Hybrid flow shop scheduling method and system with outsourcing options

Abstract

The invention belongs to the technical field of workshop production scheduling, and discloses a hybrid flow workshop scheduling method and system with outsourcing options, and the method comprises the steps: defining a problem; the method comprises the following steps: grouping workpieces, dividing the groups into an outsourcing group and an internal processing group, determining the internal processing group and a scheduling sequence and machine allocation of the workpieces in the internal processing group, and obtaining a parent population, an initial reference point and an initial file set; operating the internal processing group and the scheduling sequence of the workpieces in the internal processing group to obtain a sub-population, combining the sub-population, the parent population and the initial file set to obtain a new reference point and a new file set, determining a contribution solution and a non-contribution solution, updating the reference point and the file set by using the contribution solution, and iterating for multiple times until the model converges to obtain a final scheduling scheme. According to the method, outsourcing options and a grouping technology are combined into a hybrid flow shop scheduling problem, and a target value is optimized by a self-adaptive reference point learning and cooperative driving multi-target algorithm, so that the production efficiency can be improved, the productivity can be increased, and the enterprise pressure can be reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of workshop production scheduling, and in particular to a hybrid flow workshop scheduling method and system with outsourcing options. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the increasing competition in the industry, the hybrid flow shop scheduling problem (HFSP) has become more and more popular. As an extension of the flow shop scheduling problem, it has some essential differences from the ordinary flow shop scheduling. It is divided into multiple processing stages, and each stage has multiple unrelated parallel machines. Therefore, HFSP must consider both the scheduling order of workpieces and the selection of machines in each stage. Since all machines can process a large number of similar products at the same stage at the same time, the hybrid flow shop has the advantage of high productivity. It is widely used in the fields of papermaking, glass production, aircraft engines, etc.

[0004] However, in the actual production process of high-frequency machining systems, due to the large number of machines and workpieces, it is easy to cause some difficulties in workpiece scheduling due to reasons such as machine failure, resulting in uncoordinated resource coordination and frequent congestion between processed workpieces. Therefore, in order to reduce the pressure brought to the factory by large-scale production, it is crucial to choose a suitable production scheduling method. Grouping technology and outsourcing solutions are favored because of their advantages of improving efficiency, expanding production capacity, and reducing corporate pressure. Grouping technology is to group multiple workpieces with the same or similar properties together and regard them as a whole to study the scheduling of the whole. The setup time between groups needs to be considered, but the setup time between workpieces does not need to be considered. In this case, the setup time of the group is only related to the processing order of the previous and next groups. In this way, time can be used reasonably, productivity can be improved, and the production system can be made more flexible. Outsourcing solutions are a production model chosen by the manufacturing industry to reduce pressure. It refers to the manufacturing industry contracting workpieces to subcontractors and paying production costs. After the subcontractor completes the processing, it returns to the workshop for the next process. Generally speaking, there are two main forms of outsourcing. One is that the manufacturer contracts all workpieces to subcontractors and processes them completely externally. Alternatively, a manufacturer may outsource one of the operations of a workpiece to a subcontractor. After the subcontractor completes the processing, the workpiece will be returned to the workshop while the other operations are still being processed in the workshop. Figure 1 As shown, the second outsourcing method can arrange the workpieces more reasonably, shorten the product delivery time and reduce the cost. So far, no research has introduced the example of outsourcing the group sequence to the contractor in the hybrid flow shop scheduling.

[0005] In addition, as the energy crisis has become one of the most serious problems in today's society, people are paying more and more attention to energy consumption. The "green, low-carbon" production model has also been deeply rooted in people's hearts. Therefore, this has prompted the manufacturing industry to consider not only the changes in completion time, but also the energy consumption in the production scheduling process. Developing effective energy-saving measures and technologies is particularly important for the manufacturing industry. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a hybrid flow shop scheduling method and system with outsourcing options, combines outsourcing options and grouping technology into the hybrid flow shop scheduling problem, and proposes an adaptive reference point learning and cooperation-driven multi-objective algorithm to optimize the target value, which can improve production efficiency, expand production capacity and reduce enterprise pressure.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a hybrid flow shop scheduling method with an outsourcing option, comprising the following steps:

[0009] Define the hybrid flow shop scheduling problem based on grouping techniques and outsourcing options, and construct the desired objective function in the actual production process and the constraints that satisfy the problem;

[0010] Based on the same processing stage, the workpieces to be processed are divided into several groups, the group sequence and the workpiece sequence within the group are obtained, the group sequence is divided into an outsourcing group sequence and an internal processing group sequence, the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group are determined, the parent population is obtained, the parent population is operated, and the initial reference point and the initial archive set are obtained;

[0011] Operate on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merge the sub-population, parent population and initial archive set to obtain a merged population, obtain a new reference point and a new archive set based on the merged population, determine the contributing solutions and non-contributing solutions in the new archive set, use the contributing solutions to update the reference point and archive set, iterate multiple times until the model converges, and obtain the final scheduling plan.

[0012] As an optional implementation, it also includes an energy-saving strategy, which is specifically:

[0013] On the basis of the final scheduling plan, determine whether there is idle time between the processing of two adjacent workpieces according to the start time and completion time of the processing of two adjacent workpieces. According to the idle time, reduce the processing speed of the previous workpiece without affecting the start time of the next workpiece.

[0014] As an optional implementation, the grouping sequence is divided into an outsourcing group sequence and an internal processing group sequence, specifically:

[0015] The ratio between the internal processing time and the outsourcing cost of each group is calculated, and the grouping sequence with a ratio greater than 1 is selected as the outsourcing group sequence.

[0016] As an optional implementation, the scheduling order of the internal processing group sequence and the workpiece sequence within the group is determined, specifically:

[0017] Calculate the setup time between internal processing groups, randomly select a group as the first element of the new group sequence, and then select the group with the shortest setup time in the previous group in turn until a new group sequence is formed;

[0018] Select the workpiece with the shortest processing time in the group as the first workpiece, and then select the workpieces with the shortest completion time with the previous workpiece one by one until a complete workpiece sequence is formed.

