CN108154254B - Logistics distribution vehicle scheduling method based on improved A-x algorithm - Google Patents

Abstract

The invention relates to a method based on improved A^*The logistics distribution vehicle scheduling method of the algorithm provides a scheme of vehicle scheduling, path selection and path planning in logistics distribution: comprises a modified type A^*Algorithm and logistics distribution algorithm; wherein the improvement is^*The algorithm is used for rapidly searching the optimal path between two points and comprises the following steps: gridding a distribution area, preferably evaluating a proper distance, and searching a shortest distance by a recursive method; the logistics distribution algorithm is used for generating vehicle information sent from a distribution center to each customer node, wherein the vehicle information comprises a vehicle number, passing customer nodes, a vehicle route, a load capacity and a total route distance, and the logistics distribution algorithm comprises the following steps: calculating the distance and the route from each client node to the logistics center, and generating a distribution scheme by using an improved weighted graph algorithm. The dispatching method gives consideration to constraint conditions in vehicle paths, reduces the total transportation distance, enhances the comprehensive control and management of the logistics distribution process, and realizes economical and practical distribution lines.

Description

Logistics distribution vehicle scheduling method based on improved A-x algorithm

Technical Field

The invention relates to the technical field of car networking, in particular to a car networking system based on an improved A^*A logistics distribution vehicle scheduling method of an algorithm.

Background

Vehicle scheduling problems (VRPs) in logistics distribution paths are a typical combinatorial optimization problem and have proven to be an NP-hard problem that is difficult to solve in a finite time with accurate algorithms.

Common algorithms include Dijkstra algorithm and optimal preferential search (BFS) algorithm, but the two algorithms have certain defects, Dijkstra is a typical single-source shortest path algorithm, when a U-shaped obstacle in a map is encountered, the Dijkstra algorithm runs slowly, and the execution efficiency needs to be improved; BFS, although it is much faster than Dijkstra's algorithm, selects a long path without avoiding when encountering a U-shaped obstacle in the map, since it only considers the cost of reaching the target.

Disclosure of Invention

The invention aims to provide a rapid and convenient VRP combination optimization scheme.

The technical scheme adopted by the invention is as follows:

the invention provides a method based on an improved A^*The logistic distribution vehicle dispatching method of the algorithm comprises an improved type A^*Algorithm and logistics distribution algorithm.

The terms used in the present invention are explained as follows:

(1) path: a sequence of consecutive numbers called nodes from start to end;

(2) path weight: path length from one node to another;

(3) the following drawings: is a set of nodes and edges, usually denoted by G ═ V, E, where V is the set of all nodes and E is the set of all edges;

(4) undirected graph: is a graph with no direction of edges, and no order relationship between two vertexes, and the examples (V1, V2) and (V2, V1) represent the same edges;

(5) adjacency matrix: for an undirected graph, the adjacency matrix must be symmetrical, the diagonal of the adjacency matrix is 0, and the matrix represents the adjacent relation between each node in the graph;

(6) shortest path: there are multiple paths from the initial vertex to the end vertex in the undirected graph, and the shortest path is taken as the shortest path.

Improved A of the invention^*The algorithm is used for rapidly searching the optimal path between two points and comprises the following steps: gridding the delivery area, preferably evaluating the distance appropriately, and searching for the shortest distance three parts in a recursive method.

The logistics distribution algorithm is used for generating vehicle information sent from a distribution center to each customer node, wherein the vehicle information comprises a vehicle number, passing customer nodes, a vehicle route, a load capacity and a total route distance, and the logistics distribution algorithm comprises the following steps: calculating the distance and the route from each client node to the logistics center, and generating a distribution scheme by using an improved weighted graph algorithm.

In the present invention, the positions of the logistics center and the customer sites are known, and the maximum cargo capacity of the cargo truck is Q, and the cargo truck uses at most m cargo trucks from the logistics center to distribute the cargo to n customers_maxMaximum distance of travel L_maxThe trucks start from the logistics distribution center, return to the logistics center after completing the transportation task, and have the following constraint conditions:

(1) the using time of truck transportation is minimum;

(2) the shortest transportation distance;

(3) completing the delivery using a minimum of vehicles;

(4) the total amount of the customer goods in each distribution line is less than or equal to the maximum loading capacity of the truck;

(5) each customer site is completed by one delivery of one truck and cannot be repeated.

