Improved bipartite graph-based distributed integrated scheduling method for two vehicles

Abstract

The application proposes a two-machine distributed comprehensive scheduling method based on improved bipartite graph. The method proposes an improved bipartite graph cycle decomposition strategy; secondly, based on the sub-string structure characteristics generated by decomposition, a multi-sub-string weight calculation scheme is established; finally, a virtual and real distribution strategy of workshop is proposed, the scheduling process is simulated by pre-distributing the process set to the virtual device, the resource allocation scheme is dynamically adjusted by disassembling the sub-string, and the dual optimization of "shorter processing time and higher equipment efficiency" is realized. The method effectively solves the problem of heavy horizontal and light vertical or heavy vertical and light horizontal in the traditional scheduling method, avoids the process migration phenomenon and the additional time consumption caused thereby, improves the scheduling efficiency and equipment utilization level of the symmetric two-machine distributed scheduling, and provides a solution with theoretical value and practical significance for the field of complex product production scheduling.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer integrated manufacturing, in particular to a two-workshop distributed comprehensive scheduling method based on improved bipartite graph. Specifically, in the scheduling process of single-piece or small-batch tree-structured complex products with "processing and assembly carried out simultaneously", the optimization goal of shorter collaborative finishing time cost and higher equipment utilization rate of multiple products is simultaneously achieved, and the scheduling effect is more optimal. BACKGROUND

[0002] Under the background of fierce global manufacturing competition and continuous rise of market demand iteration rate, product manufacturing problems are facing the severe test of efficiency and cost. On the one hand, consumers' requirements for timeliness are increasingly stringent, prompting the manufacturing end to shorten the processing cycle through technological innovation to respond quickly to market dynamics; on the other hand, the digital transformation of manufacturing is accelerating, and the efficient use of equipment resources has become the key to reducing unit production cost and improving the core competitiveness of enterprises.

[0003] With the development of computer technology and the continuous evolution of social needs, the product scheduling mode of manufacturing industry has also changed accordingly. The current trend of individualization and diversification of complex products has promoted the widespread application of multi-variety small-batch production mode. The multi-process processing and complex assembly links of such products are closely related, and although traditional Flow-shop and Job-shop scheduling is effective in large-scale scheduling generation, it is difficult to achieve efficient collaborative scheduling with complex constraint relationships due to the fragmentation of the correlation between processing and assembly. Therefore, for tree-structured complex products, the comprehensive scheduling method processes the mode of decision-making processing sequence and assembly process cooperatively, further optimizes resource allocation, and achieves more optimal scheduling effect of complex product processing time and overall equipment utilization rate.

[0004] In the research of complex product integrated scheduling, the research on distributed integrated scheduling occupies an important position, among which the research on the direction of symmetrical two workshop collaborative distributed scheduling has attracted the attention of many scholars and experts. For example, some scholars have proposed a two-workshop integrated scheduling method based on the pseudo-key path method: through the three-stage strategy of process sequencing optimization, load balancing pre-scheduling and migration control mechanism, efficient scheduling is realized, but the method focuses on vertical advancement, which hinders the continuous processing of non-critical processes and increases the migration frequency of long paths. Some experts have proposed a two-workshop schedulable process balancing processing integrated scheduling method: based on the flexibility, parallelism and symmetrical two-workshop equipment configuration, the process grouping is carried out by using the workshop balancing strategy, which effectively shortens the completion time of single complex product, but this method has certain optimization space in the intensity of parallelism, optimization of vertical scheduling and strengthening of continuous processing. Some experts have proposed a two-workshop integrated scheduling method based on neighborhood rendering: a neighborhood rendering factor quantization model is created, and a pre-balancing-dynamic rendering two-stage decision architecture is established, but it is easy to cause unnecessary process migration, which weakens the process parallelism and affects the improvement of overall scheduling efficiency. SUMMARY

[0005] The purpose of the present application is to solve the problems in the prior art, and a two-workshop distributed integrated scheduling method based on improved bipartite graph is proposed.

[0006] The present application is realized by the following technical solutions, and the two-workshop distributed integrated scheduling method based on improved bipartite graph is proposed, which includes an improved bipartite graph cycle decomposition strategy, a multi-substring weight strategy and a substring pre-allocation strategy.

[0007] The improved bipartite graph cycle decomposition strategy: based on the improved bipartite graph, combined with the structural characteristics of the process tree, the process tree is reasonably divided and decomposed into several process substrings; in the improved bipartite graph, the original undirected graph is improved into a directed graph.

[0008] The multi-substring weight strategy: this strategy calculates the multi-substring weight by taking the substring processing time, the substring priority and the subsequent substring urgency value as the consideration factors, and schedules the process set in descending order of weight value;

[0009] The substring pre-allocation strategy: first, the process set is virtually scheduled by pre-allocating it to the two workshops, the processing time of the two workshops is compared, then the workshop with the shortest processing time is selected for actual allocation, and then it is further predicted whether the next to be decomposed substring can further optimize the processing time in this workshop.

[0010] Further, an iterative recursive framework is adopted in the improved bipartite graph cycle decomposition strategy. In each round of decomposition, the current substring nodes are first continuously numbered based on hierarchical traversal, and then the center node position is calculated according to the subgraph size. The center node needs to meet double criteria, that is, it needs to be located at the geometric center of the process tree to ensure the balance of the subgraph size after partitioning, and it needs to be mapped to the first element of the second vertex subset in the improved bipartite graph model to provide an initial matching base point for cross-plant resource allocation. After positioning the center node, the substring where one subset of the center node is located is cut off as a whole and is defined as an independent scheduling unit, which facilitates subsequent allocation and processing in the two plants. Then, the center positioning and improved bipartite graph partitioning operations are recursively performed on the remaining part of the process tree after partitioning. Through multiple rounds of iterative refinement, the hierarchical decomposition of the entire process tree is gradually completed.

[0011] Further, in the multi-substring weight strategy, the substring processing time is directly related to the length of time the equipment is continuously occupied, with longer time indicating higher demand for equipment resources. The substring priority is determined by the layer priority of each process in the process tree. The subsequent substring urgency value is determined by the number of subsequent to-be-scheduled substrings remaining in the current substring. The substring processing time, substring priority, and subsequent substring urgency value are calculated according to the preset entropy weight method weight formula to establish the comprehensive demand urgency value of each substring process set. The scheduling is sorted from high to low according to this value, and the substrings with more urgent demand are processed first to reduce the idle time of equipment due to waiting or migration.