[0019] As an optional implementation, the machine allocation of the internal processing group sequence and the workpiece sequence within the group is determined, specifically:

[0020] According to the principle of idle machine priority, if there is an idle machine, the internal processing group will be arranged on the idle machine and the next idle time of the machine will be calculated. If there is no idle machine, the internal processing group will be arranged on the machine with the shortest time to the next idle period.

[0021] As an optional embodiment, operations are performed on the internal processing group sequence, including inserting groups based on the group sequence, exchanging groups based on the same machine, inserting groups based on different machines, and exchanging groups based on different machines;

[0022] Operate on the sequence of artifacts within the internal processing group, including swapping artifacts based on the same group and flipping artifacts in the same group.

[0023] In a second aspect, the present invention provides a hybrid flow shop scheduling system with an outsourcing option, comprising:

[0024] A model building module is configured to: define a hybrid flow shop scheduling problem based on grouping technology and outsourcing options, and construct an objective function expected in an actual production process and constraints that satisfy the problem;

[0025] The initialization module is configured to: divide the workpieces to be processed into several groups based on the same processing stage, obtain the group sequence and the workpiece sequence within the group, divide the group sequence into an outsourcing group sequence and an internal processing group sequence, determine the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group, obtain the parent population, operate the parent population, and obtain the initial reference point and the initial archive set;

[0026] The solution module is configured to: operate on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merge the sub-population, the parent population and the initial archive set to obtain a merged population, obtain a new reference point and a new archive set based on the merged population, determine the contributing solution and the non-contributing solution in the new archive set, update the reference point and the archive set using the contributing solution, iterate multiple times until the model converges, and obtain the final scheduling plan.

[0027] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in the first aspect is performed.

[0028] In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions, wherein when the computer instructions are executed by a processor, the method described in the first aspect is performed.

[0029] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method described in the first aspect.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The present invention proposes a hybrid flow shop scheduling method and system with outsourcing options, combines outsourcing options and grouping technology into the hybrid flow shop scheduling problem, constructs a hybrid flow shop scheduling model, proposes an adaptive reference point learning and cooperative driven multi-objective algorithm to optimize the target value, and generates a high-quality initial population according to a knowledge-based hybrid initialization method in the solution process. The reference point adaptation strategy is introduced in the co-evolution algorithm to make the population evolve towards the true Pareto frontier. The co-evolution algorithm is divided into two main stages. In the first stage, six search operators based on group sequences and workpiece sequences are designed to improve the depth and diversity of the solution set. In the second stage, the excellent solutions among the non-dominated solutions generated in the first stage are used to update the reference point, which is used to select the global optimal solution for the next iteration. This is more conducive to the evolution of the population towards the true Pareto frontier. The two stages cooperate with each other to ensure the diversity and convergence of the final non-dominated solution set. In addition, considering green scheduling, an effective energy-saving strategy is designed to reduce TEC. A large number of statistical analysis experiments (KW) show that the strategies selected by ARPCMOA in initialization, co-evolution and environment selection are effective and can improve production efficiency, expand production capacity and reduce enterprise pressure.

[0032] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0034] Figure 1 is an example of the second outsourcing method;

[0035] Figure 2 An example of adjusting the reference point;

[0036] Figure 3 A flow chart of a hybrid flow shop scheduling method with outsourcing options provided in Example 1 of the present invention;

[0037] Figure 4 An example of the encoding process of a hybrid flow shop scheduling method with outsourcing options provided in Embodiment 1 of the present invention;

[0038] Figure 5 An example of a decoding process of a hybrid flow shop scheduling method with outsourcing options provided in Embodiment 1 of the present invention;

[0039] Figure 6 A schematic diagram of a hybrid flow shop scheduling method with an outsourcing option provided in Embodiment 1 of the present invention for operating a group sequence;

[0040] Figure 7 A schematic diagram of a hybrid flow shop scheduling method with outsourcing options provided in Example 1 of the present invention operating a workpiece sequence;

[0041] Figure 8 A schematic diagram of an energy-saving strategy for a hybrid flow shop scheduling method with an outsourcing option provided in Example 1 of the present invention;

[0042] Fig. 9 Horizontal trends of various parameters of a hybrid flow shop scheduling method with outsourcing options provided in Example 1 of the present invention;

[0043] Fig.10 The experimental results of non-parametric test of a hybrid flow shop scheduling method with outsourcing option and a random initialization method provided in Example 1 of the present invention;

[0044] Fig.11 The experimental results of non-parametric test of a hybrid flow shop scheduling method with outsourcing option and randomly evolving grouping sequence provided in Example 1 of the present invention;

[0045] Fig.12The experimental results of non-parametric test of a hybrid flow shop scheduling method with outsourcing options and a random evolution strategy of workpieces provided in Example 1 of the present invention;

[0046] Fig.13 The experimental results of a hybrid flow shop scheduling method with outsourcing options and a non-parametric test of random environment selection provided in Example 1 of the present invention;

[0047] Fig.14 The experimental results of non-parametric tests of a hybrid flow shop scheduling method with outsourcing options provided in Example 1 of the present invention and other algorithms;

[0048] Fig.15 It is the Pareto front distribution diagram of multiple comparison algorithms under the same instance conditions;

[0049] Fig.16 A Gantt chart of a solution to a hybrid flow shop scheduling method with an outsourcing option provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0051] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0052] It should be noted that the terms used herein are only for describing specific embodiments, and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "include" and "have" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0053] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0054] Example 1

[0055] like Figure 3 As shown, this embodiment provides a hybrid flow shop scheduling method with an outsourcing option, comprising the following steps:

[0056] S1 defines the hybrid flow shop scheduling problem based on grouping technology and outsourcing options, and constructs the desired objective function in the actual production process and the constraints that meet the problem;

[0057] S2 divides the workpieces to be processed into several groups based on the same processing stage, obtains the group sequence and the workpiece sequence within the group, divides the group sequence into an outsourcing group sequence and an internal processing group sequence, determines the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group, obtains the parent population, operates the parent population, and obtains the initial reference point and the initial archive set;

[0058] S3 operates on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merges the sub-population, the parent population and the initial archive set to obtain a merged population, obtains a new reference point and a new archive set based on the merged population, determines the contributing solutions and non-contributing solutions in the new archive set, uses the contributing solutions to update the reference point and the archive set, iterates multiple times until the model converges, and obtains the final scheduling plan.

