CN111860957A - Multi-vehicle type vehicle path planning method considering secondary distribution and balance time - Google Patents

Multi-vehicle type vehicle path planning method considering secondary distribution and balance time Download PDF

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CN111860957A
CN111860957A CN202010562320.1A CN202010562320A CN111860957A CN 111860957 A CN111860957 A CN 111860957A CN 202010562320 A CN202010562320 A CN 202010562320A CN 111860957 A CN111860957 A CN 111860957A
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truck
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route
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CN111860957B (en
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李伟
支琛
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Zhejiang University of Technology ZJUT
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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

A multi-vehicle-type vehicle path planning method considering secondary distribution and balance comprises the steps of carrying out mathematical modeling on logistics distribution problems, regarding the logistics distribution problems as a single transportation center and including secondary distribution derived VRP problems, taking the minimum cost of vehicles and the balanced vehicle working time as optimization targets, carrying out initialization clustering on customer points by using the characteristics of a Veno diagram, designing a 'borrowing-in and borrowing-out' idea to redistribute the customer points among routes, and meanwhile, enhancing the searching capability of an optimal distribution sequence in the routes by using a heuristic algorithm. And finally, verifying through an example, and obtaining different path results by adjusting given parameters so as to make decisions by a manager. The invention obtains a more reasonable path distribution result; the condition of secondary distribution can be considered, the working time of each route can be distributed in a balanced manner, a more appropriate vehicle type can be selected from multiple vehicle types for distribution tasks, and the total distribution cost can be reduced on the premise that the result meets the distribution limiting condition.

Description

Multi-vehicle type vehicle path planning method considering secondary distribution and balance time
Technical Field
The invention relates to the related fields of SPFA algorithm, Voronoi diagram, path saving algorithm, reference point-based adjacent insertion path algorithm and the like, and discloses a multi-vehicle type vehicle path planning method considering secondary distribution and balance.
Background
Modern logistics, as a 'third profit source', gradually become 'source running water' for realizing stable and high-starting-point development of national economy. In the original logistics background, the distributor mostly depends on the experience of the distributor to distribute the distribution sequence of the customer points. Nowadays, under the informatization addition of a logistics distribution center, the distribution route optimization of an algorithm greatly improves the logistics distribution efficiency. However, the optimization of logistics by theoretical algorithms is still potentially huge. In practical situations, when the customer points included in the route are close to the distribution center, a situation that "after the distributor completes the distribution task and returns to the distribution center, the actual working time of the distributor is short" may be caused, if the distributor goes to work, time utilization may be insufficient, which is a loss for the logistics company, and the distributor may be scheduled to start again to perform the secondary distribution task on the day. The balance of the working time among different distributors represents the reasonability and fairness of the workload distribution and is also an important consideration factor.
The concept was first proposed by Dantzig, 1959, at home and abroad for the problem of vehicle routing and for solving the problem of routing for the transportation of gasoline from large terminals to service stations. The depth of the VRP problem is then increasingly mined and derivative VRP-based problems and their solutions are gradually proposed. Azi Nabila et al, for the VRP problem of multiple use vehicles (vehicles), define routes for customers by revenue, demand and time windows, and introduce a branch pricing method to solve the problem. Zhang Zizhen et al developed a multi-objective modulo arithmetic (MMA) to solve the VRP problem with path balancing (VRPRB) that integrated the problem-specific local search process into a multi-objective evolutionary algorithm. Kudzuvine and the like adopt quantum bit to design chromosome structure, and quantum genetic algorithm is designed for solving the VRP problem of multiple vehicle types.
VRP is an NP-hard problem, meaning that it is difficult to solve accurately when the problem reaches a certain scale. The exact algorithm cannot traverse all combinations of routes at the computational speed of existing processors when the delivery size is slightly larger. Simple heuristic methods such as the mile reduction method and the nearest interpolation method have high calculation speed, but are also only suitable for small-sized VRP problems, and the result is poor when the calculation scale is large. The two-stage method aims at the idea of grouping before routing of client points, and is suitable for large-scale VRP problems. For example, Wangwen and the like use a k-means clustering algorithm to distribute lines, and gradually convert the problem into a small-scale traveler problem. However, the k value of the k-means clustering algorithm is inconvenient to grasp manually, which is unfavorable for limiting the time and the cargo capacity of the vehicle, and the algorithm is sensitive to noise and abnormal points, and if relatively outlier customer points exist, the clustering result is poor.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a multi-vehicle type vehicle path planning method considering secondary distribution and balance, which can calculate order information with large data volume and obtain a more reasonable path distribution result; the condition of secondary distribution can be considered, the working time of each route can be distributed in a balanced manner, a more appropriate vehicle type can be selected from multiple vehicle types for distribution tasks, and the total distribution cost can be reduced on the premise that the result meets the distribution limiting condition.
The logistics distribution Problem is mathematically modeled, is regarded as a single transportation center, comprises a derivative VRP Problem of secondary distribution, and is called a multi-Vehicle type Vehicle path Problem (CMMVRPRB) with capacity of constraint and time balance constraint, takes the minimum cost of vehicles and the balanced Vehicle working time as optimization targets, utilizes the characteristics of a Weino graph to initialize clustering of client points, designs the idea of borrowing and borrowing to redistribute the client points among routes, and simultaneously utilizes a heuristic algorithm to enhance the searching capability of an optimal distribution sequence in the routes. And finally, verifying through an example, and obtaining different path results by adjusting given parameters so as to make decisions by a manager.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a multi-vehicle type vehicle path planning method considering secondary distribution and balance time comprises the following steps:
1) reading data;
2) judging whether the distance between the clients and the time matrix are complete or not according to the data, and directly jumping to the step 3) if the distance between the clients and the time matrix are complete; if not, using SPFA shortest path algorithm to perfect distance and time matrix;
3) by using a two-stage method for reference, initializing a cluster for a client point by utilizing a first-order proximity characteristic of a Voronoi diagram;
4) respectively redistributing customer points of different lines according to the sequence of time limit, multi-vehicle type, secondary distribution and time balance by using a 'borrowing-in and borrowing-out' thought aiming at distribution limit conditions, and optimizing the distribution sequence in the lines by using 3-opt [ ]andor-opt [ ] operators during the period;
5) selecting lines according to the ascending sequence of the distance between the customer point distribution and the distribution center, carrying out 'melon division' on the lines, and distributing the lines including the customer points to other lines to serve as distribution tasks of secondary distribution;
6) finally, the maximum difference in man-hours for using the vehicle is minimized as much as possible by performing the calculation for the time of balance.
