A distributed process planning and shop floor scheduling integrated optimization method

Abstract

The application discloses a distributed process planning and workshop scheduling integrated optimization method. The application firstly classifies four decision sub-problems of the distributed process planning and workshop scheduling integrated optimization problem into two categories: selection problem and sequencing problem. Then, the selection problem is regarded as a main problem, and the sequencing problem is regarded as a sub-problem, and the two problems are solved respectively, and two groups of Benders optimality cuts and a Benders optimality cut selection strategy are designed to feed back the solving condition of the iteration to the main problem, so that the iteration between the main problem and the sub-problem is realized until the convergence rule is satisfied. The application is not only suitable for the production scene with high requirement on the calculation time, but also suitable for the production scene with high requirement on the quality of the solution. A large number of simulation experiments verify that the application can realize the fast solution of the distributed process planning and workshop scheduling integrated optimization problem, and ensure the quality of the solution.

Description

Technical Field

[0001] This invention belongs to the field of production and manufacturing technology in a distributed environment, specifically relating to a distributed process planning and workshop scheduling integrated optimization method. Background Technology

[0002] The Distributed Integrated Process Planning and Scheduling (DIPPS) problem considers the simultaneous decision-making of process planning and shop floor scheduling in a distributed manufacturing environment, thereby optimizing pre-defined performance indicators. In a distributed manufacturing environment, each workpiece can be processed by a system with multiple Flexible Manufacturing Cells (FMCs). Currently, literature research on the DIPPS problem only includes some metaheuristic algorithms, and the performance of these methods is generally poor.

[0003] In the distributed process planning and shop floor scheduling integrated optimization problem, there are H independent flexible manufacturing cells distributed across different geographical locations in a factory, M machines, and N workpieces with multiple optional process flows. Once a flexible manufacturing cell is selected for a workpiece, all operations of that workpiece must be processed within that flexible manufacturing cell; production across flexible manufacturing cells is not allowed. After all workpieces have been assigned flexible manufacturing cells, a suitable process flow needs to be selected for each workpiece, and a suitable processing machine needs to be selected for each operation within the selected process flow. Then, it needs to be ensured that each machine can process only one operation at a time, and operations belonging to the same process flow need to be processed in their pre-defined order. Furthermore, it is assumed that all flexible manufacturing cells and machines are available initially, and all workpieces can be processed by any flexible manufacturing cell. Once a workpiece has been processed in its assigned flexible manufacturing cell, it needs to be immediately transported to a buffer zone, and the transport time is fixed. Therefore, in the integrated optimization problem of distributed process planning and shop floor scheduling, the following four decision sub-problems need to be solved: selecting a flexible manufacturing unit for processing each workpiece, selecting a process flow for each workpiece with a selected flexible manufacturing unit, selecting a machine for each operation in the selected process flow, and determining the processing sequence of operations assigned to the same machine.

[0004] While industry and academia have made significant progress in addressing the Integrated Process Planning and Scheduling (IPPS) problem, the widespread use of flexible manufacturing cells in modern manufacturing systems has replaced traditional centralized manufacturing environments with flexible distributed manufacturing environments. This has resulted in methods designed for the IPPS problem not being directly applicable to solving distributed IPPS problems, which are extensions of the IPPS problem. Furthermore, current metaheuristic algorithms for distributed IPPS problems yield solutions of low quality, failing to meet the needs of actual production. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the present invention aims to provide a distributed process planning and shop floor scheduling integrated optimization method. This method can improve the quality of solutions to the distributed process planning and shop floor scheduling integrated optimization problem regardless of the scale of the production scenario, while also reducing the computation time consumed by the algorithm, thus meeting the needs of actual production. To achieve the above objective, the present invention adopts the following technical solution: a distributed process planning and shop floor scheduling integrated optimization method, comprising the following steps:

[0006] Step S1: Transform the distributed process planning and shop floor scheduling integration optimization problem into a formal description using digital symbols;

[0007] Step S2: Analyze the preset constraints of the distributed process planning and workshop scheduling integrated optimization problem;

[0008] Step S3: Obtain the target to be optimized and construct the corresponding target optimization function;

[0009] Step S4: Decompose the distributed process planning and shop floor scheduling integrated optimization problem into sub-problems based on model reconstruction: Divide the four sub-decision tasks of the distributed process planning and shop floor scheduling integrated optimization problem into two types of sub-problems (selection problem and sequencing problem). The selection problem refers to selecting a flexible manufacturing cell for processing each workpiece, selecting a process flow for each workpiece with a selected flexible manufacturing cell, and selecting a machine for each operation in the selected process flow; the sequencing problem refers to determining the processing order of operations assigned to the same machine.

