Multi-target irrelevant parallel batch scheduling method considering degradation and maintenance collaborative optimization

Abstract

The invention relates to a multi-objective irrelevant parallel batch scheduling method considering degradation and maintenance collaborative optimization. The method comprises the following steps: acquiring production task data; establishing a three-objective optimization model for minimizing maximum completion time, total completion time and total energy consumption; performing sub-problem decomposition on a multi-objective irrelevant parallel batch scheduling problem; respectively designing heuristic rules of workpiece assignment, batch formation and batch sorting based on the features of the sub-problems; and in combination with a heuristic rule, designing an MOEA / D-VNS algorithm to solve the three-objective optimization model so as to solve the problems of workpiece division and collaborative optimization and obtain a multi-objective irrelevant parallel batch scheduling scheme comprehensively considering degradation and maintenance collaborative optimization. Compared with the prior art, the method has the advantages that batch scheduling and maintenance activities can be collaboratively optimized, stable and efficient production is ensured, and the energy efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of batch scheduling, and in particular to a multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization. Background Art

[0002] Heat treatment is a typical batch manufacturing process in the production of aviation parts, which has the characteristics of high energy consumption, long processing time, and machine degradation effect. As a typical industrial production process, batch processing plays a vital role in various energy-intensive fields such as semiconductors, metal manufacturing, and aviation industry. With the rapid urbanization and modernization process, energy problems are becoming increasingly severe, and environmental pollution problems are also intensifying. Therefore, efforts are being made to strike a balance between economic growth and energy conservation and emission reduction. In order to meet this challenge, more sustainable production solutions must be developed in the field of industrial manufacturing. Among them, batch scheduling is one of the key issues. How to coordinate batch scheduling production and energy consumption to achieve a dual improvement in production efficiency and energy efficiency is an important issue that needs to be solved urgently.

[0003] In the field of operations research, batch scheduling problems are roughly divided into two categories: serial batching (s-batch) and parallel batching (p-batch). The research content on parallel batch scheduling mainly involves two types of machine environments: single machine and parallel machine. Single machine parallel batch scheduling problems focus on the optimization of a single batch processing machine, and this type of problem has received widespread attention. In contrast, parallel machine batch scheduling allows multiple batches to be processed simultaneously on multiple batch processing machines. In the heat treatment process, the high temperature environment accelerates the aging process of equipment components, causing the equipment to easily fail, thereby disrupting the original production rhythm. In order to extend the service life of the equipment and ensure stable production operation, equipment maintenance is essential. In the field of batch scheduling problems, an ant colony algorithm is designed in an existing technology to try to explore the collaborative optimization strategy of batch scheduling and maintenance. However, this study is limited to a single batch processing machine and periodic maintenance activities with a time window. In the field of batch scheduling, how to take more complex and changeable production scenarios and maintenance activities into consideration in the scheduling strategy still has a lot of research space.

[0004] In addition, equipment aging not only has a negative impact on the normal operation of the equipment, but also leads to an extension of the processing time, a phenomenon known as the degradation effect. The existence of the degradation effect further exacerbates the complexity of the batch scheduling problem because it involves the dynamic changes in the workpiece processing time. In one prior art, a hybrid ABC-TS algorithm is proposed to solve the scheduling problem of degraded workpieces with at least one maintenance activity. In another prior art, a BRKGA-DE algorithm is established to solve the degradation effect scheduling problem considering preventive maintenance in a related parallel machine environment. However, these few batch scheduling literatures considering maintenance have not yet involved issues such as energy consumption. For unrelated multi-objective parallel batch scheduling problems, due to their high-dimensional characteristics, the complexity increases significantly, thus bringing greater challenges. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-objective unrelated parallel batch scheduling method considering the collaborative optimization of degradation and maintenance. In an unrelated parallel batch processing machine environment, the degradation effect and maintenance factors are comprehensively considered to obtain a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers the collaborative optimization of degradation and maintenance. The scheme aims to significantly improve production efficiency and effectively reduce energy consumption through optimization strategies.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A multi-objective uncorrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization includes the following steps:

[0008] Step 1) Obtain production task data:

[0009] Step 2) Establish a three-objective optimization model for multi-objective unrelated parallel batch scheduling problems:

[0010] Based on the prior degradation model and preventive maintenance activities, a three-objective optimization model is established to minimize the maximum completion time, total completion time and total energy consumption.

[0011] Step 3) Sub-problem decomposition:

[0012] Decomposing the multi-objective unrelated parallel batch scheduling problem into sub-problems, wherein the sub-problems include workpiece allocation, batch formation and batch sequencing, wherein the workpiece allocation includes workpiece partitioning and workpiece assignment;

[0013] Step 4) Heuristic rule design:

[0014] Based on the characteristics of the sub-problems, heuristic rules for workpiece assignment, batch formation, and batch sorting are designed respectively;

[0015] Step 5) Design MOEA / D-VNS algorithm for collaborative optimization:

[0016] Combined with heuristic rules, the MOEA / D-VNS algorithm is designed to solve the three-objective optimization model to solve the workpiece partitioning and collaborative optimization problems, and a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers degradation and maintenance collaborative optimization is obtained.

