HEDA_RH Solution Method for Multi-order Coupled Assembly Integration Scheduling Problem

Abstract

This invention discloses a solution method for the HEDA_RH multi-stage coupled assembly integrated scheduling problem. First, a mathematical model of the processing-transportation-mixed loading multi-stage coupled integrated scheduling problem (MCISP_PTmA) integrating workshop and transportation scheduling is constructed in stages. Second, based on fully exploring the hierarchical and temporal nature of the problem's coupling constraints, an encoding method targeting only the processing stage is adopted. Two rules based on the problem's properties are proposed for each of the three stages, and the optimal rule combination is determined experimentally to achieve problem decoupling and decoding. Then, the HEDA_RH algorithm is designed to solve MCISP_PTmA. In HEDA_RH, regarding the global search, considering the two block structure characteristics of homogeneous and heterogeneous clusters among individuals, a probabilistic model update mechanism and two sampling methods are designed from a global perspective to better guide the search direction and improve solution efficiency. Regarding the local search, six heuristic search operations and replacement strategies are designed to improve solution quality while maintaining population diversity.

Description

Technical Field

[0001] This invention relates to an integrated optimization scheduling method for workshop and transportation in assembly manufacturing enterprises, covering multiple stages of production from processing and transportation to assembly. It belongs to the field of intelligent optimization scheduling technology for multi-stage coupled complex production systems. Background Technology

[0002] Against the backdrop of the national strategy to comprehensively promote intelligent manufacturing processes, hybrid production, as a mainstream method for many manufacturing enterprises to achieve flexible production, is often used in the production of products with similar processes, and is widely applied in industries such as engines, automobiles, and home appliances. How to improve the intelligence level of hybrid systems from a scheduling perspective has become one of the research hotspots in the manufacturing field in recent years, attracting much attention from the industry. For the scheduling research of existing hybrid production systems, with the enrichment of scheduling theory and the enhancement of information technology, the focus has shifted from single-system scheduling problems that only consider the mixed assembly of products to complex systems that consider the entire process from processing to assembly. However, current research in this field mainly suffers from the following problems: 1. The product structure is set too simply, considering only one assembly operation for each product, which is inconsistent with the diverse product structures and multiple assembly processes in current mixed assembly enterprises; 2. In solving complex system integration scheduling problems, existing research combines the characteristics of the problem with the design of effective heuristic rules and algorithms to improve the solution efficiency, but at the algorithm level, the problem itself and the solution algorithm are still separated, focusing on improving the performance of the algorithm itself, lacking the design of effective algorithm operations from the perspective of analyzing the characteristics of the problem, resulting in minimal improvement in the solution effect as the difficulty of the problem increases.

[0003] The multi-stage coupled integrated scheduling problem with processing-transport-mixed-mode assembly (MCISP_PTmA) is a scheduling problem integrating workshop and transportation in existing mixed production enterprises. It requires simultaneously considering the scheduling of processing, transportation, and assembly processes for all components within a multi-level bill of materials (BOM_ML) structure. Characterized by numerous coupling constraints between production stages and strong inter-stage correlations, it is a typical multi-stage coupling constraint (MCC) optimization problem. Further exploration of efficient solution methods for MCISP_PTmA that incorporates multi-stage coupling has significant theoretical implications. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for solving the multi-stage coupled integrated scheduling problem of processing, transportation, and mixed loading by combining a rule-based heuristic hybrid distribution estimation algorithm. Starting from efficient solution methods for complex system integrated scheduling under multi-stage coupling, this invention utilizes the multi-stage coupling characteristics of the problem, employing encoding only for the processing stage, with subsequent stages using rule groups to complete problem decoding. Finally, the problem coupling characteristics are integrated into a rule-based heuristic hybrid distribution estimation algorithm (HEDA_RH), combining two types of block structure features appearing in individuals to guide the global solution space search direction to improve search efficiency, and designing rule-based heuristic local search operations to improve solution quality. This invention supplements the shortcomings of existing research in this field, considering not only batch transportation from processing to assembly, but also the BOM_ML between products, and refining the assembly stage into a multi-machine assembly workshop problem with process constraints. MCISP_PTmA aims to minimize the maximum completion time, and designs a hybrid distribution estimation algorithm with fused rules for optimization.

