A logistics network node design method based on a few leaf support tree algorithm

Abstract

This invention discloses a logistics network design method based on a few-leaf support tree algorithm. The logistics and distribution network is represented by a graph G. A depth-first search algorithm is used to obtain a support tree T in graph G, with an additional output providing the degree of each vertex of support tree T. Support tree T is transformed to obtain another support tree F in graph G. Step S3 is repeated until a few-leaf support tree is obtained in graph G. Logistics centers, transfer stations, and distribution points in the logistics and distribution network are then designed based on this few-leaf support tree. This invention reduces the complexity of vehicle scheduling and operating costs in the logistics network.

Description

Technical Field

[0001] This invention relates to a logistics network design method, and more particularly to a logistics network design method based on a minimal leaf support tree algorithm, belonging to the field of logistics and distribution network technology. Background Technology

[0002] In the logistics field, if we consider logistics centers, transit stations, and delivery points in a logistics and distribution network as vertices, and the connecting channels between them as edges, then the logistics and distribution network can be modeled using a graph. When designing a distribution center-radial network, the goal is to reduce the number of last-mile delivery points, which are essentially the leaves of the supporting tree. One approach is to consolidate multiple small areas into a single transit station, and then have the transit station handle unified delivery, thereby reducing vehicle scheduling complexity and operating costs. This objective can be achieved by finding a minimal leaf supporting tree.

[0003] Using a diagram to represent a logistics and distribution network When indicating, if There is a road in the middle go through All the vertices, then Known as Hamilton Road (or H Road). If If there exists a Hamiltonian road, then this road is a very small leaf-supported tree. In this case, no transit station is needed. However, there are many other situations... There is no Hamiltonian path in the given situation. In this case, a minimal leaf support tree can be used as a substitute. Therefore, it is necessary to design a logistics network design method based on the minimal leaf support tree algorithm. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a logistics network design method based on a minimal leaf support tree algorithm, which solves the logistics and distribution network design problem under the condition that there is no Hamiltonian path in G.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for designing logistics network points based on a minimal leaf support tree algorithm includes the following steps: S1. Consider the logistics center, transit station, and distribution point in the logistics and distribution network as a vertex, and the connecting channel between the logistics center, transit station, and distribution point as an edge. The logistics and distribution network is represented by graph G. S2. Use the depth-first search algorithm to obtain a support tree T of graph G, and add an output that gives the degree of each vertex of the support tree T; S3. Based on the support tree transformation, another support tree F of graph G is obtained from the support tree T; S4. Repeat step S3 until a minimal leaf support tree of graph G is obtained, and design logistics centers, transit stations and delivery points in the logistics and distribution network based on the minimal leaf support tree.

[0007] Furthermore, the depth-first search algorithm obtains the support tree T of graph G by traversing every vertex of graph G. This represents the support tree obtained by Algorithm 1. The set of neighboring vertices, in this process, any vertex They were all marked with a number In the resulting supporting tree T, each non-root vertex has a unique parent. .

[0008] Furthermore, the depth-first search algorithm specifically includes the following steps: A1, when hour, ,and , Represents the empty set; A2, ; A3 S represents the set of all vertices in the network; A4. If for any vertex All Then output The algorithm ends if the condition is met; otherwise, w is a variable; A5 ; A6 ; A7. If Does the adjacency list contain a certain , making If yes, then go to A8; otherwise, go to A10. A8 , ,and ; A9 Transfer to A5; A10, if ,but If yes, proceed to A11; otherwise, proceed to A4. A11、 ; A12, Output Then switch to A7.

[0009] Furthermore, each vertex of the supporting tree T Each has a set of neighboring points If a vertex neighbor set If there is only one vertex, then this vertex It refers to a leaf of a supporting tree T. Let's say the supporting tree T has k leaves. .

[0010] Furthermore, the support tree transformation is as follows: from To begin, select an edge from the cotree edges of the support tree T associated with each leaf. Adding it to the supporting tree T results in a unique cycle C. If cycle C has three edges and contains a vertex with a degree of at least 3, then the cycle is considered complete. If two leaves are connected, remove the edges in cycle C that are associated with a vertex of degree at least 3, and then consider the next vertex; otherwise, consider the edges associated with... The next associated edge; if cycle C has at least four edges, and contains an edge connecting two vertices with a degree of at least 3, then delete that edge and consider the next vertex; otherwise, consider the next vertex. The next associated edge.