[0012] Further, the multi-substring weight strategy scheduling process is as follows:

[0013] Step 1: Calculate the processing time, substring priority, and subsequent substring urgency value of each substring.

[0014] Step 2: Use the entropy weight method to fuse the processing time, priority, and subsequent urgency value parameters of the substring to calculate the weight of each substring.

[0015] Step 3: Sort all substrings by weight from high to low.

[0016] Step 4: Determine whether the maximum weight of the substring is unique. If it is unique, execute Step 5; if it is not unique, execute Step 6.

[0017] Step 5: Schedule the substring with the maximum weight and jump to Step 10.

[0018] Step 6: Compare the processing time of each substring.

[0019] Step 7: Determine whether there is a substring with longer processing time. If there is, execute Step 8; if there is not, execute Step 9.

[0020] Step8: Select the longest processing substring, jump to Step10;

[0021] Step9: Compare the priority of the substring, if there is a higher priority substring, schedule the highest priority; if the substring priority is the same, compare the subsequent substring urgency value, schedule the substring with larger urgency value, jump to Step10;

[0022] Step10: Determine whether all substrings are scheduled, if yes, execute Step11, otherwise return to Step2, recalculate the weight of the remaining substring and schedule;

[0023] Step11: Establish a substring scheduling sequence and complete the scheduling process.

[0024] Further, in the substring pre-allocation strategy, first, the target substring to be scheduled is selected, and its process set is pre-allocated to the two workshop devices, the scheduling time of the process set allocated to the two workshops is calculated, and the process set is allocated to the appropriate two workshops according to the standard of less allocation time; the original target substring is optimized by disassembling to further reduce the product processing time.

[0025] Further, the substring pre-allocation strategy allocation process is as follows:

[0026] Step1: Select the target substring to be pre-allocated from the substring set of the complex product decomposition;

[0027] Step2: Pre-schedule the process set of the target substring to the workshop , workshop respectively;

[0028] Step3: Calculate the earliest time for the workshop , workshop to complete all processes after pre-scheduling the substring, denoted as MT1 and MT2, respectively, according to the process duration and device constraints;

[0029] Step4: Compare MT1 and MT2: if MT1<MT2, select workshop as the candidate; if MT2<MT1, select workshop as the candidate; if MT1=MT2, randomly select one workshop as the candidate; jump to Step5;

[0030] Step5: Partially disassemble the original target substring, calculate the earliest completion time MT' of the optimized substring in the candidate workshop;

[0031] Step6: If MT'<Min(MT1,MT2), execute Step7; otherwise, execute Step8;

[0032] Step7: Assign the optimized substring to the candidate workshop, jump to Step9;

[0033] Step8: Give up optimization, assign the original scheme substring to the candidate workshop, jump to Step9;

[0034] Step9: Whether the substring is all assigned, yes to Step10, otherwise to Step1;

[0035] Step10: After the substring is assigned, mark the occupation period and available state of the corresponding equipment in the candidate workshop to ensure that the subsequent scheduling can perceive the resource changes in real time;

[0036] Step11: Output the two-workshop Gantt chart, and the assignment is completed.

[0037] Further, the improved bipartite graph is a quadruple: , wherein: is a finite vertex set, and are mutually exclusive subsets, is a directed edge set; The specific mathematical modeling of the improved bipartite graph is as follows:

[0038] (1)

[0039] (2)

[0040] (3)

[0041] (4)

[0042] (5)

[0043] (6)

[0044] Formula (1) represents the complete division of vertices, that is, the vertex set V is strictly divided into two mutually exclusive subsets;

[0045] Formula (2) represents the completeness of the edge set, and the edge is only allowed to exist in: inside U, inside W, direction;

[0046] Formula (3) and formula (4) represent the allowed directed edges inside the U and W subsets;

[0047] Formula (5) represents that there is and only one edge from W to U, and the edge must be pointed to the next process in the U subset by the first vertex of the W subset;

[0048] Formula (6) represents the first node in the U set as the root node of the process tree, and the first node in the W set as the center node.

[0049] Further, in the scheduling process, it is assumed that in the symmetric two-plant integrated scheduling process Each process is assigned to two plants , and the two plants process in a certain order to complete the product; each plant is equipped with equipment, and each plant has the ability to independently process each process; here, the two plants have completely consistent plant environment and production processing conditions; the specific requirements are as follows:

[0050] (1) The processing and assembly operations of the process are unified as processing;

[0051] (2) The processing technology of the complex product is presented through a tree structure, wherein the nodes represent specific processing processes;

[0052] (3) Each process node contains three core parameters: process number, associated equipment number, and processing time;

[0053] (4) The equipment resource configuration of the symmetric plant is completely consistent, and the same plant is not allowed to be equipped with the same equipment;

[0054] (5) There is a process dependency between processes, and the next process can only be started after the previous process is completed;

[0055] (6) If a process and its immediately preceding process are processed in different plants, process migration will occur;

[0056] (7) The time when the last process is completed is the maximum completion time of the product.

[0057] The application also proposes an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to realize the steps of the improved bipartite graph-based two-plant distributed integrated scheduling method.

[0058] The application also proposes a computer-readable storage medium for storing computer instructions, wherein the computer instructions are executed by a processor to realize the steps of the improved bipartite graph-based two-plant distributed integrated scheduling method.

[0059] The application has the following advantages:

[0060] The improved bipartite graph-based two-machine distributed comprehensive scheduling method takes a substring as a scheduling unit, integrates three-order collaborative mechanisms of improved bipartite graph cyclic decomposition, multi-substring weight scheduling and substring pre-allocation strategy, realizes vertical and horizontal two-way collaborative optimization, effectively solves the problem of heavy vertical and light horizontal or heavy horizontal and light vertical in the traditional scheduling algorithm, reduces the process migration times, improves the scheduling efficiency and equipment utilization of two machines, and provides a solution with theoretical value and practical significance for the field of complex product comprehensive scheduling. BRIEF DESCRIPTION OF DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0062] Figure 1 It is a bipartite graph structure diagram.

[0063] Figure 2 It is an improved unidirectional bipartite graph structure diagram.

[0064] Figure 3 It is an improved tree-type bipartite graph structure diagram.

[0065] Figure 4 It is a flowchart of the improved bipartite graph cyclic decomposition strategy.

[0066] Figure 5 It is a complex product A processing process tree diagram.

[0067] Figure 6 It is a cut set diagram of the directed graph of the complex product A processing process.

[0068] Figure 7 It is a diagram of the process string S1 obtained after the first decomposition of the complex product A.

