A cable shortest path optimization method, device and medium based on an improved Astar algorithm

Abstract

The application relates to a cable shortest path optimization method based on an improved Astar algorithm, equipment and a medium, the method comprising the following steps: constructing a record matrix B, a path matrix P, a minimum heap Q and an adjacency list matrix G and initializing; updating the adjacency list matrix G according to a bridge network adjacency matrix A; updating the minimum heap Q according to a start point coordinate and an end point coordinate of a to-be-laid cable; updating the path matrix P in combination with the minimum heap Q and the adjacency list matrix G; and obtaining a laying path of the to-be-laid cable according to the updated path matrix P. The application greatly improves the operation efficiency of the Astar algorithm.

Description

Technical Field

[0001] This invention relates to the field of cable laying, and in particular to a method, device and medium for finding the shortest path of a cable based on an improved Astar algorithm. Background Technology

[0002] Cable laying is crucial in factory power system design. The length of a cable connecting a starting point and an ending point determines its procurement cost, while the total length of all cables to be laid determines the total procurement cost. Traditional manual cable route selection, though simple to operate, suffers from drawbacks such as reliance on subjective experience, slow computational efficiency, inaccurate calculations, and inability to guarantee the optimal route. However, with the continuous development of computer hardware and various path optimization algorithms, traditional manual cable route selection is gradually transforming into automatic shortest path optimization methods using intelligent algorithms.

[0003] The factory's power system consists of numerous cable trays, forming a graph network of traversable cables. Each cable tray's endpoint corresponds to a node in the graph network, and the length of each cable tray corresponds to an edge weight. Once the cable trays are determined, their corresponding graph network is also determined. For a given cable to be laid, its starting and ending points are known and determined. Finding the shortest cable laying path is equivalent to finding the shortest path between the starting and ending nodes in the graph network.

[0004] In graph theory, a graph network is typically first converted into an adjacency matrix to facilitate subsequent computation and solution. The element in the i-th row and j-th column of the adjacency matrix represents the distance between node i and node j in the graph network. Because cable trays are bidirectionally connected and have the same length in both directions, the graph formed by the cable tray network is an undirected graph, meaning its corresponding adjacency matrix is ​​a symmetric matrix with zeros on the main diagonal.

[0005] There are various methods for finding the shortest path between a given pair of nodes on a graph using shortest path algorithms, but no single algorithm can simultaneously achieve optimal solution quality and efficiency. Different types of algorithms are best suited for different scenarios. The Astar algorithm, a classic graph shortest path algorithm, also cannot simultaneously achieve optimal solution quality and efficiency. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a method, device, and medium for finding the shortest cable path based on an improved Astar algorithm.

[0007] The specific plan is as follows:

[0008] A cable shortest path optimization method based on an improved Astar algorithm includes the following steps:

[0009] S1: Construct an N×N record matrix B and initialize it, setting the diagonal elements to True and the remaining elements to False; construct an N×N path matrix P and initialize it, setting all its elements to -1; construct a min-heap Q and initialize it as an empty heap; construct an adjacency list matrix G with N rows and initialize it so that each column is empty; N represents the total number of nodes in the bridge network.

[0010] S2: Obtain the adjacency matrix A of the bridge network, traverse each element in A, and for each element, determine whether the value of the element satisfies both not equal to ∞ and not equal to 0. If so, extract the row number k1 and column number k2 corresponding to the element, and add an element with the value k2 in the row with row number k1 in G.

[0011] S3: Obtain the starting and ending coordinates of a cable to be laid. Set the node number of the cable tray network corresponding to the starting coordinates of the cable to index1 and the node number of the cable tray network corresponding to the ending coordinates to index2. Traverse each element in the row with row number index1 in G. For the i-th element, represent its value as g. i Construct the tuple (g) corresponding to this element. i ,A[index1,g i ]+h(ICM(g i ),ICM(index2))) and push it into the min-heap Q, where A[index1,g i ] indicates that the row number is index1 and the column number is g in matrix A. i The value of the element, the function ICM(.) represents solving for the coordinates corresponding to the index of the node in the bridge network, ICM(g i ) indicates that the index g in the cable tray network i The coordinates corresponding to the node, ICM(index2) represents the coordinates corresponding to the node with index2 in the bridge network, and h(.) represents the distance between the two coordinates; the smaller the value of the second element in the tuple, the higher the priority of the tuple; each time a value is taken from the min-heap Q, the tuple with the highest priority is automatically popped.

[0012] S4: Update the path matrix P by combining the min-heap Q and the adjacency list matrix G, including the following steps:

[0013] S401: Determine if the number of tuples in the min-heap Q is 0. If it is, assign True to B[index1,index2].