[0017] The multi-objective unrelated parallel batch scheduling problem is described as follows:

[0018] n independent workpieces are processed on m unrelated parallel batch processing machines. The processing time of the workpieces on different machines is different, where n is the number of workpieces and m is the number of machines;

[0019] The maximum capacity of workpieces that each unrelated parallel batch processing machine can process simultaneously is c; the processing time of each batch depends on the longest processing time of the workpieces in the batch; once the machine starts processing a workpiece, it cannot be interrupted, and no more workpieces can be added to the machine before the processing is completed;

[0020] The batches between two consecutive preventive maintenance activities constitute a block; when the number of batches processed by the machine in a block reaches the number of batches u between two consecutive maintenance activities, maintenance activities are performed immediately.

[0021] The objective function of the three-objective optimization model is expressed as:

[0022] minC max

[0023]

[0024] Among them, C max is the maximum completion time, m is the number of machines, is the completion time of machine i, TC is the total completion time, ρ i is the power of machine i, r ig is the number of locations in the g-th block on machine i, For B igr The actual processing time of B igr For G ig The batch at block position r, G ig is the g-th block on machine i, b i is the batch number on machine i, u is the batch number between two consecutive maintenance sessions, It means rounding up, TEC is the total energy consumption.

[0025] The constraints of the three-objective optimization model include:

[0026]

[0027]

[0028] Where n is the number of workpieces, x ijb and ibgr All are binary variables; x ijb ∈{0,1}, When job j is assigned to the bth batch to be processed on machine i, x ijb is equal to 1, otherwise it is equal to 0; ibgr ∈{0,1}, When the bth batch on machine i is at position r in the gth block, y ibgr is equal to 1, otherwise it is equal to 0; p ij P is the normal processing time of machine i processing job j; ib is the processing time of the bth batch processed on machine i; P igr For B igr Normal processing time; l is the machine degradation rate; S igr For B igr The start time of the batch; t0 is the setup time; C igr For B igr The end time of the batch; T is the maintenance activity time; G ig G ig The end time of the block; For machine collection, is a collection of artifacts, is the batch set on machine i, is the set of blocks on machine i, is the location set of the g-th block on machine i.

[0029] In step 4), for the workpiece assignment sub-problem, assume that all workpieces are initially divided into m parts, m is the number of machines, and the number of workpieces assigned to a machine is positively correlated with the total processing time of the machine. A JD strategy is designed as a heuristic rule for workpiece assignment. The JD strategy is implemented by the following steps:

[0030] Step 411) sorting the m partial workpieces in non-increasing order according to the number of workpieces included to form a partial workpiece list;

[0031] Step 412) Select the workpiece portion at the top of the partial workpiece list, assign it to the machine with the least power, and delete the machine from the list of available machines;

[0032] Step 413) Repeat step 412) until all workpiece parts are assigned to the machine.

[0033] In step 4), for the batch formation sub-problem, the shortest processing time priority rule is used as the heuristic rule for batch formation to reduce the deviation of the processing time of the workpieces in the batch and give priority to the workpieces with the shortest processing time; the shortest processing time priority rule is implemented by the following steps:

[0034] Step 421) sorting all the workpieces to be processed on the machine in non-decreasing order according to normal processing time to form a workpiece list;

[0035] Step 422) According to the list of workpieces obtained in step 421), the first unallocated workpiece is selected and placed into the first batch with capacity, wherein the batch capacity is c. If the current batch is full, the workpiece is placed into a new batch and the workpiece is removed from the list of unallocated workpieces.

[0036] Step 423) repeats step 422) until all workpieces are allocated and a batch list is created.

[0037] In step 4), for the batch sorting sub-problem, the completion time of the workpiece processing is determined, and the optimal batch sorting rule is designed to minimize the completion time of the workpiece processing as the heuristic rule for batch sorting, wherein:

[0038] For any machine, the completion time of workpiece processing is:

[0039]

[0040] Among them, b i is the number of batches on machine i, u is the number of batches between two consecutive maintenance sessions, r ig is the number of locations in the g-th block on machine i, d l is the machine degradation rate, r is the position index, P igr For B igr Normal processing time, B igr For G ig The batch at block position r, G ig is the g-th block on machine i, T sum and C d Represents the total maintenance time and the total setup time respectively;

[0041] The optimal batch sorting rule is implemented through the following steps:

[0042] Step 431) All batches are sorted in non-decreasing order according to processing time to form a batch list, and r=1;

[0043] Step 432) If Select the first one in the batch list batches, assigning the batches to the rth position of each block and deleting the batches from the list, otherwise, executing step 434);

[0044] Step 433) r = r + 1, go to step 432);

[0045] Step 434) Select the top of the list batches and assign the batches to the previous The r-th position of the blocks and delete these batches from the list;

[0046] Step 435) r = r + 1, if r>u, then end; otherwise, go to step 434).

