CN111860957B

CN111860957B - Multi-vehicle-type vehicle path planning method considering secondary distribution and balancing

Info

Publication number: CN111860957B
Application number: CN202010562320.1A
Authority: CN
Inventors: 李伟; 支琛
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2020-06-18
Filing date: 2020-06-18
Publication date: 2023-12-29
Anticipated expiration: 2040-06-18
Also published as: CN111860957A

Abstract

A multi-vehicle-type vehicle path planning method considering secondary distribution and balancing is characterized in that mathematical modeling is conducted on logistics distribution problems, the logistics distribution problems are regarded as single transportation centers, the two-vehicle-type vehicle path planning method comprises the derived VRP problems of secondary distribution, cost of vehicles is minimum and working time of vehicles is balanced as optimization targets, the characteristics of a Veno diagram are utilized to initialize clusters of client points, the concept of borrowing and lending is designed to conduct reassignment of the client points among routes, and meanwhile searching capacity of optimal distribution sequences in routes is enhanced by means of heuristic algorithms. Finally, the verification is carried out through the calculation example, and different path results can be obtained through adjusting given parameters so as to be used for a manager to make decisions. The invention obtains a more reasonable path distribution result; the method can consider the condition of secondary delivery, can carry out balanced distribution on the working time of each route, can select a more proper vehicle type from multiple vehicle types to carry out delivery tasks, and can make the total delivery cost smaller on the premise that the result meets the delivery limiting condition.

Description

Multi-vehicle-type vehicle path planning method considering secondary distribution and balancing

Technical Field

The invention relates to the related fields of SPFA algorithm, veno diagram, saving path algorithm, adjacent insertion path algorithm based on reference points and the like, and discloses a multi-vehicle-type vehicle path planning method considering secondary distribution and balancing.

Background

Modern logistics are used as a third profit source spring, and gradually become source running water for realizing stable and high-starting-point development of national economy. In the prior logistics background, the distribution personnel mostly rely on self experience to distribute the distribution sequence of the client points. At present, the distribution route optimization of the algorithm greatly improves the logistics distribution efficiency under the informatization of the logistics distribution center. However, the optimization of the theoretical algorithm for logistics distribution is still potentially enormous. In practical situations, when the client points included in the route are all close to the distribution center, the situation that the actual working time is less after the distributor completes the distribution task and returns to the distribution center may be caused, if the distributor leaves the work in this way, the time utilization is insufficient, and the loss is caused to the logistics company, so that the distributor can be arranged to start again to perform the secondary distribution task on the same day. The balance of the working time length among different distribution operators represents the rationality and fairness of workload distribution and is also an important consideration.

Aiming at the vehicle path problem at home and abroad, the concept is firstly proposed by Dantzig equal to 1959 and is used for solving the path planning problem of transporting gasoline from a large dock to various service stations. The depth of VRP problems is then increasingly being explored, and VRP-based derivative problems and solutions therefor are increasingly being proposed. The VRP problem for multi-use vehicles (Multiple use of vehicles) is addressed by Azi Nabila et al by defining routes for customers through revenue, demand and time windows, and introducing a branch pricing approach. Zhang zin et al have developed a multi-objective modulo-cause algorithm (MMA) to solve the VRP problem (VRPRB) with path balancing, which integrates problem-specific local search processes into a multi-objective evolutionary algorithm. Ge Xianlong and the like adopt quantum bit to design chromosome structures, and a quantum genetic algorithm is designed for solving the problem of multi-vehicle type VRP.

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 route combinations at the computational speed of the existing processor at a somewhat larger scale of delivery. Simple heuristic methods such as mileage throttle method and recent insertion method have high calculation speed, but are only suitable for small VRP problem, and have poor result when the calculation scale is large. The two-stage method aims at the concept of grouping before routing of client points, and is suitable for the problem of large VRP. For example Wang Wenrui, etc. utilize k-means clustering algorithms to distribute lines to gradually translate the problem into small-scale traveler problems. However, the k value of the k-means clustering algorithm is inconvenient to grasp manually, which is disadvantageous to the limitation of the time and load of the vehicle, and the algorithm is sensitive to noise and abnormal points, and if relatively outlier client points exist, the clustering result is often 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 balancing, which can calculate order information with large data quantity to obtain a more reasonable path distribution result; the method can consider the condition of secondary delivery, can carry out balanced distribution on the working time of each route, can select a more proper vehicle type from multiple vehicle types to carry out delivery tasks, and can make the total delivery cost smaller on the premise that the result meets the delivery limiting condition.

The method comprises the steps of carrying out mathematical modeling on logistics distribution problems, regarding the logistics distribution problems as a single transportation center, including derived VRP problems of secondary distribution, and called as multi-vehicle type vehicle path problems (Capacitated and Multi-Model Vehicle Routing Problem with Route Balancing, CMMURRPRB) with capability constraint and time balance constraint, taking minimum cost spent by vehicles and balanced vehicle working time as optimization targets, initializing customer points by utilizing the characteristics of a Veno diagram, designing the reassignment of the customer points among routes by virtue of the idea of borrowing and lending, and enhancing the searching capability of the optimal distribution sequence in the routes by utilizing a heuristic algorithm. Finally, the verification is carried out through the calculation example, and different path results can be obtained through adjusting given parameters so as to be used for a manager to make decisions.

