A path planning method based on the large-scale sparse Chinese Postman Problem

Abstract

The present invention discloses a path planning method based on the large-scale sparse Chinese Postman Problem, including: obtaining the positions of the endpoints and intersection points of the roads in the path to be optimized, and establishing an undirected road network graph with the road endpoints and intersection points as nodes; screening out the set V of odd-degree nodes in the undirected road network graph odd , constructing a complete graph formed by the shortest paths between all nodes in V odd ; clustering the odd-degree nodes in V odd to obtain multiple sub-node groups; merging the sub-node groups so that the coverage rate of the adjacent node sets of each merged sub-node group itself is above the adjacent node set coverage rate threshold; performing an even-degree processing on the merged sub-node groups; solving the shortest matching edge set within each even-degree processed sub-node group, and adding the corresponding edges in the shortest matching edge set to the undirected road network graph to form an Euler graph with all node degrees being even; determining the path starting point, and obtaining an Euler circuit starting from this starting point in the Euler graph as the optimized path.

Description

Technical Field

[0001] The invention belongs to the technical field of path planning, and in particular relates to a path planning method based on the large-scale sparse Chinese postman problem. Background Art

[0002] The Chinese Postman Problem (CPP), also known as the Arc Routing Problem (ARP), is a classic combinatorial optimization problem that can be described as finding a path starting from a given starting point, traversing all edges on the road network graph, and then returning to the starting point with the minimum total cost. This problem has a very wide range of application scenarios in reality, such as: postmen delivering letters, road exploration, police patrols, garbage trucks collecting garbage, snowplows cleaning streets, street view photography, etc.

[0003] The traditional method for solving the CPP problem is represented by the odd-even point graph operation method proposed by Guan Meigu. Its core idea is to add duplicate edges to the original graph to eliminate odd-degree nodes. In order to find the optimal duplicate edge addition scheme in the second step of this method, Edmonds and Johnson further proposed a maximum weight matching algorithm on a general graph, which finds a certain maximum matching by continuously searching for augmenting paths to obtain the optimal solution. In recent years, a variety of solutions for solving the CPP problem using heuristic methods have been proposed: Jiang Bo et al. use molecular programming algorithms and genetic algorithms to solve; TKRalphs et al. propose a solution for edge weight dynamic mixing in view of the limitations of genetic algorithms in solving the Chinese postman problem. Yu Hongbin et al. introduced the ant algorithm, which improves the two-step solution method of first matching singular points and then finding loops in the conventional case by selecting travel directions and the shortest route incentive strategy with random probability. Most of the existing work is carried out on a scale with a maximum number of nodes of only a few hundred. The traditional method can obtain the optimal path when the scale of the road network graph is small. As the scale of the road network expands, the number of nodes grows rapidly, and the solution time grows exponentially, usually taking hours or even days, which is difficult to meet the timeliness requirements of the work. Heuristic methods can effectively shorten the solution time and obtain feasible solutions that meet the requirements, but as the scale of the road network increases, the deviation between the feasible solution and the optimal solution also increases. Summary of the invention

[0004] The purpose of the present invention is to provide a path planning method based on the large-scale sparse Chinese postman problem in view of the sparse characteristics of large-scale road networks, which can improve the efficiency of path planning, and the efficiency advantage increases significantly with the increase of the scale of the road network.

[0005] The technical solution provided by the present invention is:

[0006] A path planning method based on the large-scale sparse Chinese postman problem, including:

[0007] Obtain the locations of the endpoints and intersections of the roads in the path to be optimized, and establish an undirected road network graph G=(V, E) with the road endpoints and intersections as nodes;

[0008] Among them, V is the node set and E is the edge set;

[0009] Filter out the odd-degree node set V in the undirected road network graph odd , constructed by V odd The complete graph formed by the shortest paths between all nodes in;

[0010] V odd Cluster the odd-degree nodes in to obtain multiple child node groups;

[0011] Merge the sub-node groups so that the coverage rate of the neighboring node sets of each merged sub-node group is above the threshold of the neighboring node set coverage rate;

[0012] Even-number the merged sub-node groups so that the number of nodes in each merged sub-node group is an even number;

[0013] Solving the shortest matching edge set in each even-numbered sub-node group, and adding the corresponding edges in the shortest matching edge set to the undirected road network graph to form an Euler graph in which all node degrees are even numbers;

[0014] A path starting point is determined, and an Euler circuit starting from the starting point is obtained in the Euler graph as an optimized path.