The logistics distribution problem to which the present invention refers is described below: it is known that logistics distribution centers have different types of trucks that transport goods for local distribution merchants. The rated maximum cargo capacity and the trip cost of different types of trucks are different, and the trip cost of each truck is in positive correlation with the maximum cargo capacity. The truck carrying a certain unit quantity of goods starts from the logistics center, passes through a plurality of merchants on the way so as to meet the requirements of the merchants, and returns to the logistics center after delivery is finished; and if the remaining working time is sufficient, the truck starts from the logistics center again after carrying out secondary loading, and returns to the logistics center after completing the delivery task. The working time of each truck is required to be not more than a specified value, and the balance among a plurality of routes is ensured; the actual freight volume of the truck does not exceed the rated maximum freight volume every time of transportation; minimizing the sum of the costs of transporting the required vehicles; each route is as optimal as possible for the delivery order of the customer.
On the basis of the original VRP problem, the invention considers secondary transportation, time consumption balance among routes and multiple vehicle types, and is called as the multi-vehicle type vehicle path problem with capacity of constraint and load balance constraint. Aiming at the problems, a multi-vehicle type vehicle path planning method considering secondary distribution and balance time is designed. Firstly, preprocessing order data and an incomplete distance matrix by utilizing an SPFA algorithm, and calculating a complete travel distance matrix and a complete travel time matrix containing all nodes; the algorithm initializes the clusters of the clients based on the first-order proximity of the Voronoi diagram, so that the calculation complexity is greatly reduced, and the problem caused by outliers is avoided; the idea of borrowing and lending provided by the invention can reasonably redistribute the customer points among the routes; when the calculation of the secondary distribution is considered, a customer point which is close to the distribution center is used as a tail list of the secondary distribution; during balancing, the ban table is used to prevent customer points from being repeatedly assigned. In the calculation process, the client distribution sequence in a single line is optimized by using a 2-opt algorithm and an or-opt algorithm.
The invention has the following beneficial effects: 1. reasonable path distribution results can be obtained relatively quickly for order information with large data volume. 2. The total distribution cost can be minimized on the premise of simultaneously considering secondary distribution, time consumption balance and multiple vehicle types. 3. The working time of the truck can be distributed more evenly on the premise of only increasing less time, and fairness is guaranteed.
Drawings
FIG. 1 is a flow chart of the algorithm process showing a general description of each step of the algorithm.
Fig. 2 is a relational diagram between database tables, which mainly shows the structure of different data tables of the database and the association relationship of association according to foreign key reference.
Fig. 3 is a schematic diagram of the thought of "borrowing and lending" for showing the thought meaning of the "borrowing and lending" operation in the practical use case. Where (a) shows an example of a "lending" operation, that is, when a route is used to allocate a customer point, the customer point in the route needs to be appropriately allocated to another route when the specified time limit is exceeded, so that the number of customer points in the route is reduced accordingly, and the time limit is not gradually reduced until the specified time limit is satisfied. (b) An example of the "borrowing" operation is shown, that is, when the time of use does not reach the specified time limit, the customer points in other routes can be tried to be inserted into the present route, and if the time of use meets the specified time limit, the customer points are formally transferred.
Fig. 4 is a schematic diagram of "borrowing" operation-search area division, which is used to show how to filter the client points that may be "borrowed" in the "borrowing" operation.
Fig. 5 is a schematic diagram of a vehicle model selection process showing how to select a suitable vehicle model for a distribution route.
Fig. 6 is a diagram showing calculation results, showing paths of different routes by using a high-grade map, wherein the different paths are represented by customer points and sequential lines of different colors.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 6, a multi-vehicle type vehicle path planning method considering secondary distribution and balancing time includes the steps of:
1) reading data;
2) judging whether the distance between the clients and the time matrix are complete or not according to the data, and directly jumping to the step 3) if the distance between the clients and the time matrix are complete; if not, using SPFA shortest path algorithm to perfect distance and time matrix;
3) by using a two-stage method for reference, initializing a cluster for a client point by utilizing a first-order proximity characteristic of a Voronoi diagram;
4) respectively redistributing customer points of different lines according to the sequence of time limit, multi-vehicle type, secondary distribution and time balance by using a 'borrowing-in and borrowing-out' thought aiming at distribution limit conditions, and optimizing the distribution sequence in the lines by using 3-opt [ ]andor-opt [ ] operators during the period;
5) selecting lines according to the ascending sequence of the distance between the customer point distribution and the distribution center, carrying out 'melon division' on the lines, and distributing the lines including the customer points to other lines to serve as distribution tasks of secondary distribution;
6) Finally, the maximum difference in man-hours for using the vehicle is minimized as much as possible by performing the calculation for the time of balance.
The invention uses a two-stage method for reference, firstly, a first-order proximity based on a Voronoi diagram is used for initializing a cluster for customer points, then customer points of different lines are redistributed according to the distribution limiting conditions by utilizing the 'borrowing-in and borrowing' thought proposed by a pen person according to the sequence of time-of-use limitation, multi-vehicle types, secondary distribution and time-of-use balance, during the period, the distribution sequence in the lines is optimized by using 3-opt and or-opt operators, and after the calculation of the time-of-use of secondary distribution and balance is considered respectively, the algorithm is ended.