The technical scheme adopted for solving the technical problems is as follows:

a multi-vehicle-type vehicle path planning method considering secondary distribution and balancing, comprises the following steps:

1) Reading data;

2) Judging whether the distance between clients and the time matrix are complete according to the data, and if so, directly jumping to the step 3); if not, using an SPFA shortest path algorithm to perfect a distance and time matrix;

3) By means of the two-stage method, the first-order proximity characteristic of the Voronoi diagram is utilized to initialize the cluster of the client points;

4) According to the order of time limit, multiple vehicle types, secondary distribution and time balance, the client points of different lines are redistributed according to the distribution limiting conditions by utilizing the concept of borrowing and lending, and during the period, 3-opt operator and or-opt operator are used for optimizing the distribution order in the lines;

5) According to the distribution of the client points and the distance between the distribution centers, selecting lines according to the ascending order, carrying out melon distribution, and distributing the client points to other lines to serve as distribution tasks of secondary distribution;

6) Finally, the calculation is performed for balancing, and the maximum working hour difference of the vehicle is minimized as much as possible.

The logistics distribution problem referred to by the present invention is described as follows: logistics distribution centers are known to have different types of trucks that carry goods for merchants distributed locally. The rated maximum cargo carrying capacity and the travel cost of different types of trucks are different, and the travel cost of each truck is positively correlated with the maximum cargo carrying capacity. The trucks carrying a certain unit of goods start from the logistics center and pass through a plurality of merchants in the middle to meet the requirements of the merchants, and return to the logistics center after the distribution is finished; if the remaining working time is abundant, the truck starts from the logistics center again after carrying out secondary loading, and returns to the logistics center after completing the delivery task. Wherein the working time of each truck is required to be no more than a specified value, and the balance among a plurality of routes is ensured; the actual cargo capacity of the truck does not exceed the rated maximum cargo capacity of the truck during each transportation; the sum of the costs of the vehicles required for transportation is minimized; the delivery order of each route to the customer is as optimal as possible.

The invention considers the secondary transportation, the time balance among routes and multiple vehicle types based on the original VRP problem, and is called as the multi-vehicle type vehicle path problem with capacity constraint and load balance constraint. In order to solve 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 using an SPFA algorithm, and calculating a complete driving distance matrix and a driving time matrix which comprise all nodes; the algorithm initializes the clusters for the clients based on the first-order adjacency of the Veno graph, so that the calculation complexity is greatly reduced, and the problem caused by outliers is avoided; the concept of borrowing, lending and lending can reasonably reassign client points among routes; when the calculation of the secondary distribution is considered, taking a client point which is closer to a distribution center as a tail note of the secondary distribution; during balancing, ban tables are used to prevent client points from being repeatedly allocated. In the calculation process, the 2-opt algorithm and the or-opt algorithm are utilized to optimize the client distribution sequence in a single line.

The beneficial effects of the invention are mainly shown in the following steps: 1. reasonable path allocation results can be obtained relatively quickly for order information of large data volume. 2. The total distribution cost can be minimized on the premise of simultaneously considering secondary distribution, time balance and multiple vehicle types. 3. On the premise of only increasing less time consumption, the working time of the truck can be distributed more uniformly, which ensures fairness.

Drawings

FIG. 1 is a flow chart of an algorithm process, showing a general description of each step of the algorithm.

Fig. 2 is a diagram of relationships among data warehouse tables, mainly illustrating the association between the structures of different data tables of the data warehouse and the association according to foreign key references.

Fig. 3 is a schematic diagram of the concept of "borrowing and lending", which is used to show the concept meaning of the "borrowing and lending" operation in practical use cases. Wherein (a) represents an example of "lending" operation, that is, when the time of route usage exceeds a prescribed time limit, the client points in the present route need to be appropriately allocated to other routes, so that the number of client points in the present route is reduced, and the time of use is gradually reduced until the prescribed time limit is satisfied. (b) An example of a "borrow" operation is shown in which, when the time period has not reached a predetermined time period, it is possible to try to insert a client point in another route into the present route, and when the time period has reached the predetermined time period, it is possible to formally transfer the client point.

FIG. 4 is a diagram of a "borrowing" operation-search area division showing how client points that may be "borrowed" are screened during the "borrowing" operation.

Fig. 5 is a schematic diagram of a model selection process showing how to select the appropriate model for the distribution line.

Fig. 6 is a schematic diagram showing the calculation results, showing the paths of different routes by using the Goldmap, wherein the different paths are represented by the client points of different colors and the sequential routes.