Improved A of the invention^*The algorithm is realized by the following steps:

(1) gridding a distribution area: on the premise of knowing the accurate geographic position of a client node, dividing a map into square grids (Grid) according to a certain proportion, and describing the Grid state by a two-dimensional array; the trellis pass-then trellis state is labeled □, represented as 0 in the array; if the grid is not passed then the grid status flag is

1 in the array; the path is a set of grids passing from a starting grid S to an end grid E, wherein the passing grids are called nodes, the nodes have a passable state and a non-passable state, and the passable state has two modes of moving along the XY axis direction of the grids and moving along the diagonal direction of the grids;

(2) preferably, the appropriate evaluation distance: node n (x)_n,y_n) Is from a starting point S (x)_S,y_S) And end point E (x)_E,y_E) The node reached after n steps evaluates the distance f (n) g (n) h (n), where g (n) is the distance from the starting point S to the path passed by the node n, the grid side length is d, i is a certain grid passed by the starting point a to the node nIf the grid is moved in the XY-axis direction of the grid, the distance d (i) ═ d passed by the grid, and if the grid is moved in the diagonal direction of the grid, the distance passed by the grid

h (n) is a heuristic function from the node n to the end point E, the value of which is the minimum value of the Manhattan distance and the Euclidean distance between two points, and Min () represents a function for returning the minimum value, then

If the terrain is known, and for the convenience of calculation, the manhattan distance can be directly selected, namely h (n) ═ x_n-x_E|+|y_n-y_EL, |; comparing the Euclidean distances when the Manhattan distances are the same;

(3) the shortest distance is searched for by a recursive method: with A^*(S, E) describing a better path from the starting point S to the end point E and returning a weight of the path, wherein the weight of the path is represented by L1, an open set stores all grids which are considered to find the shortest path, a closed set stores grids which are not considered any more, and a set P_minStoring the grids with the minimum f (n) values in the open sets, storing all the sets in a stack form, and constructing a linked list K, A according to a last-in first-out principle^*The algorithm of (S, E) is described as follows:

STEP 1: emptying an open set and a closed set, and putting S into the open set;

STEP 2: continuing when the open is not empty, otherwise returning to the error and exiting;

STEP 3: finding out the node n with the minimum evaluation distance in open, and putting n into P_minPerforming the following steps;

STEP 4: if n is equal to E, the end point is found, the step9 is switched to, otherwise, the operation is continued;

STEP5: removing n from the open set and adding the n into the closed set;

STEP 6: checking all grids G which can be passed around n, and skipping grids which cannot be passed;

STEP 7: adding all G not in the open set into the open set;

STEP 8: returning to STEP 2;

STEP 9: from E, pop P out in sequence_minAnd adding the linked list K into the nodes in the set until the starting point S is returned, reversely placing the linked list K to obtain a path from the starting point S to the end point E, and obtaining the weight L1 f (E) of the path.

The logistics distribution algorithm of the invention comprises the following steps:

(1) calculating the distance and route from each client node to the logistics center, wherein the address of the distribution center A is (x)_A,y_A) Address (x) of client node Vi_Vi,y_Vi) (i ═ 1,2, …, n) by modification a^*The algorithm calculates the path weight from the distribution center to each node Vi and puts the path weight into a one-dimensional array Lse Vi]＝A^*(a, Vi) (i ═ 1, …, n), and saves its path;

(2) generation of delivery plans by means of a modified weighted graph algorithm, known as delivery center A (x)_A,y_A) The client nodes and paths are described by a weighted undirected graph, G ═ V, E ═ V1, …, Vn }, E { (Vi, Vj) } (Vi ∈ V, Vj ∈ V), using a two-dimensional array L [ Vi ∈ V }][Vj]Storing the weight values between vertexes Vi to Vj, L [ Vi][Vj]＝A^*(Vi,Vj)；D[k]The travel distance to store each vehicle includes the distance to return to the distribution center, where (k ═ 1,2, …, M), M is the vehicle maximum; q [ k ]]Storing the load weight of each vehicle in driving, wherein (k is 1,2, …, M); the maximum travel distance of each vehicle is L_max(ii) a The maximum load of each vehicle is Q_max(ii) a Set V_TIs a set of unassigned vertices; set S [ k ]]Is a set of vertices assigned to the kth vehicle; a is a process variable and represents the current starting point to search the vertex of the next jump; the algorithm is described as follows:

STEP 1: initialization variable k is 1, V_T＝V；

STEP 2: initializing S [ k ] ═ phi, Q [ k ] ═ 0, D [ k ] ═ 0, and a ═ A;

STEP3：V_Tturning to STEP10 when empty, otherwise, continuing;

STEP 4: from the set V_TMiddle through modified type A^*The algorithm finds the vertex V [ i ] with the minimum distance from a]；

STEP5: judgment (Q [ k ]]+Q[V[i]]<＝Q_max)AND(D[k]+L[a][V[i]]+Lse(V[i])<＝L_max) If true, go to STEP6, otherwise go to STEP 9;

STEP6：D[k]＝D[k]+L[a,V[i]]，Q[k]＝Q[k]+Q[V[i]]，a＝V[i]；

STEP 7: let the vertex V [ i ]]Put into the set S [ k ]]In (3), delete the set V_TV [ i ] of (1)]；

STEP 8: returning to STEP 3;

STEP 9: d [ k ] + ls [ a ], k ═ k +1, return to STEP 2;

STEP 10: d [ k ] + ls [ a ], and ends.

The returned client nodes which are stored in the set S [ k ] and need to be visited by the vehicle k are the client nodes, the visiting sequence is the sequence of the elements in the set S [ k ], and all the logistics distribution vehicles only need to visit the client nodes in the set according to the corresponding vehicle.

Compared with the prior art, the invention has the following advantages:

improved A of the invention^*The algorithm combines the advantages of a conventional algorithm Dijsktra and a heuristic algorithm, different heuristic functions are used for adapting to different terrains for solving the shortest path, a weighted graph is designed in the logistics distribution algorithm for describing the road path condition, and the distribution scheme is planned by an improved recursive weighted graph search algorithm to obtain the optimal solution of the VRP.

Drawings

The invention is further described with reference to the accompanying drawings and detailed description, in which:

FIG. 1 is a schematic diagram of a U-shaped obstacle shortest path;

FIG. 2 shows a modification A^*Searching a path map in a straight-line obstacle map by an algorithm;

FIG. 3 is a schematic diagram of a weighting path;

FIG. 4 is a adjacency matrix diagram of a weighted graph.

Detailed Description

Gridding a distribution area:

as shown in fig. 1, on the premise that the precise geographic location of a client is known, a map is divided into square grids (Grid) according to a certain proportion and simplified into a two-dimensional array, each Grid is an element of the array, and the Grid mark □ represents a passable path and is marked as □

Indicating an impassable path (e.g., wall, gutter, etc.). A path is referred to as a set of points that pass through the grid from a starting point a to an end point B, where the points that pass through are referred to as "nodes," which may be any location of any shape.

Preferably, the appropriate evaluation distance:

as shown in fig. 2, a is a starting point, B is an end point, the edges of the grid are 10, g (n) is added to 10 when moving along the XY axis of the grid, g (n) is added to 14 when moving along the diagonal of the grid (where integers are taken for convenience of calculation), and the value of h (n) is the minimum value of the manhattan distance from the node to the point B and the euclidean distance, or one of them, where the manhattan distance h ═ x is selected for convenience of calculation₁-x₂|+|y₁-y₂|， L_ABThe final path weight from A to B is stored in the buffer.

