A Scheduling Method for Grouping in a Distributed Flow Shop with Setup Time

Abstract

The present invention relates to a scheduling method for grouping distributed flow shops with setup times, and the scheduling method comprises the following steps: Step 1: Construct a problem model with the objective of minimizing the makespan; Step 2: Parameter setting; Step 3: Initialization strategy; Step 4: Execute the first-stage search strategy; Step 5: First update the scheduling sequence, and determine whether the first-stage termination condition is satisfied. If it is satisfied, proceed to the next step; otherwise, continue to execute Step 4; Step 6: Execute the second-stage search strategy; Step 7: Second update the scheduling sequence, and determine whether the second-stage termination condition is satisfied. If it is satisfied, the evolution ends and the current best scheduling sequence is output; otherwise, continue to execute Step 6. The present invention solves the problem of grouping scheduling for distributed flow shops with setup times, reduces the makespan, lowers the production cost, and improves the workshop scheduling efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of workshop scheduling, and in particular to a distributed flow workshop group scheduling method with preparation time. Background Art

[0002] With the development of the economy, manufacturing has become an important pillar of the national economy. The development and application of cell manufacturing and group technology have a great impact on efficient batch manufacturing systems. In a cell manufacturing system, resources are divided into smaller organizational units, called manufacturing cells. A manufacturing cell usually consists of a series of specialized machines, and a group is composed of workpieces with similar requirements in terms of tools, settings, and operation sequences. Manufacturing cells can simplify the scheduling process, shorten production time, and improve the reliability of production systems, which is especially beneficial for highly automated systems. It is becoming one of the most important manufacturing models in modern enterprises, such as Huawei Co., Ltd., Foxconn Technology Group, and the automotive assembly industry.

[0003] Take the printed circuit board PCB as an example. PCB is an important component of electronic products. In the PCB manufacturing process, different types of PCB parts need to be scheduled. First, the PCB parts are grouped according to type, for example, the PCB is divided into the first PCB group and the second PCB group, and the number of chips loaded on the machine for processing these two different PCB groups is also different. Specifically, the number of chips loaded on the machine is unchanged when processing the first PCB group. When the first PCB group is processed and the second PCB group needs to be switched for processing, the machine must be cleaned and maintained to meet the conditions required for processing the second PCB group. Therefore, the switching time depends on the order of the PCB groups, and the switching time required between different PCB groups is also different. In this case, the scheduling problem is a group scheduling problem with sequence-related preparation time. Therefore, in the environment of collaborative scheduling of multiple manufacturing units, it can be abstracted as a distributed flow shop group scheduling problem with sequence-related preparation time. Therefore, different scheduling sequences will have a very important impact on the completion time. If the scheduling sequence is unreasonable, the production line may be idle, thereby increasing production time and reducing production efficiency. It may lead to insufficient or wasteful resource utilization, thereby increasing production costs. It may also lead to a decrease in the processing accuracy of certain processes, thereby affecting product quality. Therefore, it is a problem with important practical significance and needs to be solved urgently. Summary of the invention

[0004] To better solve the group scheduling problem of distributed flow shop with setup time, an effective scheduling method is proposed, that is, a group scheduling method for distributed flow shop with setup time, integrating the evolutionary operators into a two-stage strategy with the makespan as the optimization goal. Compared with the traditional flow shop scheduling method, the scheduling method provided by the present invention has the advantages of convenient implementation, easy adjustment of parameters, fast calculation speed, etc. It can perform multiple iterative optimizations on production scheduling to obtain a more accurate scheduling plan, avoiding errors in the scheduling process; it can effectively schedule and optimize workshop tasks according to production requirements, helping enterprises improve production efficiency; at the same time, it can balance the loads among multiple factories, avoid bottlenecks and blockages in the production process, improve the stability and reliability of the production line, and the optimized scheduling plan can reduce the idle time of materials and equipment, reduce resource waste, and thus reduce production costs.

[0005] The present invention provides a group scheduling method for distributed flow shop with setup time, including the following steps:

[0006] Step 1: With the goal of minimizing the makespan, construct a group scheduling problem model for distributed flow shop with setup time. The objective function of the group scheduling problem model for distributed flow shop with setup time is:

[0007] MinimizC max ; where, C max is the makespan;

[0008] Step 2: Parameter setting. According to the characteristics of the objective function, set the following parameters:

[0009] The threshold for distinguishing any two stages is tv, the probability value pv for selecting different search operators in the first stage, and the coefficient ω for adjusting the optimization time of the algorithm; where, 0 < tv < 1, 0 < pv < 1, ω > 0;

[0010] The termination time of the first stage: t1 = tv × (ω × m × δ);

[0011] The termination time of the second stage: t2 = (1 - tv) × (ω × m × δ);

[0012] where, m is the number of machines, m > 0; δ is the number of groups, δ > 0;

[0013] where, the probability of selecting the first search operator in the first stage is pv, and the probability of selecting the second search operator is 1 - pv;

[0014] Step 3: Initialize the strategy. Number the group sequence based on the representation method of the workpiece sequence. The group sequence is represented as Δ = {Δ1, Δ2, …, Δ l , …, Δδ}, and the construction heuristic method is used to initialize the scheduling sequence, and the combinations are reasonably arranged into the factory sequence π = {π1, π2, …, π k , …, π f};

[0015] Step 4: First-stage strategy, select the first search strategy according to the probability value pv, and select the second search strategy according to the probability value 1 - pv; wherein, the first search strategy includes first-stage destruction and reconstruction, and simulated annealing acceptance criterion; the second search strategy includes insertion-based neighborhood search and insertion-based first local intensification;

[0016] Step 5: First update the scheduling sequence, and determine whether the termination time t1 of the first stage is reached by the running time; wherein, when the running time reaches the termination time t1 of the first stage, then execute the next step; otherwise, continue to execute Step 4;

[0017] Step 6: Second-stage strategy, execute swap-based neighborhood search, second-stage destruction and reconstruction, and insertion-based second local intensification;

[0018] Step 7: Second update the scheduling sequence, and determine whether the termination time t2 of the second stage is reached by the running time; wherein, when the running time reaches the termination time t2 of the second stage, then the optimization ends, and the optimized scheduling sequence scheme and its corresponding makespan are output; otherwise, continue to execute Step 6.