[0010] Step S5: Construct a logic-based Benders decomposition (LBBD) algorithm; iteratively optimize the logic-based Benders decomposition algorithm until the final solution set is output, and parse out the final process planning selection and production scheduling arrangement.

[0011] Further, step S1 specifically involves: Let i and i′ be the workpiece indices, N be the set of workpieces, i and i′ ∈ N, |N| be the cardinality of N, representing the number of workpieces to be processed; k be the machine indices, M be the set of machines, k ∈ M; h and h′ be the indices of the flexible manufacturing units that can be used to process workpiece i, H i Let H be the set of flexible manufacturing cells that can be used to process workpiece i, where h, h′∈H i ;l, l′ are the sequence numbers of the optional process flow for workpiece i in flexible manufacturing unit h, Let h be the set of optional process flows for workpiece i in flexible manufacturing unit h. j and j′ are the sequence numbers of the operation in the l-th process flow of workpiece i in flexible manufacturing unit h. Let i be the set of operations in the l-th process flow of workpiece i in flexible manufacturing unit h. for The cardinality represents the number of operations in the l-th process flow of workpiece i in flexible manufacturing cell h, and J is equal to the largest number of operations among all workpieces. O ij This refers to the j-th process of workpiece i; For workpiece i, the j-th process in the l-th process flow of flexible manufacturing unit h express The final step (the last process); This indicates that machine k can be used for processing. otherwise express Processing time on machine k; Let A be the transport time of workpiece i in flexible manufacturing cell h; A is a sufficiently large positive integer; C max For production cycle; c i Let be the completion time of workpiece i; if workpiece i is assigned to flexible manufacturing cell h, then... otherwise If workpiece i is selected in the l-th process flow of flexible manufacturing cell h, then otherwise If the process If assigned to machine k otherwise For process The start time of processing on machine k; For process The end processing time on machine k; if process O i′j′ and process O ij All are assigned to machine k for processing, and process O i′j′ Directly or indirectly in O ij Post-processing otherwise

[0012] Furthermore, the preset constraint mentioned in step S2 is:

[0013] Select only one flexible manufacturing cell from the available options for each workpiece to process that workpiece:

[0014]

[0015] Choose only one process flow from the available process flows for the workpiece in the selected flexible manufacturing cell to process the workpiece:

[0016]

[0017] Next, a processing machine must be selected for each step of the chosen process flow for each workpiece:

[0018]

[0019] The constraints for determining the start and end times of a process are as follows:

[0020]

[0021]

[0022] Constraint (4) ensures that when Time, i.e., process If it is not assigned to machine k, then the process... The start and end times of processing on machine k are both 0. Conversely, according to constraint (5), if the process... If the process is assigned to machine k, then the operation... The difference between the end time and start time of machining on machine k must not be less than the operation time. Processing time on machine k

[0023] The processing sequence between operations assigned to the same machine is determined by the following formula.

[0024]

[0025]

[0026]

[0027] The start and end times of two adjacent processes in the same process flow are determined by the following formula.

[0028]

[0029] The completion time of each workpiece is not less than the completion time of the last machining operation of that workpiece. Therefore, the following constraints apply:

[0030]

[0031] For the objective function, the following constraints apply:

[0032]

[0033] Finally, the feasible domain of all variables is defined as follows:

[0034]

[0035] Furthermore, step S3 specifically involves minimizing the production cycle, i.e., minimizing the maximum completion time, as the performance indicator in this invention. The objective function can be derived as follows:

[0036] min C max (12)

[0037] Furthermore, step S5 specifically includes:

[0038] Step S51: Treat the selection problem as the master problem (MP) and establish a mixed-integer linear programming (MILP) model to solve the master problem. To describe this MILP model, this invention introduces a 0-1 variable yk to indicate whether a process is assigned to machine k. In addition, two continuous variables... r k and q k Used to represent the minimum start time and minimum remaining processing time on machine k, a 0-1 variable. and Used to indicate Is it the operation with the minimum start time or minimum remaining processing time on machine k? The specific mixed-integer linear programming model is as follows:

[0039] min C max (13)

[0040] st(1), (2), (3)

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Benders optimal cut (24).

