Method and system for assembling job shop scheduling based on whole block right shift repair coding

Abstract

The application belongs to the technical field of workshop scheduling, and particularly discloses an assembly job shop scheduling method and system based on whole-block right shift repair coding, which comprises the following steps: considering the machine constraint of an assembly process, a production scheduling model of an assembly job shop is constructed; the production scheduling model is iteratively solved through a meta-heuristic algorithm to obtain an assembly job shop scheduling method; and a whole-block right shift repair coding is executed in the iteration process, which can meet the complex assembly constraint relationship of a product, ensure the feasibility of a chromosome, guarantee the relative order of underlying machining processes not to be changed in the repair process, reduce the damage to an initial solution as much as possible while meeting the feasibility, and thus realize more efficient exploration of a solution space. The application can improve production stability and production efficiency, reduce the product manufacturing cycle, and improve economic benefits.

Description

Technical Field

[0001] This invention belongs to the field of workshop scheduling technology, and more specifically, relates to an assembly workshop scheduling method and system based on whole-block right-shift repair coding. Background Technology

[0002] The job shop scheduling problem (JSP) is one of the most classic and complex job shop scheduling problems. The assembly job shop scheduling problem (AJSP), in addition to the job shop problem, further considers the assembly constraints between workpieces. The final assembly start time of the product is constrained by the completion time of the required components, while the assembly start time of higher-level components is constrained by the completion time of their directly subordinate parts / sub-components. The process paths and time requirements of components in multi-level AJSPs will also exhibit high variability, often manifesting as severe pre-assembly waiting problems in real-world production.

[0003] Current research on AJSP (Automatic Job Launcher) problems mainly focuses on mathematical modeling and metaheuristic algorithm optimization. Common modeling methods optimize the machining and assembly of workpieces simultaneously. Generally, the optimization objective is the maximum completion time, constructing AJSP solution models for single and multi-product tasks, and solving them using feasible domain-based genetic algorithms. Alternatively, a genetic algorithm based on Virtual Component-Level Partition Coding (VCLDC) can be used. This algorithm can generate feasible chromosomes without adding additional constraints, expanding the search range of the solution space.

[0004] In summary, significant progress has been made in the research of the Assembly Job Shop (AJSP) problem. However, there is a lack of research on machine constraints in the assembly process within the model, and how to reduce the destructive impact of operators on the solution in the algorithm flow. To achieve collaborative optimization of machining and assembly in enterprises, there is an urgent need for a new and efficient assembly job shop optimization algorithm to solve practical production problems. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides an assembly workshop scheduling method and system based on whole block right shift repair coding, the purpose of which is to solve the problem of processing and assembly collaboration optimization in the assembly workshop.

[0006] To achieve the above objectives, according to a first aspect of the present invention, an assembly workshop scheduling method based on whole-block right-shift repair coding is proposed, comprising the following steps:

[0007] Considering the machine constraints of the assembly process, a production scheduling model for the assembly workshop is constructed; the production scheduling model is iteratively solved using a metaheuristic algorithm to obtain the scheduling method for the assembly workshop.

[0008] During iterative solution, machining and assembly processes are combined and encoded into chromosomes, with one chromosome corresponding to one solution. For each iteration's intermediate solution, a block-based right-shift repair operator is executed, which includes the following steps:

[0009] S11: Starting from the left end, search for genes on the chromosome. If the gene is a machining process, skip the gene directly. If the gene is an assembly process, mark its position on the chromosome as Ad1. Then, start the second search from the left end of the chromosome again to find the largest position among all processes under the assembly process, and mark it as Ad2.

[0010] S12: Treat the chromosome segment between positions Ad1+1 and Ad2 as a whole P, and then shift the gene at position Ad1 to the right of chromosome segment P;

[0011] S13: Starting from the current Ad1 position, repeat steps S11 and S12 until the entire chromosome has been searched and the repaired chromosome is obtained.

[0012] As a further preferred embodiment, a mutation operator is also performed on the intermediate solutions generated in each iteration, which includes the following steps:

[0013] S21: Randomly select a gene at a location marked as g, and delete the gene g from the chromosome;

[0014] S22: Based on gene g, define the range of insertable blocks from the chromosome; the method for determining the insertable blocks is as follows:

[0015] Let the range of insertable blocks be Ad3 to Ad4, and the set of positions of the subordinate processes of gene g be I. sub The set of positions of the upper-level processes of gene g is I. ab If gene g represents a machining process, then Ad3 is 1, and Ad4 is (I). ab )min-1; If gene g is the assembly process, then Ad3 is (I sub )max+1, Ad4 is determined to be (I ab )min-1;(I sub max represents set I sub The maximum position of the intermediate process, (I) ab min represents set I ab The smallest position in the intermediate process;

[0016] S23: Randomly insert gene g at any position in the insertable block.