[0019] Furthermore, the constraint conditions of the distributed flow shop group scheduling problem model with setup times include:

[0020] Ensure that each group has exactly one direct successor in the group sequence, that is

[0021]

[0022] where δ is the number of groups in the group sequence, if group l' is the direct successor of group l, then x l,l' is 1, otherwise 0;

[0023] Ensure that each group has exactly one direct predecessor in the group sequence, that is

[0024]

[0025] where δ is the number of groups in the group sequence, if group l' is the direct successor of group l, then x l,l' is 1, otherwise 0;

[0026] Ensure that the virtual group is the direct predecessor less than or equal to f times, that is

[0027]

[0028] Among them, f is the number of factories, δ is the number of groups in the group sequence. If group l' is the direct successor of group 0, then x 0,l' is 1, otherwise it is 0;

[0029] Ensure that the virtual group is a direct successor less than or equal to f times, that is

[0030]

[0031] Among them, f is the number of factories, δ is the number of groups in the group sequence. If group 0 is the direct successor of group l, then x l,0 is 1, otherwise it is 0;

[0032] Ensure that the virtual group has the same number of direct successors and direct predecessors in the group sequence, that is

[0033]

[0034] Ensure that each workpiece in the group, including two virtual workpieces, has exactly one direct predecessor and successor. In addition, ensure that the workpieces in the same group are not separated and not mixed with the workpieces in other groups, that is

[0035]

[0036]

[0037] Among them, n l is the number of workpieces in group l. If workpiece j' in the group is the direct successor of workpiece j, then y j,j',l is 1, otherwise it is 0;

[0038] Ensure that for workpiece j and workpiece j' from the same group, if workpiece j' is the direct successor of workpiece j on machine i, then the completion time of workpiece j' on machine i is not less than the completion time of workpiece j plus the processing time of workpiece j' on machine i, that is

[0039]

[0040]

[0041] Among them, c j',l,i is the completion time of workpiece j' in group l on machine i, c j,l,i is the completion time of workpiece j in group l on machine i, p j',l,i is the processing time of workpiece j' in group l on machine i, h is a sufficiently large positive number, and m is the number of machines;

[0042] Ensure that for group l' and group l, if group l' is the direct successor of group l on machine i, the completion time of workpiece j' in group l' on machine i is not less than the completion time of workpiece j in group l plus the processing time of workpiece j' on machine i and the setup time s between group l and group l'. l,l',i , that is

[0043]

[0044]

[0045] where c j',I',i is the completion time of workpiece j' in group l' on machine i, c j,l,i is the completion time of workpiece j in group l on machine i, s l,l',i is the setup time between group l and group l', and p j',l',i is the processing time of workpiece j' on machine i;

[0046] Ensure that for the first group of workpieces processed on this machine, adding the initial setup time, that is

[0047]

[0048]

[0049] where c j,l,i is the completion time of workpiece j in group l on machine i, s 0,l,i is the setup time between group l and group l', and p j,l,i is the processing time of workpiece j in group l on machine i;

[0050] Ensure that the completion time of workpiece j on machine i + 1 is greater than or equal to the processing time of workpiece j on machine i + 1 plus the completion time of workpiece j on the previous machine i, that is

[0051]

[0052]

[0053] where c j,l,i+1 is the completion time of workpiece j in group l on machine i + 1, c j,l,i is the completion time of workpiece j in group l on machine i, and p j,l,i+1 is the processing time of workpiece j in group l on machine i + 1;

[0054] Define the makespan, that is

[0055]

[0056] where cj,I,m It is the completion time of workpiece j in group l on machine m.

[0057] Furthermore, the construction heuristic method includes the following steps:

[0058] Calculate the total processing time of each group, sort the δ groups in descending order according to the total processing time, take out the first f groups in sequence, and assign them to f factories in sequence, where δ > f;

[0059] Take out the remaining δ - f groups in sequence and insert them into the best positions until all groups are extracted and inserted;

[0060] Optimize and adjust the group sequences in each factory to obtain a scheduling sequence with the minimum completion time.

[0061] Furthermore, after the initialization strategy is completed, with a probability of pv, the first search strategy is used to optimize the scheduling sequence. The operation steps of the first - stage destruction and reconstruction in the first search strategy include:

[0062] Extract D groups of workpieces from the factory sequence π, where the value range of D is 2 - 7, and sort all factories in descending order according to the completion time;

[0063] Take out one group from each factory in sequence until the number of taken - out groups is equal to D;

[0064] Re - insert the D taken - out groups into the best positions in all factories to minimize the completion time.