Data warehouse design
And establishing data tables of a data warehouse according to the vehicle path algorithm requirement and the service related data, wherein the data tables comprise a customer basic information table, a distribution center table, a cargo order table, a customer point-to-point distance table, a customer point-to-point time table and a road information table.
The basic information of the above five tables is introduced as follows:
customer basic information table (customer _ info)
The client basic information table contains client basic information and has 7 fields including a client ID, a client name, a road ID (foreign key) where the client is located, a distance between the client and the start of the road where the client is located, longitude and latitude of the client, and a direction where the client is located with respect to the road.
Distribution center basic information table (department _ info)
The distribution center basic information table contains distribution center basic information and has 7 fields including a distribution center ID, a distribution center name, a road ID (external key) where the distribution center is located, a distance between the distribution center and a start point of the road where the distribution center is located, longitude and latitude of a distribution center point, and a direction of the distribution center point relative to the road.
Goods order form (order _ info)
The order form contains information about orders, and even in the case of a central distribution center, orders of different dates may be different. There are 6 fields in the table, including order ID, customer ID (foreign key), cargo demand, time required to unload, date of order, and distribution center ID (foreign key).
Client Point-to-Point distance Table (distance _ info)
The client point-to-point distance table is used for storing the distance information between the client points after the order information is preprocessed. There are 4 fields in the table, including unique identification ID, start client ID (foreign key), end client ID (foreign key), distance.
Customer Point-to-Point timetable (time _ info)
The client point-to-point time table is used for storing the client point-to-point time information after the order information is preprocessed. There are 4 fields in the table, including unique identification ID, start client ID (foreign key), end client ID (foreign key), time.
Wherein, each table is associated according to the external key reference, and the table relationship and structure are shown in figure 2.
The model establishing process of the embodiment is as follows:
taking G ═ V, E as a distribution network, wherein V is a node set, V ═ {0,1,2,3, …, n }, 0 represents a distribution center, and the rest represent customer points; e is a collection of distance time matrixes between the distribution center and the client points, and E { (i, j) | i, j belongs to V, i ≠ j }; t is ti,jThe time required for the truck to go from point i to point j; q. q.siDemand for customer point i; x is the number ofi、yiRespectively representing the longitude and latitude of the client point i; k is a set of different vehicle models, K ═ 1,2k、ck、pk、ukRespectively representing the maximum cargo capacity, the travel cost, the provided vehicle number and the currently used vehicle number of the truck type with the number K, wherein K belongs to K; truck is the set of trucks in actual use, Truck ═ 1,2NoLine1, model number in K of No wagonNo、Line2NoThe data are ordered arrays which respectively represent the sequence of the passing points of the first delivery and the second delivery of the freight car with the No number, if the arrays are not empty, the length is not less than 2, and the starting point and the tail point are delivery centers 0, t1No、.w1NoTime and load of the one-time distribution route of the No-numbered truck, t2No、w2NoThe same, wherein No belongs to Truck; ts is the working time defined by each truck per day; b is the acceptable maximum difference in shop hours.
Up to now, a mathematical model considering the logistics problem is as follows.
Figure BDA0002545044370000081
TNo＝mint1No+mint2No＜Ts,No∈Truck (2)
max(Ti)-min(Tj)≤B,i,j∈Line (3)
w1No,w2No＜lwk,No∈Truck,k＝carTypeNo(4)
Figure BDA0002545044370000082
Figure BDA0002545044370000083
Figure BDA0002545044370000084
Figure BDA0002545044370000085
Equations (1) to (4) are target functions based on the constraint. C in the formula (1) represents that the sum of the costs of the vehicles required for transportation is minimum; the formula (2) shows that the delivery sequence of each truck to the client in the first delivery and the second delivery is optimal, so that the time consumption of each route is shortest, TNoThe sum of the time of the primary distribution route and the time of the secondary distribution route is less than the specified working time; the formula (3) represents the time balance, and represents that the difference between the longest and the shortest of the freight car in the working process meets the maximum time balance difference acceptable by the regulation; equation (4) indicates that the truck is not overloaded during each delivery task.
Equations (5) and (6) respectively represent the time required for the truck to go from the distribution center, pass through the customer site, and return to the distribution center after the delivery is completed each time the truck performs the delivery task, and the time is 0 when the truck does not need to perform the secondary delivery. And the formula (7) and the formula (8) respectively show that the cargo capacity of each delivery task of the truck is the sum of the demands of the customers passing through the route, and when the truck does not need secondary delivery, the cargo capacity is 0.