[0059] It also includes S4 energy saving strategy, which is specifically:

[0060] On the basis of the final scheduling plan, determine whether there is idle time between the processing of two adjacent workpieces according to the start time and completion time of the processing of two adjacent workpieces. According to the idle time, reduce the processing speed of the previous workpiece without affecting the start time of the next workpiece.

[0061] Firstly, the hybrid flow shop scheduling problem based on grouping technology and outsourcing options is defined, and the desired objective function in the actual production process and the constraints that satisfy the problem are constructed.

[0062] This disclosure considers a hybrid flow shop scheduling problem with grouping and outsourcing constraints, named HFGSP_OO. To solve this problem, an adaptive reference point learning and cooperation-driven multi-objective algorithm (ARPCMOA) is proposed to simultaneously optimize the maximum completion time (makespan), total energy consumption (TEC), and outsourcing cost. First, according to the characteristics of the problem, a strategy for determining the outsourced group is considered to generate a promising initial solution. Secondly, a two-stage co-evolutionary strategy is adopted to deeply explore the solution space. In the first stage, a hybrid local search (HLS) method is proposed to obtain more extreme solutions. In the second stage, a reference point adaptation mechanism is used to enhance the global search capability of the algorithm to select high-quality solutions. The two stages cooperate with each other in the iterative process, so that the group evolves towards the true Pareto frontier. In addition, an energy-saving strategy based on idle time is proposed to better optimize TEC. Finally, a large number of statistical analysis experiments (KW) show that ARPCMOA outperforms existing multi-objective algorithms.

[0063] As an extension of HFSP practical application, HFGSP_OO can be described as follows: There are n jobs (Job = {J1, J2, ..., J j ,...,J n}) are arranged in d groups (Group={G1,G2,...,G k ,...G d}) to generate group sequences. Each group sequence is processed in g stages (Stage = {S1, S2, ..., S s ,...,S g}) Each stage has m machines, (M={M1,M2,...,M i ,...,M m}), v different speeds (V = {1,2,...l,...,v}). Considering the characteristics of the problem, due to the pressure of factory production, some groups need to be outsourced to contractors at each stage. k In stage S s Outsourcing, then return the outsourcing delivery time l k,s And pay outsourcing feesW k In stage S s+1 , the previous stage S s The preparation time of is considered as its completion time. Then, in stage S s+1 Re-determine the group sequence that needs to be outsourced. For the group sequence of internal processing in each stage, it is reasonably arranged on m machines according to the principles of "first come first served" and "idle machine first". The actual processing time of the workpiece is determined by the standard processing time and the actual processing speed. It is assumed that the greater the processing speed, the shorter the processing time and the higher the energy consumption. The goal of this paper is to minimize makespan, TEC and cost.

[0064] The assumptions and limitations of this disclosure are as follows:

[0065] (1) All machines are idle at time 0.

[0066] (2) All workpieces belonging to the same group must be processed continuously without interruption.

[0067] (3) At any stage, a workpiece can only be processed by one machine. A machine can only process one workpiece at a time.

[0068] (4) All stages must process the group sequence continuously and may not be skipped or ended early.

[0069] (5) At each stage, the outsourced group sequence can be returned based on the delivery time.

[0070] (6) Energy consumption is related to the processing speed of the machine. The faster the speed, the higher the energy consumption.

[0071] The desired objective function in the actual production process is:

[0072]

[0073] TE C = PE C+IE C+SE C (5)

[0074]

[0075] The constraints that satisfy the problem are:

[0076]

[0077]

[0078]

[0079] Where n is the total number of workpieces, d is the total number of groups, m is the total number of machines, g is the total number of stages, v is the total number of speeds, G k represents the set of workpieces in the kth group, W k Indicates group G k Outsourcing costs, p j,i,s Indicates that in stage S s Next, workpiece G k On machine M i Standard processing time on Indicates that in stage S s Next, in G k and G k' The setting time matrix between Indicates that in stage S s Next, the unit sets the energy consumption, Indicates that in stage S s Next, on machine M i Unit processing energy consumption at speed l, Indicates that in stage S s In the following figure, PEC represents the total processing energy consumption, IEC represents the idle time energy consumption, SEC represents the setup time energy consumption, and PEC represents the total processing energy consumption. j,s Indicates operation O j,s Energy consumption, L represents a sufficiently large positive number, X k,s is a decision variable, when G k In stage S s Set to 1 when outsourced, otherwise set to 0, Y j,k,r is the decision variable, when workpiece J j Placed in Group G k The position of Z is set to 1, otherwise it is set to 0. k,q,i,sis a decision variable, when G k In stage S s On machine M with priority q i When processing, set it to 1, otherwise set it to 0, V j,l,s is a decision variable, when J j In stage S s When being processed at speed l, it is set to 1, otherwise it is set to 0, S j,k,s For stage S s , Group G k J j The start time of C j,k,s For stage S s , Group G k J j The completion time, t j,s For stage S s , J j The actual processing time, C k,s For group G k In stage S s The completion time, S k,s For group G k In stage S s The start time, V l,s For the machine in stage S s The actual processing speed, C max is the maximum completion time, TEC is the total energy consumption, cost is the outsourcing cost, j, j' is the workpiece subscript, k, k' is the group subscript, i is the machine subscript, l is the speed subscript, r is the workpiece priority, q is the group priority, and s is the stage subscript.