The shortest distance is searched for by a recursive method:

as shown in fig. 2, the following steps describe the process of searching for a path:

step 1: emptying open and closed sets;

step 2: putting A into an open set, finding a square which can pass around A, calculating the value of F-G + H, finding the square which is 54 marked with 1, and adding A into a closed set;

step 3: putting 1 into an open set, finding a square grid which can pass around the 1, calculating the value of F-G + H, finding the square grid which is 74 and marked by 2, and adding 1 into a closed set;

step 4: putting 2 into an open set, finding a square grid which can pass around 2, calculating the value of F-G + H, finding the square grid which is 74 and marked by 3, and adding 2 into a closed set;

step5, putting 3 into the open set, finding the square grids which can pass around the 3, calculating the value of F & ltG + H & gt, finding the square grid which is F & lt74 & gt and marked by 4, and adding 3 into the closed set;

step 6: putting 4 into an open set, finding a square which can pass around 4, calculating the value of F-G + H, finding the square which can pass around F-68 and marking the square with 5, and adding 4 into a closed set;

step 7: putting 5 into an open set, finding a square which can pass around the 5, calculating the value of F-G + H, finding the square B of F-68, and adding the 5 into a closed set;

step 8: putting B into an open set, calculating the value of F ═ G + H, F ═ 68, and adding B into a closed set;

step 9: ending circulation, returning path to A, and sequentially B-fifth-fourth-third-fifth-A, so that the shortest path from A to B is L_AB＝68。

The logistics distribution algorithm is realized as follows:

as shown in fig. 3, the vertex a is the logistics center, the vertices V1 to V6 are the customer nodes, and the logistics distribution needs to traverse all the vertices in the graph from the vertex a, satisfy the logistics distribution constraint, and obtain the optimal path solution.

The distance weights between vertices, represented as a adjacency matrix, can be obtained from FIG. 3, as shown in FIG. 4.

Regarding the undirected weight graph G (V, E) as a road from a distribution center to each customer point, wherein the distribution center A, nodes V1 to V6 are vertexes of each customer, and the weight E on each side represents the distance of the path; q_max＝4.9,L_max200, initialize k 1, set V_TAdding V1, V2, V3, V4, V5 and V6 into a set V_TSet of

Assign a to distribution center A, the vehicle load Q [1]]0, distance D [1]]＝0；

Step 1: from the set V_T{ V1, V2, V3, V4, V5, V6}, searching a vertex V2 with the minimum distance to a, and judging a condition Q [1]]+2.3<＝Q_maxAnd D [1]]+15+15<＝L_maxIf the condition is satisfied, then V2 is selected from the set V_TDelete middle, put set S [1]]In this case, S [1]]＝{V2}，Q[1]＝2.3，D[1]15, then V2 is assigned to a;

step 2: from the set V_T{ V1, V3, V4, V5, and V6} searching the vertex V6 with the minimum distance to a, and judging the condition Q [1]]+2.3<＝Q_maxAnd D [1]]+22+30<＝L_maxIf the condition is satisfied, then V6 is selected from the set V_TDelete middle, put set S [1]]In this case, S [1]]＝{V2,V6}，Q[1]＝4.6，D[1]67, V6 is assigned to a;

step 3: from the set V_T{ V1, V3, V4, V5} searching the vertex V4 with the minimum distance to a, and judging the condition Q [1]]+1.5<＝Q_maxAnd D [1]]+25+39<＝L_maxIf the first condition is not satisfied, the first vehicle is distributed completely, Q1]＝4.6,D[1]67, k 2, assign a to a and reset Q2]＝0，D[2]＝0；

Step 4: from the set V_T{ V1, V3, V4, V5} searching the vertex V3 with the minimum distance to a, and judging the condition Q [2]]+1.8<＝Q_maxAnd D [2]]+35+35<＝L_maxIf the condition is satisfied, then V3 is selected from the set V_TDelete middle, put set S [2]]In this case, S2]＝{V3}，Q[2]＝1.8，D[2]35, V3 is assigned to a;

step5: from the set V_T{ V1, V4, V5} searching the vertex V5 with the minimum distance from a, and judging the condition Q [2]]+1.3<＝Q_maxAnd D [2]]+40+37<＝L_maxIf the condition is satisfied, then V5 is selected from the set V_TDelete middle, put set S [2]]In this case, S2]＝{V3,V5}，Q[2]＝3.1，D[2]V5 is assigned to a at 75;

step 6: from the set V_T{ V1, V4} searching the vertex V4 with the minimum distance to a, and judging the condition Q [2]]+1.5<＝Q_maxAnd D [2]]+55+39<＝L_maxIf the condition is satisfied, then V4 is selected from the set V_TDelete middle, put set S [2]]In this case, S2]＝{V3,V5,V4}，Q[2]＝4.6，D[2]130, V4 is assigned to a;

step 7: from the set V_T{ V1} searching the vertex V1 with the minimum distance from a, and judging the condition Q [2]]+2.3<＝Q_maxAnd D [2]]+74+44<＝L_maxIf all the conditions of the condition are not met, the second vehicle is distributed completely，Q[2]＝4.6,D[2]169, k 3, assign a to a and reset Q3]＝0，D[3]＝0；