[0005] To achieve the above-mentioned technical objectives, the present invention is implemented through the following technical solution: A method for solving the multi-order coupled integrated scheduling problem of processing-transportation-mixed loading by combining rule-based heuristic hybrid distribution estimation algorithms includes the following steps: S1: Based on the existing three-stage integration problem of processing-transportation-mixed assembly, a method is proposed that considers part constraints and MCISP_PTmA related to the product's BOM_ML structure. S2: With minimizing the maximum completion time (Makespan) as the optimization objective, construct problem permutation models for the processing stage, transportation stage, and mixed loading stage respectively; S3: Analyze the coupling constraint characteristics present in MCISP_PTmA; S4: Based on the coupling characteristics, an encoding method is adopted for the processing stage, and decoding rules based on the nature of the problem are designed to complete the decoding of the subsequent stages; S5: Based on the encoding and decoding method, two block structures are defined in the MCISP_PTmA individual: homotypegather block (HGB) and isomerism gather block (IGB). S6: Design the HEDA_RH algorithm based on the problem properties and block structure to solve MCISP_PTmA; Preferably, the mixed assembly stage takes into account the product's BOM_ML structure, the setup time between different parts is considered in the processing stage, the impact of different transport weights on transport speed is considered in the transportation stage, and the part allocation and multi-process constraints are considered in the mixed assembly stage, thus extending the single-machine problem into a multi-machine problem. Preferably, in step S2, a mathematical model MCISP_PTmA considering part constraints and assembly process constraints in the product BOM_ML is constructed, and a permutation model with minimizing the maximum completion time as the objective function is established in stages. The specific method for establishing the model is as follows: a: Establish a processing stage model for a multi-process heterogeneous parallel machine scheduling problem with release and set-time, using a part processing process-based arrangement. Equation (1) calculates the completion time of the process under different conditions. ,in express As the first process, express For machines The first step; (1)

[0006] Component The completion time for the first stage of processing is = ; b: Establish a transportation stage model for a multi-vehicle, single-point direct transportation problem with vehicle load constraints and speed settings, using a permutation based on the part transportation sequence. Equation (2) calculates the transportation arrival time of parts under different conditions. This indicates that this is the vehicle's first trip. (2)

[0007] Component Depend on Transport Transportation completion time ; c: Establish an assembly stage model for multi-product, multi-machine assembly problems with part constraints and assembly process constraints, using a sequencing-based assembly process approach. Assembly process There may be A tight pre-assembly process. It can only begin after all preceding processes are completed; Equation (3) calculates different cases. Completion time ,in =0 indicates that this process has no preceding process. This indicates that the process is machine-based. The first step; (3)

[0008] product Assembly completion time ; d: Based on the above model, determine the optimization objective calculation formulas (4) and (5); (4) (5) Table 1 shows the meaning of the above parameters:

[0009] Preferably, in step S3, the coupling constraint characteristics of the problem in MCISP_PTmA are analyzed, specifically from the perspectives of coupling constraint hierarchy and coupling constraint temporality, as follows: Coupling constraint hierarchy analysis: MCISP_PTmA involves the product's BOM_ML, part processing process constraints, and product assembly process constraints; the assembly of the product requires that all the components arrive, and the parts can be transported, which requires that all processes of the parts be completed. The process is progressive and closely related to each level. Coupling Constraint Timing Analysis: In MCISP_PTmA, the product assembly start time is constrained by the arrival and assembly time of the required parts; the transportation start time is constrained by the completion time of the parts processing; the part processing start time in the processing stage is constrained by the process release time; therefore, the processing stage determines the start time of the latter two stages.

[0010] Preferably, in step S4, encoding is used only for the processing stage based on the temporal nature of the coupling constraints, and subsequent stage decoding is completed through rules. The specific steps of encoding and solution are as follows: Considering the multi-stage coupling characteristics present in MCISP_PTmA, the encoding method used is specific to the processing stage: a: Based on the demand and component composition of different products, form One part that needs to be processed; b: Identify each part and assign a number to each part. ,Component The corresponding part model is ; c: If the part The model number is ,So It needs to appear in the code. The second time, the first time appearing in the encoding indivual This represents the parts. No. One process; The code generated according to the above rules is considered as an individual. = ; The decoding method is as follows: a: will Input processing stage; b: Calculate using the processing machine allocation rules ; c: Parts are formed in batches using a batch transportation rule. ; d: Assign transport vehicles to different batches using vehicle allocation rules and calculate... ; e: Forming the product assembly sequence Based on this, and according to the constraints of the assembly process, products are formed through aggregation. ; f: Select assembly machines using assembly machine allocation rules to obtain the assembly completion time for different products. ; Preferably, in the decoding process, two decoding rules are used for three stages to form eight rule groups, among which the maximum load rule (MLTR) in the time range of the transportation stage, the minimum parts product priority rule (MPF) and the maximum subsequent processable product priority rule (MSPF) in the mixed loading stage are all proposed for the first time. The processing stage rules adopt the Shortest process time + Settime (SPST) rule and the Earliest completion time (ECT) rule respectively. The SPST rule assigns the process to the machine with the smallest sum of settime and processing time, while the ECT rule assigns the process to the machine that can complete processing earliest. During the transportation phase, the First Finished First Transport (FFFS) rule and the Maximum Weight-to-Load (MLTR) rule are used to batch the workpieces. FFFS sorts the parts solely based on their completion time in ascending order, and adds the weights of the parts sequentially from beginning to end. If adding a later part would cause the total weight of the batch to exceed the vehicle's load capacity, then the earlier parts will be grouped into the same batch. MLTR, based on the FFFS rule, specifies a time range... When the next component cannot meet the load constraints, consider Internal components that can meet load-bearing constraints; The above 6 rules form 8 rule groups, namely: SPST / FFFS / MPF, SPST / FFFS / MSPF, SPST / MLTR / MPF, SPST / MLTR / MSPF, ETC / FFFS / MPF, ETC / FFFS / MSPF, ETC / MLTR / MPF, and ETC / MLTR / MSPF; Preferably, in step S5, the two block structures that appear in the encoding when solving MCISP_PTmA are defined as follows: Homotype gather block (HGB): This refers to the phenomenon of clustering of similar parts, where all processes in the block involve the same type of part, and this phenomenon occurs multiple times in high-quality individuals. Isomerism gather block (IGB): Although the parts in the block are not of the same type, the block structure appears multiple times in high-quality individuals; As the population quality increases, the proportion of HGBs in individuals will increase, while the change in the number of IGBs is related to the selected statistical length and problem size. Preferably, the specific steps of the HEDA_RH algorithm in S5 are as follows: S51: Initialize the population, where... Individual units are generated using a product aggregation method; S52: Execute sampling mechanism I; S53: Execute sampling mechanism II; S54: Perform 6 heuristic operations, namely local search operations, and perform a replacement strategy once; S55: Execute S54 a total of repeat times; S56: Update the two probability matrices based on the dominant individual; Preferably, in the HEDA_RH, the steps of sampling mechanism I and sampling mechanism II for global search are as follows: Sampling Mechanism I adopts Record high-quality HGBs, initialize them using equation (6), and update them using equation (7), where For the current algebra, Position among all selected high-quality individuals Parts appear The total number of times; the specific steps of sampling mechanism I are: a: In the preserved population A high-quality individual is introduced into Spop(g); seeds are formed from the new population; b: Select seed, via Sample to generate new individuals; and determine whether the new individuals are superior to the seed; c: If the new individual is not better than the seed, then determine whether the maximum number of generation times has been reached; d: If the maximum number of generation attempts is reached, select the best newly generated individual and add it to the new population; determine whether a new individual has been generated. A new individual; (6) (7)