[0011] Furthermore, the support tree transformation specifically includes the following steps: B1, ,and F represents the resulting support tree; B2, ; B3, if Then output The algorithm ends; B4 ; B5. If If the adjacency list is empty, then go to B2; otherwise, in Select a vertex from the adjacency list ,make yes middle arrive The only road; B6 ,and ; B7. If There are 3 sides. for The leaves, and in Zhongyu and Adjacent vertices If the degree is at least 3, then , This means to remove edge wu from H, then go to B8; otherwise, go to B9. B8, in Remove from adjacency list Then switch to B2; B9. If There are two vertices and So that they are in The degree in all of them is at least 3, and yes One of the edges, then Then, turn to B8; otherwise, turn to B10. B10, in Remove from adjacency list Then switch to B5.

[0012] Compared with existing technologies, this invention has the following advantages and effects: It provides a logistics network design method based on a minimal leaf support tree algorithm, reducing vehicle scheduling complexity and operating costs in the logistics network; it is a relatively good solution when no Hamiltonian path exists in G. In some cases, it is the optimal solution. Attached Figure Description

[0013] Figure 1 This is a flowchart of a logistics network design method based on a minimal leaf support tree algorithm according to the present invention.

[0014] Figure 2 This is a schematic diagram of the logistics and distribution network according to an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of the support tree of the logistics and distribution network according to an embodiment of the present invention.

[0016] Figure 4 This is a schematic diagram of a minimal leaf support tree obtained by support tree transformation according to an embodiment of the present invention. Detailed Implementation

[0017] To illustrate in detail the technical solutions adopted by the present invention to achieve the intended technical objectives, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Furthermore, the technical means or technical features in the embodiments of the present invention can be replaced without creative effort. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0018] like Figure 1 As shown, the present invention provides a logistics network design method based on a minimal leaf support tree algorithm, comprising the following steps: S1. Consider the logistics center, transit station, and delivery point in the logistics and distribution network as vertices, and the connecting channels between them as edges. The logistics and distribution network is represented by graph G. To reduce the complexity of vehicle scheduling and operating costs in the logistics and distribution network, we design transit stations and delivery points by finding a minimal spanning tree.

[0019] S2. Use the depth-first search algorithm to obtain a support tree T of graph G, and add an output that gives the degree of each vertex of the support tree T.

[0020] S3. Based on the support tree transformation, another support tree F of graph G is obtained from the support tree T. The subgraph derived from all edges of graph G that are not in T is called the cotree of T. If any edge in the cotree of T... Adding it to T results in a unique cycle C. Then, deleting a line from cycle C that is not a cycle C... From the edges, we can obtain another supporting tree F of G.

[0021] If F is a support tree of G, and the number of leaves in the support tree obtained by any support tree transformation is no less than the number of leaves in F, then F is called a minimal leaf support tree of G.

[0022] S4. Repeat step S3 until a minimal leaf support tree of graph G is obtained, and design logistics centers, transit stations and delivery points in the logistics and distribution network based on the minimal leaf support tree.

[0023] The depth-first search algorithm obtains the support tree T of graph G by traversing every vertex of graph G. This represents the support tree obtained by Algorithm 1. The set of neighboring vertices, in this process, any vertex They were all marked with a number In the resulting supporting tree T, each non-root vertex has a unique parent. .

[0024] The depth-first search algorithm specifically includes the following steps: A1, when hour, ,and , Represents the empty set; A2, ; A3 S represents the set of all vertices in the network; A4. If for any vertex All Then output The algorithm ends if the condition is met; otherwise, w is a variable; A5 ; A6 ; A7. If Does the adjacency list contain a certain , making If yes, then go to A8; otherwise, go to A10. A8 , ,and ; A9 Transfer to A5; A10, if ,but If yes, proceed to A11; otherwise, proceed to A4. A11、 ; A12, Output Then switch to A7.