[0080] Formulas (1)-(6) represent the objective functions of makespan, TEC, and cost. Constraints (7) and (8) ensure that the workpiece is assigned to a unique group, and constraint (9) ensures that there can be only one workpiece at any position in the group. Constraint (10) ensures that each workpiece has a processing order within the group. Constraint (11) ensures that each group has a processing order. Constraint (12) ensures that only one group is processed at any position in any stage. Constraint (13) indicates that at any stage, each group processed internally can only select one machine. Constraint (14) ensures that at least one group in the stage is outsourced. Constraint (15) indicates that at any stage, the two previous and next workpieces J belonging to the same group j' and J j , J j The start time is greater than or equal to J j' Constraint (16) ensures that at any stage, J j The completion time is greater than or equal to J j' Completion time plus J jConstraints (17) and (18) represent the relationship between the start time and the end time of the same workpiece. Constraints (19) to (20) represent the relationship between the finish time and the start time of the group and workpiece. Constraints (21) to (24) represent the relationship between the start time, the end time and the setup time. Constraints (25) to (28) represent the relationship between energy consumption and the actual processing time.

[0081] The process of solving the problem disclosed in the present invention involves a method for selecting high-quality solutions from the non-dominated solution set, specifically: in the environmental selection process, when the total number of non-dominated solution sets N is greater than the population size PS required for the next iteration, several PS from the non-dominated solution set will be selected from N. However, when only certain solutions located in the same Pareto layer need to be selected, it is difficult to decide whether to keep or delete the solution. The general solution is to randomly select a solution as a possible case. However, this method has a certain degree of randomness, which will affect the quality of the solution set of the entire group. Therefore, it is very important to judge the quality of the non-dominated solution set located in the same Pareto layer. Based on this, a new distance-based method (BDQ) is proposed to determine the quality of non-dominated solutions in the same Pareto layer. The main idea is to use a reference point to select non-dominated solutions. The quality of the solution is judged by calculating the distance from the non-dominated solution to the reference point, thereby selecting a solution that is conducive to the evolution of the group. The specific steps are as follows

[0082] Step 1: Adjust the position of the reference point to ensure the diversity of non-dominated solution selection. Calculate the Euclidean distance d from the non-dominated solution set X to the reference point set R.

[0083] Step 2: Find the non-dominated solution set X that is closest to the d value of each reference point in R non , it is called contribution point, otherwise it is called non-contribution point.

[0084] Step 3: Calculate dD for each individual x and select the individual with the minimum value. This individual is called the solution with the smallest contribution and is deleted.

[0085] Step 4: Repeat steps 1-3 until a non-dominated solution that meets the quantity requirements is selected.

[0086]

[0087] As shown in step 1, before using the reference point to select contributing solutions, the position of the reference point should be adjusted. The purpose of this is to diversify the selected non-dominated solution sets and better retain the non-dominated solution sets at the extremes. This makes the non-dominated solution sets selected by the reference point located on the entire Pareto plane instead of only selecting the middle area. Figure 2There are original reference points A, C, E, and G in . A and E are far from the solution, so they should be discarded. However, in order to better retain the extreme solutions and diversify the final non-dominated solution set, the reference points on the edge should be retained as much as possible. Adjust the reference points A and E to minimize their vertical distance from the non-dominated solution. Therefore, if Figure 2 As shown, A is adjusted to B and E is adjusted to F. Reference points C and G are closest to the non-dominated solution in vertical distance, so no adjustment is required.

[0088] Based on the above knowledge, the framework of the ARPCMOA algorithm disclosed in the present invention is as follows Figure 3 As shown in the figure. First, a hybrid initialization method is used to generate the initial population. Second, a co-evolutionary algorithm with an adaptive reference point is proposed according to the actual shape of the Pareto front. As the population iterates, the reference point is continuously adjusted and updated to ensure that the quality of solutions in the population is improved. In this way, the population will evolve in a more promising direction. Finally, we propose an energy-saving speed change strategy to reduce TEC.

[0089] Before solving the problem, it is necessary to encode and decode the problem. The HFGSP_OO encoding aims to solve the following four problems: (1) assigning workpieces to group sequences. (2) dividing group sequences for internal processing and outsourcing. (3) scheduling group sequences for internal processing on machines. (4) assigning different speeds to different machines. In order to better represent the solution, a four-vector encoding is designed, such as Figure 4 (a)-(d) are shown. G represents the complete group sequence formed by dividing n workpieces into d groups, where δ = {τ1, τ2, τ3, ..., τ x} represents the sequence of workpieces within the group. π represents the scheduling sequence after outsourcing, where G out represents the outsourcing group sequence, G in represents the internal processing group sequence. M represents the workpieces arranged on different machines at different stages. V represents the processing speed of the workpiece on the machine at that stage. The speed level is ν l ={1.50,1.75,2.00,2.25,2.50}.

[0090] Decoding is divided into two different parts. In the S1 stage, the outsourced group is first judged. Then, for the internally processed group, the complete scheduling order and machine allocation are determined. According to the principle of idle machine priority, if there is an idle machine, the group is scheduled on the idle machine and the next idle time of the machine is calculated. That is, the group sequence setting time and group sequence processing time t k,sIf there is no idle machine, the group is processed on the machine with the shortest time to the next idle period. Assume that all machines are idle at the beginning, that is, 0. In the next stage, the outsourcing of the group is also determined first, and then the group sequence for internal processing is arranged on the machine according to the principle of first-come, first-served group sequence. An example of the decoding process is as follows Figure 5 shown.

[0091] During the solution process, initialization is required first. The initialization method of ARPCMOA mainly solves three sub-problems: 1) the division of internal processing of grouped sequences and outsourcing of each stage. 2) sorting the grouped sequences processed internally. 3) sorting the sequences of artifacts processed internally. Therefore, different initialization methods can be designed for different sub-problems. In order to maintain the diversity of the initial population, the random initialization method is added to form a hybrid initialization method.