[0011] Sampling Mechanism II adopts Record high-quality HGBs, initialize them using equation (8), and update them using equation (9), where The block record length is 1GB. For model learning rate, For all selected high-quality individuals, IGB blocks The number of consecutive occurrences, It is a constant; the specific steps of sampling mechanism II are as follows: a: Through Sample the first A-1 encoded bits, and read the block structure of the first A-1 bits; b: Use Equation 10 for roulette wheel betting and Perform sampling; c: Output new individuals to the new population until a population is generated. A new individual; (8) (9) (10) ( ) Preferably, the local search method in HEDA_RH includes heuristic operations and replacement strategies; the six heuristic operations are: aggregation operation based on Insert, aggregation operation based on Swap, disordered perturbation operation based on partial fragments, mixed operation of random swap and fragment swap, cross-based crossover operation, and fragmented insertion operation of a single entity. Replacement operation steps: First, sort the population, and record the half of individuals that are worse as follows: , = For the number of poor individuals, the first individual Equation (11) Statistical All individuals in the position average ,Will and Considered The column vector of dimension is calculated using equations (11) and (12) to obtain the individual. and Euclidean distance As a basis for similarity assessment; The smallest 7 individuals used to Perform the replacement; repeat the above heuristic and replacement strategy. Second-rate.

[0012] (11) (12) The beneficial effects of this invention are: First, addressing the issue that existing multi-stage production-assembly studies oversimplify product structures and fail to align with actual production in hybrid assembly enterprises, this invention further considers the BOM_ML and the MCISP_PtmA problem—a complex integrated scheduling problem involving multiple machines and multiple stages with assembly process constraints—thus improving and supplementing the model. Second, addressing the lack of research on algorithm search operations based on problem characteristics, this invention further analyzes the properties of MCISP_PtmA and proposes HEDA_RH for solving it, thereby enhancing the algorithm's search efficiency by designing a search mechanism based on problem characteristics. This invention achieves good results in terms of model completeness, depth of problem analysis, mining of coupling characteristics, and effectiveness of algorithm search, providing methodological guidance for improving the overall efficiency of production processes in complex assembly manufacturing enterprises, reducing costs, and enhancing intelligent manufacturing levels. Attached Figure Description

[0013] Figure 1 It is a multi-level BOM structure diagram of the product. Figure 2 This is a diagram of the MCISP_PTmA model; Figure 3 This is a schematic diagram illustrating the encoding process principle; Figure 4 This is a schematic diagram illustrating the decoding process. Figure 5 This is a schematic diagram of the block structure; Figure 6 It is the first-to-ship rule in the phased transportation process; Figure 7 It is the maximum load priority rule within the time specification in the batching rules of the transportation phase; Figure 8 These are the ARPD curves for different rules as a function of experimental scale; Figure 9 This is a schematic diagram of sampling mechanism I; Figure 10 This is a schematic diagram of sampling mechanism II; Figure 11 This is the flowchart of the HEDA_RH algorithm. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Example 1