Step 8: from the set V_T{ V1} searching the vertex V1 with the minimum distance from a, and judging the condition Q [3]]+2.3<＝Q_maxAnd D [3]]+44+44<＝L_maxIf the condition is satisfied, then V1 is selected from the set V_TDelete middle, put set S [3]]{ r }, in this case S [3]]＝{V1}，Q[3]＝2.3，D[3]44, V1 is assigned to a;

step 9: set V_TIs empty, Q3]＝2.3，D[3]When the cycle is finished, 88;

according to the logistics distribution algorithm, 3 vehicles are needed to complete distribution tasks; because S [1] = { V2, V6}, the first vehicle delivers vertices V2 and V6 in that order; the second vehicle sequentially delivers three vertexes V3, V5 and V4 because S [2] { V3, V5 and V4 }; s [3] = { V1}, so the third vehicle delivers V1; since Q [1] is 4.6 and D [1] is 67, the first vehicle weighs 4.6T and the travel distance is 67 km; the second vehicle weighs 4.6T and the driving distance is 169 kilometers because Q [2] is 4.6 and D [2] is 169; since Q [3] is 2.3 and D [3] is 88, the third vehicle weighs 2.3T and the travel distance is 88 km.

Claims (1)

1. Based on the improved A^*Algorithmic method for logistics distribution vehicle scheduling, characterized in that said method comprises the improvement A^*Algorithm and logistics distribution algorithm; the modification A^*The algorithm is used for rapidly searching the optimal path between two points and comprises the following steps: gridding a distribution area, preferably evaluating a proper distance, and searching a shortest distance by a recursive method; the logistics distribution algorithm is used for generating vehicle information sent from a distribution center to each customer node, wherein the vehicle information comprises a vehicle number, passing customer nodes, a vehicle route, a load capacity and a total route distance, and the logistics distribution algorithm comprises the following steps: calculating the distance and route from each client node to the logistics center, and generating a distribution scheme by an improved weighted graph algorithm;

wherein the improvement is^*The algorithm is realized by the following steps:

(1) gridding a distribution area: on the premise of knowing the accurate geographic position of the client node, dividing the map into a plurality of parts according to a certain proportionA square Grid (Grid), the state of the Grid being described in a two-dimensional array; the trellis is then labeled □ through the trellis state, represented by 0 in the array; if the grid is not passed then the grid status flag is

1 in the array; the path is a set of grids passing from a starting grid S to an end grid E, wherein the passing grids are called nodes, the nodes have a passable state and a non-passable state, and the passable state and the non-passable state can be moved along the XY axis direction of the grids and along the diagonal direction of the grids;

(2) preferably, the appropriate evaluation distance: node n (x)_n,y_n) Is from a starting point S (x)_S,y_S) And end point E (x)_E,y_E) The node reached by the n steps evaluates the distance f (n) ═ g (n) + h (n), where g (n) is the distance from the starting point S to the path passed by the node n, the side length of the grid is d, i is a certain grid passed by the starting point A to the node n, if the grid is moved along the XY axis direction of the grid, the distance d (i) ═ d passed by the grid is passed, if the grid is moved along the diagonal direction of the grid, the distance d (i) ═ d passed by the grid is passed by the grid

h (n) is a heuristic function from the node n to the end point E, the value of which is the minimum of the manhattan distance and the euclidean distance between the two points, and when Min () represents the return minimum function, h (n) is Min ((| x)_n-x_E|+|y_n-y_E|),

If the terrain is known, and for the convenience of calculation, the manhattan distance can be directly selected, namely h (n) ═ x_n-x_E|+|y_n-y_EL, |; comparing the Euclidean distances when the Manhattan distances are the same;