[0015] Preferably, the coverage rate of the neighboring node set of the sub-node group itself is calculated by the following formula:

[0016]

[0017] In the formula, Coverage ij Represents the child node group C i For the neighboring node set CN j The coverage rate of the middle nodes; N i belongs to the subnode group C i and CN j The node set of |N i | is the node set N i The number of nodes in |CN j | is the neighboring node set CN j The number of nodes in .

[0018] Preferably, the neighboring node set coverage threshold is:

[0019]

[0020] In the formula, threshold cov is the coverage threshold of the neighboring node set, and Num is the number of child node groups obtained by clustering.

[0021] Preferably, the method for even-numbering the merged sub-node group is:

[0022] Filter out the sub-node groups with an odd number of nodes as the target sub-node groups;

[0023] Calculate the shortest matching edge set between the central nodes of each target sub-node group;

[0024] Filter out the nodes in the two sub-node groups corresponding to the shortest matching edge set that are close to the edge of the sub-node group and have the smallest distance difference to the centers of the two sub-node groups, and record them as boundary nodes;

[0025] The category of the boundary node is changed so that the central node of the matching group belongs to one node group of the two sub-node groups corresponding to the shortest matching edge set to another node group.

[0026] Preferably, the shortest matching edge set in each even-numbered sub-node group is solved based on the ant colony algorithm, and multiple ants perform the following operations simultaneously:

[0027] Step 1: Randomly select an unmatched node and calculate the probability that the current node selects the remaining unmatched nodes;

[0028] Step 2: randomly select a node from the remaining unmatched nodes based on probability, and match the two;

[0029] If there are still nodes that have not been matched, repeat steps 1-2 until all nodes have been matched;

[0030] Step 3: From the matching results obtained by multiple ants, the matching result with the shortest added path length is selected as the best matching result, and the pheromone of the ant corresponding to the best matching result is updated;

[0031] Repeat steps 1-3 until the maximum number of iterations is reached, and save the overall best matching result as the final result;

[0032] In the iterative process, if the best matching result of the current iteration is better than the best matching result of the previous iteration, the current best matching result is saved as the overall best matching result.

[0033] Preferably, when the pheromone is updated, the amount of each increase is a constant.

[0034] Preferably, a density peak clustering algorithm is used to cluster V oddClustering the odd-degree nodes in includes the following steps:

[0035] Sort the nodes according to the decision value γ from large to small to obtain the node sequence;

[0036] Select decision value γ exceeding decision value threshold γ threshold The nodes are taken as the cluster center set CP1;

[0037] In the node sequence, select the node with the largest decision value neighbor difference γ from front to back. dmax The node with the largest decision value neighbor difference γ dmax The node and all the nodes before it are taken as the cluster center set CP2;

[0038] The set with more nodes in CP1 and CP2 is selected as the selected cluster center set, and the remaining nodes are clustered according to the distance relative to the cluster center point to form multiple child node groups Vc = {C1, ..., CNum};

[0039] Among them, Num is the number of child node groups obtained by clustering.

[0040] Preferably, the decision value γ is calculated by the following formula:

[0041]

[0042] In the formula, γ i represents the decision value of node i; ρmax, ρmin are the maximum and minimum values ​​of the local density of all nodes, δmax, δmin are the maximum and minimum values ​​of the relative distance of all nodes, respectively; ρ i represents the local density of node i and δ i Represents the relative distance of node i.

[0043] Preferably, the maximum decision value neighborhood difference γ dmax The calculation formula is:

[0044] γ dmax =max i≥1∩i＝N-1 (γ i+1 -γ i-1 );

[0045] Where N is the number of nodes with odd degrees; γ i+1 and γ i-1 Represent the decision values ​​of node i+1 and node i-1 respectively.

[0046] The beneficial effects of the present invention are:

[0047] The path planning method based on the large-scale sparse Chinese postman problem provided by the present invention can quickly obtain path planning results when performing path planning on a small-scale road network map; when performing path planning on a large-scale sparse road network map, it can quickly obtain better planning results, and the efficiency advantage increases significantly with the increase of the road network scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the basic process of solving the CPP problem based on the idea of ​​the operation method on the odd-even point graph described in the present invention.