[0069] Figure 8 It is a diagram of the process string S2 obtained after the second decomposition of the complex product A.

[0070] Figure 9 It is a diagram of the process strings S3 and S4 obtained after the third decomposition of the complex product A.

[0071] Figure 10 It is a flowchart of the multi-substring weight strategy scheduling.

[0072] Figure 11 It is a flowchart of the improved bipartite graph-based two-machine distributed comprehensive scheduling method.

[0073] Figure 12Process tree diagram for complex product P.

[0074] Figure 13 Process tree diagram for complex product P for first cycle decomposition.

[0075] Figure 14 Substring S obtained for complex product P for first cycle decomposition A Schematic diagram.

[0076] Figure 15 Process tree diagram for complex product P for second cycle decomposition.

[0077] Figure 16 Substring S obtained for complex product P for second cycle decomposition B Schematic diagram.

[0078] Figure 17 Substring S obtained for complex product P for recursive cycle decomposition C -S K Schematic diagram.

[0079] Figure 18 Schematic diagram for overall substring partitioning of process tree for complex product P.

[0080] Figure 19 Gantt chart for complex product P for method scheduling.

[0081] Figure 20 Gantt chart for scheduling using two-machine integrated scheduling method based on pseudo critical path.

[0082] Figure 21 Gantt chart for scheduling using two-machine integrated scheduling method with adjustable process balancing.

[0083] Figure 22 Gantt chart for scheduling using two-machine integrated scheduling method based on neighborhood rendering. DETAILED DESCRIPTION

[0084] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0085] The present application proposes a two-machine distributed integrated scheduling method based on improved bipartite graph, which includes an improved bipartite graph cycle decomposition strategy, a multi-substring weight strategy and a substring pre-allocation strategy.

[0086] The improved bipartite graph cycle decomposition strategy is based on an improved bipartite graph, combines the structural characteristics of the process tree, realizes reasonable division of the process tree, and divides the process tree into a plurality of process sub-strings; in the improved bipartite graph, the original undirected graph is improved into a directed graph;

[0087] The multi-sub-string weight strategy: the multi-sub-string weight strategy takes the sub-string processing time, sub-string priority and subsequent sub-string urgency value as consideration factors to calculate the multi-sub-string weight, and schedules the process set according to the weight value in descending order;

[0088] The sub-string pre-allocation strategy: first, the process set is virtually scheduled by pre-allocating the process set to the two workshops, the processing time of the two workshops is compared, then the workshop with the shortest processing time is selected for actual allocation, and then it is further predicted whether the sub-string to be decomposed next can further optimize the processing time in this workshop.

[0089] The essential characteristic of tree decomposition is to divide the node set of the tree-shaped complex graph into a limited number of related subsets based on the connectivity rule, to decompose the original graph into a plurality of relatively independent sub-structures, to effectively approximate the global optimal solution by distributed solving of each sub-problem and comprehensive results.

[0090] The improved bipartite graph cycle decomposition strategy proposed by the method of the application is based on the dynamic center positioning strategy of the process tree and the topological constraint of the improved bipartite graph, and realizes the recursive balanced partitioning of the process tree. Specifically, in the improved bipartite graph cycle decomposition strategy, an iterative recursive framework is adopted. In each round of decomposition, first, the current sub-string node is continuously numbered based on hierarchical traversal, then the center node position is calculated according to the size of the sub-graph, and the center node needs to meet double criteria at the same time, that is, it needs to be located at the geometric center of the process tree to ensure that the sizes of the sub-graphs after partitioning are balanced, and it also needs to be mapped to the first element of the second vertex subset in the improved bipartite graph model to provide an initial matching base point for cross-workshop resource allocation; after positioning the center node, the sub-string in which one subset (W subset) of the center node is located is cut off as a whole and is defined as an independent scheduling unit, which is convenient for subsequent allocation and processing in the two workshops; then, the center positioning and improved bipartite graph partitioning operations are continuously recursively performed on the remaining part of the process tree after partitioning, and through multiple rounds of iteration and refinement, the hierarchical decomposition of the entire process tree is gradually completed. The cycle decomposition mode not only fully utilizes the accuracy of the dynamic center positioning strategy in structure recognition, but also relies on the subset division of the improved bipartite graph to balance the independence and relevance of the scheduling unit. The specific flow chart is shown in Figure 4 .

[0091] Suppose that a complex product A contains 10 processing procedures , which are processed on a set of equipment , and the process tree is shown in Figure 5 . The following demonstrates the application process of the improved bipartite graph cycle decomposition strategy:

[0092] Step 1: asFigure 6 A5 is determined as the center node by using the dynamic center positioning strategy, the unique connection between the U and W subsets is segmented, and a substring {A7, A5} is generated, as shown in the process substring S1. Figure 7

[0093] Step 2: The process tree in the U set of the first decomposition is subjected to a second decomposition by the improved bipartite graph cycle, the center node A4 is found by using the dynamic center positioning strategy, A4 is the first node in the W set of the improved bipartite graph, and the substring in which A4 is located is entirely cut off to obtain a process substring S2, as shown in the following figure. Figure 8

[0094] Step 3: The process tree in the U set of the second decomposition is subjected to a third decomposition by the improved bipartite graph cycle to obtain process strings S3 and S4, as shown in the following figure. Figure 9

[0095] Step 4: According to the given cut set, the process tree of the complex product A is cyclically split into multiple process strings, and the specific process is as follows: {A7, A5}, {A8, A9, A6, A4}, {A3, A2}, and {A1}.

[0096] In the multi-substring weight strategy, the substring processing time is based on the total sum of process processing time, is directly related to the length of time that the equipment is continuously occupied, and the longer the time means the higher the demand for equipment resources; the substring priority is determined by the layer priority of each process in the process tree, and plays a key role in the process of complex product scheduling; the subsequent substring urgency value is determined by the number of subsequent to-be-scheduled substrings remaining in the current substring; the processing time, the priority and the subsequent urgency value of the substring are calculated according to the preset entropy weight method weight formula, the comprehensive demand urgency value of each substring process set is established, and the scheduling is sorted from high to low according to the value, and the substrings with more urgent demand are processed preferentially, so as to reduce the idle time of the equipment due to waiting or migration. The multi-substring weight scheduling flow chart is shown in the following figure. Figure 10

[0097] The multi-substring weight strategy scheduling flow is as follows:

[0098] Step 1: Calculate the processing time, the priority and the subsequent urgency value of each substring;

[0099] Step 2: Use the entropy weight method to fuse the processing time, the priority and the subsequent urgency value parameters of the substring, and calculate the weight of each substring;

