Pick-up path optimization fast calculation method based on Christofides algorithm

Abstract

The application provides a picking path optimization fast calculation method based on Christofides algorithm, which converts the path problem among various shelves in a warehouse into a traveling salesman problem including a warehouse starting point position and a warehouse ending point position, and utilizes a Christofides heuristic algorithm to calculate a minimum spanning tree list of a non-directional graph composed of shelves with the warehouse starting point position as a root node, and according to the minimum spanning tree list, a method for calculating a complete Euler path traversing the list is utilized to obtain an optimal shelf sequence; the method has simple steps, low algorithm complexity, and can obtain extremely high calculation speed; the method has good adaptability to different density picking tasks and can obtain satisfactory results.

Description

Technical Field

[0001] This invention relates to the fields of warehousing and logistics and numerical computation, and in particular to a fast calculation method for picking route optimization based on the Christofides algorithm. Background Technology

[0002] With the ever-increasing workload in the manufacturing and logistics industries, modern warehousing systems have experienced unprecedented development, transforming the warehousing industry from simply storing goods to a more comprehensive approach that integrates distribution processing and information processing. In recent years, as picking demands have shifted from large-volume, low-batch orders to diverse, low-volume orders, delivery time requirements have become increasingly shorter, placing higher demands on the response speed and picking efficiency of distribution centers.

[0003] Optimizing picking routes is a crucial issue that modern warehousing must address, as it improves efficiency in both inbound and outbound operations while reducing operational costs. In particular, current picking route calculation methods are slow when faced with high-density picking tasks and large volumes of data, failing to meet the efficiency requirements for handling large-scale picking operations. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a fast calculation method for picking path optimization based on the Christofides algorithm.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A fast calculation method for picking route optimization based on the Christofides algorithm includes the following steps:

[0007] S01: Based on the actual shelving arrangement in the warehouse, fill in the parameter values ​​in the algorithm configuration file of the intelligent warehousing system to configure the basic parameters. The basic parameters include the number of shelving rows, the number of shelving columns, the length, width, height, number of shelving layers, and number of storage units for each shelving, as well as the row spacing and column spacing.

[0008] The intelligent warehousing system is a real-time computer software system that can manage information, resources, behaviors, inventory, and distribution operations according to the business rules and algorithms in operation.

[0009] The algorithm configuration file is the parameter configuration module in the system;

[0010] S02: Obtain the picking task, warehouse start point location, and warehouse end point location from the intelligent warehousing system;

[0011] The picking task is a task or set of tasks that selects the location of goods in the warehouse; the information of each picking task includes: task ID, shelf number, warehouse number, and shelf layer number;

[0012] Warehouse starting point location: Mark the location of the nearest storage location to the warehouse entrance;

[0013] Warehouse endpoint location: Mark the location of the storage location closest to the warehouse exit;

[0014] Storage location: This refers to the number of columns on the shelf where the goods occupy.

[0015] S03: Transform the path problem between shelves in the warehouse into a Traveling Salesman Problem (TSP) that includes the starting and ending points of the warehouse. TSP: Let G = (V, E) be a graph, where V is the set of vertices and E is the set of edges. Let C = (cij) be the distance matrix associated with E. The problem is transformed into finding the shortest path through n shelves, or searching a permutation of the integer subset X = {1, 2, ..., n}. Calculate:

[0016]

[0017] Where d(v) i v i+1 ) indicates shelf v i To the shelf v i+1 The distance is calculated using the Christofides heuristic algorithm:

[0018] S04: Filter all shelves included in this picking and generate a list of shelf numbers;

[0019] S05: Add the warehouse starting point location to the shelf number list;

[0020] S06: Calculate the physical location of all shelves in the shelf number list based on the warehouse's basic parameters;

[0021] S07: Based on the physical location of the shelves, calculate the minimum spanning tree list of the undirected graph composed of the shelves, with the starting point of the warehouse as the root node;

[0022] S08: Filter the nodes in the minimum spanning tree that have an odd number of edges, and form a list of nodes with an odd number of edges;

[0023] S09: Select node pairs in the odd-numbered edge node list according to the shortest distance principle and add them to the minimum spanning tree list;

[0024] S10: Given a list of minimum spanning trees, calculate a complete Eulerian path that traverses this list, in which all nodes have an even number of edges.