[0052] Step S52: Treat the sorting problem as a sub-problem (SP). This can be obtained by solving the mixed-integer linear programming model established in step S51. and A set of values ​​is taken as known parameters in the subproblem, thus simplifying the subproblem into the classic shop floor scheduling problem, used to determine the processing order of operations assigned to the same machine and calculate the solution to the original problem. Based on this, a constraint programming (CP) model is established to solve the subproblem. To describe this constraint programming model, this invention defines the variable Ok as the set of operations that can be processed on machine k; Let i be the 0th step in the l-th process flow of FMC h. This step is fictitious, so... For use in processing procedures A collection of machines; For process The time intervals are optional (optional means they exist if they are considered in the solution; otherwise, they do not). Indicate process The time interval for processing on machine k is optional. if If it exists otherwise And size = 0; IS(O k ) for O k The set of time intervals. Furthermore, this invention introduces the function `endOf(I)` to return the end time of I if it exists, otherwise returning 0; the function `noOverlap(IS)` to specify that the time intervals in IS cannot overlap; and the function `endBeforeStart(I, I′)` to ensure that the end time of time interval I is less than the start time of time interval I′. The specific constraint programming model is as follows:

[0053]

[0054]

[0055]

[0056] Step S53: Determine whether the solutions obtained from solving the main problem and the subproblems converge. If they converge, the method ends; otherwise, design two Benders optimality cuts (classical and enhanced) based on the feasible solutions to the original problem obtained from the subproblems and the output of the main problem. Then, select the Benders optimality cut and add the selected Benders optimality cut to the mixed integer linear programming model of the main problem, and return to step S51.

[0057] Furthermore, the classic Benders optimal cut described in step S53 is as follows:

[0058]

[0059] in This represents the feasible solution obtained for the subproblem in the t-th iteration.

[0060] The enhanced Benders optimality cut described in step S53 is as follows:

[0061]

[0062] Where N s It is a set of selected tasks. This is the corresponding feasible solution.

[0063] The Benders optimal cut selection strategy described in step S53 is as follows:

[0064] Based on the above design, when the method proposed in this invention obtains a feasible solution each time, it derives two sets of Benders optimal cuts. However, if both sets of derived Benders optimal cuts are included in the main problem, the difficulty of solving the main problem increases with the number of iterations. Therefore, it is necessary to analyze the applicability of the two sets of Benders optimal cuts according to the specific situation and make a selection accordingly. Since the Benders optimal cut (29) only considers the selected workpiece... The value of the workpiece is determined by the selection criteria, while for those workpieces that are not selected... The value of is not restricted in any way, therefore Benders optimal cut (29) is more efficient than Benders optimal cut (28). For example, if the workpiece i∈N s ,have and Therefore, Benders optimality cut (28) will only restrict one solution to the main problem, while Benders optimality cut (29) can restrict multiple solutions to the main problem. This is because the unselected artifacts... The value of is unrestricted and can be arbitrarily set to 0 or 1. Therefore, when a Benders optimal cut (29) is generated, the present invention only adds the Benders optimal cut (29) containing the minimum number of workpieces to the main problem. Conversely, when no Benders optimal cut (29) is generated, the present invention adds the Benders optimal cut (28) to the main problem.

[0065] Finally, the convergence criteria described in step S53 are as follows:

[0066] 1. That is, the solutions to the subproblem and the main problem converge at the t-th iteration;

[0067] 2. That is, the solution to the main problem in the t-th iteration is equal to the best solution obtained so far for the subproblems.

[0068] The technical effects of this invention are as follows:

[0069] This invention addresses the distributed process planning and shop floor scheduling integrated optimization problem by minimizing completion time through simultaneously allocating workpieces to the most suitable flexible manufacturing cell, selecting the most suitable process flow for each workpiece, choosing the most suitable machine for each step of the selected process flow, and determining the processing sequence of steps assigned to the same machine. This invention first categorizes the four decision subproblems of the distributed process planning and shop floor scheduling integrated optimization problem into two types: selection problem and ordering problem. The selection problem is considered the main problem, and the ordering problem is treated as a subproblem. Then, two sets of Benders optimality cuts and a Benders optimality cut selection strategy are designed to feed back the solution progress of the current iteration to the main problem, thereby achieving iterative back-and-forth between the main problem and the subproblems until the convergence criterion is met. This invention is applicable not only to production scenarios with high computational time requirements but also to production scenarios with high requirements for solution quality. Finally, extensive simulation experiments verify that this invention can achieve a fast solution to the distributed process planning and shop floor scheduling integrated optimization problem and obtain solutions of good quality. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the process of the present invention;