[0065] Furthermore, after the first - stage destruction and reconstruction operation is completed, the simulated annealing acceptance criterion is performed. The simulated annealing acceptance criterion includes:

[0066] When the objective function value of the scheduling sequence generated after the first - stage destruction and reconstruction operation is not as good as that of the scheduling sequence before optimization, then accept this worse scheduling sequence with a certain probability as the scheduling sequence to be further optimized.

[0067] Furthermore, after the initialization strategy is completed, with a probability of 1 - pv, the second search strategy is used to optimize the scheduling sequence. The operation steps of the insertion - based neighborhood search in the second search strategy include:

[0068] Find the key factory from the factory sequence π. The key factory is the factory with the maximum completion time;

[0069] Randomly take out one group from the key factory, test this group at all positions in all factories, and re - insert this group into the best position with the minimum completion time.

[0070] Further, after the insertion-based neighborhood search is completed, perform the first local intensification operation based on insertion. The operation steps of the first local intensification based on insertion include:

[0071] Find the key factory from the factory sequence π, where the key factory is the factory with the largest completion time;

[0072] Successively take out workpieces one by one from the group of the key factory, test all positions in the group of the key factory for the workpieces, and insert the workpieces into the best position with the smallest completion time to obtain the best workpiece sequence for each group.

[0073] Further, after the first-phase strategy is completed, perform the second-phase strategy and execute the swap-based neighborhood search operation. The operation steps of the swap-based neighborhood search include:

[0074] Find the key factory from the factory sequence π, where the key factory is the factory with the largest completion time;

[0075] Randomly extract a group from the key factory, and find the factory with the smallest completion time, and randomly extract a group from the smallest factory;

[0076] Swap a group randomly extracted from the key factory with a group randomly extracted from the smallest factory, and find the best position to insert in the swapped factory to minimize the completion time.

[0077] Further, after the swap-based neighborhood search operation is completed, perform the second-phase destruction and reconstruction operation. The operation steps of the second-phase destruction and reconstruction include:

[0078] Extract d groups of workpieces from the factory sequence π, where the value range of d is 2 - 7, and the key factory is the factory with the largest completion time among all factories;

[0079] Randomly take out a group from the key factory successively until the number of taken-out groups is equal to d;

[0080] Re-insert the d taken-out groups into the best position of the key factory to minimize the completion time.

[0081] Further, after the second-phase destruction and reconstruction operation is completed, perform the second local intensification operation based on insertion. The operation steps of the second local intensification based on insertion include:

[0082] Find the key factory from the factory sequence π, where the key factory is the factory with the largest completion time;

[0083] Workpieces are successively taken out one by one from the group of the key factories, the workpieces are tested at all positions of the group of the key factories, and the workpieces are inserted into the best position with the minimum completion time to obtain the best workpiece sequence for each group.

[0084] The present invention provides a scheduling method for a distributed flow shop grouping with setup time, and has the following technical effects:

[0085] At the method level:

[0086] (1) Based on the iterative greedy algorithm, this method further explores the neighborhood space of a single solution, greatly improving the quality of the solution;

[0087] (2) Through the interaction between factories, the two neighborhood search strategies increase the diversity of solutions, which is conducive to finding better solutions within the search area and enhancing the global search ability;

[0088] (3) Adopting the local intensification strategy, the workpiece sequence within the group is optimized, further enhancing the adaptability of the solution and the local search ability;

[0089] (4) According to the two stages of the problem characteristics, in the first stage, the group sequence between all factories is perturbed to improve the diversity of solutions. In the second stage, the factories within the key factories are perturbed to further improve the scheduling sequence of the key factories to reduce the makespan;

[0090] At the application level:

[0091] (1) Compared with the traditional flow shop scheduling method, the method provided by the present invention has the advantages of convenient implementation, easy adjustment of parameters, fast calculation speed, etc.;

[0092] (2) It can perform multiple iterative optimizations on production scheduling, so as to obtain a more accurate scheduling plan and avoid errors in the scheduling process;

[0093] (3) It can effectively schedule and optimize the workshop tasks according to production requirements, helping enterprises improve production efficiency;

[0094] (4) It can balance the loads between multiple factories, avoid bottlenecks and blockages in the production process, improve the stability and reliability of the production line, and the optimized scheduling plan can reduce the idle time of materials and equipment, reduce resource waste, and thus reduce production costs.

[0095] Therefore, the scheduling method for a distributed flow shop grouping with setup time provided by the present invention can well solve the scheduling problem, can provide a good solution for the distributed flow shop grouping scheduling, can improve the efficiency of workshop scheduling, and reduce the completion time. Description of the Drawings

[0096] Figure 1 Schematic diagram of the implementation process of the present invention;

[0097] Figure 2 Comparison chart of the confidence interval of the present invention;

[0098] Figure 3 Comparison chart of the evolution curve of the present invention. Detailed implementation manners

[0099] Embodiments of the present invention will now be described more fully hereinafter with reference to the accompanying drawings that show embodiments of the invention. However, the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. Throughout the text, the same numbers represent the same elements.

[0100] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art, and will not be interpreted in an idealized or overly formal sense.

[0101] The present invention will be described below with reference to the flowcharts and / or block diagrams of methods, systems, and computer program products according to embodiments of the present invention. It will be understood that some of the blocks in the flowchart illustrations and / or block diagrams, and combinations of some of the blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be stored or implemented in a microcontroller, microprocessor, digital signal processor (DSP), field programmable gate array (FPGA), state machine, programmable logic controller (PLC), or other processing circuits, general purpose computer, special purpose computer, or other programmable data processing device (such as a production machine) so as to create means or apparatus for implementing the functions / actions specified in the flowchart and / or block diagram by instructions executed by a processor of the computer or other programmable data processing device.