(3) the shortest distance is searched for by a recursive method: with A^*(S, E) describing a better path from the starting point S to the end point E and returning a weight of the path, wherein the weight of the path is represented by L1, an open set stores all grids which are considered to find the shortest path, a closed set stores grids which are not considered any more, and a set P_minStoring the grids with the minimum f (n) values in the open sets, storing all the sets in a stack form, constructing a linked list K and storing a final path according to a last-in first-out principle, A^*The algorithm of (S, E) is described as follows:

STEP 1: emptying an open set and a closed set, and putting S into the open set;

STEP 2: continuing when the open is not empty, otherwise returning to the error and exiting;

STEP 3: finding out the node n with the minimum evaluation distance in open, and putting n into P_minPerforming the following steps;

STEP 4: if n is equal to E, the end point is found, the step9 is switched to, otherwise, the operation is continued;

STEP5: removing n from the open set and adding the n into the closed set;

STEP 6: checking all grids G which can be passed around n, and skipping grids which cannot be passed;

STEP 7: adding all G not in the open set into the open set;

STEP 8: returning to STEP 2;

STEP 9: from E, pop P out in sequence_minAdding a linked list K into the nodes in the set until a starting point S is returned, inversely setting the linked list K to obtain a path from the starting point S to an end point E, wherein the weight L1 of the path is f (E);

the logistics distribution algorithm comprises the following implementation steps:

(1) calculating the distance and route from each client node to the logistics center, wherein the address of the distribution center A is (x)_A,y_A) Address (x) of client node Vi_Vi,y_Vi) (i ═ 1,2, …, n) by modification a^*The algorithm calculates the path weight from the distribution center to each node Vi and puts the path weight into a one-dimensional array Lse Vi]＝A^*(a, Vi) (i ═ 1, …, n), and saves its path;

(2) the distribution scheme is generated by a modified weighted graph algorithm,known distribution center A (x)_A,y_A) The client nodes and paths are described by a weighted undirected graph, G ═ V, E ═ V1, …, Vn }, E { (Vi, Vj) } (Vi ∈ V, Vj ∈ V), using a two-dimensional array L [ Vi ∈ V }][Vj]Storing the weight values between vertexes Vi to Vj, L [ Vi][Vj]＝A^*(Vi,Vj)；D[k]The travel distance to store each vehicle includes the distance to return to the distribution center, where (k ═ 1,2, …, M), M is the vehicle maximum; q [ k ]]Storing the load weight of each vehicle in driving, wherein (k is 1,2, …, M); the maximum travel distance of each vehicle is L_max(ii) a The maximum load of each vehicle is Q_max(ii) a Set V_TIs a set of unallocated nodes; set S [ k ]]Is a set of vertices assigned to the kth vehicle; the node a is a process variable and represents the current starting point to search the vertex of the next hop; the algorithm is described as follows:

STEP 1: initialization variable k is 1, V_T＝V；

STEP 2: initializing S [ k ] ═ phi, Q [ k ] ═ 0, D [ k ] ═ 0, and a ═ A;

STEP3：V_Tturning to STEP10 when empty, otherwise, continuing;

STEP 4: from the set V_TMiddle through modified type A^*The algorithm finds the vertex V [ i ] with the minimum distance from a]；

STEP5: judgment (Q [ k ]]+Q[V[i]]<＝Q_max)AND(D[k]+L[a][V[i]]+Lse(V[i])<＝L_max) If true, go to STEP6, otherwise go to STEP 9;

STEP6：D[k]＝D[k]+L[a,V[i]]，Q[k]＝Q[k]+Q[V[i]]，a＝V[i]；

STEP 7: let the vertex V [ i ]]Put into the set S [ k ]]In (3), delete the set V_TV [ i ] of (1)]；

STEP 8: returning to STEP 3;

STEP 9: d [ k ] + ls [ a ], k ═ k +1, return to STEP 2;

STEP 10: d [ k ] + ls [ a ], end;

the returned client nodes which are stored in the set S [ k ] and need to be visited by the vehicle k are the client nodes, the visiting sequence is the sequence of the elements in the set S [ k ], and all the logistics distribution vehicles only need to visit the client nodes in the set according to the corresponding vehicle.

Images