[0071] Figure 2 This is a schematic diagram illustrating the generation of enhanced Benders optimal cuts according to a specific embodiment of the present invention;

[0072] Figure 2 (a) is the optimal scheduling scheme for all workpieces for the subproblem in a specific embodiment of the present invention;

[0073] Figure 2 (b) is the optimal scheduling scheme for the subproblem in a specific embodiment of the present invention for the selected workpiece (1, 5);

[0074] Figure 2 (c) is the optimal scheduling scheme for the subproblem in a specific embodiment of the present invention for the selected workpiece (3, 4);

[0075] Figure 3 These are schematic diagrams illustrating two convergence scenarios in a specific embodiment of the present invention;

[0076] Figure 3 (a) is a schematic diagram of the first convergence scenario in a specific embodiment of the present invention;

[0077] Figure 3 (b) is a schematic diagram of the second convergence scenario in a specific embodiment of the present invention. Detailed Implementation

[0078] refer to Figure 1 The present invention provides a method such as Figure 1The distributed process planning and shop floor scheduling integration optimization method shown includes the following steps:

[0079] Step S1: Define variable symbols to mathematically describe the integrated optimization problem of distributed process planning and shop floor scheduling;

[0080] Step S2: Analyze the constraints of the integrated optimization problem of distributed process planning and shop floor scheduling;

[0081] Step S3: Analyze the metrics to be optimized and establish the corresponding objective optimization function;

[0082] Step S4: Decompose the distributed process planning and shop floor scheduling integrated optimization problem into sub-problems based on model reconstruction: Divide the four sub-decision tasks of the distributed process planning and shop floor scheduling integrated optimization problem into two types of sub-problems (selection problem and sequencing problem). The selection problem refers to selecting a flexible manufacturing cell for processing each workpiece, selecting a process flow for each workpiece with a selected flexible manufacturing cell, and selecting a machine for each operation in the selected process flow; the sequencing problem refers to determining the processing order of operations assigned to the same machine.

[0083] Step S5: Construct a logic-based Benders decomposition algorithm; iteratively optimize the logic-based Benders decomposition algorithm until the final solution set is output; and parse to obtain the final process planning selection and scheduling arrangement.

[0084] In this embodiment, step S1 specifically involves defining the following variable symbols:

[0085] Let i and i′ be the workpiece indices, N be the set of workpieces, i and i′ ∈ N, |N| be the cardinality of N, representing the number of workpieces to be processed; k be the machine indices, M be the set of machines, k ∈ M; h and h′ be the indices of the flexible manufacturing units that can be used to process workpiece i, H i Let H be the set of flexible manufacturing cells that can be used to process workpiece i, where h, h′∈H i ;l, l′ are the sequence numbers of the optional process flow for workpiece i in flexible manufacturing unit h, Let h be the set of optional process flows for workpiece i in flexible manufacturing unit h. j and j′ are the sequence numbers of the operation in the l-th process flow of workpiece i in flexible manufacturing unit h. Let i be the set of operations in the l-th process flow of workpiece i in flexible manufacturing unit h. for The cardinality represents the number of operations in the l-th process flow of workpiece i in flexible manufacturing cell h, and J is equal to the largest number of operations among all workpieces. O ijThis refers to the j-th process of workpiece i; For workpiece i, the j-th process in the l-th process flow of flexible manufacturing unit h ( express The final step (the last process); This indicates that machine k can be used for processing. otherwise express Processing time on machine k; Let A be the transport time of workpiece i in flexible manufacturing cell h; A is a sufficiently large positive integer; C max For production cycle; c i Let be the completion time of workpiece i; if workpiece i is assigned to flexible manufacturing cell h, then... otherwise If workpiece i is selected in the l-th process flow of flexible manufacturing cell h, then otherwise If the process If assigned to machine k otherwise For process The start time of processing on machine k; For process The end processing time on machine k; if process O i′j′ and process O ij All are assigned to machine k for processing, and process O i′j′ Directly or indirectly in O ij Post-processing is assigned to machine k. otherwise