[0017] As a further preferred embodiment, the objective function in the production scheduling model is: minimizing the maximum completion time.

[0018] As a further optimization, the production scheduling model is solved iteratively using a genetic algorithm.

[0019] As a further preferred approach, the production scheduling model is iteratively solved using a genetic algorithm, including the following steps:

[0020] S31: Use a random initialization strategy to generate the initial population;

[0021] S32: Perform the block-based right shift repair operator on individuals in the initial population;

[0022] S33: Calculate the fitness of individuals in the population, and select individuals in the population according to the selection strategy to generate a new population;

[0023] S34: Perform crossover between chromosomes of individuals in the population;

[0024] S35: Perform a block-based right shift repair operator on individuals in the population;

[0025] S36: Perform mutation operator on individuals in the population;

[0026] S37: When the set maximum number of iterations or other termination conditions are met, stop the iteration and output the individual with the highest fitness in the population at this time as the optimal scheduling method; otherwise, return to step S33.

[0027] As a further preferred option, the selection strategy is an elite retention strategy and a tournament selection strategy.

[0028] According to a second aspect of the present invention, an assembly workshop scheduling system based on whole-block right-shift repair coding is provided, including a processor, the processor being used to execute the above-described assembly workshop scheduling method based on whole-block right-shift repair coding.

[0029] According to a third aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described assembly workshop scheduling method based on block right shift repair coding.

[0030] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0031] 1. This invention considers the machine constraints of the assembly process and designs an encoding method based on whole-block right shift. This encoding method can not only satisfy the complex assembly constraints of the product and ensure the feasibility of chromosomes, but also ensure that the relative order of the underlying machining processes does not change during the repair process. While satisfying feasibility, it minimizes the destruction of the initial solution, thereby achieving more efficient exploration of the solution space.

[0032] 2. This invention addresses the problem of infeasible solutions arising from mutations by designing a novel block-based insertion mutation operation, which prevents the algorithm from encountering infeasible solutions and improves the algorithm's search efficiency.

[0033] 3. This invention can provide a high-quality production scheduling solution for enterprise machining-assembly production environments, combining the advantages of flexibility and economy, and also making it convenient for enterprises to change the scheduling solution according to actual needs; it can improve production stability and efficiency, reduce product manufacturing cycle, and improve economic benefits. Attached Figure Description

[0034] Figure 1 This is a schematic diagram illustrating the process of solving the production scheduling model using a genetic algorithm according to an embodiment of the present invention;

[0035] Figure 2 Images (a) and (b) are schematic diagrams of the product structure and corresponding coded chromosomes in embodiments of the present invention.

[0036] Figure 3 This is a schematic diagram of the operation based on the whole-block right shift repair operator in an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram illustrating the theoretical advantages of the block-based right-shift repair operator in an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the mutation operator operation in an embodiment of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0040] An assembly workshop scheduling method based on whole-block right-shift repair coding provided by an embodiment of the present invention includes the following steps:

[0041] Step S1: Set preset conditions, basic parameters and constraints for the target assembly workshop, and set an optimization objective function based on minimizing the maximum completion time to construct a production scheduling model for the assembly workshop.

[0042] To effectively describe the scheduling problem, the preset conditions set in this embodiment include:

[0043] 1) At time t=0, every workpiece and device is available.

[0044] 2) Each machine can only process one workpiece or perform one assembly operation at a fixed time, and each workpiece can only be processed or assembled on one machine at a fixed time.

[0045] 3) The time for workpiece assembly, unloading, and transportation is included in the processing time.

[0046] 4) The equipment must not be interrupted during the fixed processing or assembly time.

[0047] 5) The equipment can operate continuously and has an infinite buffer.