[0102] These computer program instructions can also be stored in a computer-readable memory, which can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction apparatus. Implement the functions / actions specified in the flowchart and / or block diagram.

[0103] Computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby making the instructions executed on the computer or other programmable device possible. Other programmable devices provide steps for implementing the functions / actions specified in the flowchart and / or block diagram boxes. It should be understood that the functions / actions indicated in the boxes may not occur in the order indicated in the operation diagram. For example, depending on the functions / actions involved, two consecutively shown boxes can actually be executed substantially simultaneously, or sometimes these boxes can be executed in the reverse order. Although some diagrams include arrows on the communication paths to indicate the main direction of communication, it should be understood that communication can occur in the direction opposite to the depicted arrows.

[0104] The specific implementation process of the present invention is as follows:

[0105] Provided is a scheduling method for a distributed flow shop grouping with setup time, including the following steps:

[0106] Step 1: With the goal of minimizing the makespan, construct a scheduling problem model for a distributed flow shop grouping with setup time. The objective function of the scheduling problem model for a distributed flow shop grouping with setup time is:

[0107] MinimizC max ; where C max is the makespan;

[0108] Step 2: Parameter setting. According to the characteristics of the objective function, set the following parameters:

[0109] The threshold for distinguishing any two stages is tv, the probability value pv for selecting different search operators in the first stage, and the coefficient ω for adjusting the optimization time of the algorithm; where 0 < tv < 1, 0 < pv < 1, ω > 0;

[0110] The termination time of the first stage: t1 = tv × (ω × m × δ);

[0111] The termination time of the second stage: t2 = (1 - tv) × (ω × m × δ);

[0112] where m is the number of machines, m > 0; δ is the number of groups, δ > 0;

[0113] where the probability of selecting the first search operator in the first stage is pv, and the probability of selecting the second search operator is 1 - pv;

[0114] Step 3: Initialization strategy. Number the group sequence based on the representation method of the workpiece sequence. The group sequence is represented as Δ = {Δ1, Δ2, …, Δ l , …, Δδ}, and an initialization scheduling sequence is generated using a constructive heuristic method, and the combinations are reasonably arranged into the factory sequence π = {π1, π2, …, π k , …, π f};

[0115] Step 4: First-stage strategy, select the first search strategy according to the probability value pv, and select the second search strategy according to the probability value 1 - pv; wherein, the first search strategy includes first-stage destruction and reconstruction, simulated annealing acceptance criterion; the second search strategy includes insertion-based neighborhood search, insertion-based first local intensification;

[0116] Step 5: First update the scheduling sequence, and determine whether the termination time t1 of the first stage is reached by the running time; wherein, when the running time reaches the termination time t1 of the first stage, then execute the next step; otherwise, continue to execute Step 4;

[0117] Step 6: Second-stage strategy, execute swap-based neighborhood search, second-stage destruction and reconstruction, insertion-based second local intensification;

[0118] Step 7: Second update the scheduling sequence, and determine whether the termination time t2 of the second stage is reached by the running time; wherein, when the running time reaches the termination time t2 of the second stage, then the optimization ends, and the optimized scheduling sequence scheme and its corresponding makespan are output; otherwise, continue to execute Step 6.

[0119] Specifically, as Figure 1 shown, a distributed flow shop group scheduling optimization method with setup times provided by the present invention mainly includes the following implementation processes:

[0120] In Step 1, with the goal of minimizing the makespan, a distributed flow shop group scheduling problem model with setup times is constructed;

[0121] The objective function of the distributed flow shop group scheduling problem model with setup times is:

[0122] Minimize C maχ

[0123] where C max is the makespan;

[0124] The constraint conditions of the distributed flow shop group scheduling problem model with setup times include:

[0125] Ensure that each group has exactly one direct successor in the group sequence, that is

[0126]

[0127] where δ is the number of groups in the group sequence, and if group l' is the direct successor of group l, then χ l,l' is 1, otherwise 0;

[0128] Ensure that each group has exactly one direct predecessor in the group sequence, that is

[0129]

[0130] where δ is the number of groups in the group sequence, and if group l' is the direct successor of group l, then χ l,l' is 1, otherwise 0;

[0131] Ensure that the virtual group is a direct predecessor less than or equal to f times, that is

[0132]

[0133] where f is the number of factories, δ is the number of groups in the group sequence, and if group l' is the direct successor of group 0, then x 0,l' is 1, otherwise 0;

[0134] Ensure that the virtual group is a direct successor less than or equal to f times, that is

[0135]

[0136] where f is the number of factories, δ is the number of groups in the group sequence, and if group 0 is the direct successor of group l, then χ l,0 is 1, otherwise 0;

[0137] Ensure that the virtual group has the same number of direct successors and direct predecessors in the group sequence, that is

[0138]

[0139] Ensure that each workpiece in the group, including two virtual workpieces, has exactly one direct predecessor and successor. In addition, ensure that the workpieces in the same group are not separated and not mixed with the workpieces in other groups, that is

[0140]

[0141]

[0142] where n l is the number of workpieces in group l, and if workpiece j' in the group is the direct successor of workpiece j, then y j,j',l is 1, otherwise 0;

[0143] Ensure that for workpiece j and workpiece j' from the same group, if workpiece j' is the direct successor of workpiece j on machine i, the completion time of workpiece j' on machine i is not less than the completion time of workpiece j plus the processing time of workpiece j' on machine i, that is