Initializing a cluster based on a voronoi diagram: on the premise of large-scale customer volume, the vehicle path algorithm is an NP-hard problem, which means that an exhaustion method is infeasible, while the heuristic algorithm can only make the result tend to be optimal as much as possible, and the larger the calculation scale is, the more difficult the optimization is ensured in a certain time. The method uses a scheme of establishing an initial solution based on Voronoi proximity, converts the whole vehicle path problem into a small part of traveler problem, and reduces the complexity of an algorithm. The distribution problem includes the condition of 'multi-vehicle type', the maximum loading capacity of the vehicles is not unique, and the sum of the demand of each cluster in the initial solution is ambiguous when compared with the reference capacity. The method is improved aiming at the requirements of multiple vehicle types, and comprises the following steps:
3.1) creating a voronoi diagram for the set of nodes V, populating a first order voronoi diagram neighborhood list of customer points, wherein distribution centers are not included;
3.2) creating a queue R, and pressing all the first-order adjacent node pairs of the voronoi diagram into the queue R, wherein each client point is independently calculated as a class;
3.3) the customer point pairs i-j in R are according to t in the time matrixi,jSequencing in an ascending order;
3.4) providing the maximum cargo capacity of different vehicle types and the number of vehicles to be provided according to the vehicle type data set K, and calculating the average maximum cargo capacity w of the vehicles to be providedavgWhich satisfies the equation
Figure BDA0002545044370000101
3.5) taking out the client point pair i-j at the head of the queue in the R, and if i and j are in the same class, not operating; otherwise, judging whether the class of i and j is merged: regarding the class of the client i as ViIn the same way, obtain VjWill be class ViThe total demand of the goods is regarded as QiIn the same way, Q is obtainedjIf Q isi+Qj≤wavgMerging class Vi，Vj(ii) a Otherwise, not performing clustering operation;
3.6) repeatedly executing step 3.5) until the list R is empty; get initial cluster partition Line1 ═ Line11,Line12,…,Line1pThe Truck model is not determined when the Truck type is determined;
compared with a k-means clustering algorithm, the clustering algorithm based on the voronoi diagram only uses a first-order adjacent client point pair, so that the time complexity of operating data is greatly reduced, and the clustering performance is improved. The cluster algorithm can dynamically control the number of clusters according to the reference capacity without setting in advance. Due to the principles of voronoi diagram rendering, voronoi diagram-based clustering algorithms inherently prefer datasets with outliers. The advantages enable the clustering algorithm based on the voronoi diagram to be more suitable for point clustering in the vehicle path problem and obtaining an initial solution.
Optimization of delivery sequence within route: after the initial cluster is obtained, the initial cluster is considered as a distribution point set for one-time distribution, and at this time, the required time of each route under the optimal distribution sequence needs to be calculated. The algorithm respectively uses a saving algorithm and an adjacent insertion method based on a reference point to obtain two initial solutions, then uses a 3-opt and an or-opt local search operator to respectively carry out distribution sequence optimization of a single path on the two initial solutions, and the optimization process is as follows:
4.1) create the optimization failure number F and initialize it to 0.
4.2) obtaining the number n of the clients of the route, and obtaining the suitable optimization failure limit times FL according to different numbers n.
4.3) F ═ F +1, and the time t before optimization was calculated from equation (5)pre. Obtaining a Random number with a value of 0 or 1 by using a Random function, and performing 3-opt algorithm optimization on the line when the Random function is 0; and when the value is 1, carrying out or-opt algorithm optimization on the line. The optimized time t is obtained according to the formula (5)afterWhen t isafter＜tpreIf the optimization is successful, F is reset to 0, and the route is updated; otherwise, the route is not updated.
4.4) step 4.3) is repeatedly performed until F > FL. And returning to the optimization line, and ending the optimization process.
After the two initial solutions are respectively subjected to a line optimization process, two optimized solutions and the time t of each solution are obtained saving、tinsertThe solution with less time taken is taken as the following operation Line1NoAnd the other solution is discarded.
The idea of "borrowing in and out": fig. 3 shows the idea of "borrowing and lending". Wherein part (a) shows the "loan" operation. When allocating customer points, the specified time limit is exceeded when the optimized route takes time, t1NoWhen the number of the client points in the route is more than Ts, the client points in the route need to be properly distributed to other routes, so that the number of the client points in the route is reduced, and the time consumption can not be gradually reduced until a specified time limit is met, namely 'lending'.
(b) The "borrow" operation is partially shown. When used, it is still redundant with respect to the specified time period, i.e. t1NoIf Ts is less than Ts, the customer points closer to the route in other routes can be distributed to the route in an attempt, and if the customer points meet the specified time limit in use, the customer points are formally transferred, namely, "borrow".
After the optimization of the delivery sequence within the routes is complete, heap A is created, where each optimized route is added to represent an "unshaped" route. And then, entering a circulating operation until A is empty and jumping out. In the circulation body, A is traversed first, and the time t1 of each line in A is obtainedNoCoordinates of the midpoint of the customer in the route (cen 1X) No,cen1YNo) The average distance between the customer points included in the route and the distribution center, disAvgNoWherein
Figure BDA0002545044370000121
Figure BDA0002545044370000122
Get disavgThe largest, i.e. most distributed customer site, route Line1farAnd aiming at the route, the client points are redistributed by using the thought of borrowing and lending, and after the distribution is finished, the line in the A is removedThe number of ways far.
The "borrow" and "borrow" operations of each route to the customer site are described in detail below.
Lending: when line hours are greater than limit hours, i.e. t1far(> Ts.), customer points cust closer to the distribution center in the route need to be "borrowed" to be distributed to other lines closer. When only Line1 remains in AfarIf no other line can be lent, adding a new line and distributing the customer point cust to the newly-built line; when more than one Line1 exists in AfarAccording to the coordinates (x) of the customer point custcust,ycust) Customer midpoint coordinates (cen 1X) with other lines in ANo,cen1YNo) Determine their Euclidean distance disfar,NoI.e. by
Figure BDA0002545044370000123
Get disfar,NoMinimum Line1NoAnd assigns the customer point cust to the line. The "borrow" operation is cycled through until t1farTs is less than or equal to, the Line is 1 after jumping out of the loan cyclefarA "borrow" operation is performed.