[0100] Step 3: Sort all substrings in descending order of weight;

[0101] Step 4: Determine whether the maximum weight of the substring is unique, if yes, execute Step 5; if not, execute Step 6;​​​​

[0102] Step5: Schedule the substring with the largest weight, and jump to Step 10;

[0103] Step6: Compare the processing time of each substring;

[0104] Step7: Determine whether there is a substring with longer processing time, if yes, execute Step 8; if not, execute Step 9;

[0105] Step8: Select the substring with the longest processing time, and jump to Step 10;

[0106] Step9: Compare the priority of the substrings, if there is a substring with higher priority, schedule the one with the highest priority; if the priorities of the substrings are the same, compare the urgency values of the subsequent substrings, schedule the substring with the larger urgency value, and jump to Step 10;

[0107] Step10: Determine whether all substrings have been scheduled, if yes, execute Step 11, otherwise, return to Step 2 to recalculate the weights of the remaining substrings and schedule them;

[0108] Step11: Establish a substring scheduling sequence, and complete the scheduling process.

[0109] In the substring pre-allocation strategy, first, the target substring to be scheduled is selected, and its process set is pre-allocated to the two workshop devices, the scheduling time of the process set allocated to the two workshops is calculated, and the process set is allocated to the appropriate two workshops based on the standard of less processing time in the allocated workshop; the original target substring is optimized by disassembly to further reduce the product processing time. Through the cycle operation of "pre-scheduling-disassembly structure-dynamic allocation", the rationality of substring resource allocation is improved.

[0110] The substring pre-allocation strategy allocation process is as follows:

[0111] Step1: From the substring set decomposed from the complex product, select the target substring to be pre-allocated;

[0112] Step2: Distribute the process set of the target substring to the workshop and the workshop for pre-scheduling in turn;

[0113] Step3: Calculate the earliest time for the workshop and the workshop to complete all processes after pre-scheduling the substring based on the process time and device constraints, and record them as MT1 and MT2;

[0114] Step4: Compare MT1 and MT2: if MT1 < MT2, select the workshop is a candidate; if MT2<MT1, select the workshop as a candidate is a candidate; if MT1=MT2, select one workshop as a candidate at random; jump to Step5;

[0115] Step5: perform a partial disassembly operation on the original target substring, and calculate the earliest completion time MT' of the optimized substring in the candidate workshop;

[0116] Step6: if MT'<Min(MT1,MT2), execute Step7; otherwise, execute Step8;

[0117] Step7: distribute the optimized substring to the candidate workshop, and jump to Step9;

[0118] Step8: give up optimization, distribute the substring of the original scheme to the candidate workshop, and jump to Step9;

[0119] Step9: whether the substrings are all distributed, yes, jump to Step10, otherwise, jump to Step1;

[0120] Step10: after the substring distribution is completed, mark the occupation period and available state of the corresponding equipment in the candidate workshop to ensure that the subsequent scheduling can perceive the resource changes in real time;

[0121] Step11: output the Gantt chart of the two workshops, and the distribution is completed.

[0122] Complexity analysis: the method proposed in the present application improves the bipartite graph cycle strategy through multi-strategy collaborative optimization, and the process tree is divided by iteration and recursion, and the time complexity is . On this basis, the multi-substring weight scheduling strategy forms a scheduling sequence through the entropy weight method, and the time complexity is , and the time complexity of the workshop virtual-real distribution strategy is not more than . Finally, the overall time complexity of the algorithm is not more than .

[0123] A bipartite graph is a special graph structure composed of two disjoint vertex sets and edges connecting the vertices of the two sets. Its core feature is that all edges exist only between the two vertex sets, and there is no direct connection between the vertices in the same set. Bipartite graph is widely used in task allocation, resource matching, data clustering and other fields due to its clear modeling ability of the relationship between two types of elements. Let be an undirected graph, if the vertex set V can be divided into two disjoint non-empty subsets U and W (i.e. and ), and any edge in the edge set E has two endpoints belonging to U and W (i.e. for any , there are and or and If G is a bipartite graph, then G is called a bipartite graph, denoted as G(x). ,like Figure 1 As shown. In comprehensive scheduling research, a tree structure is used to represent the characteristics of complex products with a large number of processes and strong constraints on technological relationships. Therefore, in the improved bipartite graph, the original undirected graph is improved into a unidirectional graph, as shown. Figure 2 As shown. One-way pointing relationships are allowed between the vertices of sets U and W. The two sets have a one-way pointing relationship. The node positions are adjusted, and the structure diagram after adjustment according to the product process tree structure is shown below. Figure 3 As shown. Let the improved bipartite graph be a quadruple: ,in: For a finite set of vertices, and For mutually exclusive subsets, Given a directed edge set; the specific mathematical modeling of the improved bipartite graph is as follows:

[0124] (1)

[0125] (2)

[0126] (3)

[0127] (4)

[0128] (5)

[0129] (6)

[0130] Equation (1) represents a complete partition of vertices, that is, the vertex set V is strictly partitioned into two mutually exclusive subsets;

[0131] Equation (2) indicates the completeness of the edge set, where edges are only allowed to exist inside: U, W, ... direction;

[0132] Equations (3) and (4) indicate that directed edges are allowed within subsets U and W;

[0133] Equation (5) indicates that there exists one and only one edge from W to U, and this edge must point from the first vertex (center node) of the subset W to the next process in the subset U;

[0134] Equation (6) indicates that the first node in the U set is the root node of the process tree, and the first node in the W set is the center node.

[0135] In the scheduling process, each process is not independent, but is limited by certain constraints, which have a key impact on the rationality and efficiency of scheduling. Assuming that in the symmetric two-shop integrated scheduling process processes are allocated to two shops , which are processed by two shops in a certain order to complete the product; each shop is equipped with devices, and each shop has the ability to process each process independently; here, the two shops have completely consistent shop environment and production processing conditions, which is the core embodiment of the "symmetric" attribute. The specific requirements are as follows:

[0136] (1) The processing and assembly operations of the process are unified as processing;

[0137] (2) The processing technology of complex products is presented through a tree structure, where the nodes represent specific processing processes;

[0138] (3) Each process node contains three core parameters: process number, associated device number, and processing time;

[0139] (4) The device resource configuration of the symmetric shop is completely consistent, and the same shop is not allowed to be equipped with the same device;

[0140] (5) There is a process dependency between processes, and the next process can only start after the previous process is completed;

[0141] (6) If a process and its immediate previous process are processed in different shops, process migration will occur;

[0142] (7) The time when the last process is completed is the maximum completion time of the product.