[0144]

[0145]

[0146] where c j',l,i is the completion time of workpiece j' in group l on machine i, c j,l,i is the completion time of workpiece j in group l on machine i, p j',l,i is the processing time of workpiece j' in group l on machine i, h is a sufficiently large positive number, and m is the number of machines;

[0147] Ensure that for group l' and group l, if group l' is the direct successor of group l on machine i, the completion time of workpiece j' in group l' on machine i is not less than the completion time of workpiece j in group l plus the processing time of workpiece j' on machine i and the setup time s l,l',i between group l and group l', that is

[0148]

[0149]

[0150] where c j',l',i is the completion time of workpiece j' in group l' on machine i, c j,l,i is the completion time of workpiece j in group l on machine i, s l,l',i is the setup time between group l and group l', and p j',l',i is the processing time of workpiece j' in group l' on machine i;

[0151] Ensure that for the first group of workpieces processed on this machine, plus the initial setup time, that is

[0152]

[0153]

[0154] where c j,l,i is the completion time of workpiece j in group l on machine i, s 0,l,i is the setup time between group l and group l', and p j,l,i is the processing time of workpiece j in group l on machine i;

[0155] Ensure that the completion time of workpiece j on machine i + 1 is greater than or equal to the processing time of workpiece j on machine i + 1 plus the completion time of workpiece j on the previous machine i, that is

[0156]

[0157]

[0158] where c j,l,i+1 is the completion time of workpiece j in group l on machine i + 1, and c j,l,i is the completion time of workpiece j in group l on machine i, and p j,l,i+1 is the processing time of workpiece j in group l on machine i + 1;

[0159] Define the makespan, that is

[0160]

[0161] where c j,l,m is the completion time of workpiece j in group l on machine m.

[0162] In step 2, perform parameter setting: distinguish the threshold tv for the two stages, the probability value pv for selecting different search operators in the first stage; the termination time t1 of the first stage = tv × (ω × m × δ), where m is the number of machines, δ is the number of groups, and ω is the coefficient for adjusting the optimization time of the algorithm; the termination time t2 of the second stage = (1 - tv) × (ω × m × δ), where m is the number of machines, δ is the number of groups, and ω is the coefficient for adjusting the optimization time of the algorithm; among them, the probability of selecting the first search operator in the first stage is pv, and the probability of selecting the second search operator is 1 - pv;

[0163] In step 3, perform initialization strategy: encode the group sequence through a representation method based on the workpiece sequence, and the group sequence is represented as Δ = {Δ1, Δ2,..., Δ l ,..., Δ δ} δ is the number of groups, and use the construction heuristic method to initialize the scheduling sequence, and arrange the group sequence Δ = {Δ1, Δ2,..., Δ l ,..., Δ δ} into the factory sequence π = {π1, π2,..., π k ,..., π f}.

[0164] The factory sequence π is in the form of a two-dimensional vector, π = {π1, π2,..., π k ,..., π f}, where 1, 2,..., k,..., f are the factory numbers, f is the total number of factories, and the factory sequence π is composed of f one-dimensional vectors.

[0165] The group sequence of factory serial number k is expressed as where 1, 2, …, δ k is the group serial number in factory serial number k, and δ k is the total number of groups in factory serial number k.

[0166] The group sequence Δ is in the form of a two-dimensional vector, Δ = {Δ1, Δ2, …, Δ l , …, Δ δ}, where 1, 2, …, l, …, δ are the group serial numbers in the group sequence Δ, δ is the total number of groups in the group sequence Δ, and the group sequence Δ is composed of δ one-dimensional vectors.

[0167] The workpiece sequence of group serial number l is expressed as where 1, 2, …, n l is the workpiece serial number in group serial number l, and n l is the total number of workpieces.

[0168] Among them, the construction heuristic method is as follows:

[0169] First, calculate the total processing time of each group, sort the δ groups in descending order according to the total processing time, that is, sort in the order from large to small, take out the first f groups in turn, and assign them to f factories in turn. The number of groups ≥ the number of factories, that is, δ > f. The above operations ensure the uniformity of the allocation quantity.

[0170] Second, take out the remaining δ - f groups in turn and insert them into the best positions until all groups are extracted and inserted;

[0171] Finally, optimize and adjust the group sequences in each factory to obtain the scheduling sequence with the minimum completion time.

[0172] In step 4, perform the first-stage strategy. Select the first search strategy according to the probability value pv, and select the second search strategy according to the probability value 1 - pv. Among them, the first search strategy includes the first-stage destruction and reconstruction, and the simulated annealing acceptance criterion; the second search strategy includes the insertion-based neighborhood search and the first local reinforcement based on insertion.

[0173] The probability of pv uses the first search strategy to optimize the scheduling sequence. The specific steps of the first-stage destruction and reconstruction in the first search strategy are as follows:

[0174] First, extract D groups of workpieces from the factory sequence π. The value range of D is 2 - 7, and all factories are sorted in descending order according to the completion time;

[0175] Second, take out one group from each factory in turn until the number of groups taken out is equal to D;

[0176] Finally, insert the D groups taken out back to the best positions in all factories to minimize the completion time.

[0177] After the destruction and reconstruction operation in the first stage is completed, the simulated annealing acceptance criterion is carried out. The specific steps of the simulated annealing acceptance criterion are as follows:

[0178] When the objective function value of the scheduling sequence generated after the destruction and reconstruction operation in the first stage is not as good as that of the scheduling sequence before optimization, then accept this worse scheduling sequence with a certain probability as the scheduling sequence to be continuously optimized. In other words, if the newly generated current solution is not as good as the original solution, this solution still has a certain probability of being accepted, rather than only replacing it when the current solution is better than the original solution.