[0025] The Euler path is defined as follows: In an undirected graph, a path is found such that every edge is visited exactly once.

[0026] S11: Starting from the root node of the minimum spanning tree, retrace the Eulerian path. At each node, remove the edge associated with that node from the Eulerian path. Finally, the optimal shelf order is obtained.

[0027] S12: Group all tasks according to shelf number to form several shelf task lists. Calculate the optimal task order for each shelf task list to obtain several optimal task order lists for each shelf.

[0028] S13: Combine the optimal shelf order, calculate the picking direction for each shelf, including forward and reverse order, update the picking order of the optimal task order list for this shelf, update the final task order list, and pick according to the final task order list.

[0029] Furthermore, step S07 includes the following sub-steps:

[0030] S071: Create an undirected graph, with the warehouse starting position and each shelf with picking tasks as a node, and all nodes connected by edges. Calculate the length of all edges based on the physical location of the shelves.

[0031] S072: Using the warehouse's starting position as the root node, find all edges that the current node can access;

[0032] S073: Find the shortest edge among the edges that have been searched. This edge must have one unvisited point. Add the unvisited point to the set and record the added edge.

[0033] S074: Find all edges that can be accessed by the current set, and repeat the process of S073 until no new nodes can be added;

[0034] S075: At this point, the tree formed by all edges is the minimum spanning tree.

[0035] Furthermore, step S10 also includes the following sub-steps:

[0036] S101: The adjusted list of minimum spanning trees guarantees the basic condition for computing the Eulerian path: the graph is connected and each vertex in the graph has an even number of edges;

[0037] S102: Start the search from the root node of the minimum spanning tree;

[0038] S103: Find an edge connected to the current node, and find the next node based on this edge;

[0039] S104: Repeat S103 until the search returns to the starting point, record these edges as a loop, and remove them from the adjusted minimum spanning tree list;

[0040] S105: Find a new starting point and repeat the process from S102 to S104 until all loops are found;

[0041] S106: Connect all loops based on the nodes that appear repeatedly in multiple loops to form an Euler path.

[0042] Furthermore, step S12 also includes the following sub-steps:

[0043] S121: Concatenate multiple task lists for different storage locations according to their location numbers to obtain the optimal task order list for this shelf.

[0044] S122: If the last task in the previous storage location has more than half the total number of shelf layers, then the tasks in this storage location are arranged in descending order of shelf layer number and then spliced ​​together; otherwise, the tasks in this storage location are arranged in ascending order of shelf layer number and then spliced ​​together.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows: the Christofides heuristic algorithm has simple steps, low algorithm complexity, and can achieve extremely high computing speed; it has good adaptability to picking tasks of different densities and can obtain satisfactory results in all cases. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the implementation steps of Embodiment 1 of the present invention;

[0047] Figure 2 A schematic diagram of the warehouse racks on which the implementation configuration data of Embodiment 1 of the present invention is based;

[0048] Figure 3 This is a schematic diagram of the minimum spanning tree in Embodiment 1 of the present invention;

[0049] Figure 4 This is a schematic diagram of the Euler path in Embodiment 1 of the present invention;

[0050] Figure 5 This is a schematic diagram of the optimal shelf arrangement in Embodiment 1 of the present invention;

[0051] Figure 6 This is a schematic diagram of the optimal task sequence for each shelf in Embodiment 1 of the present invention;

[0052] Figure 7-1 This is a shelf task sequence diagram (task density approximately 20%) for Embodiment 1 of the present invention;

[0053] Figure 7-2 This is a shelf task sequence diagram (task density approximately 50%) for Embodiment 1 of the present invention;

[0054] Figure 7-3 This is a shelf task sequence diagram (task density approximately 80%) for Embodiment 1 of the present invention;

[0055] Figure 7-4 This is a comparison chart of the shelf task sequence in Embodiment 1 of the present invention (task density approximately 20%, 50%, and 80%). Detailed Implementation

[0056] To provide a further understanding of the purpose, structure, features, and functions of the present invention, detailed descriptions are provided below with reference to specific embodiments.

[0057] Example 1: As Figure 1 As shown:

[0058] A fast calculation method for picking route optimization based on the Christofides algorithm includes the following steps:

[0059] S01: Based on the actual shelving arrangement in the warehouse, fill in the parameter values ​​in the algorithm configuration file of the intelligent warehousing system to configure the basic parameters. The basic parameters include the number of shelving rows, the number of shelving columns, the length, width, height, number of shelving layers, and number of storage units for each shelving, as well as the row spacing and column spacing.