[0143] According to this, the mathematical model is established as follows:

[0144]

[0145] The meanings of each symbol are as follows:

[0146] : the start processing time of the th process on the th device; : the processing time of the th process on the th device; : the start processing time of the th process on the th device in the th shop; : the processing time of the th process on the th device in the Start processing time on the device; : In the workshop, the processing time of the first device; : The substring set assigned to the workshop; : The substring set assigned to the workshop; : The processing duration of the substring i ; : The processing duration of the substring j ; : The number of transitions between two workshops.

[0147] Formula (7) represents the time optimization goal of complex product processing, that is, minimizing the maximum completion time; formula (8) represents that each process starts processing as early as possible; formula (9) represents that on the same device in the same workshop, a process with a subsequent constraint can only start processing after the previous process has been continuously processed; formula (10) represents that a process needs to be processed after the previous process has been processed; formula (11) represents minimizing the total processing duration difference of the substrings borne by the two workshops; and formula (12) represents minimizing the transition time of the processes between the two workshops.

[0148] Related definitions and methods:

[0149] Definition 1: Process chain duration (PCD)

[0150] It refers to the sum of the processing durations of all processes in the substring established according to the improved bipartite graph algorithm, which is the critical path length of the substring and the core basis for weight calculation.

[0151] Definition 2: Process chain priority (PCP)

[0152] It refers to the arithmetic mean of the priority of all process layers in the substring. When assigning the workshop, the substring with high priority is assigned first.

[0153] Definition 3: Successor chain urgency (SCU)

[0154] It represents the number of directly succeeding substrings to be assigned after the current substring is assigned.

[0155] Definition 4: Earliest completion time (EFT)

[0156] The earliest time node from starting processing to completing all processing of a process or sub-string on the corresponding equipment in the workshop under the premise of meeting all process constraints.

[0157] Definition 5 Dynamic center positioning strategy (DCPS)

[0158] In the complex product process tree, all processes are continuously traversed and marked from the root node by level, from top to bottom and from left to right. The last marked process node is numbered as , and the position of is defined as the center node. The center node is not unique and fixed, but changes with the occurrence of sub-string loop pruning. When a sub-string is pruned, the remaining sub-tree finds a new center node.

[0159] Method 1 Vector normalization method

[0160] This method is used to eliminate the dimension effect and generate a standardized matrix. The calculation formula is:

[0161]

[0162] Where is the standardized value of the i th evaluation object on the j th index; is the corresponding original data; n is the total number of evaluation objects; i , j are the serial numbers of the evaluation objects and the indexes, respectively.

[0163] Method 2 Information entropy calculation

[0164] When using the entropy weight method to determine the weight, the index dispersion degree is first reflected through information entropy calculation. The formula is:

[0165]

[0166] Where represents the information entropy of the j th index; is the proportion of the standardized value of the i th evaluation object on the j th index to the total sum of all standardized values of the index.

[0167] Method 3 Weight optimization calculation

[0168] Based on the information entropy result, the index weight is determined. The formula is:

[0169]

[0170] wherein denotes the weight of the j th indicator; m is the total number of indicators.

[0171] Method 4 Weighted normalized matrix calculation

[0172] The normalized matrix is combined with the indicator weight to generate a weighted normalized matrix, and the formula is:

[0173]

[0174] Method 5 Distance of each substring to the positive ideal solution

[0175] The positive ideal solution (Z + ) is the optimal value in the weighted normalized value of each indicator, and the formula is:

[0176]

[0177] Method 6 Distance of each substring to the negative ideal solution

[0178] The negative ideal solution is the worst value in the weighted normalized value of each indicator, and the formula is:

[0179]

[0180] Method 7 Relative closeness

[0181] Reflects the closeness of each substring to the ideal solution, and the formula is:

[0182]

[0183] wherein, The value is closer to 1, indicating that the substring is closer to the positive ideal solution.

[0184] Embodiment

[0185] The method of the application has universality and can be flexibly applied to comprehensive scheduling research of various complex products. From the topological structure, the symmetric tree structure can be regarded as a special case of the asymmetric tree structure, therefore, in order to more fully verify the applicability of the algorithm, a randomly generated complex product P asymmetric process tree is taken as an example for illustration, as shown in the figure. The process tree P contains 24 process nodes and 4 devices, and the process node data structure is a triple (process number, corresponding device, processing time), for example, node P1 / 1 / 1 indicates that process P1 processes on device M1 for 1 hour. Figure 12

[0186] Cyclic decomposition of complex product P process tree

[0187] ​Step 1: Take process {P13} as the center node to perform improved bipartite graph partitioning of the complex product P process tree, as shown in Figure 13 . The first time, the substring S A :{P21, P18, P13} is taken as the cut set to perform decomposition, and the decomposition result is shown in Figure 14 .

[0188] Step 2: Take process {P11} as the center node to perform improved bipartite graph partitioning of the complex product P process tree, as shown in Figure 15 . The second time, the substring S B :{P11} is taken as the cut set to perform decomposition, and the decomposition result is shown in Figure 16 .

[0189] Step 3: Use the dynamic center positioning strategy, and take processes {P12}, {P10}, {P8}, {P5}, {P6}, {P4}, {P9}, {P2}, and {P1} as the center nodes in turn to perform improved bipartite graph partitioning of the complex product P process tree, and the resulting substrings are substring S C {P17, P12}, substring S D {P20, P16, P10}, substring S E {P24, P23, P22, P19, P14, P8}, substring S F {P19}, substring S G {P6}, substring S H {P15, P9, P4}, substring S I {P3}, substring S J {P7, P2}, substring S K {P1}, as shown in Figure 17 . The overall substring partitioning structure is shown in Figure 18 .

[0190] According to the multi-substring weight, a scheduling sequence is constructed

[0191] Figure 18 The 24 processes of the complex product P are divided into 11 substrings (S A -S K ), and the processing time of each substring of the complex product P, the substring priority, and the subsequent substring urgency value are calculated, as shown in Table 1.

[0192] Table 1: Substring processing time, substring priority, and subsequent substring urgency value statistics table of complex product P

[0193]

[0194] The processing time length, priority, and subsequent urgency value of the substring have different dimensions and orders, and therefore are standardized by using the entropy weight method. The standardized matrix calculated by using the vector normalization method in the method is shown in Table 2.