[0092] In order to generate a more promising solution, it is necessary to select a suitable method to determine the grouping to be outsourced. The present disclosure designs a heuristic method to divide the outsourcing grouping sequence at each stage. If the group satisfies q in formula (30) k,s If G is greater than 1, it means that outsourcing this group is more cost-effective. k Being outsourced.

[0093]

[0094] In formula (30), α represents the weight of the numerator and denominator of the formula, and its value range is [0,1], so that the sum of the weights of the upper and lower parts of the fraction is 1. represents the total processing time of the group on the stage, W k represents the outsourcing cost of the group. k,s Indicates the ratio between the processing time and outsourcing cost of a group. If it is greater than 1, it means that the proportion of internal processing time is large and the proportion of outsourcing cost is small. If it is less than 1, it means that the proportion of outsourcing cost is large and the proportion of internal processing time is small. The condition for selecting an outsourcing group is that the time spent on internal processing is too much, and the time spent on outsourcing is too little. Therefore, group sequences greater than 1 are outsourced.

[0095] In the scheduling process of HFGSP_OO, one of the important factors affecting the completion time between groups is the setup time. Based on the idea of ​​the heuristic method JPA, a method (IJPA) for sorting the internal processing group sequence is designed. First, the sum of the setup time between the internal processing groups is calculated to obtain the matrix M (the matrix M is used in the IJPA sorting method. It is obtained according to the sum of the setup time between groups. The sorting group sequence is to select the group with the smallest setup time between the current group according to the elements in the matrix M, and put it into the new group sequence). Secondly, in order to maintain the diversity of the group sequence, when generating a new group sequence, randomly select a group as the first element of the new group sequence. Then select the group with the shortest setup time in the previous group in turn until a new group sequence is formed.

[0096] According to the problem characteristics, the SPT rule is used to sort the artifacts in the internal processing group. First, the artifact with the shortest processing time in the group is selected as the first artifact. Then, the artifacts with the shortest completion time with the previous artifact are selected one by one. Finally, a complete artifact sequence is formed.

[0097] For the proposed ARPCMOA, the co-evolution part includes the population, archive set, and reference point. It is mainly divided into two stages. The first stage uses hybrid local search (HLS) to deeply explore the solution space. After the first stage of evolution is completed, the second stage uses the solution generated in the first stage to adjust and update the reference point according to the characteristics of the problem. Based on the newly generated reference point, the global optimal solution for the next iteration is obtained. In this way, a co-evolution system including the first and second stages is generated in the iterative process.

[0098] As an effective method to solve optimization problems, HLS can make the quality of the group solution set close to the optimal solution. Based on HFGSP_OO coding, six search operators are proposed to evolve the group and artifact sequences.

[0099] For group sequence operations:

[0100] Inserting groups based on the group sequence: Take out any group and reinsert it at the position with the smallest adaptation value. The specific steps are as follows: Figure 6 (a) shown.

[0101] Exchange groups based on the same machine: For a sequence of groups assigned to the same machine, select any two groups and exchange their positions. The specific steps are as follows Figure 6 (b) as shown.

[0102] Insertion groups based on different machines: After assigning group sequences to machines, select any two different machines M i and M i' From machine M iSelect the group and insert it into machine M i' The specific steps are as follows: Figure 6 (c) as shown.

[0103] Based on different machine exchange groups: After assigning group sequences to machines, select any two different machines M i and M i' . From machine M i Select Group G k and from machine M i' Select Group G k' , and exchange. The specific steps are as follows Figure 6 (d) as shown.

[0104] For operations on workpiece sequences:

[0105] Exchange artifacts based on the same group: For the artifact sequence assigned to the same group, select any two artifacts and exchange their positions. The specific steps are as follows Figure 7 (a) shown.

[0106] Flipping artifacts in the same group: For artifact sequences assigned to the same group, flip the artifact sequence to obtain a new sequence. The specific steps are as follows Figure 7 (b) as shown.

[0107] After the first phase, the reference point is updated using the reference point adaptation mechanism. There are four main steps: 1) Determine the contributing solution. 2) Update the reference point. 3) Update the archive set. 4) Environment selection.

[0108] First, the contributing solution needs to be determined. Merge the archive set Archive, the parent population Population, and the child population Off_population to obtain the merged population Total_population. Using the target value information of Total_population, the minimum and maximum values ​​of the three targets are obtained and assigned to Z, which is a matrix with two rows. The first row stores the minimum value of each target dimension, and the second row stores the maximum value of each target dimension. Using this matrix Z, the population and reference point are normalized. Since the three target values ​​are of different size scales, it is difficult to unify them in the subsequent calculation process. Therefore, the population and reference point must first be normalized. Then, the BDQ method is used to determine the contributing solution and the non-contributing solution.

[0109] Then, the reference points and archive set are updated. The update mainly uses the determined contributing solutions. The new reference points will select solutions closer to the Pareto frontier for the next iteration for population evolution. Updating the reference points is a key step in ARPCMOA. When updating the reference points, the reference points closest to the contributing solutions are selected as the new reference points. Other reference points that are far from the Pareto frontier are deleted. If the number of new reference points does not meet the required total number of reference points, the minimum value of the maximum cosine between the closer reference points and the Non_population individuals is calculated. The solution with the minimum value is selected and added to the new reference point set until the new reference points reach the required total number. The reference point update is completed, and the updated reference points are closer to the true Pareto frontier. In order to update the archive set, the archive set is designed to retain elite solutions. The first step is to determine whether the number of contributing solutions meets the archive set size. If not, the minimum value of the maximum cosine between the contributing solutions and the non-contributing solutions is calculated. Select the non-contributing solutions that meet the conditions. These solutions are merged with the contributing solutions into a new archive set. This allows the archive set to retain globally better solutions, which is conducive to updating the reference points in the next iteration.