[0048] 6) The basic parameters to be set include:

[0049] n: Total number of workpieces

[0050] m: Total number of devices

[0051] q: Total number of assembly operations

[0052] O ij The j-th process of workpiece i

[0053] J i Total number of processes for workpiece i

[0054] A ij The j-th process in assembly operation i

[0055] AJ i Total number of processes in assembly operation i

[0056] s ijk Process O ij (i=1,2,...,n; j=1,2,...,J i The start time of processing on machine k (k = 1, 2, ..., m)

[0057] c ijk Process O ij Completion time on machine k

[0058] t ijk Process O ij Processing time on machine k

[0059] s Aijk Assembly process A ij (i=1,2,...,q; j=1,2,...,AJ i The start processing time of machine k (k = 1, 2, ..., m)

[0060] c Aijk Assembly process A ij The completion time of machine k (k = 1, 2, ..., m)

[0061] t Aijk Assembly process A ij The processing time of machine k (k=1,2,...,m)

[0062] sub Ai Assembly Operation A i The set of subordinate workpieces and assembly operations

[0063] M: an infinitely large positive number

[0064]

[0065]

[0066]

[0067]

[0068] The constraints are set as follows:

[0069] s ijk +t ijk =c ijk (1)

[0070] s ijk +M(1-a ijhk )≥c ijh (2)

[0071] c pqk -c ijk +M(1-x ijpqk )≥t pqk (3)

[0072] s ijk ≥0 (4)

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Equation (1) indicates that the processing of a process cannot be interrupted; Equation (2) indicates the sequential constraint of different processes on the same workpiece; Equation (3) indicates the sequential constraint of processes on different workpieces on the same machine. Equation (4) indicates that the start time of all workpieces must be greater than or equal to 0; Equation (5) indicates that the assembly process cannot be interrupted once it starts; Equations (6) and (7) consider the constraints between the assembly operation and its subordinate processes, indicating that the start time of the assembly process must be greater than the processing time of the preceding workpiece and the assembly time of the preceding assembly. Equation (8) indicates the sequential constraint of different assembly processes in the same assembly operation; Equation (9) is the machine constraint of the assembly process, indicating the sequential constraint of different assembly processes on the same machine.

[0079] The objective function is to minimize the maximum completion time, specifically expressed as:

[0080] C max =min{max{c Aijk}}

[0081] Step S2: Perform integer coding operations on all processing and assembly processes in the entire production plan.

[0082] Specifically, considering the characteristics of the constructed production scheduling model, an integer encoding method was adopted that combines the encoding of the underlying machining processes and the upper-level assembly processes. For ease of understanding, an example is provided, such as... Figure 2 As shown in (a), it includes the bottom layer 1, 2, 3, and the top layer 4, 5, 6; workpiece 1 has 3 machining processes 1-1, 1-2, 1-3, workpiece 2 has 3 machining processes 2-1, 2-2, 2-3, and workpiece 3 has 3 machining processes 3-1, 3-2, 3-3; 1 and 2 require assembly operation 4, which includes assembly processes 4-1 and 4-2; 3 requires assembly operation 5, which includes assembly processes 5-1 and 5-2; finally, assembly operation 6 includes assembly processes 6-1 and 6-2. Figure 2 As shown in (b), this is the encoded chromosome. The number of times the process number appears in the code indicates which machining process or assembly process it is. For example, the second appearance of the number 3 indicates machining process 3-2, and the first appearance of the number 6 indicates assembly process 6-1.

[0083] During decoding, each number is read from left to right. The order in which the same number appears is the processing order of that step. In order to obtain a feasible scheduling scheme, the decoding in this embodiment adopts a left-shift strategy, that is, to arrange the steps in the chromosome from left to right, so that the steps are arranged as early as possible while satisfying various constraints.

[0084] Step S3: Solve the production scheduling model using a metaheuristic algorithm to obtain the assembly workshop scheduling method.

[0085] In this embodiment, a genetic algorithm is used to solve the problem, such as... Figure 1 As shown, it includes the following steps:

[0086] Step S31: Generate an initial population using a random initialization strategy;

[0087] There are four main parameters that affect the genetic algorithm: population size C, maximum number of iterations N, crossover rate R1, and mutation rate R2. The optimal algorithm parameters—population size C, maximum number of iterations N, crossover rate R1, and mutation rate R2—can be determined through experimental testing.

[0088] Step S32: Execute the block-based right shift repair operator to ensure the feasibility of individual solutions;

[0089] Due to the assembly constraints between problematic workpieces in the assembly workshop, randomly generated chromosomes may produce infeasible solutions during the decoding process. For example, according to Figure 2 When the chromosome with the product structure diagram encoded is decoded from left to right, assembly operation 4 will be decoded first. At this time, its subordinate workpieces 1 and 2 have not been processed yet, which will result in an infeasible solution. In order to maintain the feasibility of the chromosome, a right shift repair operator based on the whole block is introduced to repair the chromosome.