[0025] Each vertex of the supporting tree T Each has a set of neighboring points If a vertex neighbor set If there is only one vertex, then this vertex It refers to a leaf of a supporting tree T. Let's say the supporting tree T has k leaves. .

[0026] The support tree is transformed into: from To begin, select an edge from the cotree edges of the support tree T associated with each leaf. Adding it to the supporting tree T results in a unique cycle C. If cycle C has three edges and contains a vertex with a degree of at least 3, then the cycle is considered complete. If two leaves are connected, remove the edges in cycle C that are associated with a vertex of degree at least 3, and then consider the next vertex; otherwise, consider the edges associated with... The next associated edge; if cycle C has at least four edges, and contains an edge connecting two vertices with a degree of at least 3, then delete that edge and consider the next vertex; otherwise, consider the next vertex. The next associated edge.

[0027] The support tree transformation specifically includes the following steps: B1, ,and F represents the resulting support tree; B2, ; B3, if Then output The algorithm ends; B4 ; B5. If If the adjacency list is empty, then go to B2; otherwise, in Select a vertex from the adjacency list ,make yes middle arrive The only road; B6 ,and ; B7. If There are 3 sides. for The leaves, and in Zhongyu and Adjacent vertices If the degree is at least 3, then , This means to remove edge wu from H, then go to B8; otherwise, go to B9. B8, in Remove from adjacency list Then switch to B2; B9. If There are two vertices and So that they are in The degree in all of them is at least 3, and yes One of the edges, then Then, turn to B8; otherwise, turn to B10. B10, in Remove from adjacency list Then switch to B5.

[0028] The supporting tree F obtained by the supporting tree transformation for point G may not be a very few-leaf supporting tree. The supporting tree transformation can be repeated until a very few-leaf supporting tree for point G is obtained.

[0029] The present invention will be further described below with reference to specific embodiments.

[0030] like Figure 2 The logistics and distribution network shown contains 12 logistics centers, transit stations, and distribution points. These are represented by 12 vertices, and if two vertices have a connecting path, they are connected by an edge, thus forming a graph G. In this network... For logistics centers, we use a method of constructing a minimal leaf-supported tree of G to set up distribution stations and transfer stations.

[0031] Step 1. For a connected graph The depth-first search algorithm is used to obtain A support tree .

[0032] Step 2. For the supporting tree By transforming the support tree, traversing... After each leaf, we obtained Another support tree ,like The number of leaves is not less than The number of leaves, then that is A tree supported by very few leaves. Otherwise, proceed to step 3.

[0033] Step 3. Repeat the algorithm in Step 2 until you get... A tree supported by very few leaves.

[0034] like Figure 2 As shown, the present invention provides an embodiment, which is a connected graph. It has 12 vertices: .

[0035] like Figure 3 As shown, a support tree for the embodiment can be obtained by using a depth-first algorithm.

[0036] The specific process is as follows: 1. From Begin, The label is 1. Then, in Two neighboring points Select ,Will The label is 2.

[0037] 2. In 4 unlabeled neighboring points Select ,Will The label is 3. Because Two neighboring points They're all numbered, so the next step is to go back to... .exist 3 neighboring points Select The number is 4. Then, select... Unlabeled neighbor , and label it as 5.

[0038] 3. Select Unlabeled neighbor It is numbered 6.

[0039] 4. In Choose from 6 unlabeled neighboring points ,Will Numbered 7. Then, They are numbered 8 and 9 in sequence.

[0040] 5. Because All neighboring points are labeled; the next step is to backtrack. .and All neighboring points are labeled, then backtrack. .again The neighboring points are labeled, then backtrack to .

[0041] 6. In Choose from 3 unlabeled neighboring points ,Will The label is 10. Then, They are numbered 11 and 12 in sequence.

[0042] 7. Since each vertex is labeled, the algorithm ends.

[0043] like Figure 4 As shown, the process by which the smallest leaves support the tree is as follows: 1. Taking the example of the embodiment as an example Figure 3 A supporting tree is shown, denoted as At this time, in In the middle, it has 4 leaves. .

[0044] 2. Move the edge Add In the middle, the only circle was obtained. .because The degree is 3, remove the edge. This yields another support tree in the embodiment. .