[0086] In this embodiment, the constraints in step S2 include:

[0087] Select only one flexible manufacturing cell from the available options for each workpiece to process that workpiece:

[0088]

[0089] Choose only one process flow from the available process flows for the workpiece in the selected flexible manufacturing cell to process the workpiece:

[0090]

[0091] Next, a processing machine must be selected for each step of the chosen process flow for each workpiece:

[0092]

[0093] The constraints for determining the start and end times of a process are as follows:

[0094]

[0095]

[0096] Constraint (33) ensures that when Time, i.e., process If it is not assigned to machine k, then the process... The start and end times of processing on machine k are both 0. Conversely, according to constraint (34), if the process... If the process is assigned to machine k, then the operation... The difference between the end time and start time of machining on machine k must not be less than the operation time. Processing time on machine k

[0097] The processing sequence between operations assigned to the same machine is determined by the following formula.

[0098]

[0099]

[0100]

[0101] The start and end times of two adjacent processes in the same process flow are determined by the following formula.

[0102]

[0103] The completion time of each workpiece is not less than the completion time of the last machining operation of that workpiece. Therefore, the following constraints apply:

[0104]

[0105] For the objective function, the following constraints apply:

[0106]

[0107] Finally, the feasible domain of all variables is defined as follows:

[0108]

[0109] In this embodiment, step S3 specifically involves: determining that the target metric to be optimized is minimizing the production cycle, i.e., minimizing the maximum completion time. The objective function can then be obtained as follows:

[0110] min C max (41)

[0111] In this embodiment, step S5 specifically includes the following steps:

[0112] Step S51: Treat the selection problem as the main problem. Consider the variables. Using constraints (30), (31), and (32), a mixed-integer linear programming model is established to solve the main problem;

[0113] Step S52: Treat the sorting problem as a subproblem. This can be obtained by solving the mixed-integer linear programming model in step S51. and If we consider a set of values ​​as known parameters in a subproblem, then the subproblem is simplified to the classic shop floor scheduling problem, used to determine the processing order of operations assigned to the same machine and to calculate the solution to the original problem. Based on this, a constraint programming model is established to solve the subproblem;

[0114] Step S53: Determine whether the solutions obtained from solving the main problem and the subproblems converge. If they converge, the method ends; otherwise, design two Benders optimality cuts (classical and enhanced) based on the feasible solutions to the original problem obtained from the subproblems and the output of the main problem. Then, select the Benders optimality cut and add the selected Benders optimality cut to the mixed integer linear programming model of the main problem, and return to step S51.

[0115] Preferably, step S51 specifically includes:

[0116] Step S511: Consider only variables The constraints (30), (31), and (32) can be used to handle selection problems, but cannot be used to solve production cycles. Therefore, by simplifying the calculation of the maximum completion time of the workpiece, a lower bound can be obtained for the distributed process planning and shop floor scheduling integrated optimization problem:

[0117]

[0118] Step S512: By simplifying the calculation of the machine's maximum completion time, a lower bound can also be obtained for the distributed process planning and shop floor scheduling integrated optimization problem:

[0119]

[0120]

[0121] Step S513: Given Therefore, the mixed-integer linear programming model for solving the main problem can be obtained as follows:

[0122] min C max (42)

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] Benders optimal cut (49).

[0131] Step S514:

[0132] Since constraints (46) and (47) are nonlinear, the computation time for solving the lower bound increases exponentially with the problem size. Therefore, constraints (46) and (47) need to be linearized to improve computational efficiency. To describe this linearized model, this invention defines a 0-1 variable y. k This indicates whether a process has been assigned to machine k. Additionally, two continuous variables... r k and q k Used to represent the minimum start time and minimum remaining processing time on machine k, a 0-1 variable. and Used to indicate Is it the operation that generates the minimum start time or minimum remaining processing time on machine k? The specific linearized model is as follows:

[0133] min C max (50)

[0134] st(43), (44), (45)

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] Benders optimal cut (61).

