An optimization method for solving the group scheduling of distributed heterogeneous flow shops

Abstract

The present invention relates to the technical field of intelligent manufacturing workshops, in particular to an optimization method for solving the group scheduling of distributed heterogeneous flow shops, including determining the problem-solving goal of minimizing the product assembly completion time and initializing parameters; initializing the solution; generating probability random numbers, and judging whether to select to perform product and group operations or product and workpiece operations; updating the best solution, and judging whether the termination time is reached. If satisfied, the iteration ends and the current best solution is output. The application of the present invention can effectively solve the group scheduling problem of distributed heterogeneous flow shops with a product assembly stage, and improve the production efficiency of manufacturing enterprises through optimized scheduling.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed heterogeneous flow shop group scheduling in an intelligent manufacturing workshop, and particularly belongs to an optimization method for solving distributed heterogeneous flow shop group scheduling. Background Art

[0002] With the acceleration of global economic integration and the intensification of competition among enterprises, in order to make full use of resources in different regions, multi-factory cooperation or distributed scheduling schemes have gradually become active in most industrial operations. Compared with traditional flow shop scheduling, this mechanism can make full use of factory resources in different regions, shorten the production cycle, reduce logistics costs, and use intelligent technologies to quickly achieve reasonable resource allocation, optimize the efficiency of the entire supply chain system, and reduce the degree of regional isomorphism. Therefore, the distributed flow shop scheduling problem (DFSP) in a distributed manufacturing environment has been widely studied. With the continuous optimization of production lines, in the production activities in some fields, work should be processed in different groups, such as the semiconductor industry, the automotive industry, printed circuit boards (PCBs), or the electronics manufacturing industry. The grouping technology realizes grouping workpieces with similar processing attributes into the same group for processing, which not only improves the flexibility of the production system but also reduces production costs. The distributed flow shop scheduling problem with grouping constraints is called the distributed flow shop group scheduling problem (DFGSP). Currently, the research on DFGSP is mainly based on the assumption that all factories are the same. However, in the actual production process, distributed production factories are not always the same. Due to reasons such as supply chain and procurement strategies, machine brands, and wear, there are differences in the processing capabilities of machines in different factories, that is, the factories are heterogeneous. In addition, many manufacturing enterprises, such as automotive, furniture, and clothing, have processing and assembly production, that is, after the parts are processed in distributed factories, they need to be assembled into products. In this mode, the types of parts are diverse, the cooperation relationships between processes are extremely complex, and the production is difficult. Therefore, in the actual situation considering multi-factory cooperation, it is of great significance for enterprises and researchers to study an effective method to solve the distributed heterogeneous flow shop group scheduling problem with an assembly stage. Summary of the Invention

[0003] The purpose of the present invention is to provide an optimization method for solving distributed heterogeneous flow shop group scheduling, which solves the problem that the product assembly stage is not considered in the current distributed flow shop group scheduling problem.

[0004] An optimization method for solving distributed heterogeneous flow shop group scheduling provided by the present invention is characterized by including the following steps.

[0005] Step 1: Analyze the problem characteristics of the distributed heterogeneous flow shop group scheduling problem, determine the problem-solving objective of minimizing the assembly completion time, and initialize the parameters, including the probability selection parameter , the temperature coefficient , the product damage size , where the above-mentioned assembly completion time is the time when all products are assembled;

[0006] Step 2: Initialize the solution, design a heuristic method to generate the initial solution, and use it as the optimal solution;

[0007] Step 3: Generate a probability random number ;

[0008] Step 4: , perform product and group operations, including product and group damage reconstruction, group local search, product local search, and accept the new solution using the simulated annealing acceptance criterion; , perform product and workpiece operations, including workpiece damage reconstruction, workpiece local search, and product local search;

[0009] Step 5: Update the best solution, determine whether the termination time is reached. If it is satisfied, end the iteration and output the current best solution. Otherwise, return to Step 3.