[0047] The step 5) comprises the following steps:

[0048] Step 51) Artifact division based on coding:

[0049] For the parallel batch scheduling problem involving n workpieces and m machines, a chromosome consisting of n+m-1 genes is used for encoding, where the chromosome consists of two main parts: workpiece genes and split genes. Workpiece genes represent workpieces numbered from 1 to n, and split genes consist of integer arrays from n+1 to n+m-1. Split genes are used to achieve workpiece partitioning.

[0050] In the encoding process, the segmentation genes are first randomly generated, and it is ensured that the segmentation genes are not located at the beginning or end of the chromosome and are not adjacent to each other; then, the artifact genes are randomly generated in the remaining vacancies of the chromosome to complete the encoding process; after the encoding is completed, all artifacts are divided into m parts;

[0051] Step 52) Decode and calculate the target function:

[0052] Step 521) using a heuristic rule for assigning workpieces to assign each part of the workpiece to a machine;

[0053] Step 522) using the heuristic rules for batch formation to group the workpieces on each machine into batches;

[0054] Step 523) sorting the batches using the heuristic rule for batch sorting;

[0055] Step 524) Calculate three target values ​​corresponding to the chromosome;

[0056] Step 53) Aggregation function: using a normalized Chebyshev aggregation function to guide the evolution of the group by comparing the quality of individuals;

[0057] Step 54) Evolution operation:

[0058] Step 541) Crossover operator: use uniform crossover method, that is, the genes of the offspring individuals are randomly selected from the genes at the corresponding positions of the parent individuals to determine;

[0059] Step 542) Mutation operator: randomly select two working genes or one working gene and one segmentation gene, and exchange their positions in the new individuals generated by the crossover operation;

[0060] Step 55) Use MOEA / D-VNS algorithm to solve:

[0061] The solution is searched by combining the MOEA / D algorithm and the VNS algorithm, and the optimal solution is obtained as a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers the collaborative optimization of degradation and maintenance.

[0062] The normalized Chebyshev aggregation function is expressed as:

[0063]

[0064] Where x represents the solution to the problem; λ is the weight vector; f a (x) represents the a-th objective function value of solution x; represents an ideal point; for any a=1,…,L, Where Ω is the variable space; L is the number of objective functions;

[0065] The MOEA / D-VNS algorithm selects individuals in the external population and individuals in the neighborhood that have not been selected more than three times as objects, and performs the following operations on the objects:

[0066] Machine exchange: Randomly select two machines and exchange all batches on these two machines to reduce the maximum completion time;

[0067] Batch exchange: randomly select a machine and randomly select two batches at the same position in different blocks to exchange to reduce the maximum completion time;

[0068] Job swapping: randomly select a batch in a machine and remove the last job, trying to insert it into the last position of another batch in the same machine, in the attempt to choose a position that minimizes the maximum completion time.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] (1) The present invention proposes a batch scheduling problem of collaborative optimization considering degradation effects and preventive maintenance. This problem closely reflects the actual production scenario. In order to accurately describe this problem, the present invention establishes a three-objective optimization model to characterize it and achieve dual optimization of economic indicators and environmental indicators.

[0071] (2) Aiming at the collaborative model of the unrelated parallel batch scheduling problem with NP-hard characteristics, this paper deeply explores and proposes a new job allocation sub-problem, including job partitioning and job assignment. Based on the derived structural characteristics of batch formation and batch sorting, a heuristic algorithm is designed to minimize the objective function.

[0072] (3) In addition to considering traditional economic indicators such as maximum completion time and total completion time, the present invention also considers environmental indicators such as energy consumption to reflect the emphasis on sustainable development of the manufacturing industry.

[0073] (4) In view of the high-dimensional complexity and difficulty of solving the problem, the present invention designs the MOEA / D-VNS algorithm to find the optimal solution within a reasonable time. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a flow chart of the method of the present invention;

[0075] Figure 2 is a schematic diagram of a chromosome encoding method in an embodiment;

[0076] Figure 3 is a schematic diagram of an evolution process in an embodiment;

[0077] Figure 4 This is a comparison chart of algorithm performance under different parameters in an embodiment. DETAILED DESCRIPTION

[0078] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0079] In energy-intensive production processes such as heat treatment, degradation is common and persistent with the continuous use of machines, which may prolong the processing time or even cause machine failure. Therefore, in order to ensure stable and efficient production and achieve energy efficiency, it is particularly important to coordinate and optimize batch scheduling and maintenance activities. This embodiment considers preventive maintenance such as maintenance activities after processing a certain number of batches. A novel multi-objective mixed integer programming model is proposed for the scheduling problem of unrelated parallel batches, aiming to simultaneously minimize the three key indicators of maximum completion time, total completion time and total energy consumption. This embodiment decomposes the entire problem into four sub-problems, namely, workpiece partitioning, workpiece assignment, batch formation and batch sorting. In view of the NP-hard nature of this problem, three heuristic algorithms based on structural attributes are designed according to the characteristics of the last three sub-problems. At the same time, a comprehensive method (MOEA / D-VNS) combining a decomposition-based multi-objective evolutionary algorithm with a variable neighborhood search is proposed to effectively deal with workpiece partitioning and this multi-dimensional collaborative optimization problem. Finally, the performance of the proposed comprehensive algorithm is comprehensively compared with other classic evolutionary algorithms based on dominance relations. Through example verification, the effectiveness and superiority of the designed algorithm are fully demonstrated.