[0049] Figure 2 The present invention is a flow chart of the path planning method.

[0050] Figure 3 The flowchart of clustering odd-degree nodes according to the present invention.

[0051] Figure 4 This is a schematic diagram of even-numbering the number of node groups described in the present invention.

[0052] Figure 5 The figure is a flow chart of the ant colony algorithm described in the present invention.

[0053] Figure 6 A schematic diagram showing the comparison of the running time between the method of the present invention and the linear programming method.

[0054] Figure 7 This is a schematic diagram comparing the operating results of the method of the present invention and the ant colony algorithm alone.

[0055] Figure 8 This is a comparison chart of the operating efficiency of the method of the present invention and that of the ant colony algorithm alone. DETAILED DESCRIPTION

[0056] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0057] The present invention provides a path planning method based on the large-scale sparse Chinese postman problem, wherein G = (V, E) represents an undirected road network graph, wherein V (G) is a vertex set and E (G) is an edge set. Any vertex v∈V represents an intersection or a starting and ending point (endpoint) of a road on the road network graph. Any edge e ij ∈E represents two vertices v i , v j The edge between them. w(e) represents the weight of edge e, that is, the length of the edge. V(e) represents the vertex set of edge e. Add an edge e to graph G ij ′, if V(e ij ′)=V(e ij ), and w(eij ') = w(e ij ) is called e ij ' as the duplicate edge of e ij . The set of duplicate edges added to graph G is denoted as E'. The extended multigraph of G, denoted as G* = (V, E*), where E* = E U E'.

[0058] Given a vertex sequence v 1 , v 2 ,..., v n such that (v i , v i+1 ) ∈ E (1 ≤ i < n), then this vertex sequence v 1 , v 2 ,..., v n represents a path R 1 from vertex v n to vertex v v1,vn . U(R) represents the edge set of path R, and L(R) represents the sum of the weights of all edges in path R. For path R v1,vn , if v 1 = v n , then this path is called a cycle, denoted as R v1 . If for the cycle R v1 of graph G, all edges in E(G) appear and only appear once in R v1 , then this cycle is an Euler cycle, denoted as ER v1 .

[0059] Then the Chinese Postman Problem can be described as: On an undirected connected graph G, given a starting vertex v 1 , find a cycle R v1 such that U(R v1 ) = E(G) and L(R v1 ) is minimized. If G is an Euler graph, then the cycle with the minimum L(R v1 ) must be the Euler cycle of graph G. If G is not an Euler graph, then CPP is equivalent to the following problem:

[0060] 1) Find the set of duplicate edges E' of G such that the extended multigraph G* of graph G is an Euler graph and L(E') is minimized;

[0061] 2) Find the Euler cycle of G*.

[0062] On a large-scale road network graph, based on the idea of the method of operations on the parity graph, the basic process of solving the CPP problem is as Figure 1 shown, including the following two stages:

[0063] The first stage: Find the set of odd-degree nodes V odd in graph G and construct a graph from V oddThe complete graph G formed by the shortest paths between all nodes c ;

[0064] Stage 2: In the complete graph G c Find the shortest matching edge set E′ in G. c Find the repeated edge set E′ in the graph G so that the extended multigraph G * It is an Euler graph, and L(E′) is as small as possible.

[0065] Since the solution speed of the second stage is restricted by the number of odd-degree vertices in a large-scale network, which is the bottleneck for solving the entire CPP problem, the present invention mainly studies this problem.

[0066] For a given road network graph G formed by odd-degree nodes, c The method flow of the present invention for solving the shortest matching edge set is as follows: Figure 2 As shown:

[0067] 1) Use the density peak clustering method to cluster and split the odd-degree node group to form multiple sub-node groups V c .

[0068] 2) By calculating V c The coverage rate of neighboring nodes of each sub-node group in is calculated, and the coverage rate threshold is used as the standard to merge related node groups to form multiple merged sub-node groups V m .

[0069] 3) Calculate V m The minimum weight perfect matching between the node groups with an odd number of nodes in the middle, and modify the class affiliation of the boundary nodes to form multiple sub-node groups V with an even number of nodes p .

[0070] 4) At V p The ant colony algorithm is used in each node group to obtain the shortest matching edge set E′ of each node group.