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, includes the steps of:

1) Reading data;

The invention refers to a two-stage method, firstly, initializing a cluster of client points based on the first-order proximity of a Veno diagram, then, according to the sequence of time limit, multiple vehicle types, secondary distribution and time balance, reassigning the client points of different lines according to distribution limit conditions by utilizing the concept of borrowing and borrowing proposed by a pen user, during the period, optimizing the distribution sequence in the lines by using 3-opt and or-opt operators, and finishing the algorithm after the calculation of the secondary distribution and the balance is considered.

Data warehouse design

According to the vehicle path algorithm requirement and the service related data, a data table of the data warehouse is established and comprises a customer basic information table, a distribution center table, a goods 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 presented as follows:

customer base 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 a client point and a start point of the road where the client point is located, longitude and latitude of the client point, and a direction where the client point is located with respect to the road.

Distribution center basic information table (partition_info)

The distribution center basic information table contains distribution center basic information, and 7 fields comprise a distribution center ID, a distribution center name, a road ID (foreign key) where the distribution center is located, a distance between a distribution center point and a road start point where the distribution center point is located, longitude and latitude of the distribution center point, and a direction where the distribution center point is located relative to the road.

Goods order form (order_info)

The order form contains information about the order, and even with a unified distribution center, orders of different dates will be different. The table contains 6 fields including order ID, customer ID (foreign key), cargo demand, time required for unloading, order date, and distribution center ID (foreign key).

Client point-to-point distance meter (distance_info)

The client-point-to-point distance table is used for storing client-point distance information after preprocessing order information. There are 4 fields in the table, including unique identification ID, start client ID (foreign key), end client ID (foreign key), distance.

Client point-to-point timetable (time_info)

The client-to-point time table is used for storing the client-to-client time information after preprocessing the order information. 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 foreign key references, and table relation and structure are shown in fig. 2.

The model building 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 client points; e is a set of time matrices between the distribution center and the client points, E= { (i, j) |i, j ε V, i+.j }; t is t _i,j The time required for the truck to go from point i to point j; q _i The demand for customer point i; x is x _i 、y _i Respectively representing the longitude and latitude of the client point i; k is a set of different vehicle types, K= {1,2,..m }, lw _k 、c _k 、p _k 、u _k Respectively representing the maximum cargo carrying capacity, travel cost, number of vehicles provided and number of vehicles used currently of a truck model with the number of K, wherein K is E K; truck is the collection of actual trucks used, truck= {1,2,..p }, carType _No Vehicle model number in K, line1 of No. truck _No 、Line2 _No For ordered array, respectively representing the sequence of the passing points of primary distribution and secondary distribution of No truck, if the array is not empty, its length is not less than 2, and the starting point and end point are distribution centers 0, t1 _No 、w1 _No Respectively representing the time and load of a primary delivery route of a truck with the number No, t2 _No 、w2 _No Similarly, where No ε Truck; ts is the working time defined daily for each truck; b is the maximum acceptable inter-truck operating time difference.

To this end, a mathematical model that considers logistics distribution problems is as follows.

T _No ＝mint1 _No +mint2 _No ＜Ts,No∈Truck (2)

max(T _i )-min(T _j )≤B,i,j∈Line (3)

w1 _No ,w2 _No ＜lw _k ,No∈Truck,k＝carType _No (4)

The formulas (1) to (4) are objective functions based on constraint conditions. In the formula (1), C represents that the sum of the costs of the vehicles required for transportation is minimum; formula (2) shows that the delivery sequence of each truck to the customer is optimal in the primary and secondary delivery, thereby minimizing the time consumption of each route, T _No The sum of route time for primary and secondary distribution is less than the prescribed working time; the formula (3) represents time balance, and represents that the difference between the longest time and the shortest time of truck working meets the maximum time balance difference acceptable by the regulation; equation (4) indicates that the truck is not overloaded each time the delivery task is performed.

The formulas (5) and (6) respectively show that when the truck performs the delivery task each time, the truck starts from the delivery center, passes through the customer point, returns to the delivery center after delivery, and the time required by the delivery is 0 when the truck does not need secondary delivery. The formula (7) and the formula (8) respectively show that the cargo carrying capacity of each delivery task of the truck is the sum of the demand of clients passing through the route, and when the truck does not need secondary delivery, the cargo carrying capacity is 0.

Initializing clusters based on the voronoi diagram: on the premise of large-scale client quantity, the vehicle path algorithm is an NP-hard problem, which means that an exhaustion method is not feasible, the heuristic algorithm only tends to optimize the result as much as possible, and the larger the calculation scale is, the harder the optimization is ensured in a certain time. The method uses a base Yu Weinuo (Voronoi) proximity-based solution to create an initial solution, which translates the overall vehicle path problem into a small fraction of the traveler problem, reducing the complexity of the algorithm. The distribution problem includes a "multi-vehicle" condition where the maximum cargo capacity of the vehicle is not unique, which makes the initial solution of the sum of the demands of the clusters ambiguous when compared to the reference capacity. The method is improved aiming at the requirements of multiple vehicle types, and comprises the following steps:

3.1 A winor graph of node set V is created, populating a first order winor graph neighbor list of client points, wherein the distribution center is not included;

3.2 A queue R is created, all the first-order adjacent node pairs of the Voronoi diagram are pressed into the R, and each client point is independently calculated as a class;

3.3 According to t in time matrix, the client point pairs i-j in R _i,j Performing ascending sort;

3.4 Providing maximum cargo capacity of different vehicle types according to the vehicle type data set K, providing the number of vehicles, calculating to provide average maximum cargo capacity w of the vehicles _avg Which satisfies the equation

3.5 Fetching the client point pair i-j located at the head of the queue in R, if i, j are already in the same class, not performing operation; otherwise, judging whether the class where i and j are located is combined or not: consider the class in which client i resides as V _i Similarly, get V _j Will be of the class V _i The total demand for goods is regarded as Q _i In the same way, get Q _j If Q _i +Q _j ≤w _avg Merging class V _i ，V _j The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, not carrying out clustering operation;

3.6 Repeatedly executing the step 3.5) until the list R is empty; obtain the initial cluster division Line 1= { Line1 ₁ ,Line1 ₂ ,…,Line1 _p And Truck set truck= {1,2,., p }, where Truck model is not determined;

compared with a k-means clustering algorithm, the clustering algorithm based on the Veno graph only uses first-order adjacent client point pairs, so that the time complexity of operation data is greatly reduced, and the clustering performance is improved. The cluster algorithm can dynamically control the cluster number according to the reference capacity without setting in advance. Due to the principle of the drawing of the voronoi diagram, the voronoi diagram-based clustering algorithm is inherently more suitable for datasets with outliers. The above advantages make the voronoi diagram-based clustering algorithm more suitable for point clustering in vehicle path problems and obtaining an initial solution.

Optimization of the in-route delivery sequence: after the initial cluster is obtained, the initial cluster is considered as a distribution point set for one distribution, and the required time of each route under the optimal distribution sequence is needed to be calculated. The algorithm obtains two initial solutions by using a saving algorithm and an adjacent insertion method based on a reference point, and then uses 3-opt and or-opt local search operators to optimize the distribution sequence of a single path of the two initial solutions, wherein the optimization process is as follows:

4.1 The number of optimization failures F) is created and initialized to 0.

4.2 The number of clients n of the route is obtained, and the number of optimization failure limits FL is suitably obtained according to the different number n.

4.3 F=f+1, the time t before optimization is calculated according to the formula (5) _pre . Obtaining a Random number with a value of 0 or 1 by using a Random function, and optimizing a line by using a 3-opt algorithm when the value is 0; when the value is 1, the line is optimized by an or-opt algorithm. Obtaining optimized time t according to formula (5) _after When t _after ＜t _pre If the optimization is successful, F is reset to 0, and the route is updated; otherwise, the route is not updated.

4.4 Repeatedly executing the step 4.3) until F > FL. And returning to the optimizing line, and ending the optimizing process.

After the two initial solutions are respectively subjected to a line optimization process, two optimized solutions and the time t for each solution are obtained _saving 、t _insert Taking fewer solutions as the subsequent operational Line1 _No The other solution is discarded.

The idea of "borrowing in and out": fig. 3 shows the idea of "lending in and out". Wherein part (a) illustrates a "lending" operation. When the optimized route is used to exceed the specified time limit, i.e. t1, when the client point is allocated _No The number of client points in the route is reduced by appropriately allocating client points in the route to other routes, and the number of client points in the route can be gradually reduced until a prescribed time limit is met, which is referred to as "borrowing".

(b) Part of the "borrow" operation is shown. There is still a margin with respect to the prescribed time limit when in use, i.e. t1 _No If Ts is smaller than Ts, the client point closer to the route in another route can be tried to be allocated to the route, if the time of use meets the requirementAnd (3) formally transferring the client point, which is "borrowing".

After the optimization of the in-route delivery sequence is finished, a pile A is created, and each optimized route is added in the pile A to represent an 'unshaped' route. And then, the cyclic operation is carried out until A is in the empty state. In the loop body, traversing A to obtain the time t1 of each line in A _No Customer midpoint coordinates (cen 1X) in a route _No ,cen1Y _No ) Average distance distvg of customer points contained in route and distribution center _No Wherein

Fetch dis _avg Route Line1 with the largest, i.e. furthest, distribution of customer points _far And for the route, reassigning the client point by using the idea of borrowing and lending, and removing the serial number far of the line in A after the assignment is completed.

The following describes the "borrowing" and "lending" operations of each route to the client point.

Lending: when the line is used more than the limit, i.e. t1 _far > Ts, the customer point curt "lending" closer to the distribution center within the route needs to be assigned to other routes closer. When only Line1 remains in A _far I.e. no other line can be "borrowed", a adds a new line and distributes the customer point cust to the newly created line; when A has more than Line1 _far According to the coordinates (x _cust ,y _cust ) Customer midpoint coordinates (cen 1X) with other lines in A _No ,cen1Y _No ) Obtaining their Euclidean distance dis _far,No I.e.