[0080] Example 1

[0081] Specifically, this embodiment provides a multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization, such as Figure 1 As shown, the following steps are included:

[0082] Step 1) Obtain aviation parts heat treatment production task data.

[0083] Step 2) Establish a three-objective optimization model for the multi-objective unrelated parallel batch scheduling problem: Based on the prior degradation model and preventive maintenance activities, a three-objective optimization model is established to minimize the maximum completion time, total completion time and total energy consumption.

[0084] This example studies a multi-objective optimization problem in a parallel batch processing environment, and considers both degradation effects and maintenance activities. For such a complex new problem, it is necessary to first build an accurate mathematical model. The model needs to clearly define the impact of the machine's degradation effects on the workpiece processing time, and describe the constraints on machine availability and the recovery effect of preventive maintenance. This mathematical model should reflect dynamic changes to effectively guide the design of scheduling solutions.

[0085] First, this embodiment uses the degradation model proposed in the prior art, in which the actual processing time of the workpiece is defined as a linear increasing function of the start time of its processing, as shown in formula (2.1):

[0086]

[0087] in, and p ij denote the actual processing time and normal processing time of workpiece j on machine i. t denotes the time when the workpiece starts to be processed. l is the degradation rate of the machine, and it is assumed that the degradation rate of all machines is the same.

[0088] The unrelated parallel processor scheduling problem studied in this embodiment is described as follows:

[0089] 1. n independent workpieces are processed on m unrelated parallel batch processing machines. The processing time of the workpieces on different machines is different, where n is the number of workpieces and m is the number of machines.

[0090] 2. The maximum number of workpieces that each machine can process simultaneously is c. The processing time of each batch depends on the longest processing time of the workpieces in the batch. Once a machine starts processing a workpiece, it cannot be interrupted, and no more workpieces can be added to the machine before the processing is completed. The power of machine i is ρ i express.

[0091] 3. The batches between two consecutive maintenance activities constitute a block. Usually, a block contains at most u batches. Once the machine processes u batches in a block, maintenance activities are required immediately.

[0092] For convenience, the meanings of the symbols appearing in this embodiment are summarized in Table 1.

[0093] Table 1 Symbols

[0094]

[0095] In view of the unrelated parallel processor scheduling problem described above, this embodiment designs a multi-objective mixed integer programming model, namely a three-objective optimization model, which aims to minimize the maximum completion time, total completion time and total energy consumption while satisfying other production constraints such as degradation effect and machine maintenance. The three objectives of minimizing the maximum completion time, total completion time and total energy consumption correspond to equations (2.2) to (2.4) respectively:

[0096] minC max (2.2)

[0097]

[0098]

[0099] Among them, C max is the maximum completion time, m is the number of machines, is the completion time of machine i, TC is the total completion time, ρ i is the power of machine i, rig is the number of locations in the g-th block on machine i, For B igr The actual processing time of B igr For G ig The batch at block position r, G ig is the g-th block on machine i, b i is the batch number on machine i, u is the batch number between two consecutive maintenance sessions, It means rounding up, TEC is the total energy consumption.

[0100] In this model, the following production constraints need to be considered first:

[0101] 1. Each workpiece can only be assigned to one batch on one machine for processing;

[0102] 2. Each parallel batch processor can process at most c workpieces at the same time;

[0103] 3. Each batch on each machine can only be processed once at one location in the block;

[0104] The above production constraints can be described as Equation (2.5) to Equation (2.7):

[0105]

[0106] Equations (2.8) and (2.9) represent binary variables:

[0107]

[0108] Formula (2.10) shows that the processing time of each batch depends on the longest processing time of the workpiece in the batch:

[0109]

[0110] Formulas (2.11) and (2.12) are used to calculate B igr Normal processing time and actual processing time:

[0111]

[0112] Formula (2.13) calculates the completion time of each batch:

[0113]

[0114] Formula (2.14) shows that the start processing time of any batch must be greater than the completion time of the previous batch:

[0115]

[0116] Equation (2.15) shows that maintenance activities must be carried out between the two blocks:

[0117]

[0118] Equations (2.16) and (2.17) define the completion time of each block and each machine:

[0119]

[0120] Formula (2.18) defines the maximum completion time:

[0121]

[0122] Where n is the number of workpieces, x ijb and ibgr All are binary variables; x ijb ∈{0,1}, When job j is assigned to the bth batch to be processed on machine i, x ijb is equal to 1, otherwise it is equal to 0; ibgr ∈{0,1}, When the bth batch on machine i is at position r in the gth block, y ibgr is equal to 1, otherwise it is equal to 0; p ij P is the normal processing time of machine i processing job j; ib is the processing time of the bth batch processed on machine i; P igr For B igr Normal processing time; l is the machine degradation rate; S igr For B igr The start time of the batch; t0 is the setup time; C igr For B igr The end time of the batch; T is the maintenance activity time; C ig G ig The end time of the block; For machine collection, is a collection of artifacts, is the batch set on machine i, is the set of blocks on machine i, is the location set of the g-th block on machine i.