[0010] Furthermore, in Step 2, a complete solution is defined as , where , represents the processing sequence of groups in each factory, represents a factory index, is the number of factories, represents the factory the processing sequence of groups in it, , represents the factory a group in it, represents the factory the number of processing groups in it, represents the factory the th group processed in it; , represents the processing sequence of workpieces within each group, represents a group, represents the number of groups, represents the processing sequence of workpieces included in group k, represents the group the number of workpieces in it, represents the group the th workpiece in it; , represents the assembly sequence of products.

[0011] Furthermore, in step 2, the designed heuristic method is as follows:

[0012] (1) For each factory, generate an initial group sequence containing all groups and determine the processing order of the workpieces within the groups. Among them, the workpieces within the groups are sorted using the longest processing time method. The longest processing time method is described as calculating the processing time of each workpiece in the current factory and then sorting them in descending order; the group sequence is generated using the key group method. The key group method is described as finding the group with the longest processing time as the key group, and inserting the groups with processing times less than the key group in ascending order of processing time before the key group, and inserting the remaining groups in descending order of processing time after the key group;

[0013] (2) Generate an initial product assembly sequence sorted in descending order of product assembly time;

[0014] (3) Set the processing sequences of the groups in all factories to be empty;

[0015] (4) Insert the first group of all initial group sequences into all processing positions of all factories, retain the insertion that produces the minimum completion time, and delete this inserted group from all initial group sequences; repeat the above process until the initial group sequences are empty. The above completion time refers to the maximum value of the completion times of all factories;

[0016] (5) Take out the products in the initial product assembly sequence in turn and insert them into the position that minimizes the assembly completion time.

[0017] Furthermore, in step 4, the destruction and reconstruction rules for products and groups are as follows: randomly select a number of products and randomly select half of the workpieces among these products; determine the groups to which these workpieces belong and extract them from the factory processing sequences of the current solution; insert the extracted groups into the position that minimizes the assembly completion time in turn.

[0018] Furthermore, in step 4, in the local search stage of the groups, design a variable neighborhood descent strategy including 2 group neighborhood search operators to optimize the solution. Among them, the group neighborhood search operators include

[0019] Insertion of the group where the last workpiece is located. Determine the last processed workpiece in each product during the assembly stage; extract the groups where these workpieces are located from the factory processing sequences; insert the extracted groups into the position that minimizes the assembly completion time in turn;

[0020] Insertion of the key factory groups. Extract each group in the key factory in turn and insert it into the position that minimizes the assembly completion time.

[0021] Further, in step 4, during the local search phase of the product, one insertion neighborhood search operator is used to optimize the solution. Each product in the assembly sequence is sequentially extracted and inserted into the position that minimizes the assembly completion time.

[0022] Further, in step 4, the simulated annealing acceptance criterion is described as follows: the new solution is better than the current solution or the random number is less than when the new solution is accepted. Among them, the temperature involved in the simulated annealing acceptance criterion is expressed as

[0023]

[0024] where the temperature coefficient is an algorithm control parameter, is the number of factories, is the number of workpieces, is the number of machines, represents the workpiece in the factory on the machine processing time, represents the objective value of the current solution, represents the objective value of the new solution.

[0025] Further, in step 4, the disruption and reconstruction rule of the workpiece is as follows: extract half of the workpieces in all groups in the key factory and insert them into the position that minimizes the assembly completion time in their respective groups.

[0026] Further, in step 4, during the local search phase of the workpiece, a variable neighborhood descent strategy including two workpiece neighborhood search operators is designed to optimize the solution. Among them, the workpiece neighborhood search operators include

[0027] Insertion of the last workpiece: Determine the last workpiece to be processed in each product during the assembly phase; extract these workpieces from the factory processing sequence; sequentially insert the extracted workpieces into the position in their respective groups that minimizes the assembly completion time;

[0028] Insertion referring to the optimal solution sequence: The workpiece sequence in the current best solution is used as the reference sequence. Each workpiece in each group in the key factory is sequentially extracted according to the order of the reference sequence and inserted into the position in their respective groups that minimizes the assembly completion time.