[0016] Optimal rule group selection The subsequent decoding stages are completed using an encoding method and decoding rule set specific to the first stage. To find the optimal decoding rule set, the example steps are as follows: S1: Construct problem permutation models for the processing stage, transportation stage, and mixed loading stage respectively; such as... Figure 2 As shown; S2: Based on the analysis of the problem coupling characteristics, we adopt the method of encoding only for the processing stage, and complete the problem decoding in subsequent stages by designing a set of solution rules based on the problem properties; S3: Run the rule groups separately in the EDA algorithm; S4: Compare the experimental data of different rule groups and select the rule group with the best performance; Preferably, the model construction method for each stage in S1 is as follows: a. Establish a processing stage model for a multi-process heterogeneous parallel machine scheduling problem with release and set-time, using a part processing operation-based arrangement. Equation (1) calculates the completion time of the process under different conditions. ,in express As the first process, express For machines The first step; (1)

[0017] Component Completion time of the first stage of processing = ; b. Establish a transportation stage model for a multi-vehicle, single-point direct transportation problem with vehicle load constraints and speed settings, using a permutation based on the part transportation sequence. Equation (2) calculates the transportation arrival time of parts under different conditions. This indicates that this is the vehicle's first trip. (2)

[0018] Component Depend on Transport Transportation completion time ; c. Establish an assembly stage model for multi-product, multi-machine assembly problems with part constraints and assembly process constraints, using a sequencing-based assembly process approach. Assembly process There may be A tight pre-assembly process. It can only begin after all preceding processes are completed; Equation (3) calculates different cases. Completion time ,in =0 indicates that this process has no preceding process. This indicates that the process is machine-based. The first step; (3)

[0019] product Assembly completion time ; d. Determine the optimization objective calculation formulas (4) and (5) based on the above model; (4) (5) S2 analyzes the coupling characteristics of the problem in MCISP_PTmA, focusing on the hierarchy and temporal nature of coupling constraints as follows: Coupling constraint hierarchy analysis: MCISP_PTmA involves the product's BOM_ML, part processing process constraints, and product assembly process constraints; the assembly of the product requires that all the components arrive, and the parts can be transported, which requires that all processes of the parts be completed. The process is progressive and closely related to each level. Coupling Constraint Timing Analysis: In MCISP_PTmA, the product assembly start time is constrained by the arrival and assembly time of the required parts; the transportation start time is constrained by the completion time of the parts processing; the part processing start time in the processing stage is constrained by the process release time; therefore, the processing stage determines the start time of the latter two stages.

[0020] Next, based on the temporal nature of the coupling constraints, encoding is adopted only for the processing stage, and subsequent stages of decoding are completed according to rules. The specific steps of encoding and solution are as follows: Encoding method: such as Figure 3 As shown, considering the multi-level coupling characteristics present in MCISP_PTmA, the encoding method that targets only the processing stage is as follows: a: Based on the demand and component composition of different products, form One part that needs to be processed; b: Identify each part and assign a number to each part. ,Component The corresponding part model is ; c: If the part The model number is ,So It needs to appear in the code. The second time, the first time appearing in the encoding indivual This represents the parts. No. One process; The code generated according to the above rules is considered as an individual. = .

[0021] Decoding method: such as Figure 4 As shown, the decoding steps are as follows: a: will Input processing stage, b: Calculate using the processing machine allocation rules , c: Parts are formed in batches according to the batch transportation rules. , d: Assign transport vehicles to different batches using vehicle allocation rules and calculate... e: Forming the product assembly sequence Based on this, and according to the constraints of the assembly process, products are formed through aggregation. f: Select assembly machines using assembly machine allocation rules to obtain the assembly completion time for different products. .

[0022] Next, in order to complete the decoding, two decoding rules are used in three stages to form eight rule groups. The specific content of each rule is as follows: The processing stage rules adopt the Shortest Process Time + Settime (SPST) rule and the Earliest Completion Time (ECT) rule, respectively. The SPST rule assigns the operation to the machine with the smallest sum of settime and processing time, while the ECT rule assigns the operation to the machine that can complete processing earliest.

[0023] During the transportation phase, the First Finished First Transport (FFFS) rule and the Maximum Load Time Rule (MLTR) are used to batch the workpieces. FFFS sorts the workpieces solely based on their completion time in the machining phase, from smallest to largest. Figure 6 As shown, the weights of the parts are added sequentially from front to back. If adding a later part would cause the total weight of the batch to exceed the vehicle's load capacity, then the earlier parts will be grouped into the same batch. MLTR is based on the FFFS rule, as follows... Figure 7 As shown, given a time range T_range, when the next part cannot meet the load constraint, consider the parts within T_range that can meet the load constraint.

[0024] The above 6 rules form a total of 8 rule groups: SPST / FFFS / MPF, SPST / FFFS / MSPF, SPST / MLTR / MPF, SPST / MLTR / MSPF, ETC / FFFS / MPF, ETC / FFFS / MSPF, ETC / MLTR / MPF, ETC / MLTR / MSPF.

