CN108596390B - Method for solving vehicle path problem - Google Patents

Method for solving vehicle path problem Download PDF

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CN108596390B
CN108596390B CN201810374691.XA CN201810374691A CN108596390B CN 108596390 B CN108596390 B CN 108596390B CN 201810374691 A CN201810374691 A CN 201810374691A CN 108596390 B CN108596390 B CN 108596390B
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阳晗杰
邓宝松
郑箘
冯燕凌
蒋遂平
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Beijing Institute of Computer Technology and Applications
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses a method for solving the problem of vehicle path, which comprises the following steps: (1) a data preprocessing step: the method comprises the steps of collecting information of each point (including the distance from the original point to the original point, the distance from the original point to other points, the latest arrival time and the driving speed of a vehicle, calculating the dissimilarity degree between the points by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix, (2) performing cluster analysis by selecting a proper clustering method and performing iterative clustering until no super-large clusters exist in a clustering result, and (3) performing path calculation by analyzing each cluster by using a branch and limit algorithm and calculating an optimal transportation scheme of all points in each cluster from the original point to pass through the cluster.

Description

Method for solving vehicle path problem
Technical Field
The invention relates to the field of vehicle routing problems, in particular to a method for solving the vehicle routing problem.
Background
As early as 1959, Danting and Ramser presented a Vehicle Routing Problem (VRP). In 1972, it was demonstrated by Karp that the VRP problem was the NP-Hard problem. It relates to various disciplinary knowledge such as operational research, management, computer application, combined mathematics, graph theory and the like. The vehicle path problem is generally defined as: for a series of delivery points and receiving points, a proper driving route is organized, so that the vehicle sequentially passes through each point, and a certain target (shortest route, minimum cost, minimum time, minimum vehicle and the like) is achieved under the condition that certain constraint conditions (cargo demand, delivery quantity, time constraint, carrying capacity constraint, driving mileage constraint and the like) are met. The algorithms for the vehicle path problem are generally of two types: exact solutions, heuristic solutions (non-exact solutions, but relatively reasonable solutions).
Direct tree search algorithms, dynamic programming methods, branch and bound methods, integer linear programming methods, etc. are all accurate solutions that can provide accurate solutions to small-scale vehicle routing problems. But due to its characteristic that the amount of calculation increases exponentially as the size of data increases, the precise solution cannot solve the large-scale vehicle path problem.
The method is characterized in that heuristic algorithms such as a Sweep algorithm, a Chridodes two-stage method, a tabu search method, a genetic algorithm and the like can solve the problem of large-scale vehicle paths, and heuristic solutions given in limited time are relatively optimal solutions, but the problem of accurate solution of the large-scale vehicle paths cannot be solved.
Disclosure of Invention
It is an object of the present invention to provide a solution to the problem of vehicle routing, which solves the above mentioned problems of the prior art.
The invention discloses a method for solving a vehicle path problem, which comprises the following steps: (1) a data preprocessing step: collecting information of each point from an original data set, calculating the dissimilarity degree of each point by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix; (2) performing cluster analysis, comprising: step 21: selecting a clustering method; step 22: based on the dissimilarity matrix, clustering by using the selected clustering method, dividing a huge-scale data set into small-scale clusters, and after each round of clustering is finished, if a super-large cluster still exists, adjusting parameters to perform clustering analysis on the cluster until the scales of all the divided clusters meet the requirements; (3) performing a path computation comprising: analyzing each cluster by using a branch and limit algorithm, and calculating an optimal transportation scheme starting from an origin and passing through all points in each cluster; step 3 of path calculation includes: step 31: constructing a distance matrix, namely dividing all points into n clusters in the step 2, adding origin information to all points in any cluster to construct a distance matrix, wherein the n clusters can construct n distance matrices; step 32: calculating the shortest path from the origin to all the points in the cluster by using a branch and bound algorithm for each distance matrix; step 33: returning to step 32, calculating the shortest path until n clusters;
in an embodiment of the method for solving the vehicle path problem according to the present invention, the information of each point includes a distance to the origin, a distance to other points, a latest arrival time, and a traveling speed of the vehicle.
According to an embodiment of the method for solving the vehicle path problem of the present invention, in step 21, if the vehicle cargo capacity can meet the demand, a dividing method is adopted to divide the clusters; if the number of vehicles is not considered, hierarchical clustering or density-based clustering methods are used to divide the clusters.