[0029] Further, in step 4, the variable neighborhood descent strategy is as follows: take the first neighborhood structure as the current neighborhood structure. If a new solution better than the original solution is obtained by searching using the current neighborhood structure, update the original solution; if no solution better than the original solution is obtained, take the next neighborhood structure as the current neighborhood structure, otherwise continue to use the current neighborhood structure and repeat the above process. When all neighborhood structures cannot update the current solution, the local search process ends. The execution order of the two group neighborhood search operators included in the variable neighborhood descent strategy for groups is the insertion of the group where the last workpiece is located and the insertion of the key factory group. The execution order of the two workpiece neighborhood search operators included in the variable neighborhood descent strategy for workpieces is the insertion of the last workpiece and the insertion of the reference optimal solution sequence.

[0030] Among them, in the variable neighborhood descent strategy for groups, each time a group neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, execute a product insertion neighborhood search operator to optimize the solution. In the variable neighborhood descent strategy for workpieces, each time a workpiece neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, execute a product insertion neighborhood search operator to optimize the solution.

[0031] Further, in step 5, the termination time is set to , that is, the longest operation time is milliseconds, where represents the number of groups in the current instance, represents the number of machines in the current instance.

[0032] An optimization method for solving the group scheduling of distributed heterogeneous flow shops provided by the present invention is more in line with the actual production scenarios of some enterprises in reality. According to the problem characteristics and scale, the present invention proposes an improved iterative greedy algorithm to obtain high-quality solutions. Compared with some existing algorithms, the present invention solves the cooperation mechanism of two sub-problems in the group scheduling problem of distributed heterogeneous flow shops, and uses a probability selection method to select the next product-group operation or product-workpiece operation. In addition, the present invention utilizes the product assembly characteristics and adopts an effective method for processing groups and workpieces to further improve the quality of the solution. In summary, the present invention has the positive effect of reducing the product assembly completion time. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the implementation flowchart of the present invention;

[0034] Figure 2 is the convergence graph of the assembly completion time of the present invention;

[0035] Figure 3 is the average scatter plot of the present invention compared with existing algorithms. Detailed implementation manners

[0036] As Figure 1 shown, an optimization method for solving the group scheduling of a distributed heterogeneous flow shop is mainly implemented through the following steps.

[0037] Step 1: Analyze the problem characteristics of the distributed heterogeneous flow shop group scheduling problem, determine the problem-solving goal of minimizing the assembly completion time, and initialize the parameters, including the probability selection parameter , the temperature coefficient , the product damage size , where the above-mentioned assembly completion time is the time when all products are assembled.

[0038] Step 2: Initialize the solution, which involves generating an initial solution using a heuristic method and taking it as the optimal solution.

[0039] Specifically, a complete solution is defined as , where represents the processing sequence of the group in each factory, represents a factory index, is the number of factories, represents the processing sequence of the group in factory , , represents a group in factory , represents a factory the number of processing groups in, represents the factory the th group processed in; , represents the processing sequence of the workpieces within each group, represents a group, represents the number of groups, represents the processing sequence of the workpieces included in group k, represents the group the number of workpieces in, represents the group the th workpiece in; , represents the assembly sequence of the products.

[0040] The steps of the designed heuristic method are as follows,

[0041] (1) For each factory, generate an initial group sequence that includes all groups and determine the processing order of the workpieces within the groups. The workpieces within the groups are sorted using the maximum processing time method, which is described as calculating the processing time of each workpiece in the current factory and then sorting them in descending order. The group sequence is generated using the critical group method, which is described as finding the group with the longest processing time as the critical group, inserting the groups with processing times less than the critical group in ascending order of processing time before the critical group, and inserting the remaining groups in descending order of processing time after the critical group.

[0042] (2) Generate an initial product assembly sequence sorted in descending order of product assembly time.

[0043] (3) Set the processing sequences of the groups in all factories to be empty.

[0044] (4) Insert the first group of all initial group sequences into all processing positions in all factories, retain the insertion that results in the minimum completion time, and delete this inserted group from all initial group sequences. Repeat the above process until the initial group sequences are empty. The above completion time refers to the maximum value of the completion times of all factories.