[0195] Table 2 Standardized matrix of processing time length, priority, and subsequent urgency value of substring

[0196]

[0197] When the weight is determined by using the entropy weight method, the information entropy of each index is calculated first, and then the optimal weight is determined by using the weight optimization calculation. The calculation result is that the weight of the processing time length of the substring is 38.29%, the weight of the priority of the substring is 22.96%, and the weight of the subsequent urgency value of the substring is 38.75%. The weighted standardized matrix of each substring is shown in Table 3.

[0198] Table 3 Weighted standardized matrix of each substring

[0199]

[0200] Based on the weighted standardized matrix of each substring obtained above, the ideal solution can be further determined. The positive ideal solution is a vector composed of the maximum value in the weighted standardized value of each index, that is, and the negative ideal solution is a vector composed of the minimum value in the weighted standardized value of each index, that is, On this basis, the distance of each substring to the positive ideal solution and the negative ideal solution is calculated, and the relative closeness is calculated to reflect the closeness of each substring to the ideal solution, which is shown in Table 4.

[0201] Table 4 Euclidean distance, relative closeness, and scheduling order of each substring

[0202]

[0203] In summary, the scheduling order of the substring is calculated as (S E →S A →S D →S C →S H →S B →S G →S J →S F / S I →S K ).

[0204] Two-vehicle distribution process

[0205] The substring task is distributed to the two vehicles according to the sequence order, and the load balance is achieved by dynamically adjusting the distribution. The specific distribution process is as follows:

[0206] Step1: Select the highest weight substring set S E {P24, P23, P22, P19, P14, P8} as the initial allocation object, pre-allocated to two workshops devices . Since S E is the highest weight substring set, and the initial state of two workshops is idle, the first allocation uses a random allocation strategy, and selects workshop. After allocation, workshop cumulative processing time is updated to working hours, and the remaining to-be-allocated substring scheduling sequence is updated to S A → S D → S C → S H → S B → S G → S J → S F / S I → S K ;

[0207] Step2: For the second highest weight substring set S A {P21, P18, P13} in the current scheduling sequence, pre-allocated to two workshops. Based on the current load state of two workshops ( : 17 working hours, : 0 working hours), calculate the EFT of S A in two workshops, workshop MT1 is 17+S A processing time, workshop MT2 is 0+S A processing time. By comparison, the EFT of S A in workshop is shorter, so select workshop for allocation. After allocation, workshop cumulative processing time is updated to working hours;

[0208] Step3: The current to-be-allocated substring scheduling sequence is S D → S C → S H → S B → S G → S J → S F / S I → S K , select the first S D substring set in the sequence and pre-allocate it to two workshop devices. Based on the current cumulative time of two workshops ( 17 working hours (11 working hours), calculate S D EFT in Workshop 2: Workshop MT1 = 17 + SD processing time, Workshop MT2=11+S D Processing time. The comparison results show that S D exist The workshop's EFT is superior, therefore it is selected. Workshop. The evaluation considers both process constraints and time optimization effectiveness to determine S. D The substring cannot be split. Therefore, according to the atomic string S D Assigned to Workshop, after allocation The workshop's cumulative processing time remains During the working hours, the sequence of substrings to be allocated is updated to S. C →S H →S B →S G →S J →S F / S I →S K ;

[0209] Step 4: Similarly, for the current substring sequence S to be allocated C →S H →S B →S G →S J →S F / S I →S K The same cyclic allocation logic as Step 3 is used. First, the substring set is selected sequentially according to the sequence order; second, based on the real-time cumulative processing time of Workshop 2, the substring is calculated in... , For each workshop, select the workshop with the smaller EFT. Finally, perform a feasibility analysis of splitting each substring under process constraints: if splitting can shorten the EFT and meet the process connection requirements, then allocate according to the split substring; otherwise, allocate according to the atomic string.

[0210] After all substrings have been assigned, the complex product P is being processed in Workshop 2. (Gantt chart follows) Figure 19 As shown. The total processing time in the workshop is Working hours The total processing time in the workshop is Working hours.

[0211] Comparative analysis of four methods

[0212] With the complex product P as an example, the method has advantages over the representative method in the same research field in terms of total processing time, number of inter-plant transfers and equipment utilization. The inter-plant processing time is 22 man-hours, the total processing time is 23 man-hours, and the equipment utilization is 100% in the method shown in The inter-plant processing time is 20 man-hours, the total processing time is 20 man-hours, and the equipment utilization is 100% in the method shown in The inter-plant processing time is 23 man-hours, the total processing time is 23 man-hours, and the equipment utilization is 100% in the method shown in The inter-plant processing time is 19 man-hours, the total processing time is 19 man-hours, and the equipment utilization is 100% in the method shown in The inter-plant processing time is 22 man-hours, the total processing time is 22 man-hours, and the equipment utilization is 100% in the method shown in The inter-plant processing time is 19 man-hours, the total processing time is 19 man-hours, and the equipment utilization is 100% in the method shown in Figure 20 — Figure 22 —

[0213] The comparative experiment results show that the method has better performances than the other three methods in terms of processing time, overall equipment utilization and relative improvement rate of overall equipment utilization, as shown in Table 5.

[0214] Table 5 Comparative analysis of inter-plant scheduling results

[0215]

[0216] Compared with the three comparative methods, the total processing time is reduced by 11.9%, 11.9% and 9.7% respectively, and the overall equipment utilization is increased by 2.7%, 5.9% and 8.7% respectively. Therefore, the method not only shortens the total processing time of the two plants, but also simultaneously improves the equipment utilization.

[0217] The reason why the method is better is mainly because:

[0218] (1) The method adopts an improved bipartite graph cycle decomposition strategy, which pre-decomposes 24 processes in the process tree of the complex product P into 11 substring-level minimum scheduling units. When the substring is used as a scheduling carrier, the internal processes strictly follow the inherent structure of the complex product process tree, which not only guarantees the tight-precedence and tight-postcedence constraint relationship between the processes in the process tree, but also realizes the close sequence connection of the tight-postcedence processes in the substring. For example, compared with Figure 20 , the subsequent processes P5, P1 are also processed in advance due to the advance processing of process P10, and the overall inter-plant processing time is reduced by 5 man-hours. Figure 21 , the subsequent processes P19, P14, P14, P8, P3, P1 are processed in advance due to the advance processing of processes P23 and P22, and the overall inter-plant processing time is reduced by 5 man-hours. Figure 22Compared with, the process P21 is processed in advance, so that the subsequent processes P18, P13, P7 and P2 are processed in advance, and the process P14 is processed in advance, so that the subsequent processes P8, P3 and P1 are processed in advance, and the overall processing time of the two workshops is reduced by 4 working hours.