Taking dis _far,No Minimum Line1 _No And assigns a customer point cust to the line. Cycle "loan" operation until t1 _far At most Ts, skipping out the Line1 after the "lending" cycle _far A "borrow" operation is performed.

Borrowing: when the line is less than the limit, i.e. t1 _far < Ts, and in A there are more than Line1 _far This operation is performed. And creating a node set Maybe for storing the client points possibly borrowed, acquiring and merging the client points of the rest lines in the A, and storing the client points into the Maybe. Acquisition of Line1 _far Time distance d between furthest customer point furthest in the middle and the distribution center _0,furthest I.e.

d _0,furthest ＝max(d _0,i ),i∈Line1 _far (13)

. According to d _0,furthest Customer midpoint coordinates C (cen 1X) _far ,cen1Y _far ) And distribution center coordinates P (x ₀ ,y ₀ ) Drawing a shape range on a map in a certain proportion, and the graph satisfies the formula

Or (V) type

Wherein B represents a boundary point of the graph; t represents a self-defined time range; a, b and c represent corresponding proportions, and different values can obtain different shapes. Taking a=1.5, b=0.5, c=2, t for 15 minutes, making it a "cover the distribution center point P, and the closer to the customer midpoint coordinate C in the longitudinal direction, the greater the transverse radius, the union range of the gourd-like shape" and "any area reachable within 15 minutes starting from the distribution center P", as shown in fig. 4. Customer points located in the graphic range in the Maybe are screened, and then the Maybe is sorted in ascending order according to the Euclidean distance between each point of the Maybe and the point coordinate C of the customer. Traversing Maybe, for each acquisitionCustomer point adds it to the line using insertion method, and then obtains time t1Aft _far . When the limiting purpose is satisfied, i.e. t1Aft _far Ts is less than or equal to, which means that the borrowing is successful, the traversal is jumped out, and the borrowing operation is circulated until no client point which can be successfully borrowed in Maybe; when the line after the addition point is overtime, i.e. t1Aft _far And (3) not less than Ts, wherein the borrowing failure is indicated, the operation of the insertion point is rolled back, and the traversal is continued.

Each line needs to undergo a "lend-in-lend-out" process, where "lend-out" may occur, and "lend-in" must occur. The line obtained through the operation in this section shows that the time consumption meets the requirement, namely, the line does not need to be "borrowed" and any other client point can not be received any more, namely, the line can not be "borrowed", the line is marked as "shaped", after the operations such as selecting the vehicle type are carried out, the line is removed from the pile A, and then whether the circulation operation is continued is judged according to whether the line still exists in the pile A. And updating the Line1 and the Truck after the cycle is ended.

Vehicle type selection: the data relating to load capacity at the time of initial point marking of the customer points is to provide an average maximum load capacity of the vehicle, which is used only for load capacity reference and no specific model is selected. And after the operation is finished, selecting the vehicle types of the trucks with different routes.

In operation, one route Line1 per "pattern _No And selecting the vehicle type of the truck. Obtaining the demand w1 of the line _No Traversing the vehicle model set K, and calculating the carrying capacity wl of different vehicle models _k And travel cost c _k Average unit cargo delivery cost cAvg _k Which satisfies the following requirements

Taking cAvg _k The vehicle model k with the smallest result is used as the current alternative vehicle model of the route. As shown in fig. 5, each vehicle type in K is sorted according to the maximum cargo capacity (in general, the larger the maximum cargo capacity of the truck is, the larger the travel cost is), the first round of ascending search is performed from the vehicle type K, and the current search is performedThe cable model curr, if there are remaining vehicles, i.e. p _curr ＞u _curr Formally selecting the vehicle model to carry out the distribution task of the current route; if there is no remaining vehicle, the second round of descending search is performed from the vehicle model k, and if there is no remaining vehicle, the user is indicated to provide too few vehicles.

Final selected vehicle model final of the route is obtained on the premise of providing sufficient vehicles, and the vehicle model final is equal to the vehicle model final _final And performing self-increasing operation. At this time, if the vehicle type is selected in the second round of searching, the vehicle is overloaded, the route needs to be subjected to the operation of 'lending in and out' again, and the condition limitation of time and overload needs to be considered at the same time.

So far, the result obtained by the algorithm is applicable to the standard multi-vehicle type VRP problem.

Consider the calculation of the secondary delivery: in general, the remaining working time of the vehicle is insufficient before the secondary distribution task is performed, so that a customer point near the distribution center preferably uses a tail order as the secondary distribution task. The "borrow-borrow" operation of the algorithm is sequentially performed in descending order according to the Euclidean distance between the customer midpoint of each route and the distribution center, thereby knowing the distribution route Line1 for each truck _No The larger the No, the closer its distribution of customer points to the distribution center. When customer point allocation is performed by considering secondary distribution, the Line1 with the largest No is taken _close As a line "melon" its associated customer point is assigned to the secondary distribution line of other trucks; the method comprises the following steps:

5.1 A maximum number close in the Truck is obtained. Creating an array L as the secondary distribution route Line2 of the truck _close Not empty, copy it to L; otherwise, the primary distribution route Line1 of the truck is used for _close Copy to L.