Borrowing: when the line time is less than the limit time, i.e. t1 far< Ts and more than one Line1 in AfarThis operation is performed. And creating a node set Maybe for storing the client points which can be lent, acquiring, merging the client points of the rest lines in the A, and storing the client points in the Maybe. Obtaining Line1farThe time distance d between the customer point futthst farthest from the distribution center and the distribution center0,furthestI.e. by
d0,furthest＝max(d0,i),i∈Line1far(13)
. According to d0,furthestCustomer midpoint coordinate C (cen 1X)far,cen1Yfar) And a delivery center coordinate P (x)0,y0) Drawing a shape range on a map in a certain proportion, wherein the pattern satisfies the formula
Figure BDA0002545044370000131
Or formula
Figure BDA0002545044370000132
Wherein B represents a boundary point of the graph; t represents a custom time range; a, b and c represent corresponding proportions, and different values can obtain different shapes. A is 1.5, b is 0.5, C is 2, t is 15 minutes, and the range is a union of "a gourd-like shape covering the distribution center point P and having a larger lateral radius as the longitudinal direction is closer to the customer center point coordinate C" and "any region reachable within 15 minutes from the distribution center point P", as shown in fig. 4. Customer points located in the graph range in the Maybe are screened, and then the Maybe is sorted in an ascending order according to the Euclidean distance between each point of the Maybe and a point coordinate C in the customer. Traversing Maybe, adding the client points obtained each time into the line by using an insertion method, and then obtaining the time t1Aft far. When the restriction is satisfied, i.e. t1AftfarTs is less than or equal to the value of Ts, the borrowing is successful, the skipping is performed, and the borrowing operation is circulated until no client point which can be successfully borrowed in Maybe exists; line timeout after adding point, i.e. t1AftfarAnd more than or equal to Ts, indicating that the borrowing fails, rolling back the insertion point operation and continuing the traversal.
Each line needs to go through a "loan-in-loan" process, where "loan" may occur and "loan" must occur. The line obtained through the operation of the section meets the requirement when the line is used, namely the line does not need to be lent, and can not receive any other customer points, namely the line can not be lent, the line is marked as shaped, after the operations such as vehicle type selection and the like are carried out, the line is removed from the pile A, and then whether the circular operation is continued or not is judged according to whether the line still exists in the pile A. And updating Line1 and Truck after the loop is finished.
Selecting a vehicle type: in the initial point-division of the customer site, the data relating to the load capacity is to provide the average maximum load of the vehicle, which is used only for load reference and no specific vehicle type is selected. After the operation is completed, selecting the types of the trucks in different routes.
In operation, one Line1 for each "shaped" routeNoAnd selecting the vehicle type of the truck. Obtaining the required quantity w1 of the circuitNoTraversing the vehicle type set K and calculating the load capacity wl of different vehicle typeskAnd trip cost ckAverage unit cargo distribution cost of lower, cAvgkWhich satisfies the formula
Figure BDA0002545044370000141
Taking cAvgkAnd the vehicle type k with the minimum result is used as the current candidate vehicle type of the route. As shown in fig. 5, sorting the vehicle types in K according to the maximum cargo capacity (generally, the larger the maximum cargo capacity of the truck is, the larger the travel cost is), starting from the vehicle type K, performing a first round of ascending search, and for the currently searched vehicle type curr, if there are remaining vehicles in the vehicle type, that is, pcurr＞ucurrFormally selecting the vehicle type to carry out the distribution task of the current route; if no vehicle remains, the vehicle type k is searched for in a descending order of the second round, and if no vehicle remains, the user provides too few vehicles.
Obtaining the final selected vehicle type final of the route on the premise of providing sufficient vehiclesfinalAnd performing self-increment operation. At this time, if the vehicle type is selected in the second round of search, it indicates that the vehicle is overloaded, and the route needs to be subjected to the operation of "borrowing in and out" again, and the condition restrictions of time consumption and overload need to be considered at the same time.
So far, the result obtained by the algorithm is already suitable for the VRP problem of the standard multi-vehicle type.
Consider the calculation of the secondary delivery: in general, the remaining operating time of the vehicle is not sufficient before the second delivery task is performed, so that a customer site near the delivery center preferably uses a trailer as the second delivery task. The "borrowing and lending" operation of the algorithm is performed in descending order according to the Euclidean distance between the customer midpoint and the distribution center of each route, so that the distribution of each truck is knownLine1NoThe larger the No, the closer its customer site distribution is to the distribution center. When the customer point allocation is performed in consideration of the secondary distribution, the Line1 with the largest No is takencloseAs a "melon" line, its associated customer points are assigned to the secondary distribution lines of other trucks; the method comprises the following steps:
5.1) obtaining the maximum number close in the transport. Creating an array L when the secondary distribution route Line2 of the truckcloseIf not, copy it to L; otherwise, the primary distribution route Line1 of the truckcloseCopy to L.
5.2) create an array lineArr, store the numbers of all trucks except close in Truck, where lineArr ═ {1,2
Figure BDA0002545044370000151
The lineArr is assigned to the total delivery time T of each truck NoAnd (5) sorting in a descending order.
5.3) traverse the lineArr, number curr for each truck, obtain its maximum cargo capacity wlkWherein k is carTypecurr。
5.4) when L is empty, the route is represented, L is already divided by 'melon', and the step 1) is skipped. If L is not empty, if Line2currTo null, the customer point in L closest to the distribution center is assigned to Line2curr(ii) a If Line2currNot null, and the L medium is linked with Line2currThe customer point with the smallest Euclidean distance among the customer points is allocated to the Line2curr. Calculating the time of the secondary delivery t2 after inserting the customer pointcurrAnd the amount of cargo w2currIf the working time and the load of the truck curr both accord with the constraint conditions, circularly executing the step 5.4); and if the constraint condition is not met, continuously traversing the lineArr.
5.5) looping over to step 5.1) until the current line L can no longer be "melon".
5.6) updating Truck, Line1, Line2 and related data t1, t2, w1 and w 2.