[0219] (2) The method of the application adopts a multi-substring weight scheduling strategy, which improves the tightness of process continuous processing. Compared with the horizontal or vertical optimization imbalance phenomenon existing in the other three methods, the method of the application considers the vertical optimization through the substring processing time and the subsequent substring urgency value, and considers the horizontal optimization through the substring priority. Specifically, the substring processing time is taken into account, which effectively avoids the prolongation of the total processing time of the product due to the last processing of the substring with long processing time; at the same time, the subsequent substring urgency value is fully considered, which also effectively reduces the waiting time of the subsequent substring. In the longitudinal dimension, the substring processing time determines the occupation span of a single substring on the Gantt chart, and taking it into account can avoid slowing down the overall progress due to the last processing of the substring with long time consumption; the subsequent substring urgency value can promote the system to plan the processing rhythm of the previous substring in advance, reducing the waiting time consumption of the subsequent substring. In the horizontal dimension, the substring priority reflects the importance of different level substrings in the process tree, effectively avoiding the disordered state of multiple substrings in resource competition, ensuring the coordination of substrings in horizontal resource allocation, and finally realizing the double improvement of the scheduling system in time efficiency and resource utilization through the synergistic optimization in the longitudinal and horizontal dimensions.

[0220] For example, compared with Figures 20-22 , the processing time in the workshop is shortened by 1 working hour, 2 working hours and 1 working hour respectively, and the processing time in the workshop is shortened by 4 working hours, 3 working hours and 3 working hours respectively. In the method of the application, , the overall utilization rate of the equipment in the workshop reaches 83.0%, which is increased by 5.8%, 11.8% and 22.3% respectively compared with the other three methods.

[0221] (3) The method of the application adopts a substring pre-allocation strategy, which enhances the efficiency of the comprehensive scheduling cooperation of the two workshops and reduces the number of process migrations. The strategy realizes zero migration and completely avoids the additional time consumption caused by process migration due to the rationality and stability of substring scheduling, further ensuring the efficiency and continuity of production scheduling.

[0222] For example, Figure 20 , there are 3 process migrations: process P17 is processed in the workshop, its next process P12 is processed in the workshop, forming the cross-workshop migration of P17 ( ) and P12 ( ), and P16 ( There is process migration phenomenon between P10 ( ), P10 ( ) and P5 ( ); Figure 21 There are 4 times of process migration: P21 ( ) and P18 ( ), P24 ( ) and P23 ( ), P11 ( ) and P5 ( ); Figure 22 There is 1 time of process migration: P19 ( ) and P14 ( ).

[0223] The application firstly combines the topological characteristics of the process tree and the dynamic constraint conditions of the equipment resources, and proposes an improved bipartite graph cycle decomposition strategy; secondly, based on the characteristics of the sub-string structure generated by decomposition, a multi-sub-string weight calculation scheme is established; finally, a virtual and real distribution strategy of the workshop is proposed, the process set is pre-distributed to the virtual equipment to simulate the scheduling process, the resource distribution scheme is adjusted dynamically by disassembling the sub-string, and the dual optimization of "shorter processing time and higher equipment efficiency" is realized. The method effectively solves the problem of heavy horizontal and light vertical or heavy vertical and light horizontal in the traditional scheduling method, avoids the process migration phenomenon and the additional time consumption caused thereby, improves the scheduling efficiency and equipment utilization level of the symmetric two-workshop distributed scheduling, and provides a solution with theoretical value and practical significance for the field of complex product production scheduling.

[0224] The application further proposes an electronic device comprising a memory and a processor, the memory stores a computer program, and the processor realizes the steps of the two-workshop distributed comprehensive scheduling method based on the improved bipartite graph when executing the computer program.

[0225] The application further proposes a computer readable storage medium for storing computer instructions, the computer instructions are executed by a processor to realize the steps of the two-workshop distributed comprehensive scheduling method based on the improved bipartite graph.

[0226] The memory in the embodiments of the application can be a volatile memory or a nonvolatile memory, or can include both volatile and nonvolatile memory. Among them, the nonvolatile memory can be a read only memory (read only memory, ROM), a programmable read only memory (programmable ROM, PROM), an erasable programmable read only memory (erasable PROM, EPROM), an electrically erasable programmable read only memory (electrically EPROM, EEPROM) or a flash memory. The volatile memory can be a random access memory (random access memory, RAM) used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (static RAM, SRAM), dynamic random access memory (dynamic RAM, DRAM), synchronous dynamic random access memory (synchronous DRAM, SDRAM), double data rate synchronous dynamic random access memory (double data rate SDRAM, DDR SDRAM), enhanced synchronous dynamic random access memory (enhanced SDRAM, ESDRAM), synchronous link dynamic random access memory (synchlink DRAM, SLDRAM) and direct memory bus random access memory (direct rambus RAM, DR RAM). It should be noted that the memory of the method described in the application is intended to include but not limited to these and any other suitable type of memory.

[0227] In the above embodiments, all or part of the methods can be implemented by software, hardware, firmware, or any combination thereof. When implemented by software, all or part of the computer program product can be implemented. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode. The computer readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available media can be magnetic media (such as floppy disk, hard disk, magnetic tape), optical media (such as high-density digital video disc (digital video disc, DVD)), or semiconductor media (such as solid state disc (solid state disc, SSD)) and the like.

[0228] In the implementation process, each step of the above method can be completed by integrated logic circuit of hardware in the processor or instruction in the form of software. The steps of the method disclosed in the embodiments of the present application can be directly embodied as hardware processor execution completion, or executed by hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory, and combines the hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0229] The above describes the two-car distributed comprehensive scheduling method based on improved bipartite graph. The principles and implementation methods of the present application are described by specific examples. The above embodiment is only used to help understand the method and core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation and application range will be changed; according to the above, the content of the specification should not be understood as the limitation of the present application.