[0045] (5) Take out the products in the initial product assembly sequence in turn and insert them into the position that results in the minimum assembly completion time.

[0046] Step 3, generate a probability random number .

[0047] Step 4, , perform product and group operations, including product and group destruction and reconstruction, local search of groups, local search of products, and accepting new solutions using the simulated annealing acceptance criterion. , perform product and workpiece operations, including workpiece destruction and reconstruction, local search of workpieces, and local search of products.

[0048] Specifically, the product and group destruction and reconstruction rule is to randomly select products and randomly select half of the workpieces in these d products; determine the groups to which these workpieces belong and extract them from the factory processing sequences in the current solution; insert the extracted groups into the position that results in the minimum assembly completion time in turn.

[0049] In the local search stage of the groups, design a variable neighborhood descent strategy that includes 2 group neighborhood search operators to optimize the solution. Among them, the group neighborhood search operators include,

[0050] Insertion of the group where the last workpiece is located. Determine the last workpiece processed in each product during the assembly stage; extract the groups to which these workpieces belong from the factory processing sequences; insert the extracted groups into the position that results in the minimum assembly completion time in turn.

[0051] Insertion of the key factory groups, extracting each group in the key factories in turn and inserting it at the position that minimizes the assembly completion time.

[0052] In the local search stage of the product, a solution is optimized using one insertion neighborhood search operator. Each product in the assembly sequence is extracted in turn and inserted at the position that minimizes the assembly completion time.

[0053] The simulated annealing acceptance criterion is described as: the new solution is better than the current solution or the random number is less than then the new solution is accepted, where the temperature involved in the simulated annealing acceptance criterion is expressed as

[0054]

[0055] where the temperature coefficient is an algorithm control parameter, is the number of factories, is the number of workpieces, is the number of machines, represents the workpiece in the factory on the machine processing time, represents the objective value of the current solution, represents the objective value of the new solution.

[0056] The destruction and reconstruction rule of the workpiece is: extract half of the workpieces in all groups in the key factories and insert them respectively at the position that minimizes the assembly completion time in their own groups.

[0057] In the local search stage of the workpiece, a variable neighborhood descent strategy including two workpiece neighborhood search operators is designed to optimize the solution. Among them, the workpiece neighborhood search operators include

[0058] Insertion of the last workpiece, determining the last workpiece to be processed in each product during the assembly stage; extracting these workpieces from the factory processing sequence; inserting the extracted workpieces in turn into their own groups at the position that minimizes the assembly completion time;

[0059] Insertion referring to the optimal solution sequence, the workpiece sequence in the current best solution is used as the reference sequence, and each workpiece in each group in the key factories is extracted in the order of the reference sequence and inserted into its own group at the position that minimizes the assembly completion time.

[0060] The variable neighborhood descent strategy is as follows: take the first neighborhood structure as the current neighborhood structure. If a new solution better than the original solution is obtained by searching using the current neighborhood structure, then update the original solution; if no solution better than the original solution is obtained, then take the next neighborhood structure as the current neighborhood structure, otherwise continue to use the current neighborhood structure and repeat the above process. When all neighborhood structures cannot update the current solution, the local search process ends. The execution order of the two group neighborhood search operators included in the variable neighborhood descent strategy for groups is: insertion of the group where the last workpiece is located, insertion of the key factory group. The execution order of the two workpiece neighborhood search operators included in the variable neighborhood descent strategy for workpieces is: insertion of the last workpiece, insertion of the reference optimal solution sequence.

[0061] Among them, in the variable neighborhood descent strategy for groups, each time a group neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, then execute the product insertion neighborhood search operator once to optimize the solution; in the variable neighborhood descent strategy for workpieces, each time a workpiece neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, then execute the product insertion neighborhood search operator once to optimize the solution.

[0062] Step 5, update the best solution, and determine whether the termination time is reached. If it is satisfied, end the iteration and output the current best solution, otherwise return to Step 3.

[0063] Specifically, the termination time is fixed at , that is, the longest evolution time is limited to milliseconds, where represents the number of groups included in the current instance, represents the number of machines included in the current instance.