In an embodiment of the method for solving the vehicle path problem according to the present invention, step 22: the clusters with the specified number of points larger than n/1000 are super-large clusters, the clusters are divided into p clusters after the first round of clustering is carried out by using a selection method, and if the super-large clusters A exist, the nodes of the A comprise: a is1,a2,……,akAnd selecting the nodes in the A from the dissimilarity matrix, constructing a dissimilarity matrix of k rows and k columns, adjusting parameters of a clustering method, and performing clustering analysis to obtain a series of new clusters until all the clusters are not oversized clusters.
According to an embodiment of the method for solving the vehicle path problem of the present invention, in step 31, the clusters divided in step 2 are processed one by one, and it is assumed that a cluster a exists, and the node a includes: a is1,a2,……,akAnd (2) selecting the information of each point and the origin of the node A from the distance matrix, constructing a k + 1-order distance symmetric matrix, and forming n different distance matrices if the clustering result in the step 2 is n clusters.
According to an embodiment of the method for solving the vehicle path problem, the data preprocessing step 1 specifically includes: in step 11, a view or a table is made on the original database, assuming that the number of points is n, the attributes of the table include: any two of the n points, e.g. point i to origin distance liDistance l from point j to originjLatest arrival time t of point iiAnd the latest arrival time t of point jjInserting the information of n points into the table to make an n-order symmetric matrix, storing the distance value l between the point i and the point j in the ith row and j columnij. The vehicle running speed is constant v, and the distance matrix is:
Figure BDA0001639231790000031
step 12: calculating the dissimilarity degree of any two points, wherein: distance l between two pointsijThe smaller the dissimilarity is; the distance between the two points is smaller compared with the distance proportion of the two points from the origin, and the dissimilarity is smaller; the larger the point variable transportation time is, the smaller the time-dependent rejection of other points is, and the smaller the dissimilarity with other points is; the larger the difference of the latest arrival time of the two points is, the smaller the time correlation repulsion between the two points is; mathematical formula of the dissimilarity between two points:
Figure BDA0001639231790000032
and (4) calculating the dissimilarity degree between any two points according to the formula and the data acquired in the step (11).
In an embodiment of the method for solving the problem of vehicle routing according to the present invention, step 12 is performed in a loop until all d are calculatedij. Constructing an n-order dissimilarity degree symmetric matrix, wherein the value of the ith row and the jth column is the dissimilarity degree d between a point i and a point jij。
The invention provides a method for solving the problem of vehicle paths, which fully considers the constraint of each factor in the problem of vehicle paths and improves the feasibility of final results by using a data processing method of cluster analysis. The method of cluster analysis is used for decomposing a large-scale problem into a series of small-scale problems, a branch-and-bound algorithm is used for obtaining an accurate solution of each small-scale problem, a heuristic solution of the whole problem is obtained in a limited time in the mode, and the accuracy of the whole heuristic solution is improved through the aggregation of similar points of the cluster analysis and the accuracy of the branch-and-bound algorithm.
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FIG. 1 is a flow chart illustrating a method of solving a vehicle path problem according to the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
Fig. 1 is a flow chart illustrating a method of solving a vehicle path problem according to the present invention, as shown in fig. 1, the method comprising the steps of:
(1) a data preprocessing step: collecting information of each point (including a distance to an origin, a distance with other points, a latest arrival time and a vehicle running speed v (all vehicle speeds are the same)) from an original data set, calculating the dissimilarity degree between the points by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix;
(2) a clustering analysis step: selecting a proper clustering method, and iteratively clustering until no super-large cluster exists in a clustering result;
(3) a path calculation step: each cluster is analyzed using a branch and bound algorithm to calculate the best transportation scheme in each cluster from the origin through all points in the cluster.
As shown in fig. 1, for an embodiment, the characteristics of each of the cluster analysis algorithm and the branch-and-bound algorithm are fully utilized to improve the accuracy and feasibility of the algorithm result, the method includes the following steps:
(1) a data preprocessing step: collecting information of each point (including a distance to an origin, a distance with other points, a latest arrival time and a vehicle running speed v (all vehicle speeds are the same)) from an original data set, calculating the dissimilarity degree between the points by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix;
(2) a clustering analysis step: selecting a proper clustering method, and iteratively clustering until no super-large cluster exists in a clustering result;
(3) a path calculation step: each cluster is analyzed using a branch and bound algorithm to calculate the best transportation scheme in each cluster from the origin through all points in the cluster.