[0060] An intelligent warehousing system is a real-time computer software system that can manage information, resources, behaviors, inventory, and distribution operations according to operational business rules and algorithms.

[0061] The algorithm configuration file is the module for configuring parameters in the system.

[0062] The specific configuration in this embodiment is as follows, such as... Figure 2 As shown:

[0063]

[0064]

[0065] S02: Obtain the picking task, warehouse start point location, and warehouse end point location from the intelligent warehousing system;

[0066] Picking task: A task or set of tasks that selects goods from their storage locations; information for each picking task includes: task ID, shelf number, storage location number, and shelf level.

[0067] Warehouse starting point location: Mark the location of the nearest storage location to the warehouse entrance;

[0068] Warehouse endpoint location: Mark the location of the storage location closest to the warehouse exit;

[0069] Storage location: This refers to the column number of the shelf space occupied by the goods.

[0070] In this embodiment, the specific picking task is as follows:

[0071] {'start':[1, 1, 10],

[0072] 'end': [6, 1, 1],

[0073] 'task': [[0, 6, 4, 12],

[0074] [1, 3, 1, 7],

[0075] [2, 3, 1, 8],

[0076] [3, 13, 5, 5]

[0077] [4, 6, 1, 4],

[0078] [5, 18, 2, 2],

[0079] [6, 13, 3, 1],

[0080] [7, 3, 4, 7]

[0081] [8, 14, 2, 8],

[0082] [9, 18, 4, 9],

[0083] [10, 14, 5, 5], [11, 3, 4, 2],

[0084] [12, 15, 2, 3], [13, 6, 5, 5]

[0085] [14, 13, 3, 2], [15, 15, 2, 11], [16, 14, 4, 5], [17, 6, 6, 3]

[0086] [18, 6, 6, 10], [19, 13, 1, 2], [20, 14, 3, 12], [21, 14, 5, 9], [22, 15, 5, 1], [23, 6, 5, 8]

[0087] [24, 3, 3, 12], [25, 6, 3, 10], [26, 6, 2, 2],

[0088] [27, 15, 6, 10], [28, 18, 4, 12], [29, 14, 1, 8],

[0089] [30, 14, 6, 7]

[0090] [31, 18, 4, 10],

[0091] [32, 14, 2, 3],

[0092] [33, 6, 5, 12],

[0093] [34, 13, 5, 6]

[0094] [35, 18, 4, 4]

[0095] [36, 14, 6, 9]

[0096] [37, 6, 5, 10]

[0097] [38, 14, 3, 8],

[0098] [39, 15, 2, 8]]}

[0099] S03: Transform the path problem between shelves in the warehouse into a Traveling Salesman Problem (TSP) that includes the starting and ending points of the warehouse. TSP: Let G = (V, E) be a graph, where V is the set of vertices and E is the set of edges. Let C = (cij) be the distance matrix associated with E. The problem is transformed into finding the shortest path through n shelves, or searching a permutation of the integer subset X = {1, 2, ..., n}. Calculate:

[0100]

[0101] Where d(v) i v i+1 ) indicates shelf v i To the shelf v i+1 The distance is calculated using the Christofides heuristic algorithm.

[0102] S04: Filter all shelves included in this picking and generate a list of shelf numbers.

[0103] In this embodiment, specifically:

[0104] Find the shelf numbers contained in all tasks: [3, 6, 13, 14, 15, 18]

[0105] S05: Add the warehouse starting point location to the shelf number list.

[0106] In this embodiment, specifically:

[0107] Set the starting shelf number as: [1, 3, 6, 13, 14, 15, 18]

[0108] S06: Calculate the physical location of all shelves in the shelf number list based on the warehouse's basic parameters. In this embodiment, the specific distance matrix is:

[0109] 1 0 22 23 68 79 90 91 3 22 0 45 46 57 68 69 6 23 45 0 45 56 67 68 13 68 46 45 0 11 22 23 14 79 57 56 11 0 11 34 15 90 68 67 22 11 0 45 18 91 69 68 23 34 45 0

[0110] S07: Based on the physical location of the shelves, calculate the minimum spanning tree list of the undirected graph composed of the shelves, with the starting position of the warehouse as the root node:

[0111] List of minimum spanning trees, such as Figure 3 As shown:

[0112] [(1,3),

[0113] (1, 6),

[0114] (6, 13),

[0115] (13, 14),

[0116] (14, 15),

[0117] (13, 18)).