[0014] S402: Determine if B[index1,index2] equals True. If yes, exit the loop and proceed to S407; otherwise, proceed to S403.

[0015] S403: Extract a tuple from the min-heap Q and denote the value of the first element in the tuple as cur;

[0016] S404: Determine if B[index1,cur] is equal to True. If yes, return S401; otherwise, assign True to B[index1,cur].

[0017] S405: Traverse each element in line G with line number cur; for the i-th element, represent its value as ad_node. i And determine whether B[index1,ad_node] is satisfied at the same time. i ] is False and A[index1,ad_node i ]>(A[index1,cur]+A[cur,ad_node i If so, then A[index1,ad_node] will be set to [index1,ad_node]. i The value is assigned to A[index1,cur]+A[cur,ad_node]. i ], and at the same time set P[index1,ad_node i After assigning the value to cur, construct the tuple (ad_node) corresponding to the i-th element. i A[index1,ad_node i ]+h(ICM(ad_node i ),ICM(index2))) and push it into the min-heap Q;

[0018] S406: Continuously loop through steps S401-S405 until the condition in step S402 that B[index1,index2] equals True is met and the loop ends.

[0019] S5: Obtain the laying path of the cable to be laid based on the updated path matrix P.

[0020] Furthermore, when traversing each element in A, the traversal is performed in order from left to right and from top to bottom.

[0021] Furthermore, if the value of A[index1,index2] in the adjacency matrix A of the cable tray network to be laid is equal to ∞, it is determined that there is no path between the starting device and the ending device of the cable to be laid, and the laying of the cable is skipped.

[0022] Furthermore, step S5 specifically includes the following steps:

[0023] S501: Initialize the path node list path = [index1], and initialize the path index index4 = index2;

[0024] S502: Determine if P[index1,index4] equals -1. If yes, proceed to S504; otherwise, proceed to S503.

[0025] S503: In the path, insert index4 after index1, and assign index4 the value P[index1,index4], then return to S502;

[0026] S504: Construct the laying path of the j-th cable according to the order of the nodes contained in the path.

[0027] A terminal device for finding the shortest cable path based on an improved Astar algorithm includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method described in the embodiments of the present invention.

[0028] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above in the embodiments of the present invention.

[0029] The present invention adopts the above technical solution, which reduces the search time for the minimum element value in the open list in each loop by using a min-heap; and reduces the search for invalid paths by using an adjacency list matrix. The combination of the two greatly improves the running efficiency of the Astar algorithm, and this improvement becomes more and more obvious as the scale of the power system expands. Attached Figure Description

[0030] Figure 1 The diagram shown is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0031] To further illustrate the various embodiments, the present invention provides accompanying drawings. These drawings are part of the disclosure of the present invention, primarily used to illustrate the embodiments, and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementations and the advantages of the present invention.

[0032] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0033] Example 1:

[0034] This invention provides a method for finding the shortest cable path based on an improved Astar algorithm, such as... Figure 1 As shown, the method includes the following steps:

[0035] S1: Initialize the cable sequence number j = 1; construct an N×N record matrix B and initialize it, setting the diagonal elements to True and the remaining elements to False; construct an N×N path matrix P and initialize it, setting all its elements to -1; construct a min-heap Q and initialize it as an empty heap; construct an adjacency list matrix G with N rows and initialize each column to be empty; N represents the total number of nodes in the cable tray network.

[0036] S2: Obtain the adjacency matrix A of the bridge network, traverse each element in A, and for each element, determine whether the value of the element satisfies both ∞ and 0. If so, extract the row number k1 and column number k2 corresponding to the element, and add an element with the value k2 in the row with row number k1 in G.

[0037] Before proceeding to step S2, it is necessary to first construct the bridge network adjacency matrix A. In this embodiment, it is constructed through the following steps:

[0038] S201: Obtain the cable tray information for each cable tray corresponding to the cable to be laid.

[0039] In this embodiment, the cable tray information for each cable tray (i.e., each segment of cable tray) is represented by an array r, that is: the cable tray information r of the i-th segment of cable tray. i =[id i ,s_p i (x i1 ,y i1 ,z i1 ),e_p i (x i2 ,y i2 ,z i2 ),length i Where i∈[1,m] represents the i-th cable tray segment, m represents the total number of cable trays; id represents the cable tray identifier, identified by a globally unique string; s_p i (x i1 ,y i1 ,z i1 ) and e_p i (x i2 ,y i2 ,z i2 ) represent the coordinates of the starting and ending points of the cable tray, respectively, x, y, z∈(-∞,∞); length∈(0,∞) represents the length of the cable tray.