Balancing the working time of each truck: in the process of balancing, a large number of trucks more are required to distribute some of the customer points distributed by the trucks to a small number of trucks less, and the distributed customer points are required to be reasonable for the trucks less. On the premise that the balance result still does not meet the balance requirement, a situation that two trucks continuously distribute the same customer point to each other may occur, which may cause dead cycles, in this embodiment, a ban stack is provided to store the numbers of truck passes, once a truck is distributed with the distribution customer points of other trucks, and the numbers are stored in the ban, the distribution customer point of the truck "can only go out" in the subsequent customer distribution, which effectively eliminates the above problems, and the steps when balancing the trucks are used are as follows:
6.1) create heap ban, initially empty. Obtaining an acceptable maximum working time difference B;
6.2) obtaining the maximum working time difference balance of each truck in the current result, if the balance is less than or equal to B, finishing the calculation, and returning the result. Otherwise, finding the truck less with the shortest working time, and acquiring the distribution route Line1 of the truck lessless、Line2lessAnd associated data t1less、t2less、w1less、w2less；
6.3) create the array AvailArr, where the wagon numbers are stored in addition to the wagon less and ban heap stores. When Line2lessIf the goods are empty, sorting the AvailArr in a descending order according to the working time of the trucks contained in the AvailArr; when Line2lessIf not, the customer midpoint cen2 of the line is obtainedlessTraversing AvailArr to obtain the customer midpoint cen of the primary distribution or secondary distribution line of each truck1or2Where the priority of the secondary distribution line is higher, cen2 is foundlessWith each cen1or2The AvailArr performs ascending sequencing on the trucks according to the Euclidean distance;
6.4) traversing AvailArr, and in the traversing process, for each truck, if the truck has a secondary distribution route, taking the truck, otherwise, taking the truck with the primary distribution route, regarding all the selected routes as currL, and sequencing the currL in an ascending order according to the distance between a customer point contained in the currL and a distribution center. While traversing AvailArr, we nests and traverses currL, while trying to assign the currently experienced customer point to a line Line2lessIn Line2lessAfter the distribution sequence is optimized, if the working time of the truck is not overtime and the goods are not overloaded, the distribution is successful, and the step 6.2) is skipped;
6.5) in step 6.4), if the allocation is still unsuccessful after traversing availArr, it indicates that the calculation for balancing can no longer be performed, and the calculation is ended and the result is returned.
And (3) realizing a vehicle path algorithm: according to the related concepts and steps described in the above stages, a multi-vehicle type vehicle path planning method in consideration of secondary distribution and balancing is realized. In this embodiment, a distribution demand order form (730 clients in total) of a logistics distribution center for one day is simulated, client information, distribution center information, order information, and a time and distance matrix between a client and the distribution center are loaded before an algorithm is executed, and then the algorithm is run to obtain a distribution path result, and the result is shown on a map as shown in fig. 6.
The vehicle path planning method provided by the embodiment can calculate order information with large data volume to obtain a more reasonable path distribution result, can consider the situation of secondary distribution, perform balanced distribution on the working time of each route, can select a more appropriate vehicle type from a plurality of vehicle types to perform distribution tasks, and can reduce the total distribution cost on the premise that the result meets the distribution limit condition.

Claims (7)

1. A multi-vehicle path planning method considering secondary delivery and balancing time, the method comprising the steps of:
1) reading data;
2) judging whether the distance between the clients and the time matrix are complete or not according to the data, and directly jumping to the step 3) if the distance between the clients and the time matrix are complete; if not, using SPFA shortest path algorithm to perfect distance and time matrix;
3) by using a two-stage method for reference, the first-order proximity characteristic of the voronoi diagram is utilized to initialize the cluster of the client points;
4) respectively redistributing customer points of different lines according to the sequence of time limit, multi-vehicle type, secondary distribution and time balance by using a 'borrowing-in and borrowing-out' thought aiming at distribution limit conditions, and optimizing the distribution sequence in the lines by using 3-opt [ ]andor-opt [ ] operators during the period;
5) selecting lines according to the ascending sequence of the distance between the customer point distribution and the distribution center, carrying out 'melon division' on the lines, and distributing the lines including the customer points to other lines to serve as distribution tasks of secondary distribution;
6) finally, the maximum difference in man-hours for using the vehicle is minimized as much as possible by performing the calculation for the time of balance.
2. The multi-vehicle type vehicle path planning method considering secondary distribution and balancing as claimed in claim 1, wherein in step 1), G ═ (V, E) is taken as a distribution network, where V is a node set, V ═ 0,1,2,3, …, n }, 0 denotes a distribution center, and the rest denote customer points; e is a collection of distance time matrixes between the distribution center and the client points, and E { (i, j) | i, j belongs to V, i ≠ j }; t is t i,jThe time required for the truck to go from point i to point j; q. q.siDemand for customer point i; x is the number ofi、yiRespectively representing the longitude and latitude of the client point i; k is a set of different vehicle models, K ═ 1,2k、ck、pk、ukRespectively representing the maximum cargo capacity, the travel cost, the provided vehicle number and the currently used vehicle number of the truck type with the number K, wherein K belongs to K; truck is the set of trucks in actual use, Truck ═ 1,2NoLine1, model number in K of No wagonNo、Line2NoThe data are ordered arrays which respectively represent the sequence of the passing points of the first delivery and the second delivery of the freight car with the No number, if the arrays are not empty, the length is not less than 2, and the starting point and the tail point are delivery centers 0, t1No、.w1NoTime and load of the one-time distribution route of the No-numbered truck, t2No、w2NoThe same, wherein No belongs to Truck; ts is the working time defined by each truck per day; b is the acceptable maximum working time difference of the goods shop;
to this end, a mathematical model considering the logistics distribution problem is as follows:
Figure RE-FDA0002638009630000011
TNo＝mint1No+mint2No＜Ts,No∈Truck (2)
max(Ti)-min(Tj)≤B,i,j∈Line (3)
w1No,w2No＜lwk,No∈Truck,k＝carTypeNo(4)
Figure RE-FDA0002638009630000021
Figure RE-FDA0002638009630000022
Figure RE-FDA0002638009630000023
Figure RE-FDA0002638009630000024
equations (1) to (4) are objective functions based on the constraint condition, and C in equation (1) represents that the sum of the costs of the vehicles required for transportation is minimum; the formula (2) shows that the delivery sequence of each truck to the client in the first delivery and the second delivery is optimal, so that the time consumption of each route is shortest, T NoThe sum of the time of the primary distribution route and the time of the secondary distribution route is less than the specified working time; the formula (3) represents the time balance, and represents that the difference between the longest and the shortest of the freight car in the working process meets the maximum time balance difference acceptable by the regulation; formula (4) shows that the truck is not overloaded during each delivery task;
the formula (5) and the formula (6) respectively represent the time required for the truck to return to the distribution center after the truck starts from the distribution center and passes through the customer point and the distribution is finished when the truck executes the distribution task each time, and the time is 0 when the truck does not need secondary distribution; and the formula (7) and the formula (8) respectively show that the cargo capacity of each delivery task of the truck is the sum of the demands of the customers passing through the route, and when the truck does not need secondary delivery, the cargo capacity is 0.