[0118] Furthermore, step S07 includes the following sub-steps:

[0119] The minimum spanning tree method is used to solve the optimal picking order between shelves. Starting from the starting point, each step selects one of the unselected edges so that it does not form a cycle with the selected edges, and this edge is the shortest among the unselected edges, thus gradually forming the minimum spanning tree.

[0120] S071: Create an undirected graph, with the warehouse starting position and each shelf with picking tasks as a node, and all nodes connected by edges. Calculate the length of all edges based on the physical location of the shelves.

[0121] S072: Using the warehouse's starting position as the root node, find all edges that the current node can access;

[0122] S073: Find the shortest edge among the edges that have been searched. This edge must have one unvisited point. Add the unvisited point to the set and record the added edge.

[0123] S074: Find all edges that can be accessed by the current set, and repeat the process of S073 until no new nodes can be added;

[0124] S075: At this point, the tree formed by all edges is the minimum spanning tree.

[0125] S08: Filter the nodes in the minimum spanning tree that have an odd number of edges to form a list of nodes with odd edges. In this embodiment, the list of nodes with odd edges is as follows:

[0126] 3 1 13 3 15 1 18 1

[0127] S09: Select node pairs in the odd-numbered edge node list according to the shortest distance principle and add them to the minimum spanning tree list.

[0128] In this embodiment, the updated minimum spanning tree list includes the addition of two entries: (3, 13) and (15, 18).

[0129] [(1,3),

[0130] (1, 6),

[0131] (6, 13),

[0132] (13, 14),

[0133] (14, 15),

[0134] (13, 18),

[0135] (3, 13),

[0136] (15, 18)]

[0137] S10: Based on the list of minimum spanning trees, calculate the complete Eulerian path traversing this list, where all nodes in the Eulerian path have an even number of edges. In this embodiment, the Eulerian path is: [1, 3, 13, 14, 15, 18, 13, 6, 1]. Figure 4 As shown.

[0138] Furthermore, step S10 also includes the following sub-steps:

[0139] S101: The adjusted list of minimum spanning trees guarantees the basic condition for computing the Eulerian path: the graph is connected and each vertex in the graph has an even number of edges;

[0140] S102: Start the search from the root node of the minimum spanning tree;

[0141] S103: Find an edge connected to the current node, and find the next node based on this edge;

[0142] S104: Repeat S103 until the search returns to the starting point, record these edges as a loop, and remove them from the adjusted minimum spanning tree list;

[0143] S105: Find a new starting point and repeat the process from S102 to S104 until all loops are found;

[0144] S106: Connect all loops based on the nodes that appear repeatedly in multiple loops to form an Euler path;

[0145] An Eulerian path is defined as follows: In an undirected graph, a path is found such that every edge is visited exactly once.

[0146] S11: Starting from the root node of the minimum spanning tree, retrace the Eulerian path. At each node visited, remove the edges associated with that node from the Eulerian path. This ultimately yields the optimal shelf order. Therefore, in this embodiment, as... Figure 5 As shown in the figure (the horizontal axis represents the warehouse length (m) and the vertical axis represents the warehouse width (m)), the optimal shelf order is: [1, 3, 13, 14, 15, 18, 6].

[0147] First, calculate the optimal shelf order among the shelves in the current warehouse, and then solve the picking order for each shelf. The complex picking order is divided into two modules for separate processing.

[0148] S12: Group all tasks according to shelf number to form several shelf task lists. For each shelf task list, calculate the optimal task order for that shelf, obtaining several optimal task order lists for that shelf. In this embodiment, for example... Figure 6 (As shown in the diagram, the horizontal axis represents the warehouse length (m), and the vertical axis represents the warehouse width (m).) The task list sorted by shelf number is as follows:

[0149]

[0150]

[0151] like Figures 7-1 to 7-4 (The horizontal axis in the figure represents the warehouse length (m), and the vertical axis represents the warehouse width (m)). As shown in the figure, (the lines in the figure only represent the order of tasks, not the time travel route). Comparative analysis shows that the Christofides heuristic algorithm has simple steps, low algorithm complexity, and can achieve extremely high calculation speed. It has good adaptability to picking tasks of different densities and can achieve satisfactory results.