5.2 Array lineArr storing the numbers of all trucks in the Truck except close, where linearr= {1, 2..p }, andlineArr is based on its total delivery time T per truck _No And (5) sorting in a descending order.

5.3)Traversing lineArr, numbering curr for each truck to obtain the maximum cargo capacity wl _k Where k=cartype _curr 。

5.4 When L is empty, representing route L has been "melon" and jump to step 1). If L is not space, if Line2 _curr For null, the nearest customer point in L to the distribution center is allocated to Line2 _curr The method comprises the steps of carrying out a first treatment on the surface of the If Line2 _curr Not empty, and Line2 in L _curr Customer point allocation to Line2 with minimum euclidean distance of customer points _curr . Time t2 for calculating secondary distribution after inserting customer point _curr And cargo amount w2 _curr If the working time and the load of the truck curr meet the constraint conditions, circularly executing the step 5.4); if the constraint condition is not met, continuing to traverse lineArr.

5.5 Loop to step 5.1) until the current line L can no longer be "melon".

5.6 Update the Truck, line1, line2 and related data t1, t2, w1, w2.

Balancing the working time of each truck: in the process of balancing, more trucks are used to distribute part of the customer points distributed by the trucks to fewer 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, the situation that two trucks continuously distribute the same customer point to each other can happen, which can cause a dead cycle, the embodiment proposes to use a ban stack to store the numbers of the trucks less, once the trucks are distributed with the delivery customer points of other trucks, the numbers of the delivery customer points of the trucks are stored in ban, the delivery customer points of the trucks can 'only go in and out' in the following customer distribution, which effectively eliminates the problems, and the steps when balancing the trucks are as follows:

6.1 A heap ban is created, initially empty. Obtaining an acceptable maximum working time difference B;

6.2 And (3) obtaining the maximum working time difference balance of each truck in the current result, if the balance is less than or equal to B, ending the calculation, and returning the result. Otherwise, finding the truck less with the shortest working time and obtaining the distribution route Line1 _less 、Line2 _less Related data t1 _less 、t2 _less 、w1 _less 、w2 _less ；

6.3 An array AvailArr is created in which truck numbers other than the truck less and ban heap stores are stored. When Line2 _less For empty, ordering AvailArr in descending order according to the working time of the trucks it contains; when Line2 _less Not empty, obtain customer point cen2 of the line _less Traversing AvailArr to obtain customer point cen of primary distribution or secondary distribution line of each truck _1or2 Wherein the priority of the secondary distribution line is higher, and cen2 is determined _less And each cen _1or2 According to the Euclidean distance, carrying out ascending order sequencing on trucks by AvailArr according to the Euclidean distance;

6.4 In the traversal process, taking a secondary distribution route for each truck, or taking a primary distribution route, regarding the selected routes as currL, and sorting currL according to the distance between the contained client point and the distribution center. Nesting traversal currL during traversal of AvailArr, and attempting to assign a currently experienced client point to Line2 during traversal of currL _less In Line2 _less After optimizing the distribution sequence, if the working time of the truck is not overtime and the goods are not overloaded, representing successful distribution, jumping to the step 6.2);

6.5 If the allocation is still unsuccessful after traversing AvailArr, indicating that the calculation for balancing is no longer possible, ending the calculation and returning the result in step 6.4).

Implementing a vehicle path algorithm: according to the related concepts and steps described in the above stages, a multi-vehicle type vehicle path planning method considering secondary distribution and balancing is realized. In this embodiment, a daily delivery demand order form (730 clients in total) of a logistics delivery center is simulated, client information, delivery center information, order information, time and distance matrix of the client and the delivery center are loaded before an algorithm is executed, then the algorithm is operated to obtain a delivery path result, and the result is displayed on a map as shown in fig. 6.

According to the vehicle path planning method, order information with large data volume can be calculated to obtain a more reasonable path distribution result, secondary distribution conditions can be considered, working time of each route can be distributed in an equalizing mode, a more proper vehicle type can be selected from multiple vehicle types to carry out distribution tasks, and total distribution cost can be reduced on the premise that the result meets distribution limiting conditions.