3. The method for planning the path of the multi-vehicle considering the secondary delivery and balance as claimed in claim 1 or 2, wherein in the step 3), the scheme of creating the initial solution based on the voronoi proximity is used to convert the overall vehicle path problem into a small part of the traveler problem, so as to reduce the complexity of the algorithm, the delivery problem includes the condition of "multi-vehicle type", the maximum cargo capacity of the vehicle is not unique, and this makes the sum of the demands of the initial solutions of each cluster ambiguous when compared with the reference capacity, and the steps are as follows:
3.1) creating a voronoi diagram for the set of nodes V, populating a first order voronoi diagram neighborhood list of customer points, wherein distribution centers are not included;
3.2) creating a queue R, and pressing all the first-order adjacent node pairs of the voronoi diagram into the queue R, wherein each client point is independently calculated as a class;
3.3) the customer point pairs i-j in R are according to t in the time matrixi,jSequencing in an ascending order;
3.4) providing the maximum cargo capacity of different vehicle types and the number of vehicles to be provided according to the vehicle type data set K, and calculating the average maximum cargo capacity w of the vehicles to be providedavgWhich satisfies the equation
Figure RE-FDA0002638009630000031
3.5) taking out the client point pair i-j at the head of the queue in the R, and if i and j are in the same class, not operating; otherwise, judging whether the class of i and j is merged: regarding the class of the client i as ViIn the same way, obtain VjWill be class ViThe total demand of the goods is regarded as QiIn the same way, Q is obtainedjIf Q isi+Qj≤wavgMerging class Vi，Vj(ii) a Otherwise, not performing clustering operation;
3.6) repeat step 3.5) until a list is reachedR is null; get initial cluster partition Line1 ═ Line11,Line12,…,Line1pAnd Truck set Truck ═ 1, 2.
4. The multi-vehicle type vehicle path planning method considering secondary delivery and balancing as recited in claim 2, wherein in the step 4), two initial solutions are obtained by using an economic algorithm and an adjacent interpolation method based on a reference point, and then single-path delivery sequence optimization is performed on the two initial solutions by using a 3-opt local search operator and an or-opt local search operator, and the optimization process is as follows:
4.1) creating an optimization failure frequency F and initializing the optimization failure frequency F to be 0;
4.2) obtaining the number n of the customers of the route, and obtaining the suitable optimization failure limiting times FL according to different numbers n;
4.3) F ═ F +1, and the time t before optimization was calculated from equation (5)preObtaining a Random number with a value of 0 or 1 by using a Random function, and performing 3-opt algorithm optimization on the line when the Random function is 0; when the value is 1, carrying out or-opt algorithm optimization on the line, and obtaining the optimized time t according to the formula (5)afterWhen t isafter＜tpreIf the optimization is successful, F is reset to 0, and the route is updated; otherwise, not updating the route;
4.4) repeatedly executing the step 4.3) until F is larger than FL, returning to the optimization line, and ending the optimization process.
5. The method as claimed in claim 3, wherein in the step 4), after the two initial solutions are respectively subjected to the route optimization process, the two optimized solutions and the time t of each solution are obtainedsaving、tinsertThe solution with less time taken is taken as the following operation Line1NoThe other solution is discarded;
after the optimization of the distribution sequence in the route is finished, a pile A is created, and each optimized route is added in the pile A to represent an unshaped route; then entering into circulation operation until A is Jumping out when empty; in the circulation body, A is traversed first, and the time t1 of each line in A is obtainedNoCoordinates of the midpoint of the customer in the route (cen 1X)No,cen1YNo) The average distance between the customer points included in the route and the distribution center, disAvgNoWherein
Figure RE-FDA0002638009630000041
Figure RE-FDA0002638009630000042
Get disavgThe largest, i.e. most distributed customer site, route Line1farAnd aiming at the route, the client points are redistributed by using the thought of borrowing and lending, and after the distribution is finished, the serial number far of the line in the A is removed;
lending operation: when line hours are greater than limit hours, i.e. t1farWhen the route is more than Ts., customer points cust which are closer to the distribution center in the route need to be allocated to other lines which are closer; when only Line1 remains in AfarIf no other line can be lent, adding a new line and distributing the customer point cust to the newly-built line; when more than one Line1 exists in AfarAccording to the coordinates (x) of the customer point custcust,ycust) Customer midpoint coordinates (cen 1X) with other lines in ANo,cen1YNo) Determine their Euclidean distance disfar,NoI.e. by
Figure RE-FDA0002638009630000043
Get disfar,NoMinimum Line1NoAnd assigns customer cut to the line, looping the "borrow" operation until t1farTs is less than or equal to, the Line is 1 after jumping out of the loan cyclefarExecuting a borrowing operation;
Borrowing operation: when the line time is less than the limit time, i.e. t1far＜Ts，And more than one Line1 in AfarExecuting the operation; creating a node set Maybe for storing the client points which may be "borrowed", acquiring, merging the client points of the rest of the lines in A, storing the client points in Maybe, and acquiring Line1farThe time distance d between the customer point futthst farthest from the distribution center and the distribution center0,furthestI.e. by
d0,furthest＝max(d0,i),i∈Line1far(13)
According to d0,furthestCustomer midpoint coordinate C (cen 1X)far,cen1Yfar) And a delivery center coordinate P (x)0,y0) Drawing a shape range on a map in a certain proportion, wherein the pattern satisfies the formula
Figure RE-FDA0002638009630000051
Or formula
Figure RE-FDA0002638009630000052
Wherein B represents a boundary point of the graph; t represents a custom time range; a, b and C represent corresponding proportions, different values are obtained to obtain different shapes, a is 1.5, b is 0.5, C is 2, t is 15 minutes, the shape is a combined range of a gourd-like shape which covers a distribution center point P and is larger in transverse radius as the longitudinal direction is closer to a client midpoint coordinate C, and a region which takes the distribution center P as a starting point and can reach any region within 15 minutes is selected from Maybe, client points which are located in a graph range are sorted in ascending order according to Euclidean distance between each point and the client midpoint coordinate C, the client points obtained each time are traversed, the client points are added into the line by using an insertion method, and then the time of use t1Aft is obtained farWhen the restriction is satisfied, i.e., t1AftfarTs is less than or equal to the value of Ts, the borrowing is successful, the skipping is performed, and the borrowing operation is circulated until no client point which can be successfully borrowed in Maybe exists; line timeout after adding point, i.e. t1AftfarNot less than Ts, means "borrow in"And if the operation fails, rolling back the insertion point operation and continuing the traversal.