[0110] Finally, the environment selection strategy is used to select solutions for the population of the next iteration. First, the parent population Population and the child population Off_population are merged and arranged in the order of non-dominated solutions. Assume that the size of the selected population is PS. As shown in formula (31), starting from the first Pareto layer, the non-dominated solution sets are added to the new population in sequence. When added to the i-th Pareto layer, if the number of solution sets in the new population exceeds PS, it is necessary to select (PS-Num(New_population)) individuals in the i-th layer. Among them, New_population is added after the (i-1)-th Pareto layer. High-quality individuals should be selected and put into the new population to ensure the quality of solutions in subsequent iterations. Therefore, the BDQ method is used to determine the non-dominated solutions that need to be retained and deleted in the i-th layer.

[0111] New_population=New_population+Solutions Pareto layer(i)(31)

[0112] For TEC, energy consumption is related to speed. The energy-saving strategy adopted in this paper is to optimize TEC by reducing the processing speed of the workpiece without changing the completion time. The specific steps are as follows: for the group sequence processed in each stage, according to the speed of each workpiece in operation O j,s The start time and the end time determine whether there is idle time. Then get the idle time matrix. j,sIf there is idle time afterwards, the processing speed will be reduced. j+1,s The start time remains unchanged, so when TEC is reduced, the construction period remains unchanged, thus achieving energy saving.

[0113] like Figure 8 As shown, it needs to first find the workpiece with free time and find O 1,2 There is free time later. Therefore, the O 1,2 processing speed, extending O 1,2 processing time. However, 3,2 The start time remains the same, so the machine's makespan does not change. Thus, TEC decreases while the makespan remains the same.

[0114] The results were verified experimentally.

[0115] To verify the effectiveness of the proposed ARPCMOA, we used the following test instances, where the number of groups is {10, 20, 30} and the number of machines is {2, 3, 4}. The setup time is divided into three types: large, medium, and small. We denote it as {1, 2, 3}. Therefore, a total of 3 × 3 × 3 = 27 instances were tested. The standard processing time of each instance is evenly distributed between [1, 8]. The outsourcing cost is distributed between [1, 7], [1, 8], [1, 9]. The setup time is divided into three levels: [1, 10], [1, 20], and [1, 30]. Here "20 × 3 × 2" means that the number of groups is 20, there are 3 available machines for each processing stage, and the setup time is medium-sized. The CPU runtime n × m × d × k / 1000 milliseconds is used as the stopping criterion, where k = 5. In addition, to verify the performance of ARPCMOA, the multi-objective performance evaluation criteria hypervolume (HV) and inverted generational distance (IGD) are also used. Then, statistical analysis was performed based on the experimentally derived HV and IGD values ​​to test whether there were significant differences between the compared algorithms.

[0116] Parameter setting: ARPCMOA has two main parameters that affect the performance of the algorithm, namely, the population size (PS) and the number of iterations (EP) of the entire evolutionary part. Taguchi test was used to test the parameter levels suitable for ARPCMOA, as shown in Table 1. Table 2 shows the orthogonal array of 16 combinations of four levels of two parameters. Each combination was run ten times under the same instance to obtain the HV values ​​listed in Table 2. Table 3 shows the delta value and level between the two parameters. It can be seen that PS has a greater impact on the algorithm, followed by EP. Fig. 9 The horizontal trend of each parameter is shown. Fig. 9 It can be seen that the optimal parameter level is 30 for PS and 25 for EP.

[0117] Table 1. Parameter values

[0118]

[0119] Table 2. Orthogonal array

[0120]

[0121]

[0122] Table 3. Comparison results

[0123]

[0124] Evaluation of the MILP model:

[0125] To test the quality of the solutions generated by ARPCMOA, we built a mathematical model using IBM ILOG CPLEX 12.7 and designed 16 small-scale instances to verify it. Here, n = {5, 8, 10, 15}, d = {2, 3}, and m = {2, 3}. The maximum CPU running time is 1800s, and the number of threads is assumed to be 3. The results show that: (1) For smaller instances, both the mathematical model and ARPCMOA can obtain the optimal solution and find the most suitable group for outsourcing. (2) As the instance size increases, the performance of the mathematical model gradually decreases, and the gap between the two becomes larger and larger.

[0126] Validity analysis of each part of ARPCMOA.

[0127] Analysis of the effectiveness of initialization: In order to demonstrate the effectiveness of the hybrid initialization method proposed in this paper, ARPCMOA is compared with the random initialization method (marked as A1). The rest of the examples remain the same. Each instance is run 10 times under the same conditions. The results show that ARPCMOA has 17 better values ​​in terms of the evaluation index HV. In the comparison of IGD, ARPCMOA has 17 better values. The average values ​​are better than the random initialization level. In addition, according to Fig.10 , box plots drawn with the RPI values ​​of HV and IGD show that ARPCMOA outperforms A1 in both cases. Since the data do not conform to a normal distribution, the nonparametric test Kruskal-Wallis (KW) method was used. Fig.10 As shown in the figure, the p-value of HV is 0.041004 and the p-value of IGD is 0.042868, both of which are less than the significance level (0.05). Therefore, the null hypothesis is rejected and there is a significant difference between ARPCMOA and A1. This proves the effectiveness of the proposed hybrid initialization method.

[0128] Analysis of the effectiveness of group sequence evolution: To demonstrate the effectiveness of the group sequence evolution operation, we compared ARPCMOA with a randomly evolved group sequence (denoted as A2). Each algorithm instance was run 10 times. The box plots drawn using the RPI values ​​of HV and IGD are shown in Figure 2. Fig.11 In addition, a KW test experiment was also conducted for non-parametric tests, and the p-values ​​obtained were as follows Fig.11 shown.

[0129] The results show that ARPCMOA has 16 better values ​​than HV. And IGD has 17 better values. The average values ​​of ARPCMOA are better than A2. Fig.11 It can be seen that ARPCMOA has a higher HV value and a lower IGD value. In addition, the p-value of HV is 0.022378 and the p-value of IGD is 0.015807, both less than 0.05. It can be seen that there is a significant difference between ARPCMOA and A2. Therefore, the group sequence evolution strategy is an effective evolution method.