The data preprocessing step 1 includes:
step 11: and (5) data acquisition. From the raw data set, the following information is collected for any point: distance to origin (warehouse), distance to other points, latest arrival time, vehicle speed v (all vehicle speeds are the same);
step 12: and calculating the dissimilarity degree of any two points. The reasonability of the dissimilarity degree has a crucial influence on the accuracy of the clustering result. In the vehicle path problem, time and distance are the most important information. The dissimilarity between the two points must be calculated reasonably according to the information collected in step 11;
step 13: and constructing a dissimilarity matrix. Calculating the dissimilarity degree between any two points of all nodes in the data set, and constructing a dissimilarity degree matrix;
the cluster analysis step 2 includes:
step 21: and (5) selecting a clustering method. Based on the dissimilarity matrix, clustering by using a proper clustering method; the proper clustering method needs to consider the high efficiency of clustering and the reasonability of results, and the most proper clustering method is selected according to the actual application condition;
step 22: and (5) clustering. And based on the dissimilarity matrix, clustering by using the selected clustering method. The purpose of clustering is to partition a large-scale data set into smaller-scale clusters. Therefore, the step is an iterative process, and after each round of clustering is finished, if the super-large clusters still exist, the parameters are adjusted to perform clustering analysis on the clusters until the scales of all the divided clusters meet the requirements;
the path calculation step 3 includes:
step 31: a distance matrix is constructed. And 2, dividing all points into n clusters, and adding the origin information to all points in a certain cluster to construct a distance matrix. n clusters can construct n distance matrixes;
step 32: the path is computed using a branch and bound method. Calculating the shortest path from the origin to all the points in the cluster by using a branch and bound algorithm for each distance matrix;
step 33: path computation for all clusters is completed. Looping step 32 until the shortest path is calculated for all n clusters;
as shown in fig. 1, for an embodiment of the method for solving the vehicle path problem, the data preprocessing step 1 specifically includes:
step 11: and (5) data acquisition is carried out. From the raw data set, the following information is collected for any point: distance to origin (warehouse), distance to other points, latest arrival time, vehicle speed v (all vehicle speeds are the same);
in implementation, a view or a table may be made on the original database, assuming that the number of points is n, and the attributes of the table include: any two of the n points, e.g. point i to origin distance liDistance l from point j to originjLatest arrival time t of point iiAnd the latest arrival time t of point jjAnd inserting the information of n points into the table. Making an n-order symmetric matrix, i row and j column, storing the distance value l between the points i and jij. The vehicle running speed is constant at v. The distance matrix is as follows:
Figure BDA0001639231790000071
step 12: the dissimilarity between any two points is calculated. The reasonability of the dissimilarity degree has a crucial influence on the accuracy of the clustering result. In the vehicle path problem, time and distance are the most important information. Performing reasonable calculation on the information acquired in the step 11 to obtain a result when the two points are different in degree;
in practice, the distance and time information of the points are taken into account. The invention obtains the following principle through mathematical simulation and empirical demonstration:
distance l between two pointsijThe smaller the dissimilarity is;
the distance between the two points is smaller compared with the distance proportion of the two points from the origin, and the dissimilarity is smaller;
the larger the point-variable transportation time (difference between the latest arrival time and the actual transportation time from the origin), the smaller the time-dependent rejection with other points, and the smaller the degree of dissimilarity with other points;
the larger the difference of the latest arrival time of the two points (the ratio of the latest arrival time difference between the two points to the latest arrival time mean value of the two points) is, the smaller the time correlation repulsion between the two points is;
according to the above principle, a mathematical formula for calculating the degree of dissimilarity between two points is provided:
Figure BDA0001639231790000081
according to the formula and the data collected in step 11, the dissimilarity between any two points can be calculated.