Claims

1. A method for planning a path of a multi-vehicle model in consideration of secondary distribution and balancing, the method comprising the steps of:

1) Reading data;

3) Initializing a cluster for the client points by using the first-order proximity characteristic of the voronoi diagram;

6) Finally, calculating aiming at balancing the working time of each truck, and minimizing the maximum working hour difference of the used vehicles;

in the step 1), g= (V, E) is taken as a distribution network, wherein V is a node set, v= {0,1,2,3, …, n },0 represents a distribution center, and the rest represents client points; e is a set of time matrices between the distribution center and the client points, E= { (i, j) |i, j ε V, i+.j }; t is t _i,j The time required for the truck to go from point i to point j; q _i The demand for customer point i; x is x _i 、y _i Respectively representing the longitude and latitude of the client point i; k is a set of different vehicle types，K＝{1,2,...,m}，lw _k 、c _k 、p _k 、u _k Respectively representing the maximum cargo carrying capacity, travel cost, number of vehicles provided and number of vehicles used currently of a truck model with the number of K, wherein K is E K; truck is the collection of actual trucks used, truck= {1,2,..p }, carType _No Vehicle model number in K, line1 of No. truck _No 、Line2 _No For ordered array, respectively representing the sequence of the passing points of primary distribution and secondary distribution of No truck, if the array is not empty, its length is not less than 2, and the starting point and end point are distribution centers 0, t1 _No 、w1 _No Respectively representing the time and load of a primary delivery route of a truck with the number No, t2 _No 、w2 _No Similarly, where No ε Truck; ts is the working time defined daily for each truck; b is the maximum acceptable working time difference between trucks;

to this end, the mathematical model that considers the logistics distribution problem is as follows:

T _No ＝min t1 _No +min t2 _No ＜Ts,No∈Truck (2)

max(T _i )-min(T _j )≤B,i,j∈Line (3)

w1 _No ,w2 _No ＜lw _k ,No∈Truck,k＝carType _No (4)

formulas (1) to (4) are objective functions based on constraint conditions, wherein C in formula (1) represents that the sum of costs of vehicles required for transportation is minimum; formula (2) shows that the delivery sequence of each truck to the customer is optimal in the primary and secondary delivery, thereby minimizing the time consumption of each route, T _No The sum of route time for primary and secondary distribution is less than the prescribed working time; the formula (3) represents time balance, and represents that the difference between the longest time and the shortest time of truck working meets the maximum time balance difference acceptable by the regulation; the formula (4) shows that the truck is not overloaded when carrying out each delivery task;

the formulas (5) and (6) respectively show that when the truck performs the delivery task each time, the truck starts from the delivery center, passes through the customer point, returns to the delivery center after delivery, and the time required by the delivery is 0 when the truck does not need secondary delivery; the formula (7) and the formula (8) respectively show that the cargo carrying capacity of each delivery task of the truck is the sum of the demand of clients passing through the route, and when the truck does not need secondary delivery, the cargo carrying capacity is 0;

in the step 4), two initial solutions are obtained by using a saving algorithm and an adjacent insertion method based on a reference point, and then the two initial solutions are respectively subjected to single-path distribution sequence optimization by using a 3-opt local search operator and an or-opt local search operator, wherein the optimization process is as follows:

4.1 Creating the optimization failure times F and initializing the optimization failure times F to 0;

4.2 Obtaining the number of clients n of the route, and obtaining the proper optimization failure limiting times FL according to different numbers n;

4.3 F=f+1, the time t before optimization is calculated according to the formula (5) _pre Obtaining a Random number with a value of 0 or 1 by using a Random function, and optimizing a line by using a 3-opt algorithm when the value 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) _after When t _after ＜t _pre If the optimization is successful, F is reset to 0, and the route is updated; otherwise, the route is not updated;

4.4 Repeatedly executing the step 4.3) until F is more than FL, returning to the optimization line, and ending the optimization process;

in the step 4), after the line optimization process is performed on the two initial solutions, two optimized solutions and the time t of each solution are obtained _saving 、t _insert Taking fewer solutions as the subsequent operational Line1 _No The other solution is discarded;

after the optimization of the distribution sequence in the route is finished, creating a pile A, and adding each optimized route in the pile A to represent an unshaped route; then, the circulation operation is carried out until A is a space time jump; in the loop body, traversing A to obtain the time t1 of each line in A _No Customer midpoint coordinates (cen 1X) in a route _No ,cen1Y _No ) Average distance distvg of customer points contained in route and distribution center _No Wherein

Fetch dis _avg Route Line1 with the largest, i.e. furthest, distribution of customer points _far And for the route, reassigning the client point by using the idea of borrowing and lending, and removing the serial number far of the line in A after the assignment is completed;

lending operation: when the line is used more than the limit, i.e. t1 _far More than Ts, the client point curt 'lending' which is closer to the distribution center in the route is required to be distributed to other closer routes; when only Line1 remains in A _far I.e. no other line can be "borrowed", a adds a new line and distributes the customer point cust to the newly created line; when A has more than Line1 _far According to the coordinates (x _cust ,y _cust ) Customer midpoint coordinates (cen 1X) with other lines in A _No ,cen1Y _No ) To obtain themEuclidean distance dis _far,No I.e.