[0123] Step 3) Sub-problem decomposition: The multi-objective unrelated parallel batch scheduling problem is decomposed into sub-problems, including workpiece allocation (including workpiece partitioning and workpiece assignment), batch formation, and batch sequencing.

[0124] The core of the collaborative optimization problem studied in this embodiment can be regarded as a novel batch scheduling problem, which is usually decomposed into multiple sub-problems to be solved one by one. In an unrelated parallel machine environment, workpieces need to be divided and assigned to each parallel machine. This link is called workpiece allocation. Subsequently, the workpieces assigned to each machine are organized into different batches, and the processing order of these batches is reasonably arranged. This link is called the batch scheduling process. Whether it is workpiece allocation or batch scheduling process, each sub-problem has optimization space. In particular, for the sub-problems of the two batch scheduling processes, the processing time of the batch depends not only on the workpieces in the batch, but also on the dual effects of degradation effects and maintenance activities. In addition, maintenance activities will also affect the arrangement of the batch order. Therefore, the solution to these two sub-problems requires the derivation and analysis of the structural properties of the problem and the design of appropriate batch scheduling rules.

[0125] For the workpiece allocation link, the sub-problem of workpiece assignment is affected by the characteristics of unrelated parallel machines. As the initial and primary problem, the workpiece partitioning problem is suitable for iterative optimization using evolutionary strategies. In addition, this problem considers multi-dimensional indicators such as economy and environment, so a multi-objective optimization algorithm that can handle high-dimensional features is required. The algorithm needs to strike a reasonable balance between multiple conflicting objectives while taking into account global and local search efficiency.

[0126] Step 4) Heuristic rule design: Based on the characteristics of the sub-problems, heuristic rules for workpiece assignment, batch formation, and batch sorting are designed respectively.

[0127] Many parallel batch scheduling problems are well known for their NP-hard complexity even in a single-machine environment. Given the inherent complexity of these problems, the unrelated parallel processor model discussed in this embodiment is even more strongly NP-hard, and therefore requires an effective heuristic algorithm to solve.

[0128] Step 41) Design of heuristic rules for the workpiece assignment sub-problem

[0129] Job assignment is the process of assigning pending jobs to available machines. Since each machine has different processing capabilities and the time required to process the same job is also different, this will lead to different energy consumption levels, which will have a significant impact on the overall scheduling performance. Therefore, the job assignment process must not be random, but should take into account the machine processing capabilities to achieve energy-efficient job assignment.

[0130] Lemma 1: Given two sequences V x and V y , where V x and V y The values ​​of are all positive numbers. If the monotonicity of the two series is opposite, then the sum of the products of the corresponding elements ∑V x Vy Minimum.

[0131] Assume that all workpieces are initially divided into m parts. Since the problem studied in this embodiment is the scheduling problem of compatible jobs in an unrelated parallel machine environment. Compatible jobs follow similar technical standards and specifications, which helps to keep the processing time fluctuations between different machines within a very small threshold. In an unrelated parallel machine environment, the power differences between machines are significant. Taking these factors into account, it is reasonable to assume that the number of workpieces assigned to a machine is positively correlated with the total processing time of the machine. Therefore, more attention can be paid to the impact of machine performance differences on the workpiece assignment problem. This embodiment designs job-dispatch (JD) as a heuristic rule for workpiece assignment.

[0132] The JD strategy is implemented through the following steps:

[0133] Step 411) sorting the m partial workpieces in non-increasing order according to the number of workpieces included to form a partial workpiece list;

[0134] Step 412) Select the workpiece portion at the top of the partial workpiece list, assign it to the machine with the least power, and delete the machine from the list of available machines;

[0135] Step 413) repeats step 412) until all workpiece parts are assigned to the machine.

[0136] Step 42) Heuristic rule design for batch formation subproblem

[0137] When all the workpieces have been assigned to the machines, they are waiting to form a batch. To optimize the efficiency of batch formation, this embodiment uses the First Fit Shortest Processing Time (FFSPT) rule as the heuristic rule for batch formation to reduce the deviation of the processing time of workpieces in the batch and give priority to the workpieces with the shortest processing time.

[0138] The shortest processing time priority rule is implemented through the following steps:

[0139] Step 421) sorting all the workpieces to be processed on the machine in non-decreasing order according to normal processing time to form a workpiece list;

[0140] Step 422) According to the list of workpieces obtained in step 421), the first unallocated workpiece is selected and placed into the first batch with capacity, wherein the batch capacity is c. If the current batch is full, the workpiece is placed into a new batch and the workpiece is removed from the list of unallocated workpieces.

[0141] Step 423) repeats step 422) until all workpieces are allocated and a batch list is created.

[0142] Step 43) Heuristic rule design for batch sorting subproblem

[0143] At this stage, all workpieces have been assigned to machines and batches have been formed. Batch sequencing is crucial when considering both degradation effects and maintenance activities. At this stage, the present embodiment derives some structural features based on the degradation model and preventive maintenance activities.