[0152] Here, density refers to the ratio of the number of storage locations involved in this picking task to the total number of storage locations. For a 10-row, 5-layer rack with a total of 50 compartments, if this picking task involves 14 of these compartments, then the density is 14 / 50 = 28%.

[0153] Since different picking tasks have different densities, and even significant differences, one or more algorithms are selected to deal with different densities when calculating the picking order. Some algorithms are fast when the density is low or moderate, but the calculation difficulty increases when the density is too high, and the overall calculation speed will be greatly reduced. However, the Christofides heuristic algorithm is highly adaptable, the calculation process is more stable, and the speed is faster.

[0154] Furthermore, step S12 also includes the following sub-steps:

[0155] S121: Concatenate multiple task lists for different storage locations according to their location numbers to obtain the optimal task order list for this shelf.

[0156] S122: If the last task in the previous storage location has more than half the total number of shelf layers, then the tasks in this storage location are arranged in descending order of shelf layer number and then spliced ​​together; otherwise, the tasks in this storage location are arranged in ascending order of shelf layer number and then spliced ​​together. In this embodiment, the shelf arrangement is as follows, as shown in the figure:

[0157] Shelf #3: 11, 7, 1, 2, 24

[0158] Shelf #6: 26, 17, 4, 13, 23, 18, 37, 25, 0, 33

[0159] Shelf #13: 6, 14, 19, 3, 34

[0160] Shelf #14: 32, 16, 10, 30, 38, 8, 29, 21, 36, 20

[0161] Shelf #15: 22, 12, 39, 27, 15

[0162] Shelf number 18: 5, 35, 9, 31, 28.

[0163] S13: Based on the optimal shelf order, calculate the picking direction for each shelf, including forward and reverse order, update the picking order of the optimal task order list for this shelf, update the final task order list, and pick according to the final task order list.

[0164] The picking direction for each shelf is solved individually, and then combined with the picking sequence to obtain the final task sequence list.

[0165] Most recent sequential task number:

[0166] 11, 7, 1, 2, 24, 6, 14, 19, 3, 34, 20, 36, 21, 29, 8, 38, 30, 10, 16, 32, 22, 12, 39, 27, 15, 5, 35, 9, 31, 28, 33, 0, 25, 37, 18, 23, 13, 4, 17, 26.

[0167] Furthermore: The picking direction of the shelves is determined sequentially according to the optimal shelf order. If the previous shelf is in forward order, and the distance from the end point of the previous shelf to the start point of the current shelf is less than the distance from the end point of the previous shelf to the end point of the current shelf, then the picking direction of the current shelf is in forward order; otherwise, it is in reverse order.

[0168] If the previous shelf is in reverse order, and the distance from the starting point of the previous shelf to the starting point of the current shelf is less than the distance from the starting point of the previous shelf to the ending point of the current shelf, then the picking direction of the current shelf is in forward order; otherwise, it is in reverse order.

[0169] If the current picking direction of the shelf is in ascending order, the optimal task order list for this shelf is added to the final task order list. If it is in descending order, the optimal task order list for this shelf is reversed before being added to the final task order list.

[0170] According to the calculation method of this invention, given basic warehouse parameters, warehouse starting point location, warehouse ending point location, and picking task list, it can quickly perform calculations and obtain high-quality results. It can process a large number of picking tasks (around 10,000) in a very short time (approximately 1 second) and obtain excellent calculation results. This can meet the needs of picking personnel for handling large numbers of tasks and real-time interaction.

[0171] The present invention has been described in the above-described embodiments; however, these embodiments are merely examples for implementing the present invention. It must be noted that the disclosed embodiments do not limit the scope of the present invention. Conversely, any modifications and refinements made without departing from the spirit and scope of the present invention are within the scope of patent protection of the present invention.