[0025] In S3, to compare the effectiveness of different rule groups, the rule groups were iterated through the EDA algorithm. All algorithm programs were implemented in Matlab 2020b, and the experimental equipment consisted of an i7-11800h CPU and 16GB of RAM. The material structure, process time, and product demand at different scales are shown in Tables 2-7. Furthermore, the experimental data are as follows: =2000kg, =3500m, =400m / min, =5, =5, =11, =8 Table 2 Product Composition Information

[0026] Table 3 Part Information

[0027] Table 4 Processing Procedure Information

[0028] [Note]: Inf indicates that the process cannot be performed on this machine. Table 5 Setting Time Information

[0029] Table 6 Assembly Process Information

[0030] Table 7 15 Experimental Scales

[0031] Runtime of experiments of different scales (seconds) is calculated by equation (6), and the vehicle transport speed in the experiment is set to... To compare the effectiveness of rule sets, the experimental method was as follows: 15 problems of different sizes were solved using the EDA algorithm with 8 different rule sets. For problems of the same size, each rule set was applied in the same time interval. The algorithm was run independently 20 times. In Table 8, "best" represents the optimal value, "worst" represents the worst value, and "avg" represents the average value. The experiment shows that the latter four rule groups yield better results, and ETC / FFFS / MPF achieve optimal solutions in most problem sizes. However, the latter three rule groups also show good performance in other scales, and the data indicates that the differences between the latter four rule groups are relatively small.

[0032] (6) To further compare the solution efficiency of the latter four rules, equation (7) calculates the average relative percentage deviation (ARPD) of the latter four rule groups under different scales, where To obtain the result using the rules, This represents the optimal value obtained by all rules at this scale, where n=20 is the number of experiment repetitions. ARPD reflects the results obtained by different rules and... The smaller the value, the better, considering the degree of deviation and fluctuation at different scales.

[0033] (7) Combined with Table 8 Figure 8 The following conclusions can be drawn: 1) The ETC rule is significantly better than the SPST rule; 2) The ETC / FFFS / MPF rule group is significantly better than other rule groups in all scales. Table 8-1 Data from the rule comparison experiment

[0034] Table 8-2 Data from the Rule Comparison Experiment

[0035] Preferably, the subsequent content is implemented using rule groups ETC / FFFS / MPF, that is, the processing stage allocation rule adopts the earliest completion time rule (ETC), the transportation stage parts batching rule adopts the first-to-completion-first-shipment rule (FFFS), and the product assembly sequencing rule adopts the least-parts-first-product rule (MPF).

[0036] Example 2

[0037] IGB block length Value selection experiment IGB block record length The value of will determine the actual effect of sampling mechanism II, matrix The size of the value will affect the time and space overhead of the algorithm. If the setting is too large, it will cause... Matrix space overhead is large and records a lot of invalid block information; if If the setting is too small, it will not be able to effectively record the block structure, resulting in poor sampling results. Therefore, further determination is needed. The value of is determined to find the most efficient value for different problem sizes. Values, respectively for With different values ​​of 2, 3, 4, and 5, the algorithm was run independently 20 times for 15 different problem sizes within the HEDA_HR framework. Key parameter settings are shown in Table 10. To ensure... Value only applies to the sampling mechanism To generate an impact, let the parameter of the new population proportion be set. =0, =0.6.

[0038] The steps for this example are as follows: S1: Establish the MCISP_PTmA problem permutation model S2: Select ETC / FFFS / MPF rule groups for encoding and decoding. S3: Construct the HEDA_HR algorithm that includes sampling mechanism II. S4: Retrieve from HEDA_RH respectively Experiments were conducted at different scales: =2, 3, 4, 5. The construction steps of HEDA_HR are as follows: a: Initialize the population, where Individual units are generated using a product aggregation method; b: Execute sampling mechanism I; c: Execute sampling mechanism II; d: Perform 6 heuristic operations, namely local search operations, and perform a replacement strategy once; e: Execute S54 a total of repeat times; f: Update the two probability matrices based on the dominant individual; The steps of sampling mechanism I and sampling mechanism II are as follows: Sampling Mechanism I adopts Record high-quality HGBs, initialize them using Equation 8, and update them using Equation 9, where... For the current algebra, Position among all selected high-quality individuals Parts appear The total number of times. The specific steps of sampling mechanism I are as follows: a: In the preserved population A high-quality individual is introduced into Spop(g); seeds are formed from the new population; b: Select a seed, then... Sample to generate new individuals; and determine whether the new individuals are superior to the seed; c: If the new individual is not better than the seed, then determine whether the maximum number of generation times has been reached; d: If the maximum number of generation attempts is reached, select the best newly generated individual and add it to the new population; determine whether a new individual has been generated. A new individual; (8) (9)

[0039] Sampling Mechanism II adopts Record high-quality HGBs, initialize them using equation (10), and update them using equation (11), where The block record length is 1GB. For model learning rate, For all selected high-quality individuals, IGB blocks The number of consecutive occurrences, It is a constant. The specific steps of sampling mechanism II are as follows: a: Through Sample the first A-1 encoded bits, and read the block structure of the first A-1 bits; b: Use Equation 12 to perform roulette wheel betting. and Perform sampling; c: Output new individuals to the new population until a population is generated. A new individual; (10) (11) (12) ( )

[0040] The local search method in HEDA_RH includes heuristic operations and replacement strategies. The six heuristic operations are shown in the table below: Table 9 Heuristic Operation Steps

[0041] Replacement operation steps: First, sort the population, and record the half of individuals that are worse as follows: , = For the number of poor individuals, the first individual Equation (13) Statistical All individuals in the position average ,Will and Considered The column vector of dimension is calculated using equation (14) to obtain the individual. and Euclidean distance As a basis for similarity assessment. The smallest 7 individuals used to Perform the replacement. Repeat the above heuristic and replacement strategy. Second-rate.