[0040] S202: Initialize the index count n = 0, A is an empty n×n matrix, initialize the coordinate index dictionary CIM to be empty, and initialize the index coordinate dictionary ICM to be empty.

[0041] S203: Iterate through the cable tray information for each segment of the cable tray in sequence. i This continues until i = m, meaning all cable tray information has been traversed. For each cable tray segment, the following processing is performed:

[0042] judge Is it true? If so, then {s_p} i (x i1 ,y i1 ,z i1 Store {n:s_p} in CIM, and store {n:s_p} in CIM. i (x i1 ,y i1 ,z i1 Store in ICM; simultaneously determine Is it true? If so, then {e_p} i (x i2 ,y i2 ,z i2 Store {n:e_p} in CIM, and store {n:e_p} in CIM. i (x i2 ,y i2 ,z i2 Store in ICM. s_p i (x i1 ,y i1 ,z i1 ):n represents a key-value pair, s_p i (x i1 ,y i1 ,z i1 ) is the key, and n is the value; n:e_p i (x i2 ,y i2 ,z i2 ) also represents a key-value pair, where n is the key and s_p i (x i1 ,y i1 ,z i1 ) is the value.

[0043] Incrementing n by 1 results in a matrix A of increased order. All new elements in A are assigned the value ∞, except for the diagonal elements, which are set to 0.

[0044] Get index2 = CIM[e_p] i (x i2 ,y i2 ,z i2 Update matrix A according to the following formula;

[0045] A[index1,index2]=A[index2,index1]=length i

[0046] S3: Obtain the starting and ending coordinates of a cable to be laid. Set the node number of the cable tray network corresponding to the starting coordinates of the cable to index1 and the node number of the cable tray network corresponding to the ending coordinates to index2. Traverse each element in the row with row number index1 in G. For the i-th element, represent its value as g. i Construct the tuple (g) corresponding to this element. i ,A[index1,g i ]+h(ICM(g i ),ICM(index2))) and push it into the min-heap Q, where A[index1,g i ] indicates that the row number is index1 and the column number is g in matrix A. i The values ​​of the elements are expressed in the same way as those below, and will not be repeated here. The function ICM(.) represents solving for the coordinates corresponding to the index of a node in a cable tray network. ICM(g i ) indicates that the index g in the cable tray network i The coordinates of the node with index 2 in the cable tray network are given by ICM(index2). h(.) represents the distance between the two coordinates, calculated as follows: The first element represents the starting coordinate, and e(x2,y2,z2) represents the ending coordinate. The smaller the value of the second element in the tuple, the higher the priority of the tuple. Each time a value is retrieved from the min-heap Q, the tuple with the highest priority is automatically popped.

[0047] In this embodiment, each element in A is traversed in order from left to right and from top to bottom.

[0048] In this embodiment, when acquiring cables to be laid, all cables to be laid are arranged in order of priority from high to low, and cables with higher priority are acquired first. The process ends when all cables to be laid have been processed.

[0049] S4: Update the path matrix P by combining the min-heap Q and the adjacency list matrix G, including the following steps:

[0050] S401: Determine if the number of tuples in the min-heap Q is 0. If it is, assign True to B[index1,index2].

[0051] S402: Determine if B[index1,index2] equals True. If yes, exit the loop and proceed to S407; otherwise, proceed to S403.

[0052] S403: Extract a tuple from the min-heap Q and denote the value of the first element in the tuple as cur.

[0053] S404: Determine whether B[index1,cur] equals True. If it does, return S401; otherwise, assign True to B[index1,cur].

[0054] S405: Traverse each element in line G with line number cur; for the i-th element, represent its value as ad_node. i And determine whether B[index1,ad_node] is satisfied at the same time. i ] is False and A[index1,ad_node i ]>(A[index1,cur]+A[cur,ad_node i If so, then A[index1,ad_node] will be set to [index1,ad_node]. i The value is assigned to A[index1,cur]+A[cur,ad_node]. i ], and at the same time set P[inode1,ad_node i After assigning the value to cur, construct the tuple (ad_node) corresponding to the i-th element. i A[index1,ad_node i ]+h(ICM(ad_node i ),ICM(index2))) and push it into the min-heap Q, where ICM(ad_node) i ) indicates that the index of the cable tray network is ad_node i The coordinates corresponding to the nodes.

[0055] S406: Continuously loop through steps S401-S405 until the condition in step S402 that B[index1,index2] equals True is met and the loop ends.