[0146] Preferably, step S52 specifically includes:

[0147] Define variable O k Let k be the set of operations that can be processed on machine k. Let i be the 0th step in the l-th process flow of FMC h. This step is fictitious, so... For use in processing procedures A collection of machines; For process The time intervals are optional (optional means they exist if they are considered in the solution; otherwise, they do not). Indicate process The time interval for processing on machine k is optional. if If it exists otherwise And size = 0; IS(O k ) for O k The set of time intervals. Furthermore, this invention introduces the function `endOf(I)` to return the end time of I if it exists, otherwise returning 0; the function `noOverlap(IS)` to specify that the time intervals in IS cannot overlap; and the function `endBeforeStart(I, I′)` to ensure that the end time of time interval I is less than the start time of time interval I′. The specific constraint programming model is as follows:

[0148]

[0149]

[0150]

[0151] Preferably, step S53 specifically includes:

[0152] Step S531: The Benders optimality cut, designed based on the feasible solution of the primal problem obtained from the subproblems and the output of the primal problem, is intended to ensure that if the solution obtained by the proposed method in this iteration is only a feasible solution, then in subsequent iterations, the Benders optimality cut is added to the primal problem to ensure that when the values ​​of the variables in the primal problem are the same as those in the current iteration, the solution obtained by the primal problem is greater than or equal to the feasible solution obtained by the subproblems in the current iteration. This is because the output of the primal problem is... and A set of values, so by changing any one of them... The value of is used to obtain two different solutions, and based on this, the classic Benders optimality cut is designed as follows:

[0153]

[0154] in This represents the feasible solution obtained for the subproblem in the t-th iteration.

[0155] Step S532: It is well known that the effectiveness of the Benders optimality cut is crucial to the convergence speed of the logic-based Benders decomposition algorithm. Unfortunately, since the Benders optimality cut (65) considers all values ​​of 1... Therefore, the Benders optimality cut (65) only affects a small subset of the solutions to the main problem. In the extreme case, by constraining with the Benders optimality cut (65), the main problem obtains a set of solutions in the (t+1)th iteration. Only one value differs from its value in the t-th iteration. Therefore, Benders optimality cut (65) performs poorly in practical applications, and a more efficient Benders optimality cut needs to be designed to improve the computational efficiency of the logic-based Benders decomposition algorithm. Therefore, this invention obtains an upper bound for the distributed process planning and shop floor scheduling integrated optimization problem by combining a scheduling rule-based algorithm and a constraint programming model. The design motivation of this hybrid method is that the minimum production cycle of the distributed process planning and shop floor scheduling integrated optimization problem is determined by the maximum completion time of the workpiece or machine. Therefore, in this hybrid method, the flexible manufacturing cell and process flow of each workpiece are selected using scheduling rules (by selecting the processing time and the minimum process flow for each workpiece). It should be noted that although the machine with the minimum processing time is selected for each process flow when calculating the processing time of each process flow, all available machines for each process flow must be considered during the machine selection process to make the load of each machine as balanced as possible. Finally, this hybrid method uses a constraint programming model to sort the processes assigned to the same machine to calculate the upper bound. The pseudocode of the hybrid method is shown below.

[0156]

[0157]

[0158] Based on this upper bound, the enhanced Benders optimality cut designed in this invention is as follows. In each iteration, once a solution to the subproblem is obtained, and this solution is greater than the current upper bound, this invention selects a certain number of artifacts (greater than or equal to 2 but less than n) from the output of the main problem. The value of n is determined by... The decision, in which T max This sets the maximum computation time for the logic-based Benders decomposition algorithm. If n > N, we set n = N. If n < 2, this invention sets n = 2. Then, this invention calculates the minimum production cycle corresponding to the selected workpiece set. If the obtained minimum production cycle is still greater than the current upper bound, then this invention designs the following enhanced Benders optimality cut:

[0159]

[0160] Where N s It is a set of selected tasks. This is the corresponding feasible solution.

[0161] It is worth noting that if the feasible solution obtained by the logic-based Benders decomposition algorithm is better than the current upper bound, then the feasible solution is used to update the current upper bound.