[0130] Validity analysis of artifact sequence evolution:

[0131] To show the effectiveness of the artifact sequence operation, ARPCMOA is compared with the artifact random evolution strategy (denoted as A3). Other strategies remain unchanged. The two compared algorithms are run 10 times under the condition of the same instance size. The box plots drawn according to the RPI values ​​of HV and IGD and the p-values ​​obtained from the non-parametric KW experiment are shown in Fig.12 shown.

[0132] The results show that ARPCMOA produces 18 higher HV values ​​and 17 lower IGD values. From the average HV and IGD values ​​listed in the last row, ARPCMOA is superior. Fig.12 The superiority of the ARPCMOA algorithm can also be seen from the box plots of the RPI values ​​of HV and IGD using the two algorithms. Finally, from the KW experiment, it can be concluded that the p-value of HV is 0.010997 and the p-value of IGD is 0.029785, both less than 0.05. Therefore, it can be proved that the operation on the order of workpieces is effective.

[0133] Analysis of the effectiveness of environmental selection:

[0134] The environment selection strategy adopted in this paper is to use the continuously updated reference point to select the population required for the next iteration. To verify the effectiveness of this method, we compared ARPCMOA with random environment selection (denoted as A4). Except for the environment selection, the rest of this paper remains the same. Under the condition of the same instance size, the two comparison algorithms are run 10 times. The box plots drawn according to the RPI values ​​of HV and IGD are shown in Fig.13In addition, a KW test experiment was also performed for non-parametric tests, and the p-values ​​obtained were as follows Fig.13 shown.

[0135] The results show that in the comparison of HV and IGD values, ARPCMOA obtained 17 better HV values ​​and 16 better IGD values. This shows that the environmental selection strategy helps the group to select more promising solutions for iteration. On average, ARPCMOA achieved better results in both HV and IGD. Fig.13 The box plot in also verifies this result well. Finally, from the KW experiment, it can be concluded that the p value of HV is 0.01838 and the p value of IGD is 0.021313, both of which indicate that there is a significant difference. Therefore, it can be proved that the operation of environmental selection is effective.

[0136] Comparison with other advanced algorithms: To evaluate the performance of ARPCMOA, three state-of-the-art algorithms are selected for comparison, namely CCMO, KCA, and NSGAII. The parameter settings, encoding and decoding of these three comparison algorithms are the same as ARPCMOA, and the CPU running time as the stopping criterion is also the same.

[0137] CCMO proposes a collaborative evolution framework for the complexity problem of handling multiple objectives and constraints (CMOP) simultaneously. The evolution of two populations is used to solve the CMOP problem and the auxiliary problem of CMOP respectively. The purpose is to solve the multi-objective optimization problem by solving the auxiliary problem. A new type of weak cooperation between populations is proposed, and the experimental results prove the superiority of the proposed algorithm. KCA, as a knowledge-based collaborative algorithm, is used to solve the distributed permutation flow workshop problem. Different strategies for optimizing factory allocation, workpiece sequence and speed scale are proposed for different target values. Among them, the green scheduling problem is well solved by utilizing the guiding role of the critical path. The collaborative search of multiple strategies further improves the performance of the algorithm. As one of the classic multi-objective optimization methods, NSGAII is a multi-objective genetic algorithm based on non-dominated sorting. It is not only fast, but also adopts an elite selection strategy to select candidate solutions. The quality of the solution

[0138] This is determined by calculating the crowding distance, which makes the solution set more likely to converge to the true Pareto front.

[0139] In order to make a comprehensive comparison, the HV and IGD values ​​of 27 instances of the four algorithms were calculated. The results show that ARPCMOA has a higher HV value and a lower IGD value than the other three algorithms. And the average values ​​of these two indicators are better. The box plots made using the RPI of HV and IGD are shown in Figure 2. Fig.14As shown, the effect is also quite good. Finally, the KW values ​​of the four algorithms were statistically analyzed, and the p values ​​of HV and IGD were 4.6236e-13 and 1.4364e-15, respectively, both less than 0.05. This shows that the difference is significant, which fully demonstrates the effectiveness and advancement of ARPCMOA.

[0140] In addition, in order to further verify the effectiveness of the proposed ARPCMOA. Fig.15 The Pareto front distribution of the four compared algorithms under 2033 and 3022 instance conditions is shown. Fig.15 It can be seen that the Pareto front of ARPCMOA is closer to the origin, indicating that it has stronger convergence. From the number of solution sets of the four compared algorithms, it can be concluded that ARPCMOA has far more non-dominated solutions than the other three compared algorithms, which indicates that its diversity is better. The above two examples show that when solving HFGSP_OO, ARPCMOA obtains high-quality initial solutions through an effective initialization method. The co-evolutionary algorithm with adaptive reference point enables the population to have better diversity and convergence, thereby obtaining more non-dominated solutions. Finally, the energy-saving strategy is used to reduce TEC to optimize the target value. Fig.16 A Gantt chart of a solution in the HFGSP_OO instance 1022 is shown.

[0141] Example 2

[0142] This embodiment provides a hybrid flow shop scheduling system with an outsourcing option, including:

[0143] A model building module is configured to: define a hybrid flow shop scheduling problem based on grouping technology and outsourcing options, and construct an objective function expected in an actual production process and constraints that satisfy the problem;

[0144] The initialization module is configured to: divide the workpieces to be processed into several groups based on the same processing stage, obtain the group sequence and the workpiece sequence within the group, divide the group sequence into an outsourcing group sequence and an internal processing group sequence, determine the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group, obtain the parent population, operate the parent population, and obtain the initial reference point and the initial archive set;

[0145] The solution module is configured to: operate on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merge the sub-population, the parent population and the initial archive set to obtain a merged population, obtain a new reference point and a new archive set based on the merged population, determine the contributing solution and the non-contributing solution in the new archive set, update the reference point and the archive set using the contributing solution, iterate multiple times until the model converges, and obtain the final scheduling plan.