Claims

1. A fast calculation method for picking route optimization based on the Christofides algorithm, characterized by: Includes the following steps: S01: Based on the actual shelving arrangement in the warehouse, fill in the parameter values ​​in the algorithm configuration file of the intelligent warehousing system to configure the basic parameters. The basic parameters include the number of shelving rows, the number of shelving columns, the length, width, height, number of shelving layers, and number of storage units for each shelving, as well as the row spacing and column spacing. The intelligent warehousing system is a real-time computer software system that can manage information, resources, behaviors, inventory, and distribution operations according to the business rules and algorithms in operation. The algorithm configuration file is the parameter configuration module in the system; S02: Obtain the picking task, warehouse start point location, and warehouse end point location from the intelligent warehousing system; The picking task: the task or a collection of tasks that selects the location of goods in the warehouse; The information for each picking task includes: task ID, shelf number, location number, and shelf layer number; Warehouse starting point location: Mark the location of the nearest storage location to the warehouse entrance; Warehouse endpoint location: Mark the location of the storage location closest to the warehouse exit; Storage location: This refers to the number of columns on the shelf where the goods occupy. S03: Transform the path problem between shelves in the warehouse into a Traveling Salesman Problem (TSP) that includes the starting and ending points of the warehouse. TSP: Let G = (V, E) be a graph, where V is the set of vertices and E is the set of edges. Let C = (cij) be the distance matrix associated with E. The problem is transformed into finding the shortest path through n shelves, or searching a permutation of the integer subset X = {1, 2, ..., n}. Calculate: ； in This represents the distance between shelves, calculated using the Christofides heuristic algorithm: S04: Filter all shelves included in this picking and generate a list of shelf numbers; S05: Add the warehouse starting point location to the shelf number list; S06: Calculate the physical location of all shelves in the shelf number list based on the warehouse's basic parameters; S07: Based on the physical location of the shelves, calculate the minimum spanning tree list of the undirected graph composed of the shelves, with the starting point of the warehouse as the root node; S08: Filter the nodes in the minimum spanning tree that have an odd number of edges, and form a list of nodes with an odd number of edges; S09: Select node pairs in the odd-numbered edge node list according to the shortest distance principle and add them to the minimum spanning tree list; S10: Given a list of minimum spanning trees, calculate a complete Eulerian path that traverses this list, in which all nodes have an even number of edges. The Euler path is defined as follows: In an undirected graph, a path is found such that every edge is visited exactly once. S11: Starting from the root node of the minimum spanning tree, retrace the Eulerian path. At each node, remove the edge associated with that node from the Eulerian path. Finally, the optimal shelf order is obtained. S12: Group all tasks according to shelf number to form several shelf task lists. Calculate the optimal task order for each shelf task list to obtain several optimal task order lists for each shelf. Step S12 also includes the following sub-steps: S121: Concatenate multiple task lists for different storage locations according to their location numbers to obtain the optimal task order list for this shelf. S122: If the last task of the previous storage location has more than half the total number of shelf layers, then the tasks of this storage location are arranged in descending order of shelf layer number and then spliced ​​together; otherwise, the tasks of this storage location are arranged in ascending order of shelf layer number and then spliced ​​together. S13: Combine the optimal shelf order, calculate the picking direction for each shelf, including forward and reverse order, update the picking order of the optimal task order list for this shelf, update the final task order list, and pick according to the final task order list.

2. The fast calculation method for picking path optimization based on the Christofides algorithm as described in claim 1, characterized in that: Step S07 includes the following sub-steps: S071: Create an undirected graph, with the warehouse starting position and each shelf with picking tasks as a node, and all nodes connected by edges. Calculate the length of all edges based on the physical location of the shelves. S072: Using the warehouse's starting position as the root node, find all edges that the current node can access; S073: Find the shortest edge among the edges that have been searched. This edge must have one unvisited point. Add the unvisited point to the set and record the added edge. S074: Find all edges that can be accessed by the current set, and repeat the process of S073 until no new nodes can be added; S075: At this point, the tree formed by all edges is the minimum spanning tree.

3. The fast calculation method for picking path optimization based on the Christofides algorithm as described in claim 1, characterized in that: Step S10 also includes the following sub-steps: S101: The adjusted list of minimum spanning trees guarantees the basic condition for computing the Eulerian path: the graph is connected and each vertex in the graph has an even number of edges; S102: Start the search from the root node of the minimum spanning tree; S103: Find an edge connected to the current node, and find the next node based on this edge; S104: Repeat S103 until the search returns to the starting point, record these edges as a loop, and remove them from the adjusted minimum spanning tree list; S105: Find a new starting point and repeat the process from S102 to S104 until all loops are found; S106: Connect all loops based on the nodes that appear repeatedly in multiple loops to form an Euler path.

Images