[0144] Property 1: For any machine, the completion time of a workpiece is:

[0145]

[0146] Among them, T sum and C d Represents the total maintenance time and the total setup time respectively.

[0147] This property can be proved by mathematical induction:

[0148] For the g-th block in machine i, when r=1, the completion time is:

[0149]

[0150] When r = 2, the completion time is:

[0151]

[0152] Therefore, the total completion time of the g-th block is:

[0153]

[0154] Therefore, the total completion time of machine i is:

[0155]

[0156] Obviously, the total maintenance time and the setup time for each block are all constants. Therefore, for convenience they are treated as T sum and C d Therefore, minimizing It can be achieved of minimization.

[0157] Therefore, based on Lemma 1 and Property 1, the following optimal batch sorting rule is designed to minimize the time:

[0158] Step 431) All batches are sorted in non-decreasing order according to processing time to form a batch list, and r=1;

[0159] Step 432) If Select the first one in the batch list batches, assigning the batches to the rth position of each block and deleting the batches from the list, otherwise, executing step 434);

[0160] Step 433) r = r + 1, go to step 432);

[0161] Step 434) Select the top of the list batches and assign the batches to the previous The r-th position of the blocks and delete these batches from the list;

[0162] Step 435) r = r + 1, if r>u, then end; otherwise, go to step 434).

[0163] Step 5) Design MOEA / D-VNS algorithm for collaborative optimization: Combined with heuristic rules, the MOEA / D-VNS algorithm is designed to solve the three-objective optimization model to solve the workpiece partitioning and collaborative optimization problems, and obtain a multi-objective unrelated parallel batch scheduling solution that comprehensively considers degradation and maintenance collaborative optimization.

[0164] Step 5) comprises the following steps:

[0165] Step 51) Artifact division based on coding:

[0166] For the parallel batch scheduling problem involving n workpieces and m machines, a chromosome consisting of n+m-1 genes is used for encoding, where the chromosome consists of two main parts: workpiece genes and split genes. Workpiece genes represent workpieces numbered from 1 to n, and split genes consist of integer arrangements from n+1 to n+m-1. Split genes are used to achieve workpiece partitioning.

[0167] During the encoding process, the split genes are first randomly generated. This method introduces randomness in the initial solution, expands the solution space, and provides potentially better solutions. In order to improve the quality of these population initial solutions, it is necessary to ensure that the split genes are neither located at the beginning or end of the chromosome nor adjacent to each other. Subsequently, artifact genes are randomly generated in the remaining vacancies of the chromosome to complete the encoding process. Through an iterative process, the chromosome will evolve towards a better scheduling solution. After the encoding is completed, all artifacts are divided into m parts.

[0168] like Figure 2An encoded chromosome is shown, which considers a scheduling problem with 7 workpieces and 4 machines, where 1-7 represent workpiece genes, 8*, 9* and 10* represent split genes, and after encoding, all workpieces are divided into 4 parts according to the split genes.

[0169] Step 52) Decode and calculate the target function.

[0170] Based on the coding division, the proposed heuristic method can be used to generate a corresponding scheduling scheme for each chromosome. At the same time, the objective function value can also be derived based on the scheduling scheme. The decoding process is as follows:

[0171] Step 521) assigning each partial workpiece to a machine using the JD strategy;

[0172] Step 522) using the FFSPT rule to batch the workpieces on each machine;

[0173] Step 523) sorting the batches using the optimal batch sorting rule;

[0174] Step 524) Calculate the three target values ​​corresponding to the chromosome.

[0175] Step 53) Aggregate Function

[0176] The aggregation function guides the evolution of the group by comparing the quality of individuals. Considering the different magnitudes of the three optimization objectives, the traditional Chebyshev aggregation function will cause the algorithm's search direction to bias towards targets with large magnitudes, making it difficult to generate uniformly distributed solutions. This embodiment uses a normalized Chebyshev aggregation function:

[0177]

[0178] Where x represents the solution to the problem; λ is the weight vector; f a (x) represents the a-th objective function value of solution x; represents an ideal point; for any a=1,…,m, Where Ω is the variable space; L is the number of objective functions.

[0179] Step 54) Evolution operation:

[0180] Step 541) Crossover operator: Since the genes in this embodiment are composed of integers, a uniform crossover method is used. Specifically, the genes of the offspring individuals are determined by randomly selecting genes at corresponding positions from the parent individuals. Through this crossover operation, more genetic information of the parent individuals can be retained.

[0181] Step 542) Mutation operator: Randomly select two working genes or a working gene and a splitting gene, and exchange their positions in the new individuals generated by the crossover operation to introduce new genetic changes.

[0182] It is worth noting that duplicate genes may appear in the initial sub-chromosome, which will lead to illegal scheduling schemes, so a repair strategy is needed to correct the sub-chromosome to ensure its feasibility. The core idea of ​​this repair strategy is to identify and remove duplicate genes, and then replace them with missing genes to restore the legitimacy of the chromosome. Figure 3 The crossover mutation process and the implementation of the repair strategy are intuitively demonstrated.