[0071] Subsequently, duplicate edges are added to the original graph according to the shortest matching edge set E′ of each node group to form an Euler graph G*, and an Euler circuit starting from any starting point is obtained in G*.

[0072] In order to effectively and reasonably reduce the size of each node group, the present invention uses a density peak clustering algorithm to segment the node group. The process of density peak clustering is as follows: Figure 3 shown.

[0073] For an odd-degree undirected complete graph G c For any odd-degree point xi, calculate the local density ρi and relative distance δi of the point.

[0074] The local density ρi of the odd-degree point xi is a quantitative standard for the density of nodes around the node, which is defined as follows:

[0075]

[0076] Where, d ij is the Euclidean distance between node i and node j, dc is the cutoff distance of the node, and χ(x) is the cutoff kernel function.

[0077] Relative distance δ i It refers to the minimum distance between a node and other nodes with higher density, which is defined as follows:

[0078]

[0079] In order to intuitively i and the relative distance δ i Determine the cluster center and use the decision value γ i Combining the two, the relevant definition is as follows:

[0080]

[0081] Among them, ρmax and ρmin are the maximum and minimum values ​​of the local density of all nodes, and δmax and δmin are the maximum and minimum values ​​of the relative distances of all nodes.

[0082] The decision value γi can intuitively see the characteristics of each node as a cluster center, but the original density peak clustering algorithm does not provide a method to automatically select the relevant cluster center, but manually selects it according to the decision diagram, which introduces a certain degree of subjectivity and uncertainty. In this regard, the FS-LSSCPP method will use the decision value threshold γ threshold and the maximum decision value neighbor difference γ dmax Automatically select cluster centers to improve the usability of the algorithm. i After sorting from large to small, the process of selecting cluster centers is as follows:

[0083] (1) Use the decision value threshold to determine the cluster center set CP1 = {V 1 ,…V i}: According to the sorted decision value γ sequence, select the decision value γ from front to back and exceed the decision value threshold γ threshold The nodes are taken as the cluster center set CP1, and the general threshold is 0.5.

[0084] (2) Use the maximum decision value proximity difference to determine the cluster center set CP2 = {V 1 ,…V j}: According to the sorted decision value γ sequence, select the one with the largest decision value neighbor difference γ from front to back. dmax The node and all the nodes before it are taken as the cluster center set CP2.

[0085] Maximum decision value neighbor difference γ dmax The definition of is as shown in formula (4), which represents the change trend of the decision value at the node.

[0086] γ dmax =max i≥1∩i≤N-1 (γ i+1 +γ i+1 ) (4)

[0087] Both methods of selecting cluster centers perform sequential operations on the same ordered sequence of center points, so CP1 and CP2 have an inclusion relationship. The set with the larger number of nodes in CP1 and CP2 is selected as the selected cluster center set, and the remaining nodes are clustered according to the distance relative to the cluster center point to form Num sub-node groups V c ={C 1 ,…,C Num}.

[0088] The effectiveness of the shortest matching edge set is related to the number of neighboring nodes contained in the subnode group. Too few neighboring nodes in the subnode group will reduce the selection range of node matching, thereby increasing the length of the Euler circuit path with a high probability. In order to effectively improve the effectiveness of the shortest matching edge set, the present invention uses subnode group merging to increase the number of neighboring nodes in the node group.

[0089] Neighboring node set CN i is the child node group C i The node set consisting of each node and its neighboring nodes in includes:

[0090] a) Child node group C i All nodes in

[0091] b) Child node group C i Each node in G c The nodes corresponding to the first m smallest weight edges.

[0092] Neighboring node set coverage ij :Represents the sub-node group C i For the neighboring node set CN j The coverage degree of the middle node is as follows:

[0093]

[0094] Where N i belongs to the subnode group C i and CNj The node set of |N i | is the node set N i The number of nodes in the j | is the neighboring node set CN j The number of nodes.

[0095] Neighboring node set coverage rate threshold: the reference standard for merging sub-node groups. When the neighboring node set coverage rate threshold and the number of sub-node groups satisfy the following relationship, the availability of the shortest matching edge set is better, as shown in formula (6):

[0096]

[0097] In the formula, threshold cov is the coverage threshold of the neighboring node set, and Num is the number of clusters.