[0146] It should be noted that the above modules correspond to the steps described in Example 1, and the examples and application scenarios implemented by the above modules and the corresponding steps are the same, but are not limited to the contents disclosed in the above Example 1. It should be noted that the above modules, as part of the system, can be executed in a computer system such as a set of computer executable instructions.

[0147] In further embodiments, there is also provided:

[0148] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in Embodiment 1 is performed. For the sake of brevity, it will not be described in detail here.

[0149] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0150] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0151] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the method described in Example 1 is completed.

[0152] The method in Example 1 can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it is not described in detail here.

[0153] A computer program product includes a computer program, and when the computer program is executed by a processor, the method described in embodiment 1 is implemented.

[0154] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer executable instructions, such as instructions included in a program module, which are executed in a device on a real or virtual processor of the target to perform the process / method as described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of program modules can be combined or divided between program modules as needed. Machine executable instructions for program modules can be executed in local or distributed devices. In distributed devices, program modules can be located in local and remote storage media.

[0155] The computer program code for implementing the method of the present invention can be written in one or more programming languages. These computer program codes can be provided to the processor of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the computer or other programmable data processing device, causes the function / operation specified in the flow chart and / or block diagram to be implemented. The program code can be executed completely on a computer, partially on a computer, as an independent software package, partially on a computer and partially on a remote computer or completely on a remote computer or server.

[0156] In the context of the present invention, computer program codes or related data may be carried by any appropriate carrier to enable a device, apparatus or processor to perform the various processes and operations described above. Examples of carriers include signals, computer readable media, and the like. Examples of signals may include electrical, optical, radio, acoustic or other forms of propagation signals, such as carrier waves, infrared signals, and the like.

[0157] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0158] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A hybrid flow shop scheduling method with outsourcing options, characterized in that: The following steps are involved: Define the hybrid flow shop scheduling problem based on grouping techniques and outsourcing options, and construct the desired objective function in the actual production process and the constraints that satisfy the problem; Based on the same processing stage, the workpieces to be processed are divided into several groups, the group sequence and the workpiece sequence within the group are obtained, the group sequence is divided into an outsourcing group sequence and an internal processing group sequence, the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group are determined, the parent population is obtained, the parent population is operated, and the initial reference point and the initial archive set are obtained; Operate on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merge the sub-population, parent population and initial archive set to obtain a merged population, obtain a new reference point and a new archive set based on the merged population, determine the contributing solutions and non-contributing solutions in the new archive set, use the contributing solutions to update the reference point and archive set, iterate multiple times until the model converges, and obtain the final scheduling plan.

2. A hybrid flow shop scheduling method with outsourcing options as claimed in claim 1, characterized in that: It also includes energy-saving strategies, which are specifically: On the basis of the final scheduling plan, determine whether there is idle time between the processing of two adjacent workpieces according to the start time and completion time of the processing of two adjacent workpieces. According to the idle time, reduce the processing speed of the previous workpiece without affecting the start time of the next workpiece.

3. A hybrid flow shop scheduling method with outsourcing options as claimed in claim 1, characterized in that: The grouping sequence is divided into an outsourcing group sequence and an internal processing group sequence, specifically: The ratio between the internal processing time and the outsourcing cost of each group is calculated, and the grouping sequence with a ratio greater than 1 is selected as the outsourcing group sequence.

4. A hybrid flow shop scheduling method with outsourcing options as claimed in claim 1, characterized in that: Determine the scheduling order of the internal processing group sequence and the sequence of workpieces within the group, specifically: Calculate the setup time between internal processing groups, randomly select a group as the first element of the new group sequence, and then select the group with the shortest setup time in the previous group in turn until a new group sequence is formed; Select the workpiece with the shortest processing time in the group as the first workpiece, and then select the workpieces with the shortest completion time with the previous workpiece one by one until a complete workpiece sequence is formed.

5. A hybrid flow shop scheduling method with outsourcing options as claimed in claim 4, characterized in that: Determine the machine allocation for the internal processing group sequence and the workpiece sequence within the group, specifically: According to the principle of idle machine priority, if there is an idle machine, the internal processing group will be arranged on the idle machine and the next idle time of the machine will be calculated. If there is no idle machine, the internal processing group will be arranged on the machine with the shortest time to the next idle period.

6. A hybrid flow shop scheduling method with outsourcing options as claimed in claim 1, characterized in that: operating on the internal processing group sequence, including inserting groups based on the group sequence, exchanging groups based on the same machine, inserting groups based on different machines, and exchanging groups based on different machines; Operate on the sequence of artifacts within the internal processing group, including swapping artifacts based on the same group and flipping artifacts in the same group.

7. A hybrid flow shop scheduling system with outsourcing options, characterized in that: include: A model building module is configured to: define a hybrid flow shop scheduling problem based on grouping technology and outsourcing options, and construct an objective function expected in an actual production process and constraints that satisfy the problem; The initialization module is configured to: divide the workpieces to be processed into several groups based on the same processing stage, obtain the group sequence and the workpiece sequence within the group, divide the group sequence into an outsourcing group sequence and an internal processing group sequence, determine the scheduling order and machine allocation of the internal processing group sequence and the workpiece sequence within the group, obtain the parent population, operate the parent population, and obtain the initial reference point and the initial archive set; The solution module is configured to: operate on the internal processing group sequence and the workpiece sequence within the group to obtain a sub-population, merge the sub-population, the parent population and the initial archive set to obtain a merged population, obtain a new reference point and a new archive set based on the merged population, determine the contributing solution and the non-contributing solution in the new archive set, update the reference point and the archive set using the contributing solution, iterate multiple times until the model converges, and obtain the final scheduling plan.

8. An electronic device, characterized in that: The method comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method according to any one of claims 1 to 6 is completed.

9. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the method described in any one of claims 1 to 6.

10. A computer program product, characterized in that The invention comprises a computer program, which, when executed by a processor, implements the method according to any one of claims 1 to 6.

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