Step 13: a dissimilarity matrix is constructed. Calculating the dissimilarity degree between any two points of all nodes in the data set, and constructing a dissimilarity degree matrix;
in practice, step 12 is cycled through until all d's have been calculatedij. A dissimilarity matrix (n-th order symmetric matrix) is constructed. Wherein, the value of the ith row and the jth column is the dissimilarity d between the point i and the point jij. The dissimilarity matrix is as follows:
Figure BDA0001639231790000082
the step 2 of cluster analysis comprises:
step 21: a clustering method is selected. Based on the dissimilarity matrix, clustering by using a proper clustering method; the proper clustering method needs to consider the high efficiency of clustering and the reasonability of results, and the most proper clustering method is selected according to the actual application condition;
in implementation, a suitable clustering method is selected according to application requirements. If the number of vehicles is limited (k), the freight volume of the vehicles can satisfy the demand certainly, and a dividing method can be adopted to divide clusters; if the number of vehicles is not considered, the clusters may be divided using a hierarchical clustering or density-based clustering, etc.
Step 22: and (6) clustering. And based on the dissimilarity matrix, clustering by using the selected clustering method. The purpose of clustering is to partition a large-scale data set into smaller-scale clusters. Therefore, the step is an iterative process, and after each round of clustering is finished, if a super-large cluster still exists, parameters are adjusted to perform clustering analysis on the cluster until the scales of all the divided clusters meet the requirements;
in the implementation, clusters with the number of the specified points larger than val (for example, val is n/1000) are super-large clusters, and after the first round of clustering is performed by using a selection method, the clusters are divided into clustersp clusters. If there is a super-large cluster A (nodes include: a)1,a2,……,ak) The nodes in a are selected from the dissimilarity matrix, and a dissimilarity matrix of k rows and k columns is constructed (using the method described above). And adjusting parameters of the clustering method, and performing clustering analysis to obtain a series of new clusters. The above process is repeated until all clusters are not oversized.
Step 3 of path calculation includes:
step 31: a distance matrix is constructed. And 2, dividing all points into n clusters, and adding the origin information to all points in a certain cluster to construct a distance matrix. n clusters can construct n distance matrixes;
in practice, the clusters divided in step 2 are processed one by one. Assume that there is a cluster A (nodes include: a)1,a2,……,ak). These points and the origin information are selected from the distance matrix, and a distance matrix (symmetric matrix of k +1 order) is constructed. If the clustering result in the step 2 is n clusters, n different distance matrixes need to be generated.
Step 32: the path is computed using a branch and bound method. Calculating the shortest path from the origin to all the points in the cluster by using a branch and bound algorithm for each distance matrix;
in practice, the distance matrices generated in step 31 are individually derived using a branch and bound algorithm.
Step 33: path computation for all clusters is completed. Looping step 32 until the shortest path is calculated for all n clusters;
in practice, the process loops through step 32 until all data is processed, and checks whether each path is reasonable according to the quantity and time of the goods.
The invention discloses a method for solving a Vehicle Routing Problem (VRP), which comprises the following steps: (1) a data preprocessing step: collecting information of each point (including a distance to an origin, a distance with other points, a latest arrival time and a vehicle running speed v (all vehicle speeds are the same)) from an original data set, calculating the dissimilarity degree between the points by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix; (2) a clustering analysis step: selecting a proper clustering method, and iteratively clustering until no super-large cluster exists in a clustering result; (3) a path calculation step: each cluster is analyzed using a branch and bound algorithm to calculate the best transportation scheme in each cluster from the origin through all points in the cluster.
The invention provides an algorithm for solving the problem of vehicle path, which is an accurate solution algorithm for small-scale problems, and provides a heuristic solution with high accuracy and feasibility for large-scale problems. Compared with the existing vehicle path problem algorithm, the method has the advantages that the large-scale data set is divided into a series of small-scale problems through clustering, so that the complexity of the problems is reduced, and the problems can be completed within a limited time; secondly, a reasonable dissimilarity degree calculation method is provided, and the rationality of a clustering result is improved; and thirdly, an algorithm combining clustering division and branch and bound is used, so that the accuracy of the result is improved. Therefore, the invention provides a reasonable solution for solving the problem of vehicle path. The effective solution of vehicle route problem can greatly optimize commodity circulation haul route, improve logistics efficiency, shorten logistics time, reduce logistics cost.