[0183] Step 55) The MOEA / D-VNS algorithm is used to solve and obtain the optimal solution as a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers degradation and maintenance collaborative optimization.

[0184] The MOEA / D algorithm is good at global search and can obtain the optimal solution more quickly. In order to avoid local optimality, this embodiment introduces variable neighborhood search VNS to improve local search capabilities.

[0185] In order to balance the global search and local search capabilities, the MOEA / D-VNS algorithm selects individuals in the external population and individuals in the neighborhood that have not been selected more than three times as objects, and performs the following operations on the objects to find a better solution:

[0186] Machine exchange: Randomly select two machines and exchange all batches on these two machines to reduce the maximum completion time;

[0187] Batch exchange: randomly select a machine and randomly select two batches at the same position in different blocks to exchange to reduce the maximum completion time;

[0188] Job swapping: randomly select a batch in a machine and remove the last job, trying to insert it into the last position of another batch in the same machine, in the attempt to choose a position that minimizes the maximum completion time.

[0189] The pseudo code of MOEA / D-VNS algorithm can be found in Table 2.

[0190] Table 2 MOEA / D-VNS algorithm

[0191]

[0192]

[0193]

[0194] Example 2

[0195] In this embodiment, the simulation experiment generates test cases according to the actual characteristics of the heat treatment process, and conducts in-depth exploration under various parameter configurations. The specific parameter settings of these cases are shown in Tables 3, 4, and 5. In order to conduct a more comprehensive comparative analysis, several key parameters will change in different scenarios, such as: the number of machines u, the number of workpieces n, the maximum capacity of the batch processing machine c, and the number of batches d between two maintenance activities, etc.

[0196] Table 3 Example parameter settings

[0197] parameter m n <![CDATA[P l ]]> c u Numeric {3,4} {40,80,160} 0.1 {2,3} {2,3}

[0198] Table 4 Machine power information

[0199] Machine number M1 M2 M3 M4 Power ρ(kW) 20 30 10 15

[0200] Table 5 Processing time data

[0201]

[0202] This example comprehensively compares the proposed algorithm MOEA / D-VNS with two of the most popular advantage-based multi-objective algorithms NSGA-II and -III. In order to comprehensively evaluate the performance of the algorithm, this example selects two commonly used performance indicators: Inverted Generational Distance (IGD) and Hypervolume (HV). The specific calculation formulas of these two indicators are as follows:

[0203]

[0204] d is a set of Pareto front solutions, and P is an approximate solution obtained by the designed algorithm. v=(v1,...,v l ) T Represents P * A solution in , d(v,P) represents the Euclidean distance from P to the nearest point in v.

[0205]

[0206] X is the solution set obtained by the designed algorithm. R is the reference point, set to (1,1,1). x is the normalized solution of X, and v(x,R) represents the volume of the hypercube formed by all solutions in the solution set.

[0207] The IGD indicator is used to measure the closeness between the solutions in the solution set and the true Pareto front. Specifically, the smaller the IGD value, the closer the solutions in the solution set are to the true Pareto front, that is, the higher the degree of convergence to the true Pareto front. The HV indicator measures the size of the hypervolume covered by the solution set in the target space. It calculates the volume dominated by the solution set in the target space. The higher the HV value, the better the trade-off between multiple objectives in the multi-objective optimization problem, and the richer the diversity of solutions.

[0208] The experiment will compare the performance of the three algorithms in various scenarios with the initial population size, maximum number of iterations, crossover rate and mutation rate of 50, 100, 0.8 and 0.1 respectively. In order to minimize the interference caused by the randomness of the experiment, each algorithm was run 10 times and the average value was taken as the final experimental result to ensure the accuracy and reliability of the conclusion.

[0209] The purpose of Experiment 1 is to compare the performance of MOEA / D, NSGA-II and NSGA-III algorithms at different scales. The experiment uses three different scale instances, which are 40, 80 and 160 workpieces on three batch processing machines with a capacity of 3, and a maintenance activity is performed after every three consecutive batches.

[0210] The comparison results of MOEA / D-VNS with the other two algorithms are listed in detail in Tables 6 and 7, where the significant values ​​are shown in bold. It can be clearly seen from Table 6 that the average values ​​of the MOEA / D-VNS algorithm on the three optimization objectives are the best at the three scales. The results in Table 7 further confirm the superiority of the MOEA / D-VNS algorithm. Compared with the other two algorithms, the average values ​​of the MOEA / D-VNS algorithm on the two key performance indicators also occupy a leading position. However, in very few cases, in terms of the best and worst values, these two indicators are slightly inferior to the other two algorithms. But overall, its comprehensive performance is still very outstanding.

[0211] Table 6 Three objective function values ​​of different algorithms (m=3, c=3, u=3)

[0212]

[0213]

[0214] Table 7 Performance of two indicators of different algorithms (m=3,c=3,u=3)

[0215]

[0216]

[0217] Considering that factors such as the number of machines, the maximum capacity of the machines, and the number of batches between two consecutive maintenance activities may have a significant impact on the performance of the algorithm, this embodiment designs Experiment 2 to deeply compare the performance of various algorithms when these three parameters change. This experiment specifically selects a small-scale scene containing 50 workpieces as the test environment.