[0162] Figure 2 This is an illustrative example of generating enhanced Benders optimal cuts. Assume there are two independent flexible manufacturing cells located in different geographical locations within a factory, 10 machines, and 6 workpieces with multiple optional process flows. Figure 2 (a) shows the optimal scheduling scheme considering all jobs, with a minimum production cycle of 109, which is greater than the current upper bound (100). Therefore, we can generate an enhanced Benders optimality cut for this instance. Here, we take n=2 as an example and obtain... Figure 2 (b) and Figure 2 (c). From Figure 2 In (b), we can see that when N s When the interval is {1, 5}, the corresponding minimum production cycle is 93, which is less than the current upper bound (100), therefore no enhanced Benders optimality cut is generated. Meanwhile, from... Figure 2 In (c), we can see that when N s When the interval is {3, 4}, the corresponding minimum production cycle is 108, which is greater than the current upper bound (100). Therefore, the enhanced Benders optimality cut can be generated as shown below:

[0163]

[0164] Step S533: Based on the above design, when the logic-based Benders decomposition algorithm obtains a feasible solution each time, it derives two sets of Benders optimal cuts. However, if both sets of derived Benders optimal cuts are included in MP, the difficulty of solving the main problem increases with the number of iterations. Therefore, it is necessary to analyze the applicability of the two sets of Benders optimal cuts according to the specific situation and make a selection. Since the Benders optimal cut (66) only considers the selected workpiece... The value of the workpiece is determined by the selection criteria, while for those workpieces that are not selected... The value of is not restricted in any way, therefore Benders optimal cut (66) is more efficient than Benders optimal cut (65). For example, if the workpiece i∈N s ,have and Therefore, Benders optimality cut (65) will only restrict one solution to the main problem, while Benders optimality cut (66) can restrict multiple solutions to the main problem. This is because the unselected artifacts... The value of is unrestricted and can be arbitrarily set to 0 or 1. Therefore, when a Benders optimal cut (66) is generated, we only add the Benders optimal cut (66) containing the minimum number of workpieces to the main problem. Conversely, when no Benders optimal cut (66) is generated, we add the Benders optimal cut (65) to the main problem.

[0165] Step S534: As Figure 3 As shown, the convergence criterion for the solution of the logic-based Benders decomposition algorithm is as follows:

[0166] 1. That is, the solutions to the subproblem and the main problem converge at the t-th iteration;

[0167] 2. That is, the solution to the main problem in the t-th iteration is equal to the best solution obtained so far for the subproblems.

[0168] To test the performance of this invention, a dataset consisting of up to 120 workpieces and 20 machines was constructed in the simulation experiment. This dataset contains 34 production scenarios, which can be divided into 4 groups according to the number of workpieces: Group A (maximum 8 workpieces), Group B (10 to 30 workpieces), Group C (36 to 54 workpieces), and Group D (56 to 120 workpieces).

[0169] The algorithm of this invention was tested on the aforementioned 34 different production scenarios. Simultaneously, within the same production scenario, the logic-based Benders decomposition algorithm (LBBD) proposed in this invention was compared with mixed-integer linear programming (MILP), constrained programming (CP), and an improved genetic algorithm (GA). 1 ), Extended Genetic Algorithm (GA) 2 The algorithm was compared with the improved Imperialist Competition Algorithm (ICA). Because these metaheuristic-based comparison algorithms are randomized, they were run independently 30 times for each production scenario, and the minimum production cycle value was taken as the final result for that scenario. The experimental results are shown in Table 1.

[0170] Table 1 Experimental Results

[0171]

[0172] As can be seen from Table 1, compared to GA 1 GA 2 Compared to ICA, the logic-based Benders decomposition algorithm proposed in this invention has significant advantages. Specifically, compared to GA... 1 Although the logic-based Benders decomposition algorithm of this invention consumes more computation time, the solutions obtained by the logic-based Benders decomposition algorithm of this invention are far better than those obtained by GA for 34 production scenarios. 1 Obtained. Compared to GA 2 Compared to ICA, the logic-based Benders decomposition algorithm of this invention achieves simultaneous improvements in both solution accuracy and efficiency. Furthermore, compared to MILP and CP, the logic-based Benders decomposition algorithm proposed in this invention has a slightly longer solution time in small-scale production scenarios. This is because small-scale production scenarios are essentially simple distributed process planning and shop floor scheduling integrated optimization problems, with a limited number of feasible scheduling schemes. Therefore, MILP and CP can find the optimal solution for these production scenarios in a very short time. However, in the logic-based Benders decomposition algorithm proposed in this invention, the solution obtained from the main problem is a lower bound of the distributed process planning and shop floor scheduling integrated optimization problem, so issues such as… Figure 3The convergence scenario shown in (b) occurs when the subproblem has obtained the optimal solution to the Distributed Process Planning and Shop Floor Scheduling (MILP) integrated optimization problem, but the solution obtained for the main problem is only a lower bound of the MILP integrated optimization problem. Therefore, the logic-based Benders decomposition algorithm proposed in this invention cannot converge until the solution obtained for the main problem equals the optimal solution to the MILP integrated optimization problem. For medium- and large-scale production scenarios, MILP sometimes fails to find feasible solutions for some production scenarios. In comparison, the logic-based Benders decomposition algorithm of this invention demonstrates an overwhelming advantage, not only obtaining better solutions but also consuming less computation time.

