitted from the statistical parameters of different Euclidean distances.

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