CN108596390A - A method of solving Vehicle Routing Problems - Google Patents
A method of solving Vehicle Routing Problems Download PDFInfo
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- CN108596390A CN108596390A CN201810374691.XA CN201810374691A CN108596390A CN 108596390 A CN108596390 A CN 108596390A CN 201810374691 A CN201810374691 A CN 201810374691A CN 108596390 A CN108596390 A CN 108596390A
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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
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
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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
- G06Q10/00—Administration; Management
- G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
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Abstract
The invention discloses a kind of methods solving Vehicle Routing Problems, including：(1) data prediction step：The information for concentrating acquisition each to put from initial data (includes the distance to origin, at a distance from other points, arrival time, the travel speed of vehicle calculate the distinctiveness ratio between each point using distinctiveness ratio calculation formula, construct dissimilarity matrix the latest；(2) clustering step：Select suitable clustering method, iteration cluster, until super large cluster is not present in cluster result；(3) path computing step：Each cluster is analyzed using Branch-and-Bound Algorithm, calculates the best traffic program from origin by all the points in cluster in each cluster.A kind of method solving Vehicle Routing Problems of the present invention, is divided into a series of small-scale problems by large-scale dataset by clustering, reduces the complexity of problem, be allowed in finite time to complete.
Description
Technical field
The present invention relates to Vehicle Routing Problems field, especially a kind of method solving Vehicle Routing Problems.
Background technology
Early in nineteen fifty-nine, Danting and Ramser just propose Vehicle Routing Problems (Vehicle Routing
Problem, VRP).It 1972, is proved by Karp, VRP problems are NP-Hard problems.It is related to operational research, management, meter
The subjects knowledge such as the application of calculation machine, Combinational Mathematics, graph theory.Vehicle Routing Problems are commonly defined as：To a series of delivery points and
Receive a little, organize traffic route appropriate, make vehicle in an orderly manner by each point, meet certain constraints (cargo demand,
Traffic volume, time-constrain, carrying capacity constraint, mileage travelled constraint etc.) under, reach certain target (distance is most short, expense most
The small, time as possible less, vehicle it is few etc. as possible).There are two types of the algorithms of Vehicle Routing Problems is general：Rigorous solution, heuristic solution
(non-precisely solution, but relatively reasonable solution).
Direct tree search algorithm, dynamic programming method, branch and bound method, integral linear programming method etc. are all rigorous solutions,
They can provide accurate solution for small-scale Vehicle Routing Problems.But due to it as data scale increases, calculation amount is exponentially
The characteristic of growth, rigorous solution can not solve large-scale Vehicle Routing Problems.
The heuritic approaches such as Sweep algorithms, Chrisofides two-phase methods, TS algorithm, genetic algorithm can solve
Large-scale Vehicle Routing Problems, the heuristic solution that can be provided in finite time is opposite optimal solution, but can not solve to advise greatly
The problem of vehicle route of mould accurately solves.
Invention content
The purpose of the present invention is to provide a kind of methods solving Vehicle Routing Problems, for solving the above-mentioned prior art
Problem.
A kind of method solving Vehicle Routing Problems of the present invention, wherein including：(1) data prediction step：From original number
The distinctiveness ratio between each point is calculated using distinctiveness ratio calculation formula according to the information that concentrated collection is each put, constructs distinctiveness ratio square
Battle array；(2) clustering is carried out, including：Step 21：Select clustering method；Step 22：Based on dissimilarity matrix, using selected
Clustering method clustered, data set in large scale is divided into the cluster of scale is smaller, often wheel cluster after the completion of, if according to
So there are super large clusters, then adjusting parameter is to cluster progress clustering, until the scale of all clusters of division is all met the requirements；
(3) path computing is carried out, including：Each cluster is analyzed using Branch-and-Bound Algorithm, calculates and goes out from origin in each cluster
Best traffic program of the hair by all the points in cluster；In the step 3 of path computing, including：Step 31：Distance matrix is constructed, if
In step 2, all the points are divided into n cluster, all the points in either cluster are added into origin information, construction one is apart from square
Battle array, n cluster can construct n distance matrix；Step 32：Branch-and-Bound Algorithm is used to each distance matrix, is calculated from original
The shortest path that point sets out by all the points in this cluster；Step 33：Return to step 32, until n cluster all calculates shortest path；
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein the information each put includes arriving
The distance of origin, at a distance from other points, the travel speed of arrival time and vehicle the latest.