The invention can provide a heuristic solution for the NP-difficult vehicle path problem within a limited time, and compared with other algorithms of the same type, the result is more reasonable and more accurate in certain aspects. In the aspect of practical application, the logistics industry becomes an important power source for pulling national economic development and improving the living standard of residents, and the effective solution of the vehicle path problem has great effects on optimizing the logistics path, improving the logistics efficiency, shortening the logistics time, reducing the logistics cost and the like.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (6)

1. A method of resolving a vehicle path problem, comprising:
(1) a data preprocessing step: collecting information of each point from an original data set, calculating the dissimilarity degree of each point by using a dissimilarity degree calculation formula, and constructing a dissimilarity degree matrix;
(2) performing cluster analysis, comprising:
step 21: selecting a clustering method;
step 22: based on the dissimilarity matrix, clustering by using the selected clustering method, dividing a huge-scale data set into small-scale clusters, and after each round of clustering is finished, if a super-large cluster still exists, adjusting parameters to perform clustering analysis on the cluster until the scales of all the divided clusters meet the requirements;
(3) performing path computation, including:
analyzing each cluster by using a branch and limit algorithm, and calculating an optimal transportation scheme starting from an origin and passing through all points in each cluster;
step 3 of path calculation includes:
step 31: constructing a distance matrix, namely dividing all points into n clusters in the step 2, adding origin point information to all points in any cluster to construct a distance matrix, wherein n clusters can construct n distance matrices;
step 32: calculating the shortest path from the origin to all the points in the cluster by using a branch and bound algorithm for each distance matrix;
step 33: returning to step 32, calculating the shortest path until n clusters;
the data preprocessing step 1 specifically includes:
in step 11, a view or a table is made on the original database, assuming that the number of points is n, the attributes of the table include: any two of the n points, e.g. point i to origin distance liDistance l from point j to originjLatest arrival time t of point iiAnd the latest arrival time t of point jjInserting the information of n points into the table to make an n-order symmetric matrix, storing the distance value l between the point i and the point j in the ith row and j columnijThe vehicle running speed is constant v, and the distance matrix is:
Figure FDA0003342096220000021
step 12: calculating the dissimilarity degree of any two points, wherein:
distance l between two pointsijThe smaller the dissimilarity is;
the distance between the two points is smaller compared with the distance proportion of the two points from the origin, and the dissimilarity is smaller;
the larger the point variable transportation time is, the smaller the time-dependent rejection of other points is, and the smaller the dissimilarity with other points is;
the larger the difference of the latest arrival time of the two points is, the smaller the time correlation repulsion between the two points is;
mathematical formula of the dissimilarity between two points:
Figure FDA0003342096220000022
and (4) calculating the dissimilarity degree between any two points according to the formula and the data acquired in the step (11).
2. A method of resolving a vehicle path problem as claimed in claim 1, wherein the information of each point includes a distance to an origin, a distance to other points, a latest arrival time, and a traveling speed of the vehicle.
3. The method for solving the vehicle path problem as claimed in claim 1, wherein in step 21, if the vehicle cargo capacity can satisfy the demand, the cluster is divided by using a dividing method; if the number of vehicles is not considered, hierarchical clustering or a density-based clustering method is used to divide the clusters.
4. A method of resolving a vehicle path problem as claimed in claim 1, wherein step 22: the clusters with the number of the specified points larger than n/1000 are super-large clusters and are usedAfter the first round of clustering is carried out by the selected method, the cluster is divided into p clusters, if a super-large cluster A exists, the node of the cluster A comprises the following steps: a is1,a2,……,akAnd selecting the nodes in the A from the dissimilarity matrix, constructing a dissimilarity matrix of k rows and k columns, adjusting parameters of a clustering method, and performing clustering analysis to obtain a series of new clusters until all the clusters are not oversized clusters.
5. The method for solving the vehicle routing problem of claim 1, wherein in step 31, the clusters divided in step 2 are processed one by one, and the node a is assumed to exist as a cluster a, and comprises: a is1,a2,……,akAnd (2) selecting the information of each point and the origin of the node A from the distance matrix, constructing a k + 1-order distance symmetric matrix, and forming n different distance matrices if the clustering result in the step 2 is n clusters.
6. The method of resolving a vehicle path problem of claim 1,
step 12 is repeated until all d are calculatedijConstructing a symmetric matrix with n-order dissimilarity, wherein the value of the ith row and the jth column is the dissimilarity d between the point i and the point jij。
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