[0056] It should be noted that if, after the algorithm iteration is completed, the value of A[index1,inode2] in the adjacency matrix A of the cable tray network to be laid is equal to ∞, it is determined that there is no path between the starting device and the ending device of the cable to be laid, and the laying of the cable is skipped; if it is not equal to ∞, the laying path of the cable to be laid is obtained through step S5.

[0057] S5: Obtain the laying path of the cable to be laid based on the updated path matrix P.

[0058] In this embodiment, step S5 specifically includes the following steps:

[0059] S501: Initialize the path node list path = [index1], and initialize the path index index4 = index2;

[0060] S502: Determine if P[index1,index4] equals -1. If yes, proceed to S504; otherwise, proceed to S503.

[0061] S503: In the path, insert index4 after index1, and assign index4 the value P[index1,index4], then return to S502;

[0062] S504: Construct the laying path of the j-th cable according to the order of the nodes contained in the path.

[0063] The Astar algorithm requires obtaining the minimum node in the open list during each iteration and may add new nodes. Storing data into an unordered list has a time complexity of O(1), and retrieving the minimum value requires traversing each element in the list, with a time complexity of O(n). A min-heap, on the other hand, is a tree-like structure stored in array form. Unlike a regular binary tree, the value of each node is less than or equal to the value of its child nodes, making its unique data structure particularly suitable for storing and retrieving ordered data. Storing data into a min-heap requires comparing it with the parent node. If the new element is less than the parent node, it needs to be swapped with the parent node. This process continues upwards until the heap property is satisfied, with a total time complexity of O(logn). Since the root node of a min-heap is the minimum value, it can be accessed directly without any comparison or swapping operations, so the time complexity for retrieving the minimum value from the min-heap is O(1). In summary, the time complexity of a single insertion and retrieval operation using a min-heap in one iteration of the Astar algorithm is O(n-logn) less than that of an unordered list. Therefore, using a min-heap instead of an unordered list can improve the computational efficiency of the Astar algorithm. Especially as the scale of power systems expands, the number of bridge nodes increases proportionally, causing the total number of iterations in the Astar algorithm to increase exponentially, making the efficiency improvement brought by the min-heap even more significant.

[0064] Furthermore, due to the unique design of power systems, the adjacency matrix formed by their cable tray networks is a sparse matrix, meaning that most values ​​are infinity (∞). Paths corresponding to these infinity values ​​cannot be used to optimize the already explored paths in step S405. However, the standard Astar algorithm, unaware of the specific locations of these infinity values, must traverse and evaluate every possible expansion node. Using an adjacency list, however, records the information of the other nodes actually connected to each node, thus avoiding the search of many meaningless paths in step S405 and saving significant search time. Moreover, the sparsity of the cable tray network becomes increasingly pronounced as the scale of the power system expands. Specifically, this is reflected in the adjacency matrix, where the proportion of infinity values ​​gradually increases. At this point, the efficiency improvement of the Astar algorithm by using an adjacency list matrix becomes even more significant.

[0065] In summary, the min-heap reduces the search time for the minimum element in the open list during each iteration, while the adjacency list reduces the search for invalid paths. Together, these two features significantly improve the efficiency of the Astar algorithm, and this improvement becomes increasingly pronounced as the scale of power systems expands.

[0066] Example 2:

[0067] The present invention also provides a terminal device for optimizing the shortest cable path based on the improved Astar algorithm, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the method embodiment described above in Embodiment 1 of the present invention.

[0068] Furthermore, as an executable solution, the cable shortest path optimization terminal device based on the improved Astar algorithm can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The cable shortest path optimization terminal device based on the improved Astar algorithm may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above-described structure of the cable shortest path optimization terminal device based on the improved Astar algorithm is merely an example and does not constitute a limitation on the cable shortest path optimization terminal device based on the improved Astar algorithm. It may include more or fewer components, or combine certain components, or different components. For example, the cable shortest path optimization terminal device based on the improved Astar algorithm may also include input / output devices, network access devices, buses, etc., and this embodiment of the invention does not limit this.

[0069] Furthermore, as an executable solution, the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the cable shortest path optimization terminal device based on the improved Astar algorithm, connecting all parts of the terminal device via various interfaces and lines.

[0070] The memory can be used to store the computer programs and / or modules. The processor implements various functions of the cable shortest path optimization terminal device based on the improved Astar algorithm by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function; the data storage area may store data created based on the use of the mobile phone. In addition, the memory may include high-speed random access memory and non-volatile memory, such as hard disk, RAM, plug-in hard disk, SmartMedia Card (SMC), Secure Digital (SD) card, Flash Card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0071] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method described in the embodiments of the present invention.