[0173] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Those skilled in the art can modify or make equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention. The scope of protection of the present invention should be determined by the claims.

Claims

1. A distributed process planning and shop floor scheduling integrated optimization method, characterized in that, Includes the following steps: Step S1: Transform the distributed process planning and shop floor scheduling integration optimization problem into a formal description using digital symbols; Step S2: Analyze the preset constraints of the integrated optimization problem of distributed process planning and workshop scheduling; Step S3: Obtain the target to be optimized and construct the corresponding target optimization function; Step S4: Decompose the distributed process planning and shop floor scheduling integrated optimization problem into sub-problems based on model reconstruction: Divide the four sub-decision tasks of the distributed process planning and shop floor scheduling integrated optimization problem into two types of sub-problems: selection problem and sequencing problem. The selection problem refers to selecting a flexible manufacturing unit for processing each workpiece, selecting a process flow for each workpiece with a selected flexible manufacturing unit, and selecting a machine for each operation in the selected process flow. The sequencing problem refers to determining the processing order of operations assigned to the same machine. Step S5: Construct a logic-based Benders decomposition algorithm; iteratively optimize the logic-based Benders decomposition algorithm until the final solution set is output; finally, obtain the process planning selection and scheduling arrangement, specifically as follows: Step S51: Treat the selection problem as the main problem and establish a mixed-integer linear programming model to solve the main problem; Step S52: Treat the sorting problem as a subproblem, and obtain the solution by solving the mixed-integer linear programming model established in step S51. and If a set of values ​​is taken as known parameters in a subproblem, the subproblem degenerates into a classic shop floor scheduling problem. A constraint programming model is then established to solve the subproblem. Step S53: Determine whether the solutions obtained from solving the main problem and the subproblems converge. If they converge, the method ends; otherwise, design classic Benders optimality cuts and enhanced Benders optimality cuts based on the feasible solutions to the original problem obtained from the subproblems and the output of the main problem. Then, select the Benders optimality cuts and finally add the selected Benders optimality cuts to the mixed-integer linear programming model of the main problem, and return to step S51.

2. The distributed process planning and shop floor scheduling integrated optimization method as described in claim 1, characterized in that, Specifically, step S1 is as follows: Let... This is the workpiece's serial number. A collection of workpieces. , for The base number represents the number of workpieces to be processed; This is the machine's serial number. A collection of machines. ; For use in machining workpieces The serial number of the flexible manufacturing unit. For use in machining workpieces A collection of flexible manufacturing units, ; For workpiece In flexible manufacturing units The sequence number of the optional process flow. For workpiece In flexible manufacturing units A collection of optional process flows, ; For workpiece In flexible manufacturing units The first in The sequence number of each process step in the technological process. For workpiece In flexible manufacturing units The first in A collection of processes in a technological flow. , for The base number represents the workpiece. In flexible manufacturing units The first in The number of steps in a process flow Equal to the largest of all workpieces , ; For workpiece The One process; For workpiece In flexible manufacturing units The first in The first in the process flow One process; Indicates machine Used for processing ,otherwise ; express In the machine Processing time; For workpiece In flexible manufacturing units The transit time; It is a sufficiently large positive integer; For the production cycle; For workpiece Completion time; If the workpiece Assigned to flexible manufacturing unit Middle ,otherwise If the workpiece In flexible manufacturing units The Middle If a process flow is selected, then ,otherwise If the process Assigned to machine but ,otherwise ; For process In the machine Start processing time; For process In the machine The end processing time on the process; if the process and process All allocated to machines Upper processing, and process Directly or indirectly Post-processing ,otherwise .

3. The distributed process planning and shop floor scheduling integrated optimization method as described in claim 1, characterized in that, The convergence criterion described in step S53 is as follows: First, the solutions to the subproblems and the main problem are in the... It converges on the second iteration; the third... In the next iteration, the solution to the main problem is equal to the best solution obtained so far for the subproblems.

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