[0179] With a probability of 1 - pv, adopt the second search strategy to optimize the scheduling sequence. Among them, the specific steps of the insertion-based neighborhood search in the second search strategy are as follows:

[0180] First, find the key factory from the factory sequence π. The key factory is the factory with the largest completion time.

[0181] Finally, randomly take out a group from the key factory, test it at all positions in all factories, and re-insert this group into the best position with the minimum completion time.

[0182] After the insertion-based neighborhood search is completed, perform the first local strengthening operation based on insertion. The specific steps of the first local strengthening based on insertion are as follows:

[0183] First, find the key factory from the factory sequence π. The key factory is the factory with the largest completion time.

[0184] Secondly, take out the workpieces from the groups of the key factory one by one, test the positions of this workpiece in all groups of the key factory, and insert the workpiece into the best position with the minimum completion time to obtain the best workpiece sequence for each group. Specifically, take out the workpieces in the first group of the key factory one by one, test its positions in the first group, and insert it into the best position with the minimum completion time. For the remaining groups in the key factory, perform the operations as those in the first group of the key factory in sequence to obtain the best workpiece sequence for each group.

[0185] This application improves the global search ability and increases the diversity of solutions through the operation of the first-stage strategy.

[0186] In step 5, perform the first update of the scheduling sequence, and determine whether the first-stage termination time t1 is reached by the running time; among them, when the running time reaches the first-stage termination time t1, then execute the next step; otherwise, continue to execute step 4.

[0187] In step 6, perform the second-phase strategy: sequentially execute swap-based neighborhood search, second-phase destruction and reconstruction, and insertion-based second local intensification.

[0188] After the first-phase strategy is completed, perform the second-phase strategy. Perform the swap-based neighborhood search operation. The specific steps of the swap-based neighborhood search are as follows:

[0189] First, find the key factory from the factory sequence π. The key factory is the factory with the largest completion time.

[0190] Second, randomly extract a group from the key factory, and find the factory with the smallest completion time, and extract a group from the smallest factory.

[0191] Finally, swap the two groups, that is, randomly extract a group from the key factory and swap it with a group randomly extracted from the smallest factory, and find the best position to insert in the swapped factories to minimize the completion time.

[0192] After the swap-based neighborhood search operation is completed, perform the second-phase destruction and reconstruction operation. The specific steps of the second-phase destruction and reconstruction are as follows:

[0193] First, extract d groups of workpieces from the factory sequence π. The value range of d is 2 - 7. The key factory is the factory with the largest completion time among all factories.

[0194] Second, randomly take out a group from the key factory in turn until the number of taken-out groups is equal to d.

[0195] Finally, insert the d taken-out groups into the best position of the key factory in turn to minimize the completion time.

[0196] After the second-phase destruction and reconstruction operation is completed, perform the insertion-based second local intensification operation. The specific steps of the insertion-based local intensification are as follows:

[0197] First, find the key factory from the factory sequence π. The key factory is the factory with the largest completion time.

[0198] Second, take out the workpieces from the groups of the key factory one by one, test the workpieces at all positions in the groups of the key factory, and insert the workpieces into the best position with the smallest completion time to obtain the best workpiece sequence for each group. Specifically, take out the workpieces in the first group of the key factory one by one, test it at all positions in the first group, and insert it into the best position with the smallest completion time. For the remaining groups in the key factory, perform the operations as in the first group of the key factory in turn to obtain the best workpiece sequence for each group.

[0199] This application enhances the local search ability through the operation of the second-stage strategy, further improving the quality of the solution.

[0200] In step 7, the second updated scheduling sequence is carried out, and it is judged whether the termination time t2 of the second stage is reached by the running time; among them, when the running time reaches the termination time t2 of the second stage, the optimization ends, and the optimized scheduling sequence scheme and its corresponding makespan are output; otherwise, step 6 is continued to be executed.

[0201] This application cooperates with each other through the first-stage strategy and the second-stage strategy to achieve the balance between search and optimization. Next, the present invention will be further described and illustrated through specific embodiments:

[0202] The simulation experiment uses 810 standard test cases. Among them, the number of groups δ = {20, 40, 60}, the number of machines m = {2, 4, 6}, the number of factories f = {2, 3, 4, 5, 6, 7}, the number of workpieces in each group and the processing time of the workpieces are uniformly distributed in the range of [1, 10], and the three setup times are randomly generated from the uniformly distributed integers [1, 20][1, 40][1, 60] respectively. In a specific example of the present invention, taking the threshold value tv = 0.9 for distinguishing the two stages and the probability value pv = 0.7 for selecting different search operators in the first stage as examples, detailed description and experimental verification are carried out.

[0203] The iterative greedy algorithm based on effective two stages proposed by the present invention, abbreviated as tIGA, is compared with the iterative greedy algorithm IG, the improved iterative greedy algorithm TIG, and the evolutionary algorithm EA to verify the effectiveness of the present invention. These several comparison algorithms are all high-performance optimization algorithms proposed in recent years. In order to reduce the error of the experiment and make the calculation results more effective and general, each test case is executed 5 times to generate statistical results. The relative percentage deviation Relativepercentageincrease, RPI, is used as the performance evaluation index, and the calculation formula of RPI i =(C i -C best ) / C best ×100, where C i represents the makespan obtained when a specific algorithm solves a specific test case, while C best represents the minimum makespan obtained when solving the above same test case among these 4 algorithms. Obviously, the smaller the RPI value, the smaller the makespan found, and the better the performance.