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein in step 21, if vehicle is transported
Goods amount energy meet demand, then using division methods come cluster dividing；If without considering vehicle fleet size, hierarchical clustering or base are used
Carry out cluster dividing in the clustering method of density.
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein step 22：Regulation point quantity is big
It is super large cluster in the cluster of n/1000, after carrying out first round cluster using the method for selection, p cluster is divided into, if there is super large
The node of cluster A, A includes：a1,a2,……,ak, then from the node selected in dissimilarity matrix in A, the phase of a k rows k row is constructed
Different degree matrix adjusts the parameter of clustering method, carries out clustering, a series of new clusters is obtained, until all clusters are not super
Until big cluster.
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein in step 31, processing one by one walks
Rapid 2 mark off the cluster come, if there are cluster A, A nodes include：a1,a2,……,ak, each point of A nodes is selected from distance matrix
And the information of origin, construct k+1 rank apart from symmetrical matrix, it is a not at n if step 2 cluster result is n cluster
The same distance matrix.
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein data prediction step 1 is specific
Including：In step 11, a view or table are done in original database, it is assumed that the quantity of point is n, and the attribute of table includes：In n point
Any two points, such as point i to initial point distance li, point j to initial point distance lj, point i arrival time t the latestiAnd point j is reached the latest
Time tj, the information of n point is inserted into table, a n rank symmetrical matrix is made, between the i-th row j row storages point i and point j away from
From value lij.Constant Vehicle Speed is v, and distance matrix is：
Step 12：The distinctiveness ratio of any two points is calculated, wherein：Distance between two points lijSmaller, distinctiveness ratio is smaller；2 points it
Between distance it is respectively smaller from the distance proportion of origin compared to 2 points, distinctiveness ratio is smaller；The variable haulage time of point is bigger, with other
The time correlation repellency of point is smaller, smaller with the distinctiveness ratio of other points；2 points the latest arrival time otherness it is bigger, 2 points it
Between time correlation repellency it is smaller；The mathematical formulae of distinctiveness ratio between 2 points：
According to above-mentioned formula and the collected data of step 11, the distinctiveness ratio between any two points is calculated.
One embodiment of the method according to the present invention for solving Vehicle Routing Problems, wherein cycle carries out step 12, until
Calculate all dij.N rank distinctiveness ratio symmetrical matrixes are constructed, the value of the i-th row jth row is the distinctiveness ratio d of point i and point jij。
The present invention provides a kind of methods solving Vehicle Routing Problems, it fully considers each factor in Vehicle Routing Problems
Binding character improve the feasibility of final result using the data processing method of clustering.Use the side of clustering
Extensive PROBLEM DECOMPOSITION is a series of small-scale problems, each small-scale problem can be obtained using Branch-and-Bound Algorithm by method
Accurate solution, the heuristic solution of entire problem has been obtained in finite time, has passed through the " similar of clustering in this way
Point " polymerism, the accuracy of Branch-and-Bound Algorithm improve the accuracy of entire heuristic solution.
Description of the drawings
Fig. 1 show a kind of flow chart for the method solving Vehicle Routing Problems of the present invention.
Specific implementation mode
To keep the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to the present invention's
Specific implementation mode is described in further detail.
Fig. 1 show a kind of flow chart for the method solving Vehicle Routing Problems of the present invention, as shown in Figure 1, this method packet
Include following steps：
(1) data prediction step：From initial data concentrate acquisition each put information (include the distance to origin, with
The distance of other points, the latest arrival time, the travel speed v (all vehicle speeds are the same) of vehicle), use distinctiveness ratio to calculate public
Formula calculates the distinctiveness ratio between each point, constructs dissimilarity matrix；
(2) clustering step：Select suitable clustering method, iteration cluster, until super large is not present in cluster result
Until cluster；
(3) path computing step：Each cluster is analyzed using Branch-and-Bound Algorithm, is calculated in each cluster from origin
The best traffic program to set out by all the points in cluster.
As shown in Figure 1, for a kind of embodiment, cluster algorithm and the respective characteristic of Branch-and-Bound Algorithm are given full play to
The accuracy and feasibility of arithmetic result are improved, this approach includes the following steps：
(1) data prediction step：From initial data concentrate acquisition each put information (include the distance to origin, with
The distance of other points, the latest arrival time, the travel speed v (all vehicle speeds are the same) of vehicle), use distinctiveness ratio to calculate public
Formula calculates the distinctiveness ratio between each point, constructs dissimilarity matrix；
(2) clustering step：Select suitable clustering method, iteration cluster, until super large is not present in cluster result
Until cluster；
(3) path computing step：Each cluster is analyzed using Branch-and-Bound Algorithm, is calculated in each cluster from origin
The best traffic program to set out by all the points in cluster.