[0098] The goal of merging sub-node groups is to make the neighboring node set coverage rate of each sub-node group greater than or equal to the neighboring node set coverage rate threshold. The number of neighboring nodes m in a sub-node group is related to the total number of odd-degree nodes in the road network graph, which is generally 1% of the total number of odd-degree nodes. The number of sub-node groups will affect the size of the coverage rate threshold. If there are fewer sub-node groups, the node distribution is relatively concentrated, and a higher neighboring node coverage rate threshold is required to ensure the availability of the shortest matching edge set. If there are many sub-node groups, the node distribution is relatively dispersed, and there are fewer nodes inside each sub-node group, and the neighboring node coverage rate threshold requirement should be appropriately reduced.

[0099] The process of merging sub-node groups is as follows:

[0100] (1) Calculate the neighboring node set and neighboring node coverage rate of each sub-node group in Vc.

[0101] (2) Merge the related sub-node groups in Vc until the neighboring node coverage of each sub-node group meets the neighboring node coverage threshold.

[0102] The number of sub-node groups after the merger is n, and the sub-node group after the merger is recorded as V m .

[0103] The specific merging process is shown in Table 1:

[0104] 1) Calculate the coverage rate of each sub-node group in Vc to itself and the neighboring node sets of other sub-node groups ii ,Coverage ij .

[0105] 2) Determine each sub-node group C in turn i , if the coverage rate of the current sub-node group to its own neighboring node set is Coverageii , not less than the neighboring node set coverage threshold threshold cov , then skip the current child node group.

[0106] 3) If Coverage ii Less than the neighboring node set coverage threshold threshold cov , then select the sub-node group with the maximum coverage of the neighboring node set of the current sub-node group from the remaining sub-node groups, and set Coverage ji Coverage Value and Coverage ii Add them together and record in C1 that the current sub-node group i needs to be merged with the sub-node group j.

[0107] 4) Repeat step 3) until Coverage ii Not less than threshold cov .

[0108] 5) When the coverage of all sub-node groups exceeds the threshold, all sub-node groups are merged according to the records in C1 to form the merged sub-node groups V m .

[0109] Table 1

[0110]

[0111] V m The number of nodes in each sub-node group may be an odd number, while the search for the shortest matching edge set E′ requires that the number of nodes in the set be an even number. Therefore, the node groups with an odd number of nodes need to be even-numbered before subsequent matching operations can be performed.

[0112] like Figure 4 As shown, the process of making the number of group nodes even is as follows: first determine the central node of all sub-node groups with odd number of nodes, then determine the minimum weight perfect matching set between the center points of the groups; finally, between two node groups with matching relationship, select a boundary node to move between groups. Among them, the minimum weight perfect matching is the shortest matching edge set: a matching that contains all vertices and has the smallest sum of matching edge weights. The boundary node refers to the node with the smallest distance difference from the center points of the two groups in the two node groups with matching relationship. Since the number of odd-degree node groups is even, the number of nodes in the adjusted sub-node groups is even. There are many ways to establish the minimum weight perfect matching set between the center points of odd-degree node groups. If the number of nodes is large, the ant colony algorithm can be used to achieve it.

[0113] As shown in Table 2, the specific process of making the number of group nodes even-numbered is:

[0114] 1) Vm The center node in each sub-node group is the target, and the minimum weight perfect matching E between each center node is calculated. m .

[0115] Among them, the sub-node group that did not participate in the merger selects the cluster center when it was clustered as the central node; the new sub-node group formed by merging multiple sub-node groups selects the cluster center with the highest ranking when clustering as the central node.

[0116] 2) For E m For the matching edge i in , find the sub-node groups a and b corresponding to the two matching points of the matching edge i; find the node in the two sub-node groups that is close to the edge of the sub-node groups and has the smallest distance difference to the center of the two sub-node groups (i.e., the center node of the matching group).

[0117] 1) Modify the class of the central node of the matching group and change its class to another matching sub-node group.

[0118] 2) Repeat 2) and 3) until E is traversed. m All matching edges in .