[0042] (13) (14) The parameter settings in HEDA_RH are shown in Table 10, and the experimental results are shown in Table 11. Table 11 shows that in the experiments of the first nine problem scales, =3 yielded 6 optimal values ​​and 7 optimal averages; in the latter 6 problem-scale experiments, =4 yielded 3 optimal values ​​and 6 relatively good average values.

[0043] Table 10 HEDA_RH Key Parameter Settings

[0044] Table 11 Different Scales Experimental results of value selection

[0045] Example 3

[0046] Validation of HEDA_RH Solution for MCISP_PTmA Since MCISP_PTmA is a novel scheduling problem, no literature has yet provided a solution. To verify the effectiveness of the algorithm, HEDA_RH is compared with the semi-permutation genetic algorithm (SPGA) and discrete bat algorithm (IHBA) published in international journals for solving ensemble scheduling problems similar to MCISP_PTmA. SPGA and IHBA use the optimal parameters set in the literature, while the key parameters for HEDA_RH are set as in Table 1, and [further details omitted]. =0.3, =0.3. The experimental data are the same as those in Tables 2-7 of Example 1. Furthermore, based on the experimental results in Example 2, the data were selected in the comparative experiments of the first 9 groups of problem sizes. =3, selected in the comparative experiments of the last 6 problem sizes. =4. Each algorithm uses rule groups ETC / FFFS / MPF to calculate completion time, and the coding is the same: part coding based on processing steps.

[0047] Different algorithms in 15 different problem sizes within a specified time Each algorithm was run independently 20 times. Table 12 shows the best, worst, and average values ​​(avg) obtained by HEDA_RH, SPGA, and IHBA at different scales. The experiments show that HEDA_RH achieves better values ​​than the other two algorithms across 15 scales and obtains a better average value across 13 scales. This demonstrates that HEDA_RH can effectively solve MCISP_PTmA.

[0048] Table 12 Comparison of experimental results between HEDA_RH, SPGA, and IHBA.

[0049]

Claims

1. A method for solving a multi-order coupled integrated scheduling problem of processing-transportation-mixed loading by combining a rule-based heuristic hybrid distribution estimation algorithm, characterized in that, Includes the following steps: S1: Based on the existing three-stage integration problem of processing-transportation-mixed assembly, we propose the MCISP_PTmA problem, which considers the multi-level bill of materials (BOM) structure of the product and the multi-level coupling integration scheduling problem of processing-transportation-mixed assembly. S2: With minimizing the maximum completion time (Makespan) as the optimization objective, construct problem permutation models for the processing stage, transportation stage, and mixed loading stage respectively; S3: Analyze the coupling constraint characteristics present in MCISP_PTmA; S4: Based on the coupling characteristics, an encoding method is adopted for the processing stage, and decoding rules based on the nature of the problem are designed to complete the decoding of the subsequent stages; S5: Based on the encoding and decoding method, two block structures are defined in the MCISP_PTmA individual: homotype gather block (HGB) and isomerism gather block (IGB). S6: Design the HEDA_RH algorithm based on the problem properties and block structure to solve MCISP_PTmA; In step S4, encoding is used only for the processing stage based on the temporal nature of coupling constraints, and subsequent stage decoding is completed through rules. The specific steps of encoding and solution are as follows: Considering the multi-stage coupling characteristics present in MCISP_PTmA, the encoding method used is specific to the processing stage: a: Based on the demand and component composition of different products, form One part that needs to be processed; b: Identify each part and assign a number to each part. ,Component The corresponding part model is ; c: If the part The model number is ,So It needs to appear in the code. The first time, the first time appearing in the encoding indivual This represents the parts. No. One process; The code formed according to the above rules is regarded as an individual. = ; The decoding method is as follows: a: will Input processing stage; b: Calculate using the processing machine allocation rules ; c: Parts are formed in batches using a batch transportation rule. ; d: Assign transport vehicles to different batches using vehicle allocation rules and calculate... ; e: Forming the product assembly sequence Based on this, and according to the constraints of the assembly process, products are formed through aggregation. ; f: Select assembly machines using assembly machine allocation rules to obtain the assembly completion time for different products. ; In S5, the two block structures that appear in the encoding when solving MCISP_PTmA are defined as follows: Homotype gather block (HGB): This refers to the phenomenon of clustering of similar parts, where all processes in the block involve the same type of part, and this occurs multiple times in high-quality individuals. Isomerism gather block (IGB): Although the parts in the block are not of the same type, the block structure appears multiple times in high-quality individuals; As the population quality increases, the proportion of HGBs in individuals will increase, while the change in the number of IGBs is related to the selected statistical length and problem size. The specific steps of the HEDA_RH algorithm in S6 are as follows: S51: Initialize the population, where... Individual units are generated using a product aggregation method; S52: Execute sampling mechanism I; S53: Execute sampling mechanism II; S54: Perform 6 heuristic operations, namely local search operations, and perform a replacement strategy once; S55: Execute S54 a total of repeat times; S56: Update the two probability matrices based on the dominant individual; In HEDA_RH, the steps of sampling mechanism I and sampling mechanism II for global search are as follows: Sampling Mechanism I adopts Record high-quality HGBs, initialize them using equation (6), and update them using equation (7), where For the current algebra, Position among all selected high-quality individuals Parts appear The total number of times; the specific steps of sampling mechanism I are: a: In the preserved population A high-quality individual is introduced into Spop(g); seeds are formed from the new population; b: Select seed, then... New individuals are generated through sampling; And determine whether the new individual is superior to the seed; c: If the new individual is not better than the seed, then determine whether the maximum number of generation times has been reached; d: If the maximum number of generation attempts is reached, select the best newly generated individual and add it to the new population; determine whether a new individual has been generated. A new individual; （6） （7） Sampling Mechanism II adopts Record high-quality HGBs, initialize them using equation (8), and update them using equation (9), where The block record length is 1GB. For model learning rate, For all selected high-quality individuals, IGB blocks The number of consecutive occurrences, It is a constant; the specific steps of sampling mechanism II are as follows: a: Through Sample the first A-1 encoded bits, and read the block structure of the first A-1 bits; b: Use formula (10) to perform roulette wheel betting and Perform sampling; c: Output new individuals to the new population until a population is generated. A new individual; (8) （9） （10） ( )。 2. The method for solving the multi-stage coupled integrated scheduling problem of processing-transportation-mixed loading using a rule-based heuristic hybrid distribution estimation algorithm as described in claim 1, characterized in that... The mixed assembly stage takes into account the product's BOM_ML structure, the setup time between different parts during the processing stage, the impact of different transport weights on transport speed during the transportation stage, and the parts allocation and multi-process constraints during the mixed assembly stage, and extends the single-machine problem into a multi-machine problem.