[0072] If the integrated module / unit of the cable shortest path optimization terminal device based on the improved Astar algorithm is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), and a software distribution medium, etc.

[0073] Although the invention has been specifically shown and described in conjunction with preferred embodiments, those skilled in the art should understand that various changes in form and detail may be made to the invention without departing from the spirit and scope of the invention as defined in the appended claims, all of which shall be within the scope of protection of the invention.

Claims

1. A method for finding the shortest cable path based on an improved Astar algorithm, characterized in that, Includes the following steps: S1: Construct an N×N record matrix B and initialize it, setting the diagonal elements to True and the remaining elements to False; construct an N×N path matrix P and initialize it, setting all its elements to -1; construct a min-heap Q and initialize it as an empty heap; construct an adjacency list matrix G with N rows and initialize it so that each column is empty; N represents the total number of nodes in the bridge network. S2: Obtain the adjacency matrix A of the bridge network, traverse each element in A, and for each element, determine whether the value of the element satisfies both not equal to ∞ and not equal to 0. If so, extract the row number k1 and column number k2 corresponding to the element, and add an element with the value k2 in the row with row number k1 in G. S3: Obtain the starting and ending coordinates of a cable to be laid. Set the node number of the cable tray network corresponding to the starting coordinates of the cable to index1 and the node number of the cable tray network corresponding to the ending coordinates to index2. Traverse each element in the row with row number index1 in G. For the i-th element, represent its value as g. i Construct the tuple (g) corresponding to this element. i ,A[index1,g i ]+h(ICM(g i ),ICM(index2))) and push it into the min-heap Q, where A[index1,g i ] indicates that the row number is index1 and the column number is g in matrix A. i The value of the element, the function ICM(.) represents solving for the coordinates corresponding to the index of the node in the bridge network, ICM(g i ) indicates that the index g in the cable tray network i The coordinates corresponding to the node, ICM(index2) represents the coordinates corresponding to the node with index2 in the bridge network, and h(.) represents the distance between the two coordinates; the smaller the value of the second element in the tuple, the higher the priority of the tuple; each time a value is taken from the min-heap Q, the tuple with the highest priority is automatically popped. S4: Update the path matrix P by combining the min-heap Q and the adjacency list matrix G, including the following steps: S401: Determine if the number of tuples in the min-heap Q is 0. If it is, assign True to B[index1,index2]. S402: Determine if B[index1,index2] equals True. If yes, exit the loop and proceed to S407; otherwise, proceed to S403. S403: Extract a tuple from the min-heap Q and denote the value of the first element in the tuple as cur; S404: Determine if B[index1,cur] is equal to True. If yes, return S401; otherwise, assign True to B[index1,cur]. S405: Traverse each element in line G with line number cur; for the i-th element, represent its value as ad_node. i And determine whether B[index1,ad_node] is satisfied at the same time. i ] is False and A[index1,ad_node i ]>(A[index1,cur]+A[cur,ad_node i If so, then A[index1,ad_node] will be set to [index1,ad_node]. i The value is assigned to A[index1,cur]+A[cur,ad_node]. i ], and at the same time set P[index1,ad_node i After assigning the value to cur, construct the tuple (ad_node) corresponding to the i-th element. i A[index1,ad_node i ]+h(ICM(ad_node i ),ICM(index2))) and push it into the min-heap Q; S406: Continuously loop through steps S401-S405 until the condition B[index1,index2] equals True in step S402 is met and the loop ends. S5: Obtain the laying path of the cable to be laid based on the updated path matrix P.

2. The cable shortest path optimization method based on the improved Astar algorithm according to claim 1, characterized in that: When traversing each element in A, the traversal is performed in the order from left to right and from top to bottom.

3. The cable shortest path optimization method based on the improved Astar algorithm according to claim 1, characterized in that: After step S4 is completed, if the value of A[index1,index2] in the adjacency matrix A of the cable tray network to be laid is equal to ∞, it is determined that there is no path between the starting device and the ending device of the cable to be laid, and the laying of the cable is skipped.

4. The cable shortest path optimization method based on the improved Astar algorithm according to claim 1, characterized in that: Step S5 specifically includes the following steps: S501: Initialize the path node list path = [index1], and initialize the path index index4 = index2; S502: Determine if P[index1,index4] equals -1. If yes, proceed to S504; otherwise, proceed to S503. S503: In the path, insert index4 after index1, and assign index4 the value P[index1,index4], then return to S502; S504: Construct the laying path of the j-th cable according to the order of the nodes contained in the path.

5. A terminal device for optimizing the shortest cable path based on an improved Astar algorithm, characterized in that: It includes a processor, a memory, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 4.

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