[0090] Specifically, such as Figure 3 As shown, the block-based right-shift repair operator includes steps S11 to S13:

[0091] S11: Search for genes on the chromosome starting from the left end. If it is a machining process of the bottom node, skip it directly. If it is an assembly process, mark its position in the chromosome as Ad1. Then, perform a second search from the left end to find the largest position among all processes under this assembly process, and record it as Ad2.

[0092] S12: Treat the chromosome segment between Ad1+1 and Ad2 as a whole P, and then shift the gene base at position Ad1 to the right relative to chromosome segment P. The chromosome after the shift is used to repair the Ad1 gene.

[0093] S13: Continue searching from Ad1, repeating steps S11 and S12 until the entire chromosome has been searched, and the repaired chromosome will be obtained.

[0094] After applying the right-shift repair operator, the chromosome encoding will no longer generate assembly constraint conflicts. At the same time, this repair operator does not disrupt the relative order between machining operations, greatly reducing the destructive impact of the repair operator on the initial solution, and maintaining the diversity of the initial population while repairing.

[0095] Specifically, the reason why the right-shift repair operator will not disrupt the machining process is as follows:

[0096] During right shift repair, the chromosome can be considered to be divided into four segments: chromosome segment O1, assembly process A, chromosome segment P, and chromosome segment O2, as shown below. Figure 4 As shown. Assembly step A is a rightward shift based on fragment P. Since the rightward shift only occurs between A and P, the gene positions in O1 and O2 remain unchanged, therefore the relative order of the underlying processes in O1 and O2 remains unchanged. For fragment P, it is "leftward shifted" relative to A. Since A only contains one assembly step and not the underlying processes, we only need to focus on the relative positions of O1, O2, and P. Figure 4 It can be seen that the relative positions of O1, O2 and P did not change before and after the right shift operation. P was always before O1 and after O2. Therefore, the relative order of the underlying processes in O1, P and O2 did not change. This proves that encoding based on the whole block right shift will not change the relative order of the underlying processes of the chromosome.

[0097] Step S33: Calculate the fitness of the population and select from the population according to the selection strategy to generate a new population;

[0098] The preferred selection strategies are elite retention and tournament selection. First, the top 10% of fittest individuals in the population are directly retained in the next population. Then, a tournament selection strategy is used for the remaining individuals. Each time, a certain number of individuals are removed from the original population (sampling with replacement), and the best one is selected to enter the offspring population. This process is repeated until the new population size reaches the original population size.

[0099] Step S34: Perform crossover between chromosomes of individuals in the population;

[0100] Step S35: Execute the block-based right shift repair operator to ensure the feasibility of individual solutions after the crossover;

[0101] Step S36: Execute the mutation operator;

[0102] Specifically, such as Figure 5 As shown, the operation of the mutation operator includes steps S21 to S23:

[0103] S21: Randomly select a gene at a location marked as g, and delete the gene g from the chromosome.

[0104] S22: Based on gene g, define the range of insertable blocks from the chromosome; the method for determining insertable blocks is as follows:

[0105] Let the range of insertable blocks be Ad3 to Ad4, and the set of positions of the subordinate processes of gene g be I. sub (I of the underlying process) sub (I is an empty set), and the set of positions of the upper-level processes is I. ab If gene g represents the underlying machining process, Ad3 is 1, and Ad4 is (I). ab If it is an assembly process, then Ad3 is determined as (I min-1); sub )max+1, Ad4 is determined to be (I ab min-1 (for the topmost root node Ad4, this represents the chromosome length). For example, ... Figure 2 and Figure 5 As shown, the selected 4 is the assembly process, its subordinate processes are 1 and 2, and its upper-level process is 6. Therefore, Ad3 is to the right of the last occurrence position of 1 and 2 in the chromosome, and Ad4 is to the left of the earliest occurrence position of 6 in the chromosome.

[0106] S23: Randomly insert gene g at any position in the insertable block.

[0107] Step S37: When the set maximum number of iterations or other termination conditions are met, stop the iteration and output the optimal solution; otherwise, return to step S33.

[0108] Specifically, the selection strategy of the genetic algorithm ensures that individuals with high fitness are continuously retained. At the same time, due to the operation of crossover and mutation operators, the population is prevented from converging towards dominant individuals too early, thereby increasing the global search capability of the algorithm to a certain extent.

[0109] The following are specific examples:

[0110] In a certain scheduling task, there are 15 workpieces, 5 processing machines, 10 assembly operations, and 5 assembly machines. The equipment numbers and processing times corresponding to the workpiece processing steps are shown in Table 1, and the equipment numbers and processing times corresponding to the assembly steps of the assembly operations are shown in Table 1.