[0064] To better prove the effectiveness of the present invention, the following will further describe and explain the present invention through experimental analysis of a series of examples of the present invention.

[0065] The test data includes 540 instances, which are created based on the number of factories , the number of groups , the number of machines , the number of products . , , , , and the workpiece processing time is uniformly distributed within the range of , and the assembly completion time of the product is uniformly distributed within the range of .

[0066] The CPU time is used as the termination time of the comparison algorithm, and the termination time is set to milliseconds, where represents the number of groups in the current example, and represents the number of machines in the current example.

[0067] In terms of algorithm parameters, in order to better solve and optimize the distributed heterogeneous flow shop scheduling problem, the probability selection parameter is set to = 0.7, the temperature coefficient is set to = 1.4, and the product damage size is set to = 0.4.

[0068] As Figure 2 and Figure 3 shown, the uIG algorithm of the present invention is experimentally compared with three improved iterative greedy algorithms: the two-stage iterative greedy algorithm TIG, the effective two-stage iterative greedy algorithm tIG, and the iterative greedy algorithm IGP with job acceleration. In order to make these algorithms adapt to the problems to be solved, necessary modifications are required, including using unified instances and following the details of their respective original algorithms during the adaptive process. Each example is executed 10 times repeatedly to generate statistical results. The present invention uses the Relative percentage increase (RPI) as the performance evaluation index, and the calculation formula of RPI is RPI = (C - C best ) / C best * 100%, where C represents the product assembly completion time obtained when a specific algorithm solves the example, and C best represents the optimal product assembly completion time obtained by all algorithms in all runs. Obviously, the smaller the RPI value, the better the algorithm performance.

[0069] In summary, the application of the present invention effectively reduces the product assembly completion time, successfully solves the group scheduling problem of the distributed heterogeneous flow shop, thereby greatly improving the production efficiency of the factory and providing strong support for the optimal scheduling in the actual production scenario.

Claims

1. An optimization method for solving distributed heterogeneous flow shop group scheduling, characterized in that: The following steps are included: Step 1: Analyze the characteristics of the distributed heterogeneous flow shop group scheduling problem, determine the problem-solving goal of minimizing the assembly completion time, and initialize the parameters, including the probability selection parameters. , Temperature coefficient , product damage size , where the above assembly completion time is the time when all products are assembled; Step 2, initialize the solution, design a heuristic method to generate an initial solution, and use it as the optimal solution; the heuristic method steps are: (1) For each factory, an initial group sequence containing all groups is generated and the processing order of the workpieces in the group is determined. The workpieces in the group are sorted using the maximum processing time method. The maximum processing time method is described as calculating the processing time of each workpiece in the current factory and then sorting them in descending order. The group sequence is generated using the key group method. The key group method is described as finding the group with the longest processing time as the key group. The groups with processing time less than the key group are inserted before the key group in ascending order of processing time, and the remaining groups are inserted after the key group in descending order of processing time. (2) Generate an initial product assembly sequence by sorting the products in descending order of assembly time; (3) Set the processing sequence of all groups in the factory to empty; (4) Insert the first group of all initial group sequences into all processing positions of all factories, retain the insertion that produces the minimum completion time, and delete this inserted group from all initial group sequences; repeat the above process until the initial group sequence is empty, and the above completion time refers to the maximum completion time of all factories; (5) taking out the products in the initial product assembly sequence one by one and inserting them into the position that minimizes the assembly completion time; Step 3: Generate a random number with probability ; Step 4, , perform product and group operations, including destructive reconstruction of products and groups, local search of groups, local search of products, and acceptance of new solutions using simulated annealing acceptance criteria; , perform product and workpiece operations, including destruction and reconstruction of workpieces, local search of workpieces, and local search of products; among them, In the local search phase of the group, a variable neighborhood descent strategy containing two group neighborhood search operators is designed to optimize the solution. The group neighborhood search operators include: Insertion of the last workpiece group, determine the last workpiece to be processed in each product during the assembly phase; extract the groups of these workpieces from the factory processing sequence; insert the extracted groups in turn to the position that minimizes the assembly completion time; Insertion of key factory groups, extracting each group in the key factory in turn and inserting it to the position that minimizes the assembly completion time; In the local search phase of the workpiece, a variable neighborhood descent strategy containing two workpiece neighborhood search operators is designed to optimize the solution. The workpiece neighborhood search operators include: Insertion of the last workpiece: determine the last workpiece to be processed in each product during the assembly phase; extract these workpieces from the factory processing sequence; insert the extracted workpieces into the group in sequence to the position that minimizes the assembly completion time; Referring to the insertion of the optimal solution sequence, the workpiece sequence in the current optimal solution is used as the reference sequence. Each workpiece in each group in the key factory is extracted in sequence according to the order of the reference sequence and inserted into the position in the group that minimizes the assembly completion time. The variable neighborhood descent strategy is to use the first neighborhood structure as the current neighborhood structure. If a new solution better than the original solution is obtained by searching with the current neighborhood structure, the original solution is updated; if no solution better than the original solution is obtained, the next neighborhood structure is used as the current neighborhood structure, otherwise the current neighborhood structure is continued to be used and the above process is repeated. When all neighborhood structures cannot update the current solution, the local search process ends; the execution order of the two group neighborhood search operators included in the variable neighborhood descent strategy for groups is the insertion of the group where the last workpiece is located and the insertion of the key factory group; the execution order of the two workpiece neighborhood search operators included in the variable neighborhood descent strategy for workpieces is the insertion of the last workpiece and the insertion of the reference optimal solution sequence; In the variable neighborhood descent strategy of the group, each time a group neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, the product insertion neighborhood search operator is executed once to optimize the solution; in the variable neighborhood descent strategy of the workpiece, each time a workpiece neighborhood search operator is used, it is necessary to determine whether the current solution is updated. If it is updated, the product insertion neighborhood search operator is executed once to optimize the solution; Step 5: Update the best solution and determine whether the termination time has been reached. If so, end the iteration and output the current best solution. Otherwise, return to step 3.