[0119] Table 2

[0120]

[0121] In order to ensure the shortest total path length of the constructed Euler graph and improve the solving speed, the present invention adopts the ant colony algorithm to solve each sub-node group V p The internal shortest matching edge set E′. V p When each sub-node group in the algorithm is solved in turn using the ant colony algorithm, multiple ants perform the following operations at the same time. The specific process is as follows Figure 5 :

[0122] (1) Randomly select an unmatched node and calculate the probability of the current node selecting the remaining unmatched nodes based on the relevant information factors and the path length between nodes. The calculation method is as follows

[0123]

[0124] In the formula, τ ij is the pheromone concentration between node i and node j, η ij is the distance heuristic information between node i and node j, p ij is the probability of node i choosing node j for matching, Unmatched is the set of unmatched nodes, α is the pheromone heuristic factor, and β is the distance heuristic factor. The distance heuristic information is as follows:

[0125]

[0126] After obtaining the selection probabilities of the remaining unmatched nodes, the current node will randomly select nodes for matching based on this probability.

[0127] (2) Randomly select a node from the remaining unselected nodes based on the probability calculated in (1) and match the two. If there are still unmatched nodes, repeat (1) and (2) until all nodes have been matched.

[0128] (3) After all ants have completed the matching of all nodes, they select the matching result with the shortest added path length from the matching results obtained by multiple ants, and modify the pheromone on the relevant matching path based on this result.

[0129] (4) If the best matching result of the current iteration is better than the best matching result of the previous iteration, save the current best matching result as the overall best matching result. If the maximum number of iterations has not been reached, repeat (1)(2)(3)(4) until the maximum number of iterations is reached.

[0130] (5) When the maximum number of iterations is reached, the saved overall best matching result is used as the final result.

[0131] The corresponding edges in the shortest matching edge set of each sub-node group are added to the original undirected graph to form an Euler graph with all node degrees being even. The Hierholzer or Fleury algorithm can then be used to find an Euler circuit starting from any starting point.

[0132] After an iteration, the pheromone needs to be updated according to the result of the iteration. The traditional pheromone update is the superposition of each ant's pheromone update, and the increase in pheromone is related to the length of the path currently being searched. In this scheme, pheromone is affected by paths of different lengths and a fixed total amount of pheromone, but paths of different lengths may produce pheromone sizes of different magnitudes, which may cause the pheromone to increase abnormally, resulting in abnormal overall convergence. In addition, all ants will update the pheromone, and the update of pheromone with poor availability will cause the overall convergence in the wrong direction, thereby increasing the difficulty of finding a usable solution. Therefore, the elite ant strategy is adopted in the improved scheme, and only the ant with the shortest path updates the pheromone in one iteration. At the same time, the increase in pheromone is changed to an increase in a constant Px each time, thereby avoiding the problem of different magnitudes of pheromones. As shown in formula (7):

[0133] τ′ ij =τ ij +Px,ij∈MA (7)

[0134] In the formula, τ ij and τ′ ijare the pheromone concentrations between nodes i and j before and after the update, MA is the matching result set of elite ants, ij is the specific path in the matching result set, and Px is the pheromone constant. The value of the pheromone constant Px is better when it is between 0.05 and 0.1.

[0135] Test example

[0136] This test case was conducted on the Win10 platform and Visual Studio 2019 environment. The input was a complete graph of odd-degree nodes, in which all nodes were odd-degree nodes, and the path lengths between nodes in the complete graph of odd-degree nodes were randomly generated to simulate the randomness between different path lengths in the actual road network environment, thereby eliminating the errors in the experimental results caused by the particularity of the data; the output was the added length and running time of the repeated path.

[0137] (1) Comparison of solution results for small-scale CPP problems

[0138] In order to prove that the matching results obtained by the method of the present invention (FS-LSSCPP) are close to the matching results with the shortest path length, the results of the method of the present invention (FS-LSSCPP) and the results obtained by the deterministic algorithm under the same scale should be compared. However, due to the limitation that the deterministic algorithm can handle a small scale of problems, the results within the scope of the deterministic algorithm are compared here, and then extended to large-scale situations. The deterministic algorithm uses a linear programming method, and the comparison of the resulting path lengths under 170 nodes is shown in Table 3 (unit: m). The FS-LSSCPP algorithm uses 1000 iterations and 5 running averages.

[0139] It can be seen from Table 3 that the FS-LSSCPP algorithm can obtain the same repeated path length as the linear programming under smaller scale, that is, the FS-LSSCPP algorithm can obtain the optimal solution under small scale.