In the data prediction step 1, including：
Step 11：Data collection steps.It is concentrated from initial data, following information is acquired to arbitrary point：To origin (warehouse)
Distance, at a distance from other points, arrival time the latest, the travel speed v of vehicle (all vehicle speeds are the same)；
Step 12：The distinctiveness ratio of any two points calculates step.The reasonability of distinctiveness ratio to the accuracy of cluster result have to
Close important influence.In Vehicle Routing Problems, time and distance are most important information.Must be to pass through when 2 distinctiveness ratios
The result that the information acquired in step 11 is reasonably calculated；
Step 13：Dissimilarity matrix constitution step.It is different between calculating any two points to all nodes that data are concentrated
Degree constructs dissimilarity matrix；
In the clustering step 2, including：
Step 21：Clustering method selects step.Based on dissimilarity matrix, clustered using suitable clustering method；It closes
Suitable clustering method needs to consider the reasonability of the high efficiency and result of cluster, most suitable poly- according to practical situations selection
Class method；
Step 22：Sorting procedure.Based on dissimilarity matrix, clustered using selected clustering method.The mesh of cluster
Be the cluster that data set in large scale is divided into scale is smaller.Therefore, this step is the process that an iteration carries out, and is often taken turns
After the completion of cluster, if still remain super large cluster, adjusting parameter carries out clustering to the cluster, until all clusters of division
Scale is all met the requirements；
In the path computing step 3, including：
Step 31：Construct distance matrix.All the points are divided into n cluster by step 2, and all the points in certain cluster are added
Origin information constructs a distance matrix.N cluster can construct n distance matrix；
Step 32：Path is calculated using branch and bound method.Branch-and-Bound Algorithm is used to each distance matrix, is calculated
Go out the shortest path by all the points in this cluster from origin；
Step 33：Complete the path computing of all clusters.Circulation step 32, until n cluster all calculates shortest path；
As shown in Figure 1, one embodiment of method for solving Vehicle Routing Problems, wherein data prediction step 1 are specific
Including：
Step 11：Carry out data acquisition.It is concentrated from initial data, following information is acquired to arbitrary point：To origin (warehouse)
Distance, at a distance from other points, arrival time the latest, the travel speed v of vehicle (all vehicle speeds are the same)；
When implementing, a view or table can be done in original database, it is assumed that the quantity of point is n, and the attribute of table includes：
Any two points in n point, such as point i to initial point distance li, point j to initial point distance lj, point i arrival time t the latestiAnd point j is most
Late arrival time tj, the information of n point is inserted into table.Make a n rank symmetrical matrix, the i-th row j row storage point i and point j it
Between distance value lij.Constant Vehicle Speed is v.Distance matrix is as follows：
Step 12：Calculate the distinctiveness ratio of any two points.The reasonability of distinctiveness ratio has the accuracy of cluster result heavy to closing
The influence wanted.In Vehicle Routing Problems, time and distance are most important information.By being adopted in step 11 when 2 distinctiveness ratios
The result that the information of collection is reasonably calculated；
When implementing, distance and temporal information a little is considered.The present invention is proved by mathematical simulation and experience, is obtained
Following principle：
Distance between two points lijSmaller, distinctiveness ratio is smaller；
Distance between two points are respectively smaller from the distance proportion of origin compared to 2 points, and distinctiveness ratio is smaller；
The variable haulage time (difference of arrival time and the actual transportation time from origin the latest) of point is bigger, with other
The time correlation repellency of point is smaller, smaller with the distinctiveness ratio of other points；
2 points (reaching time-difference reaches time average to arrival time otherness the latest with 2 points the latest between 2 points the latest
Ratio) it is bigger, illustrate that the time correlation repellency between 2 points is smaller；
According to mentioned above principle, the mathematical formulae for calculating distinctiveness ratio between 2 points is provided：
According to above-mentioned formula and the collected data of step 11, the distinctiveness ratio between any two points can be calculated.