[0204] Figure 2 is an intuitive representation of the optimization results of all algorithms. Specifically, from Figure 2From the RPI values, it can be seen that the RPI results of tIGA are significantly better than those of other algorithms. Secondly are EA and TIG, and the algorithm with the worst performance is IG. In addition, Figure 3 The evolution curves of the four algorithms over time are given with the makespan as the index. From Figure 3 it can be seen that as time increases, the evolution curve of the method of the present invention is significantly lower than that of the comparative algorithms, indicating that the method of the present invention has very good convergence and can converge to the best value at a relatively fast convergence speed.

[0205] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. After those skilled in the art read this application, any acts of making various modifications or changes to the present invention with reference to the above embodiments are within the scope of the claims of the present invention pending approval.

Claims

1. A scheduling method for grouping a distributed flow shop with setup time, characterized in that, It includes the following steps: Step 1: A distributed flow shop group scheduling problem model with setup times is constructed with the goal of minimizing the makespan. The objective function of the distributed flow shop group scheduling problem model with setup times is as follows: MinimizeC max ; Among them, C max is the makespan; Step 2: Parameter setting. According to the characteristics of the objective function, the following parameters are set: The threshold for distinguishing any two stages is \(t_v\), the probability value \(p_v\) for selecting different search operators in the first stage, and the coefficient \(\omega\) for adjusting the optimization time of the algorithm; where \(0 < t_v < 1\), \(0 < p_v < 1\), and \(\omega>0\); The termination time of the first stage: \(t_1 = t_v\times(\omega\times m\times\delta)\); The termination time of the second stage: \(t_2=(1 - t_v)\times(\omega\times m\times\delta)\); where \(m\) is the number of machines, \(m>0\); \(\delta\) is the number of groups, \(\delta>0\); where the probability of selecting the first search operator in the first stage is \(p_v\), and the probability of selecting the second search operator is \(1 - p_v\); Step 3: Initialize the strategy. Number the group sequence based on the representation method of the workpiece sequence. The group sequence is represented as Δ = {Δ1, Δ2, …, Δ l , …, Δ δ}, and use the constructive heuristic method to initialize the scheduling sequence, and reasonably arrange the groups into the factory sequence π = {π1, π2, …, π k , …, π f}; Step 4: The first-stage strategy. The first search strategy is selected according to the probability value \(p_v\), and the second search strategy is selected according to the probability value \(1 - p_v\); where the first search strategy includes first-stage destruction and reconstruction, and simulated annealing acceptance criterion; the second search strategy includes insertion-based neighborhood search and insertion-based first local intensification; Step 5: First update the scheduling sequence. It is judged whether the termination time \(t_1\) of the first stage is reached by the running time; where when the running time reaches the termination time \(t_1\) of the first stage, the next step is executed; otherwise, Step 4 is continued; Step 6: The second-stage strategy. Execute swap-based neighborhood search, second-stage destruction and reconstruction, and insertion-based second local intensification; Step 7: Second update the scheduling sequence. It is judged whether the termination time \(t_2\) of the second stage is reached by the running time; where when the running time reaches the termination time \(t_2\) of the second stage, the optimization ends, and the optimized scheduling sequence scheme and its corresponding makespan are output; otherwise, Step 6 is continued.

2. The scheduling method for a distributed flow shop group with setup times according to claim 1, wherein The constraint conditions of the distributed flow shop group scheduling problem model with setup times include: Ensure that each group has and only has one direct successor in the group sequence, that is where δ is the number of groups in the group sequence, and x is 1 if group l' is a direct successor of group l, and 0 otherwise; l,l' is 1, and 0 otherwise; Ensure that each group has and only has one direct predecessor in the group sequence, that is where δ is the number of groups in the group sequence, and x is 1 if group l' is a direct successor of group l, and 0 otherwise; l,l' otherwise it is 0; Ensure that the virtual group is the direct predecessor less than or equal to \(f\) times, that is where f is the number of factories, δ is the number of groups in the group sequence, and x 0,l' is 1 if group l' is a direct successor of group 0, and 0 otherwise; 0,l' is 1, otherwise it is 0; Ensure that the virtual group is the direct successor less than or equal to \(f\) times, that is where f is the number of factories, δ is the number of groups in the group sequence, and x is 1 if group 0 is the direct successor of group l, and 0 otherwise; l,0 is 1, otherwise it is 0; Ensure that the virtual group has the same number of direct successors and direct predecessors in the group sequence, that is Ensure that each workpiece in the group, including two virtual workpieces, has and only has one direct predecessor and successor. In addition, ensure that the workpieces in the same group are not separated and are not mixed with the workpieces in other groups, that is where n l is the number of workpieces in group l, and y j,j',l is 1 if workpiece j' in the group is the direct successor of workpiece j, and 0 otherwise; Ensure that for workpiece \(j\) and workpiece \(j'\) from the same group, if workpiece \(j'\) is the direct successor of workpiece \(j\) on machine \(i\), then the completion time of workpiece \(j'\) on machine \(i\) is not less than the completion time of workpiece \(j\) plus the processing time of workpiece \(j'\) on machine \(i\), that is where c j',l,i is the completion time of job j' in group l on machine i, and c j,l,i is the completion time of job j in group l on machine i, p j',l,i is the processing time of job j' in group l on machine i, h is a positive number large enough, and m is the number of machines; Ensure that for group l' and group l, if group l' is the direct successor of group l on machine i, the completion time of workpiece j' of group l' on machine i is not less than the completion time of workpiece j of group l plus the processing time of workpiece j' on machine i and the setup time s between group l and group l'. l,l',i That is Among them, c j',l',i is the completion time of workpiece j' in group l' on machine i, c j,l,i is the completion time of workpiece j in group l on machine i, s l,l',i is the setup time between group l and group l', p j',l',i is the processing time of workpiece j' in group l' on machine i; Ensure that for the first group of workpieces processed on this machine, plus the initial setup time, that is where c j,l,i is the completion time of job j in group l on machine i, s 0,l,i is the setup time between group l and group l', p j,l,i is the processing time of job j in group l on machine i; Ensure that the completion time of workpiece j on machine i + 1 is greater than or equal to the processing time of workpiece j on machine i + 1 plus the completion time of workpiece j on the previous machine i, that is Among them, c j,l,i+1 is the completion time of workpiece j in group l on machine i + 1, c j,l,i is the completion time of workpiece j in group l on machine i, p j,l,i+1 is the processing time of workpiece j in group l on machine i + 1; Define the makespan, that is where c j,l,m is the completion time of job j on machine m in group l.