[0140] Table 3 Comparison of FS-LSSCPP and linear programming results under different numbers of odd-degree nodes

[0141]

[0142] (2) Comparison of solution time for small-scale CPP problems

[0143] Comparison of the computational time of 1000 iterations of FS-LSSCPP algorithm and linear programming method at the same scale, such as Figure 6 As shown in the figure. When the number of nodes is small, the time required for the two algorithms to solve is short and the difference is not large. As the number of nodes increases, the efficiency advantage of the FS-LSSCPP algorithm increases significantly. When there are 170 nodes, the FS-LSSCPP algorithm is about 8 times more efficient than the linear programming method.

[0144] Depend on Figure 6 It can be seen that although the deterministic algorithm can obtain the optimal solution, the overall calculation time increases rapidly with the increase of node scale. When the node scale is too large, the required solution cannot be obtained within an acceptable time. The duration of the FS-LSSCPP algorithm is mainly related to the number of iterations and the duration of a single ant colony. As far as the node scale is concerned, the overall duration will increase slowly and linearly with the increase of the node scale. Even in large-scale cases, a feasible solution can still be obtained within a limited time.

[0145] (3) Comparison of solution results for large-scale CPP problems

[0146] The method (FS-LSSCPP) of the present invention uses a clustering algorithm to segment the original odd-degree point group according to the sparse characteristics of nodes in the road network graph before using the ant colony algorithm for solving. Next, the improvement of the result availability and overall efficiency of the FS-LSSCPP method after introducing clustering compared with the single ant colony algorithm will be given.

[0147] The FS-LSSCPP algorithm reduces the size of the node group through clustering, effectively improving the operating efficiency, and improves the coverage of adjacent nodes in the sub-node group through cluster merging, which is beneficial to reduce the length of the effective repeated path found by the subsequent ant colony algorithm. Figure 7 The comparison of the running results of the FS-LSSCPP algorithm and the single ant colony algorithm under different scale nodes is shown. It can be seen that as the node scale increases, the FS-LSSCPP algorithm has a clear advantage in the results of repeated path length.

[0148] (4) Comparison of solution time for large-scale CPP problems

[0149] Using clustering methods, a large-scale node group can be divided into multiple small-scale node groups, thereby reducing the solution space and improving operation efficiency. Figure 8 The operation efficiency of node groups of different sizes under the ant colony algorithm and FS-LSSCPP algorithm is demonstrated. Figure 8 As shown in the figure, with the increase of node scale, the computational efficiency advantage of FS-LSSCPP algorithm becomes more obvious.

[0150] From the comparison of the operating efficiency of the ant colony algorithm and the FS-LSSCPP algorithm, it can be seen that under different scale nodes, the time required for the FS-LSSCPP algorithm to solve the problem is significantly reduced, and as the scale of the node increases, the efficiency is improved more obviously.

[0151] The present invention combines the ideas of divide and conquer and inspiration to propose a fast solution method for the large-scale sparse Chinese postman problem, which can effectively reduce the required time and obtain the optimal Euler circuit within the number of iterations. Through analysis, calculation and experimental comparison, it is shown that: under the node scale supported by the deterministic algorithm, the method of the present invention can obtain the optimal Euler circuit with a high probability and greatly reduce the required time; in the case of large-scale nodes, it can effectively improve the computing efficiency and reduce the required time while ensuring the effectiveness of the results.

[0152] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A path planning method based on the large-scale sparse Chinese Postman Problem, characterized in that, it includes: Obtain the positions of the endpoints and intersection points of the roads in the path to be optimized, and establish an undirected road network graph G=(V, E) with the road endpoints and intersection points as nodes; wherein, V is the set of nodes and E is the set of edges; Filter out the set V of odd-degree nodes in the undirected road network graph odd , and construct a complete graph formed by the shortest paths between all nodes in V odd ​ Cluster the odd-degree nodes in V odd to obtain multiple sub-node groups; Merge the sub-node groups so that the coverage rate of the adjacent node sets of each merged sub-node group is above the adjacent node set coverage rate threshold; Perform an even-number processing on the merged sub-node groups so that the number of nodes in each merged sub-node group is even; Solve the shortest matching edge set within each even-numbered sub-node group, and add the corresponding edges in the shortest matching edge set to the undirected road network graph to form an Euler graph with all node degrees being even; Determine the path starting point, and obtain an Euler circuit starting from this starting point in the Euler graph as the optimized path.