Step 13：Construct dissimilarity matrix.To all nodes that data are concentrated, the distinctiveness ratio between any two points is calculated,
Construct dissimilarity matrix；
When implementing, cycle carries out step 12, until calculating all dij.Construct dissimilarity matrix (the symmetrical square of n ranks
Battle array).Wherein, the value of the i-th row jth row is the distinctiveness ratio d of point i and point jij.Dissimilarity matrix is as follows：
Clustering step 2 includes：
Step 21：Select clustering method.Based on dissimilarity matrix, clustered using suitable clustering method；Suitably
Clustering method needs to consider the reasonability of the high efficiency and result of cluster, and most suitable cluster side is selected according to practical situations
Method；
When implementing, suitable clustering method is selected according to application demand.If vehicle is limited (k), vehicle volume of freight
Sure meet demand can be used division methods and carry out cluster dividing；If without consider vehicle fleet size, can use hierarchical clustering or
The methods of density clustering carrys out cluster dividing.
Step 22：It is clustered.Based on dissimilarity matrix, clustered using selected clustering method.The mesh of cluster
Be the cluster that data set in large scale is divided into scale is smaller.Therefore, this step is the process that an iteration carries out, and is often taken turns
After the completion of cluster, if still remain super large cluster, adjusting parameter carries out clustering to the cluster, until all clusters of division
Scale is all met the requirements；
When implementing, it is specified that cluster of the point quantity more than val (such as val=n/1000) is super large cluster, the side of selection is used
After method carries out first round cluster, it is divided into each clusters of p.If there is super large cluster A, (node includes：a1,a2,……,ak), from different
The node in selection A in matrix is spent, the dissimilarity matrix (making with the aforedescribed process) of a k rows k row is constructed.Adjust clustering method
Parameter, carry out clustering, obtain a series of new clusters.It repeats the above process, until all clusters are not super large cluster.
In the step 3 of path computing, including：
Step 31：Construct distance matrix.All the points are divided into n cluster by step 2, and all the points in certain cluster are added
Origin information constructs a distance matrix.N cluster can construct n distance matrix；
When implementing, processing step 2 marks off the cluster come one by one.Assuming that there are cluster A, (node includes：a1,a2,……,
ak).The information that these points and origin are selected from distance matrix, constructs a distance matrix (symmetrical matrix of k+1 ranks).Such as
Fruit step 2 cluster result is n cluster, then needs to generate n different distance matrixs.
Step 32：Path is calculated using branch and bound method.Branch-and-Bound Algorithm is used to each distance matrix, is calculated
Go out the shortest path by all the points in this cluster from origin；
When implementing, the distance matrix that step 31 generates is come out one by one using Branch-and-Bound Algorithm.
Step 33：Complete the path computing of all clusters.Circulation step 32, until n cluster all calculates shortest path；
When implementing, cycle carries out step 32, until all data processings are complete, according to goods amount and time check each path
Whether rationally.
The invention discloses the method for solution Vehicle Routing Problems (Vehicle Routing Problem, VRP) a kind of,
The step of this method includes：(1) data prediction step：Concentrate information that acquisition each puts (including to origin from initial data
Distance, at a distance from other points, arrival time the latest, the travel speed v (all vehicle speeds are the same) of vehicle), use is different
Calculation formula is spent, the distinctiveness ratio between each point is calculated, constructs dissimilarity matrix；(2) clustering step：The suitable cluster of selection
Method, iteration cluster, until super large cluster is not present in cluster result；(3) path computing step：Use Branch-and-Bound Algorithm
Each cluster is analyzed, the best traffic program from origin by all the points in cluster in each cluster is calculated.
The present invention provides a kind of algorithms solving Vehicle Routing Problems, and for small-scale problem, he is an essence
True resolving Algorithm, for large-scale problem, the heuristic solution that it is provided has very high accuracy and feasibility.With existing vehicle
Routing problem algorithm is compared, and the beneficial effects of the present invention are large-scale dataset is divided into a series of small rule by clustering
Modulus problem reduces the complexity of problem, is allowed in finite time to complete；Secondly, it is proposed that a kind of rational different
Computational methods are spent, the reasonability of cluster result is improved；Again, the algorithm being combined using clustering and branch-and-bound, is carried
The high accuracy of result.Therefore the present invention proposes a rational solution to solve Vehicle Routing Problems.Vehicle road
Effective solution of diameter problem can greatly optimize logistics transportation route, improve logistic efficiency, shorten logistics time, reduce logistics
Cost.