[0111] Table 1. Equipment Numbers and Processing Times Corresponding to Workpiece Machining Processes

[0112]

[0113] Table 2. Equipment Numbers and Processing Times Corresponding Assembly Processes for Assembly Operations

[0114]

[0115] The genetic algorithm based on whole-block right-shift repair proposed in this invention is compared with genetic algorithms based on virtual component partitioning, process chain constraint encoding, and feasible region repair. To ensure algorithm fairness, the parameters are uniformly set as follows: population size is set to 1000, mutation rate is set to 0.1, crossover rate is set to 0.8, and maximum number of iterations is set to 100. Each algorithm is run independently 10 times, and the comparison index is the minimum and average values ​​of the 10 runs. The algorithm results are shown in Table 3.

[0116] Table 3 Algorithm Execution Results

[0117]

[0118] As can be seen from Table 3, the algorithm proposed in this invention performs better than the other three algorithms, proving its rationality and effectiveness in solving such problems in assembly workshops.

[0119] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for scheduling assembly line operations based on whole-block right-shift repair coding, characterized in that, Includes the following steps: Considering the machine constraints of the assembly process, a production scheduling model for the assembly workshop is constructed; the production scheduling model is iteratively solved using a metaheuristic algorithm to obtain the scheduling method for the assembly workshop. During iterative solution, machining and assembly processes are combined and encoded into chromosomes, with one chromosome corresponding to one solution. For each iteration's intermediate solution, a block-based right-shift repair operator is executed, which includes the following steps: S11: Starting from the left end, search for genes on the chromosome. If the gene is a machining process, skip it; if the gene is an assembly process, mark its position on the chromosome. Ad 1. Then, starting from the left end of the chromosome, perform a second search to find the maximum position among all processes under this assembly process, denoted as . Ad 2; S12: Position Ad 1+1 to Ad The chromosome segment between 2 is treated as a whole P, and then... Ad The gene at position 1 shifts to the right of chromosome segment P; S13: Based on the current situation Ad Starting from position 1, repeat steps S11 and S12 until the entire chromosome has been searched and the repaired chromosome is obtained.

2. The assembly workshop scheduling method based on whole-block right-shift repair coding as described in claim 1, characterized in that, The intermediate solutions generated in each iteration are also subjected to a mutation operator, which includes the following steps: S21: Randomly select a gene at a location marked as g, and delete the gene g from the chromosome; S22: Based on gene g, define the range of insertable blocks from the chromosome; the method for determining the insertable blocks is as follows: Let the range of insertable blocks be... Ad 3 to Ad 4. The set of positions of the subordinate processes of gene g is: I sub The set of positions of the upper-level processes of gene g is I ab If gene g is a machining process, then Ad 3 is 1. Ad 4 is ( I ab )min-1; If gene g is an assembly process, then Ad 3 is ( I sub max+1, Ad 4 is determined to be ( I ab )min-1; I sub max represents the set I sub The maximum position of the intermediate process, ( I ab min represents the set I ab The smallest position in the intermediate process; S23: Randomly insert gene g at any position in the insertable block.

3. The assembly workshop scheduling method based on whole-block right-shift repair coding as described in claim 1, characterized in that, In the production scheduling model, the objective function is to minimize the maximum completion time.

4. The assembly workshop scheduling method based on whole-block right-shift repair coding as described in claim 2, characterized in that, The production scheduling model is solved iteratively using a genetic algorithm.

5. The assembly workshop scheduling method based on whole-block right-shift repair coding as described in claim 4, characterized in that, The production scheduling model is solved iteratively using a genetic algorithm, including the following steps: S31: Use a random initialization strategy to generate the initial population; S32: Perform the block-based right shift repair operator on individuals in the initial population; S33: Calculate the fitness of individuals in the population, and select individuals in the population according to the selection strategy to generate a new population; S34: Perform crossover between chromosomes of individuals in the population; S35: Perform a block-based right shift repair operator on individuals in the population; S36: Perform mutation operator on individuals in the population; S37: When the set maximum number of iterations or other termination conditions are met, stop the iteration and output the individual with the highest fitness in the population at this time as the optimal scheduling method; otherwise, return to step S33.

6. The assembly workshop scheduling method based on whole-block right-shift repair coding as described in claim 5, characterized in that, The selection strategies are the elite retention strategy and the tournament selection strategy.

7. An assembly workshop scheduling system based on whole-block right-shift repair coding, characterized in that, Includes a processor for executing the assembly shop scheduling method based on block right shift repair coding as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the assembly workshop scheduling method based on block right shift repair coding as described in any one of claims 1-6.

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