6. The multi-vehicle type vehicle path planning method considering secondary delivery and balancing as claimed in claim 5, wherein in the step 5), the calculation considering secondary delivery: since the remaining operating time of the vehicles is not sufficient before the second delivery task is performed, the customer points near the delivery center are preferably regarded as the second delivery tasks by the trailer, and the "borrowing and lending" operation is performed in descending order according to the euclidean distance between the customer points of the routes and the delivery center, whereby it can be known that the delivery route Line "Line 1 for each truck is providedNoThe larger the No, the closer the distribution center is to the customer points, and when the customer point distribution is performed in consideration of the secondary distribution, the Line1 with the largest No is takencloseAs a "melon" line, its associated customer points are assigned to the secondary distribution lines of other trucks; the method comprises the following steps:
5.1) obtaining the maximum number close in the Truck, creating an array L, and when the secondary distribution route Line2 of the TruckcloseIf not, copy it to L; otherwise, the primary distribution route Line1 of the truckcloseCopying to L;
5.2) create an array lineArr, store the numbers of all trucks except close in Truck, where lineArr ═ {1,2
Figure RE-FDA0002638009630000053
The lineArr is assigned to the total delivery time T of each truckNoSorting in a descending order;
5.3) traverse the lineArr, number curr for each truck, obtain its maximum cargo capacity wlkWherein k is carTypecurr；
5.4) when L is empty, representing the route, L is already 'melon finished', jump to step 5.1), L is not empty, if Line2currTo null, the customer point in L closest to the distribution center is assigned to Line2curr(ii) a If Line2currNot null, and the L medium is linked with Line2currThe customer point with the smallest Euclidean distance among the customer points is allocated to the Line2currCalculating the time of the second delivery t2 after inserting the customer pointcurrAnd the amount of cargo w2currIf the working time and the load of the truck curr both accord with the constraint conditions, circularly executing the step 5.4); if the constraint condition is not met, continuously traversing the lineArr;
5.5) circularly skipping to the step 1) until the current line L can not be divided by 'melon';
5.6) updating Truck, Line1, Line2 and related data t1, t2, w1 and w 2.
7. The multi-vehicle type vehicle path planning method considering secondary delivery and balancing as claimed in claim 1 or 2, wherein in the step 6), the working time of each truck is balanced: in the process of balancing, more trucks more are certainly distributed to less trucks less, the distributed customer points are more reasonable for the trucks less, and on the premise that the balancing result does not meet the balancing requirement, the situation that two trucks continuously distribute the same customer point to each other may occur, which may cause dead cycles.
6.1) creating a heap ban, initially emptying, and acquiring an acceptable maximum working time difference B;
6.2) obtaining the maximum working time difference balance of each truck in the current result, if the balance is less than or equal to B, finishing the calculation, and returning the result; otherwise, finding the truck less with the shortest working time, and acquiring the distribution route Line1 of the truck less less、Line2lessAnd associated data t1less、t2less、w1less、w2less；
6.3) create the array AvailArr, where the wagon numbers are stored in addition to wagon less and ban heap, when Line2lessEmpty, with AvailArr according to the truck it containsSorting the working time in a descending order; when Line2lessIf not, the customer midpoint cen2 of the line is obtainedlessTraversing AvailArr to obtain the customer midpoint cen of the primary distribution or secondary distribution line of each truck1or2Where the priority of the secondary distribution line is higher, cen2 is foundlessWith each cen1or2The AvailArr performs ascending sequencing on the trucks according to the Euclidean distance;
6.4) traversing the AvailArr, wherein in the traversing process, for each truck, if the truck has a secondary distribution route, the truck takes the secondary distribution route, otherwise, the truck takes the primary distribution route, all the selected routes are regarded as currLs, the currLs are sorted in an ascending order according to the distances between the customer points contained in the currLs and the distribution centers, the currLs are nested and traversed in the traversing process of the AvailArr, and in the traversing process of the currLs, the customer points currently experienced are tried to be distributed to the Line2lessIn Line2lessAfter the distribution sequence is optimized, if the working time of the truck is not overtime and the goods are not overloaded, the distribution is successful, and the step 6.2) is skipped;
6.5) in step 6.4), if the allocation is still unsuccessful after traversing availArr, it indicates that the calculation for balancing can no longer be performed, and the calculation is ended and the result is returned.
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