2. The optimization method for solving distributed heterogeneous flow shop group scheduling according to claim 1 is further characterized in that: In step 2, a complete solution is defined as ,in , represents the processing sequence of the group in each factory, Represents a factory index, is the number of factories, Indicates factory The processing sequence of the middle group, , Representative Factory A group in Representative Factory The number of processing groups, Representative Factory Processing groups; , represents the processing sequence of workpieces in each group, Represents a group, represents the number of groups, Representative Group The processing sequence of the workpieces included in Representative Group The number of workpieces in Representative Group The Workpieces; , representing the assembly sequence of the product.

3. The optimization method for solving distributed heterogeneous flow shop group scheduling according to claim 1 is further characterized in that: In step 4, the destruction and reconstruction rules of products and groups are: randomly selected products and randomly select this Half of the workpieces in a product; Determine the groups to which these workpieces belong and extract them from the factory processing sequence of the current solution; insert the extracted groups in sequence to the position that minimizes the assembly completion time.

4. The optimization method for solving distributed heterogeneous flow shop group scheduling according to claim 1 is further characterized in that: In step 4, during the local search phase of the product, an insertion neighborhood search operator is used to optimize the solution, extracting each product in the assembly sequence in turn and inserting it to the position that minimizes the assembly completion time.

5. The optimization method for solving distributed heterogeneous flow shop group scheduling according to claim 2 is further characterized in that: In step 4, the simulated annealing acceptance criterion is described as: the new solution is better than the current solution or the random number Less than When the new solution is accepted, the temperature involved in the simulated annealing acceptance criterion is It is expressed as, Among them, the temperature coefficient is the algorithm control parameter, is the number of factories, is the number of workpieces, is the number of machines, Representative workpiece In the factory Machine The processing time on represents the target value of the current solution, Represents the target value of the new solution.

6. The optimization method for solving distributed heterogeneous flow shop group scheduling according to claim 1 is further characterized in that: In step 4, the destruction and reconstruction rule of the artifacts is to extract half of the artifacts in all groups in the critical factory and insert them into the position in the group that minimizes the assembly completion time.

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