2. The path planning method based on the large-scale sparse Chinese Postman Problem according to claim 1, characterized in that, The coverage rate of the adjacent node set of the sub-node group is calculated by the following formula: Where Coverage ij represents the coverage rate of the child node group C i for the nodes in the neighboring node set CN j ; N i is the set of nodes that belong to both the child node group C i and CN j ; |N i | is the number of nodes in the node set N i ; |CN j | is the number of nodes in the neighboring node set CN j .

3. The path planning method based on the large-scale sparse Chinese Postman Problem according to claim 2, characterized in that, The adjacent node set coverage rate threshold is: where threshold cov is the coverage rate threshold of the neighboring node set, and Num is the number of child node groups obtained by clustering.

4. The path planning method based on the large-scale sparse Chinese Postman Problem according to claim 3, characterized in that, The method for performing an even-number processing on the merged sub-node groups is: Select the sub-node groups with an odd number of nodes as the target sub-node groups; Calculate the shortest matching edge set between the central nodes of each target sub-node group; Select the nodes that are close to the edge of the sub-node group and have the smallest distance difference to the centers of the two sub-node groups in the two sub-node groups corresponding to the shortest matching edge set, and record them as boundary nodes; Change the genus of the boundary nodes so that the attribution of the matching group central node is changed from one node group in the two sub-node groups corresponding to the shortest matching edge set to the other node group.

5. The path planning method based on the large-scale sparse Chinese Postman Problem according to claim 3 or 4, characterized in that, Based on the ant colony algorithm, solve the shortest matching edge set within each even-numbered sub-node group, and multiple ants perform the following operations simultaneously: Step 1: Randomly select an unmatched node, and calculate the probability of the current node selecting the remaining unmatched nodes; Step 2: Randomly select a node from the remaining unmatched nodes according to the probability, and match the two; If there are still nodes that have not been matched, repeat steps 1-2 until all nodes have been matched; Step 3: Select the matching result with the shortest added path length from the matching results obtained by multiple ants as the best matching result, and update the pheromone of the ant corresponding to the best matching result; Repeat steps 1-3 until the maximum number of iterations is reached, and save the overall best matching result as the final result; wherein, during the iteration process, if the best matching result of the current time is better than the best matching result of the previous iteration, then save the current best matching result as the overall best matching result.

6. The path planning method based on the large-scale sparse Chinese Postman Problem according to claim 5, It is characterized in that when updating the pheromone, the increment each time is a constant.

7. The path planning method based on the large-scale sparse Chinese postman problem according to claim 6, It is characterized in that Use the density peak clustering algorithm to cluster the odd-degree nodes in V odd , including the following steps: sort the nodes in descending order according to the decision value γ to obtain a node sequence; Select nodes where the decision value γ exceeds the decision value threshold γ threshold as the clustering center set CP1; Select the node with the largest proximity difference γ of decision values from front to back in the node sequence dmax as well as the node with the largest proximity difference γ of decision values dmax and all the nodes before it as the clustering center set CP2; select the set with the larger number of nodes in CP1 and CP2 as the selected set of cluster centers, and cluster the remaining nodes according to the distance from the relative cluster center points to form multiple sub-node groups Vc = {C1,..., CNum}; wherein, Num is the number of sub-node groups obtained by clustering.

8. The path planning method based on the large-scale sparse Chinese postman problem according to claim 7, It is characterized in that the decision value γ is calculated by the following formula: In the formula, γi represents the decision value of node i; ρmax and ρmin are respectively the maximum and minimum values of the local densities of all nodes, and δmax and δmin are respectively the maximum and minimum values of the relative distances of all nodes; ρi represents the local density of node i, and δi represents the relative distance of node i.

9. The path planning method based on the large-scale sparse Chinese postman problem according to claim 8, It is characterized in that The proximity difference γ of the maximum decision value dmax The calculation formula is as follows: γ dmax = max i≥1∩i≤N-1 (γ i+1 - γ i-1 ); where N is the number of odd-degree nodes; γ i+1 and γ i-1 represent the decision values of node i + 1 and node i - 1, respectively.

Images