3. The scheduling method for grouping distributed flow shops with setup times according to claim 1, characterized in that The construction heuristic method includes the following steps: Calculate the total processing time of each group, sort the δ groups in descending order according to the total processing time, take out the first f groups in turn, and assign them to f factories in turn, where δ > f; Take out the remaining δ - f groups in turn and insert them into the best positions until all groups are extracted and inserted; Optimize and adjust the group sequences in each factory to obtain a scheduling sequence with the minimum completion time.

4. The scheduling method for grouping distributed flow shops with preparation time according to claim 1, characterized in that, After the initialization strategy is completed, with a probability of pv, the first search strategy is used to optimize the scheduling sequence. The operation steps of the first-stage destruction and reconstruction in the first search strategy include: Extract D groups of workpieces from the factory sequence π, where the value range of D is 2 - 7, and arrange all factories in descending order according to the completion time; Take out one group from each factory in turn until the number of groups taken out is equal to D; Re-insert the D groups taken out into the best positions in all factories to minimize the completion time.

5. The scheduling method for the group of distributed flow shops with preparation time according to claim 1 or 4, characterized in that, After the first-stage destruction and reconstruction operation is completed, the simulated annealing acceptance criterion is performed. The simulated annealing acceptance criterion includes: When the objective function value of the scheduling sequence generated after the first-stage destruction and reconstruction operation is not as good as the objective function value of the scheduling sequence before optimization, then accept this worse scheduling sequence with a certain probability as the scheduling sequence to be continuously optimized.

6. The scheduling method for grouping distributed flow shops with preparation time according to claim 1, characterized in that After the initialization strategy is completed, with a probability of 1 - pv, the second search strategy is used to optimize the scheduling sequence. The operation steps of the insertion-based neighborhood search in the second search strategy include: Find the key factory from the factory sequence π, and the key factory is the factory with the maximum completion time; Randomly take out one group from the key factory, test this group in all positions of all factories, and re-insert this group into the best position with the minimum completion time.

7. The scheduling method for the grouped distributed flow shop with preparation time according to claim 1 or 6, characterized in that After the insertion-based neighborhood search is completed, perform the first local intensification operation based on insertion. The operation steps of the first local intensification based on insertion include: Find the key factory from the factory sequence π, and the key factory is the factory with the maximum completion time; Take out the workpieces from the groups of the key factory one by one in turn, test these workpieces in all positions of the groups of the key factory, and insert these workpieces into the best position with the minimum completion time to obtain the best workpiece sequence for each group.

8. The scheduling method for grouping distributed flow shops with preparation time according to claim 1, wherein After the first-stage strategy is completed, perform the second-stage strategy and execute the swap-based neighborhood search operation. The operation steps of the swap-based neighborhood search include: Find the key factory from the factory sequence π, and the key factory is the factory with the maximum completion time; Randomly extract a group from the key factory, and find the factory with the minimum completion time, and randomly extract a group from the smallest factory; Exchange a group randomly extracted from the key factory with a group randomly extracted from the smallest factory, and find the best position to insert in the exchanged factories to minimize the completion time.

9. The scheduling method for the distributed flow shop grouping with preparation time according to claim 8, wherein, After the neighborhood search operation based on exchange is completed, perform the second-stage destruction and reconstruction operation. The operation steps of the second-stage destruction and reconstruction include: Extract d groups of workpieces from the factory sequence π, where the value range of d is 2-7, and the key factory is the factory with the maximum completion time among all factories; Randomly take out a group from the key factory in turn until the number of taken-out groups is equal to d; Re-insert the d taken-out groups into the best position of the key factory to minimize the completion time.

10. The scheduling method for grouping distributed flow shops with preparation time according to claim 9, characterized in that, After the second-stage destruction and reconstruction operation is completed, perform the second local intensification operation based on insertion. The operation steps of the second local intensification based on insertion include: Find the key factory from the factory sequence π, and the key factory is the factory with the maximum completion time; Take out the workpieces from the groups of the key factory one by one in turn, test all positions of the groups of the key factory for the workpieces, and insert the workpieces into the best position with the minimum completion time to obtain the best workpiece sequence for each group.

Images