，

Fetch dis _far,No Minimum Line1 _No And assigns a customer point cut to the line, loops the "lend" operation until t1 _far At most Ts, skipping out the Line1 after the "lending" cycle _far Executing a borrowing operation;

borrowing operation: when the line is less than the limit, i.e. t1 _far < Ts, and in A there are more than Line1 _far This operation is performed; creating node set Maybe for storing client points possibly "borrowed" to obtain and combine the client points of other lines in A, storing them in Maybe to obtain Line1 _far Time distance d between furthest customer point furthest in the middle and the distribution center _0,furthest I.e.

d _0,furthest ＝max(d _0,i ),i∈Line1 _far (13)，

According to d _0,furthest Customer midpoint coordinates C (cen 1X) _far ,cen1Y _far ) And distribution center coordinates P (x ₀ ,y ₀ ) Drawing a shape range on a map in a certain proportion, and the graph satisfies the formula

Or (V) type

Wherein B represents a boundary point of the graph; t represents a self-defined time range; a, b and C represent corresponding proportions, different values will obtain different shapes, a=1.5, b=0.5, c=2 and t is taken for 15 minutes, customer points located in the graphic range in the Maybe are screened, and then the Maybe is carried out according to the Euclidean distance between each point and the coordinate C of the customer pointsAscending sort, traversing Maybe, adding the client point obtained each time into the line by using an insertion method, and obtaining time t1Aft _far When the limiting purpose is satisfied, i.e. t1Aft _far Ts is less than or equal to, which means that the borrowing is successful, the traversal is jumped out, and the borrowing operation is circulated until no client point which can be successfully borrowed in Maybe; when the line after the addition point is overtime, i.e. t1Aft _far Not less than Ts, indicating "borrow" failure, rollback the insertion point operation, and continuing traversing;

in the step 5), the calculation of the secondary distribution is considered, and the steps are as follows:

5.1 Obtaining the largest number close in the Truck, creating an array L, and when the secondary distribution route Line2 of the Truck is _close Not empty, copy it to L; otherwise, the primary distribution route Line1 of the truck is used for _close Copy to L;

5.2 Array lineArr storing the numbers of all trucks in the Truck except close, where linearr= {1, 2..p }, andlineArr is based on its total delivery time T per truck _No Sorting in a descending order;

5.3 Traversing lineArr, numbering curr for each truck to obtain the maximum cargo capacity wl thereof _k Where k=cartype _curr ；

5.4 If L is empty, representing that the route L has been divided by melon, jumping to step 1), if L is not empty, if Line2 _curr For null, the nearest customer point in L to the distribution center is allocated to Line2 _curr The method comprises the steps of carrying out a first treatment on the surface of the If Line2 _curr Not empty, and Line2 in L _curr Customer point allocation to Line2 with minimum euclidean distance of customer points _curr Calculated time t2 for secondary delivery after inserting the client point _curr And cargo amount w2 _curr If the working time and the load of the truck curr meet the constraint conditions, circularly executing the step 5.4); if the constraint condition is not met, continuing to traverse the lineArr;

5.5 A step of circularly jumping to the step 5.1) until the current line L can not be divided by the melon any more;

5.6 Update the Truck, line1, line2 and related data t1, t2, w1, w2.

2. The method for planning a multi-vehicle path taking into account the secondary distribution and balancing of claim 1, wherein in the step 3), the solution of creating an initial solution based on the minox proximity is used to transform the overall vehicle path problem into a small part of the tourist problem, and the algorithm complexity is reduced, and the steps are as follows:

3.6 Repeatedly executing the step 3.5) until the list R is empty; obtain the initial cluster division Line 1= { Line1 ₁ ,Line1 ₂ ,…,Line1 _p And Truck set truck= {1,2,..p }, where Truck model is not determined.

3. The method for planning a path of a multi-vehicle type vehicle in consideration of secondary distribution and balancing according to claim 1, wherein in the step 6), the working time of each truck is balanced, and the step of balancing the truck time is as follows:

6.1 A heap is created, and is initially empty, and an acceptable maximum working time difference B is obtained;

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, ending calculation, and returning the result; otherwise, finding the truck less with the shortest working time and obtaining the distribution route Line1 _less 、Line2 _less Related data t1 _less 、t2 _less 、w1 _less 、w2 _less ；

6.3 Array AvailArr, in which truck numbers other than truck less and ban heap stores are stored, when Line2 _less For empty, ordering AvailArr in descending order according to the working time of the trucks it contains; when Line2 _less Not empty, obtain customer point cen2 of the line _less Traversing AvailArr to obtain customer point cen of primary distribution or secondary distribution line of each truck _1or2 Wherein the priority of the secondary distribution line is higher, and cen2 is determined _less And each cen _1or2 According to the Euclidean distance, carrying out ascending order sequencing on trucks by AvailArr according to the Euclidean distance;

6.4 Traversing AvailArr, taking a secondary delivery route if a secondary delivery route exists for each truck in the traversing process, taking a primary delivery route if the secondary delivery route does not exist, regarding the selected routes as currL, sorting the currL according to the ascending sequence of the distance between the contained client points and the delivery center, nesting and traversing the currL in the traversing process of AvailArr, and trying to distribute the currently experienced client points to a Line2 in the traversing process of the currL _less In Line2 _less After optimizing the distribution sequence, if the working time of the truck is not overtime and the goods are not overloaded, representing successful distribution, jumping to the step 6.2);