[0045] 3. There are 3 leaves in it Associate any leaf with Add the edges in the remaining tree In the process, the number of leaves in the support tree obtained using Algorithm 2 will not decrease, therefore This is a very small leaf support tree in the embodiment.

[0046] In an embodiment, it is possible to Set up delivery stations, and Set up a transfer station.

[0047] This invention provides a logistics network design method based on a minimal leaf support tree algorithm, reducing vehicle scheduling complexity and operating costs in the logistics network; it is a relatively good solution when no Hamiltonian path exists in G. In certain cases, it is the optimal solution. The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A logistics network site design method based on a minimal leaf support tree algorithm, characterized by Includes the following steps: S1. Consider the logistics center, transit station, and distribution point in the logistics and distribution network as a vertex, and the connecting channel between the logistics center, transit station, and distribution point as an edge. The logistics and distribution network is represented by graph G. S2. Use the depth-first search algorithm to obtain a support tree T of graph G, and add an output that gives the degree of each vertex of the support tree T; S3. Based on the support tree transformation, another support tree F of graph G is obtained from the support tree T; S4. Repeat step S3 until a minimal leaf support tree of graph G is obtained, and design logistics centers, transit stations and delivery points in the logistics and distribution network based on the minimal leaf support tree.

2. The logistics network design method based on a minimal leaf support tree algorithm according to claim 1, characterized in that: The depth-first algorithm gets the support tree T of the graph G by traversing each vertex of the graph G, The neighbor set of vertex in the support tree obtained by algorithm 1, in which each vertex is marked with a number , and each non-root vertex has a unique father in the obtained support tree T.

3. The method of claim 2, wherein the method is characterized by: The depth-first search algorithm specifically includes the following steps: A1, when hour, ,and , Represents the empty set; A2、 ； A3 S represents the set of all vertices in the network; A4. If for any vertex All Then output The algorithm ends if the condition is met; otherwise, w is a variable; A5、 ； A6、 ； A7. If Does the adjacency list contain a certain , making If yes, then go to A8; otherwise, go to A10. A8 , ,and ; A9 Transfer to A5; A10, if ,but Go to A11; Otherwise, transfer to A4; A11、 ； A12, Output Then switch to A7.

4. The logistics network design method based on a minimal leaf support tree algorithm according to claim 1, characterized in that: Each vertex of the supporting tree T Each has a set of neighboring points If a vertex neighbor set If there is only one vertex, then this vertex It refers to a leaf of a supporting tree T. Let's say the supporting tree T has k leaves. .

5. The logistics network design method based on a minimal leaf support tree algorithm according to claim 4, characterized in that: The support tree transformation is as follows: from To begin, select an edge from the cotree edges of the support tree T associated with each leaf. Adding it to the supporting tree T results in a unique cycle C. If cycle C has three edges and contains a vertex with a degree of at least 3, then the cycle is considered complete. If two leaves are connected, remove the edges in cycle C that are associated with a vertex of degree at least 3, and then consider the next vertex; otherwise, consider the edges associated with... The next associated edge; if cycle C has at least four edges, and contains an edge connecting two vertices with a degree of at least 3, then delete that edge and consider the next vertex; otherwise, consider the next vertex. The next associated edge.

6. The logistics network design method based on a minimal leaf support tree algorithm according to claim 4, characterized in that: The support tree transformation specifically includes the following steps: B1, ,and F represents the resulting support tree; B2、 ； B3, if Then output The algorithm ends; B4、 ； B5. If If the adjacency list is empty, then go to B2; otherwise, in Select a vertex from the adjacency list ,make yes middle arrive The only road; B6 ,and ; B7. If There are 3 sides. for The leaves, and in Zhongyu and Adjacent vertices If the degree is at least 3, then , This means to remove edge wu from H, then go to B8; otherwise, go to B9. B8, in Remove from adjacency list Then switch to B2; B9. If There are two vertices and So that they are in The degree in all of them is at least 3, and yes One of the edges, then Then, turn to B8; otherwise, turn to B10. B10, in Remove from adjacency list Then switch to B5.

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