3. The method for solving the multi-stage coupled integrated scheduling problem of processing-transportation-mixed loading using a rule-based heuristic hybrid distribution estimation algorithm as described in claim 1, characterized in that... In step S2, an MCISP_PTmA mathematical model considering part constraints and assembly process constraints in the product BOM_ML is constructed. A permutation model with minimizing the maximum completion time as the objective function is established in stages. The specific method for establishing the model is as follows: a: Establish a processing stage model for a multi-process heterogeneous parallel machine scheduling problem with release and set-time, using a part processing operation-based arrangement. Equation (1) calculates the completion time of the process under different conditions. ,in express As the first process, express For machines The first step; （1） Component The completion time for the first stage of processing is = ; b: Establish a transportation stage model for a multi-vehicle, single-point direct transportation problem with vehicle load constraints and speed settings, using a permutation based on the part transportation sequence. Equation (2) calculates the transportation arrival time of parts under different conditions. This indicates the vehicle's first trip. (2) Component Depend on Transport Transportation completion time ; c: Establish an assembly stage model for multi-product, multi-machine assembly problems with part constraints and assembly process constraints, using a sequencing-based assembly process approach. Assembly process There may be A tight pre-assembly process. It can only begin after all preceding processes are completed; Equation (3) calculates different cases. Completion time ,in =0 indicates that this process has no preceding process. This indicates that the process is machine-based. The first step; （3） product Assembly completion time ; d: Based on the above model, determine the optimization objective calculation formulas (4) and (5); （4） （5）。 4. The method for solving the multi-order coupled integrated scheduling problem of processing-transportation-mixed loading using a rule-based heuristic hybrid distribution estimation algorithm as described in claim 1, characterized in that... In section S3, the coupling constraint characteristics of the problem in MCISP_PTmA are analyzed, specifically from the perspectives of coupling constraint hierarchy and coupling constraint temporality, as follows: Coupling constraint hierarchy analysis: MCISP_PTmA involves the product's BOM_ML, part processing process constraints, and product assembly process constraints; the assembly of the product requires that all the components arrive, and the parts can be transported, which requires that all processes of the parts be completed. The process is progressive and closely related to each level. Coupling Constraint Timing Analysis: In MCISP_PTmA, the product assembly start time is constrained by the arrival and assembly time of the required parts; the transportation start time is constrained by the completion time of the parts processing; the part processing start time in the processing stage is constrained by the process release time; therefore, the processing stage determines the start time of the latter two stages.