The present invention can provide a heuristic solution in finite time for the Vehicle Routing Problems of NP difficulty, compared to other
Same type algorithm, its result are more rationally more accurate in some aspects.In terms of practical application, logistic industry has become drawing
Dynamic national economic development and the important motivity source for improving Living consumption, effective solution Vehicle Routing Problems are in optimization object
Flow path, raising logistic efficiency, shortening logistics time, reduction logistics cost etc. have great function.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations
Also it should be regarded as protection scope of the present invention.
Claims (7)
1. a kind of method solving Vehicle Routing Problems, which is characterized in that including：
(1) data prediction step：The information that acquisition is each put is concentrated from initial data, using distinctiveness ratio calculation formula, is calculated
Distinctiveness ratio between each point constructs dissimilarity matrix；
(2) clustering is carried out, including：
Step 21：Select clustering method；
Step 22：It based on dissimilarity matrix, is clustered using selected clustering method, data set in large scale is divided
For the cluster of scale is smaller, often after the completion of wheel cluster, if still remaining super large cluster, adjusting parameter carries out cluster point to the cluster
Analysis, until the scale of all clusters of division is all met the requirements；
(3) path computing is carried out, including：
Each cluster is analyzed using Branch-and-Bound Algorithm, is calculated in each cluster from origin by all the points in cluster
Best traffic program；
In the step 3 of path computing, including：
Step 31：Construction distance matrix adds all the points in either cluster if in step 2, all the points are divided into n cluster
Upper origin information, constructs a distance matrix, and n cluster can construct n distance matrix；
Step 32：Branch-and-Bound Algorithm is used to each distance matrix, is calculated from origin by all the points in this cluster
Shortest path；
Step 33：Return to step 32, until n cluster all calculates shortest path.
2. the method for solving Vehicle Routing Problems as described in claim 1, which is characterized in that the information each put includes to original
The distance of point, with other put at a distance from, the travel speed of arrival time and vehicle the latest.
3. the method for solving Vehicle Routing Problems as described in claim 1, which is characterized in that in step 21, if vehicle is transported
Goods amount energy meet demand, then using division methods come cluster dividing；If without considering vehicle fleet size, hierarchical clustering or base are used
Carry out cluster dividing in the clustering method of density.
4. the method for solving Vehicle Routing Problems as described in claim 1, which is characterized in that step 22：Regulation point quantity is big
It is super large cluster in the cluster of n/1000, after carrying out first round cluster using the method for selection, p cluster is divided into, if there is super large
The node of cluster A, A includes：a1,a2,……,ak, then from the node selected in dissimilarity matrix in A, the phase of a k rows k row is constructed
Different degree matrix adjusts the parameter of clustering method, carries out clustering, a series of new clusters is obtained, until all clusters are not super
Until big cluster.
5. the method for solving Vehicle Routing Problems as described in claim 1, which is characterized in that in step 31, processing one by one walks
Rapid 2 mark off the cluster come, if there are cluster A, A nodes include：a1,a2,……,ak, each point of A nodes is selected from distance matrix
And the information of origin, construct k+1 rank apart from symmetrical matrix, it is a not at n if step 2 cluster result is n cluster
The same distance matrix.
6. the method for solving Vehicle Routing Problems as described in claim 1, which is characterized in that data prediction step 1 is specific
Including：
In step 11, a view or table are done in original database, it is assumed that the quantity of point is n, and the attribute of table includes：In n point
Any two points, such as point i to initial point distance li, point j to initial point distance lj, point i arrival time t the latestiAnd point j is reached the latest
Time tj, the information of n point is inserted into table, a n rank symmetrical matrix is made, between the i-th row j row storages point i and point j away from
From value lij.Constant Vehicle Speed is v, and distance matrix is：
Step 12：The distinctiveness ratio of any two points is calculated, wherein：
Distance between two points lijSmaller, distinctiveness ratio is smaller；
Distance between two points are respectively smaller from the distance proportion of origin compared to 2 points, and distinctiveness ratio is smaller；
The variable haulage time of point is bigger, smaller with the time correlation repellency of other points, smaller with the distinctiveness ratio of other points；
2 points the latest arrival time otherness it is bigger, the time correlation repellency between 2 points is smaller；
The mathematical formulae of distinctiveness ratio between 2 points：
According to above-mentioned formula and the collected data of step 11, the distinctiveness ratio between any two points is calculated.
7. the method for solving Vehicle Routing Problems as claimed in claim 6, which is characterized in that
Cycle carries out step 12, until calculating all dij.N rank distinctiveness ratio symmetrical matrixes are constructed, the value of the i-th row jth row is
The distinctiveness ratio d of point i and point jij。
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