Claims

1. A two-car distributed integrated dispatching method based on an improved bipartite graph, characterized in that, The method comprises an improved bipartite graph cycle decomposition strategy, a multi-substring weight strategy and a substring pre-allocation strategy; The improved bipartite graph cycle decomposition strategy is based on an improved bipartite graph, combines the structural characteristics of the process tree, and realizes the rational division of the process tree, which is divided into a plurality of process substring; In the improved bipartite graph, the original undirected graph is improved into a directed graph; The multi-substring weight strategy takes the processing time of the substring, the priority of the substring and the subsequent substring urgency value as the consideration factors to calculate the multi-substring weight, and schedules the process set according to the weight value in descending order; The substring pre-allocation strategy firstly virtually schedules the process set by pre-allocating the process set to the two workshops, compares the processing time of the two workshops, then selects the workshop with the shortest processing time for actual allocation, and further pre-judges whether the next substring to be decomposed can further optimize the processing time in this workshop; In the improved bipartite graph cycle decomposition strategy, an iterative recursive framework is adopted. In each round of decomposition, first, the current substring node is continuously numbered based on hierarchical traversal, then the center node position is calculated according to the subgraph size, and the center node needs to meet double criteria at the same time, that is, it needs to be located at the geometric center of the process tree to ensure the balance of the subgraph size after division, and it also needs to be mapped to the first element of the second vertex subset in the improved bipartite graph model to provide an initial matching base point for cross-workshop resource allocation; after positioning the center node, the substring in one subset of the center node is cut off as a whole and is divided into an independent scheduling unit, which is convenient for subsequent allocation and processing in the two workshops; then, the center positioning and improved bipartite graph division operation are continuously performed on the remaining part of the process tree after division, and through multiple rounds of iteration and refinement, the hierarchical decomposition of the entire process tree is gradually completed; Let the improved bipartite graph be a quadruple: where: is a finite vertex set, and are mutually exclusive subsets, is a directed edge set; the improved bipartite graph is mathematically modeled as follows: Formula (1) represents vertex complete partition, that is, the vertex set V is strictly divided into two mutually exclusive subsets; Formula (2) represents edge set completeness, and edges are only allowed to exist in: U, W, direction; Formula (3) and formula (4) represent that there are directed edges inside the U and W subsets; Formula (5) represents that there is only one edge from W to U, and the edge must be pointed from the first vertex of the W subset to the next process in the U subset; Formula (6) represents that the first node in the U set is the root node of the process tree, and the first node in the W set is the center node; In the multi-substring weight strategy, the processing time of the substring is based on the total processing time of the process, which is directly related to the length of the continuous occupation of the equipment. The longer the length, the higher the demand for equipment resources. The priority of the substring is determined by the layer priority of each process in the process tree. The subsequent substring urgency value is determined by the number of subsequent to-be-scheduled substrings remaining in the current substring. The processing time of the substring, the priority of the substring and the subsequent substring urgency value are calculated according to the preset entropy weight method weight formula, the comprehensive demand urgency value of each substring process set is established, the scheduling is sorted from high to low according to this value, the substrings with more urgent demand are processed first, and the idle time of the equipment due to waiting or migration is reduced.

2. The method of claim 1, wherein, The multi-substring weight strategy scheduling process is as follows: Step 1: calculate the processing time, priority and subsequent substring urgency value of each substring; Step 2: use the entropy weight method to fuse the processing time, priority and subsequent urgency value of the substring to calculate the weight of each substring; Step3: Sort all substrings by weight from high to low; Step4: Determine whether the maximum weight of the substring is unique, if it is unique, execute Step5; if it is not unique, execute Step6; Step5: Schedule the substring with the maximum weight, jump to Step10; Step6: Compare the processing time of each substring; Step7: Determine whether there is a substring with longer processing time, if there is, execute Step8; if there is not, execute Step9; Step8: Select the substring with the longest processing time, jump to Step10; Step9: Compare the priority of the substring, if there is a substring with higher priority, schedule the one with the highest priority; if the priority of the substrings is the same, compare the urgency value of the subsequent substrings, schedule the substring with the larger urgency value, jump to Step10; Step10: Determine whether all substrings have been scheduled, if they have, execute Step11, otherwise return to Step2, recalculate the weight of the remaining substrings and schedule them; Step11: Establish the substring scheduling sequence and complete the scheduling process.

3. The method of claim 1, wherein, In the substring pre-allocation strategy, first, the target substring to be scheduled is selected, and its process set is pre-allocated to the two workshop devices. The scheduling time of this process set is calculated for the two workshops, and the process set is allocated to the appropriate two workshops based on the criterion of less processing time in the allocated workshop. The original target substring is optimized by disassembly to further reduce the product processing time.

4. The method of claim 3, wherein, The substring pre-allocation strategy allocation process is as follows: Step1: Select the target substring to be pre-allocated from the substring set of the complex product decomposition; Step 2: sequentially assign the process set of the target substring to the workshops , the workshops perform pre-scheduling; Step 3: Calculate the earliest time of completing all processes of the substring after pre-scheduling, respectively, according to the process time and equipment constraints , workshop The earliest time of completing all processes is recorded as MT1, MT2. Step 4: Compare MT1 and MT2: if MT1 < MT2, select the shop as a candidate if MT2 < MT1, select the shop as a candidate if MT1 = MT2, select one of the shops as a candidate at random Jump to Step5; Step5: Perform partial disassembly on the original target substring, and calculate the earliest completion time MT' of the optimized substring in the candidate workshop; Step6: If MT' < Min(MT1, MT2), execute Step7; otherwise, execute Step8; Step7: Allocate the optimized substring to the candidate workshop, jump to Step9; Step8: Give up optimization and allocate the original substring of the scheme to the candidate workshop, jump to Step9; Step9: Determine whether all substrings have been allocated, if they have, jump to Step10, otherwise jump to Step1; Step10: After the substring allocation is completed, mark the occupation period and available state of the corresponding devices in the candidate workshop to ensure that the subsequent scheduling can sense the changes in resources in real time; Step11: Output the Gantt chart of the two workshops, and the allocation is complete.

5. The method of claim 1, wherein, In the scheduling process, it is assumed that in the symmetric two-workshop integrated scheduling process There are Two workshops that process in a certain order to complete the product; each workshop is equipped with A certain number of devices, and each has the ability to process each process independently; here, the two workshops have completely consistent workshop environment and production processing conditions; the specific requirements are as follows: (1) The processing and assembly operations of the process are unified into the processing category; (2) The processing technology of the complex product is presented through a tree structure, where the nodes represent specific processing processes; (3) Each process node contains three core parameters: process number, associated device number, and processing time; (4) The device resource configuration of the symmetrical workshop is completely identical, and the same device is not allowed in the same workshop; (5) There is a process dependency between processes, and the next process can only start after the previous process is completed; (6) If a process and its immediate previous process are processed in different workshops, process migration will occur; (7) The time when the last process is completed is the maximum completion time of the product. 6.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The computer program is executed by the processor to implement the steps of the method of any one of claims 1-5.

7. A computer readable storage medium for storing computer instructions, characterized in that, The computer program is executed by the processor to implement the steps of the method of any one of claims 1-5.

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