5. The method for solving the multi-order coupled integrated scheduling problem of processing-transportation-mixed loading using a rule-based heuristic hybrid distribution estimation algorithm as described in claim 1, characterized in that... In the decoding process, two decoding rules are used to form eight rule groups for three stages. Among them, the maximum load rule MLTR in the time range of the transportation stage, the minimum part product priority rule MPF and the maximum subsequent processable product priority rule MSPF in the mixed loading stage are all proposed for the first time. The processing stage rules adopt the minimum setup time rule (SPST) and the earliest completion time rule (ECT), respectively. The SPST rule assigns the operation to the machine with the minimum sum of setup time and processing time, while the ECT rule assigns the operation to the machine that can complete processing earliest. During the transportation phase, the First-to-Complete, First-Transport rule (FFFS) and the Maximum Load-to-Time rule (MLTR) are used to batch the workpieces. FFFS sorts the parts only according to the completion time of the processing stage from smallest to largest, and adds the weights of the parts from front to back. If adding a later part would cause the total weight of the current batch of parts to exceed the vehicle's load capacity, then the previous parts will be grouped into the same batch. MLTR builds upon the FFFS rule by providing a time range. When the next component cannot meet the load constraints, consider Internal components that can meet load-bearing constraints; The above 6 rules form 8 rule groups, namely: SPST / FFFS / MPF, SPST / FFFS / MSPF, SPST / MLTR / MPF, SPST / MLTR / MSPF, ETC / FFFS / MPF, ETC / FFFS / MSPF, ETC / MLTR / MPF, and ETC / MLTR / MSPF.

6. The method for solving the multi-stage coupled integrated scheduling problem of processing-transportation-mixed loading using a rule-based heuristic hybrid distribution estimation algorithm as described in claim 1, characterized in that... The local search method in HEDA_RH includes heuristic operations and replacement strategies; the six heuristic operations are: Insert-based aggregation operation, Swap-based aggregation operation, fragment-based disorder perturbation operation, mixed operation of random swap and fragment swap, Cross-based crossover operation, and fragment insertion operation of a single entity; their specific operations are as follows: Aggregation operations based on Insert: Step 1: Select two individuals and Each cut length is splicing the fragments together ; Step 2: Remove middle Repeated times exceeded Part of the ( ); Step 3: Statistics middle Missing number Insert the missing parts into After the same part in the middle until =0, resulting in a new encoding. ; Step 4: Repeat steps 1-3 no more than [number missing] times. Next, until ,Will Output as a new individual ; Swap-based aggregation operations: Step 1: Select an individual Choose any position from them ,remember The part model is , Except All external parts are model number The subscript set is ; Step 2: Choose any subscript ,like Then from The two before and after , , , Randomly select position As Position; if Then from One before and one after , Randomly select position As Position, if Then let each and ; Step 3: [The sentence is incomplete and requires more context to be translated accurately.] and implement The operation yields a new code. ; Step 4: Repeat steps 1-3 no more than [number missing] times. Next, until ,Will Output as a new individual ; Disorder perturbation operation based on partial segments: Step 1: Select an individual Let the length of the perturbation segment be... ; Step 2: Randomly select the starting position of a perturbation segment. , ; Step 3: Generate a string containing 1 to random disorder make , ; Step 4: The above steps will be repeated no more than [number missing]. Next, until ,Will The output is Otherwise, output all generated... The individual with the highest fitness; Mixed operations of random swap and fragment swap: Step 1: Select an individual ,from Select two non-overlapping positions and swap them to obtain swap repeats no more than Next until The completion time is less than ; Step 2: Divided into A segment, making , =1; Step 3: Randomly generate intervals Two unique numbers and Then execute Operation obtained ; Step 4: If Its fitness is better than Output For new individuals ; Step 5: If ,but And return to step 3; Step 6: If ,but Return to step 2; otherwise, output... The individual with the highest fitness is ; Cross-based cross operations Step 1: Select two individuals and Randomly generate cross bits ( ); Step 2: to Partial insertion to Previously formed new code ,Will arrive Fragment insertion Previously formed new code ; Step 3: Put and The number of repetitions exceeds parts It needs to be deleted, among which It is necessary to traverse from back to front and perform deletions. This results in two new codes that conform to the encoding rules, one from front to back. and ; Step 4: Repeat steps 1-3 no more than [number missing] times. Next, until and The fitness of a certain individual is better than and ,Will[ , , , The two individuals with the highest fitness are output as the new individual. and ; Fragmented insertion operation of a single entity Step 1: Select an individual Randomly generate the length of the inserted segment ; Step 2: From Randomly select a length of Inserted fragment and will In Fragment deletion ; Step 3: Put Insert into A new code is obtained by retrieving any position from the given code. ; Step 4: Repeat steps 1-3 no more than [number missing] times. Next, until ,Will Output as a new individual ; Replacement operation steps: First, sort the population, and record the half of individuals that are worse as follows: , = For the number of poor individuals, the first individual Equation (11) Statistical All individuals in the position average ,Will and Considered The column vector of dimension is calculated using equations (11) and (12) to obtain the individual. and Euclidean distance As a basis for similarity assessment; The smallest 7 individuals to Perform the replacement; repeat the above heuristic and replacement strategy. Second-rate; （11） （12）。

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