[0218] pass Figure 4 From the IGD scoring results shown, it can be clearly observed that when the above three key parameters change, the MOEA / D-VNS algorithm significantly outperforms the NSGA-II and NSGA-III algorithms in terms of the average IGD scores obtained. This result strongly proves the advantages of the proposed MOEA / D-VNS algorithm over other algorithms in dealing with these parameter changes.

[0219] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A multi-objective uncorrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization, characterized in that: The following steps are involved: Step 1) Obtain production task data: Step 2) Establish a three-objective optimization model for multi-objective unrelated parallel batch scheduling problems: Based on the prior degradation model and preventive maintenance activities, a three-objective optimization model is established to minimize the maximum completion time, total completion time and total energy consumption. Step 3) Sub-problem decomposition: Decomposing the multi-objective unrelated parallel batch scheduling problem into sub-problems, wherein the sub-problems include workpiece allocation, batch formation and batch sequencing, wherein the workpiece allocation includes workpiece partitioning and workpiece assignment; Step 4) Heuristic rule design: Based on the characteristics of the sub-problems, heuristic rules for workpiece assignment, batch formation, and batch sorting are designed respectively; Step 5) Design MOEA / D-VNS algorithm for collaborative optimization: Combined with heuristic rules, the MOEA / D-VNS algorithm is designed to solve the three-objective optimization model to solve the workpiece partitioning and collaborative optimization problems, and a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers degradation and maintenance collaborative optimization is obtained.

2. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: The multi-objective unrelated parallel batch scheduling problem is described as follows: n independent workpieces are processed on m unrelated parallel batch processing machines. The processing time of the workpieces on different machines is different, where n is the number of workpieces and m is the number of machines; The maximum capacity of workpieces that each unrelated parallel batch processing machine can process simultaneously is c; the processing time of each batch depends on the longest processing time of the workpieces in the batch; once the machine starts processing a workpiece, it cannot be interrupted, and no more workpieces can be added to the machine before the processing is completed; The batches between two consecutive preventive maintenance activities constitute a block; when the number of batches processed by the machine in a block reaches the number of batches u between two consecutive maintenance activities, maintenance activities are performed immediately.

3. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: The objective function of the three-objective optimization model is expressed as: minC max Among them, C max is the maximum completion time, m is the number of machines, is the completion time of machine i, TC is the total completion time, ρ i is the power of machine i, r ig is the number of locations in the g-th block on machine i, For B igr The actual processing time of B igr For G ig The batch at block position r, G ig is the g-th block on machine i, b i is the batch number on machine i, u is the batch number between two consecutive maintenance sessions, It means rounding up, TEC is the total energy consumption.

4. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 3 is characterized in that: The constraints of the three-objective optimization model include: Where n is the number of workpieces, x ijb and ibgr All are binary variables; x ijb ∈{0,1}, When job j is assigned to the bth batch to be processed on machine i, x ijb is equal to 1, otherwise it is equal to 0; ibgr ∈{0,1}, When the bth batch on machine i is at position r in the gth block, y ibgr is equal to 1, otherwise it is equal to 0; p ij P is the normal processing time of machine i processing job j; ib is the processing time of the bth batch processed on machine i; P igr For B igr Normal processing time; l is the machine degradation rate; S igr For B igr The start time of the batch; t0 is the setup time; C igr For B igr The end time of the batch; T is the maintenance activity time; C ig G ig The end time of the block; For machine collection, is a collection of artifacts, is the batch set on machine i, is the set of blocks on machine i, is the location set of the g-th block on machine i.

5. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: In step 4), for the workpiece assignment sub-problem, assume that all workpieces are initially divided into m parts, m is the number of machines, and the number of workpieces assigned to a machine is positively correlated with the total processing time of the machine. A JD strategy is designed as a heuristic rule for workpiece assignment. The JD strategy is implemented by the following steps: Step 411) sorting the m partial workpieces in non-increasing order according to the number of workpieces included to form a partial workpiece list; Step 412) Select the workpiece portion at the top of the partial workpiece list, assign it to the machine with the least power, and delete the machine from the list of available machines; Step 413) Repeat step 412) until all workpiece parts are assigned to the machine.

6. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: In step 4), for the batch formation sub-problem, the shortest processing time priority rule is used as the heuristic rule for batch formation to reduce the deviation of the processing time of the workpieces in the batch and give priority to the workpieces with the shortest processing time; the shortest processing time priority rule is implemented by the following steps: Step 421) sorting all the workpieces to be processed on the machine in non-decreasing order according to normal processing time to form a workpiece list; Step 422) According to the list of workpieces obtained in step 421), the first unallocated workpiece is selected and placed into the first batch with capacity, wherein the batch capacity is c. If the current batch is full, the workpiece is placed into a new batch and the workpiece is removed from the list of unallocated workpieces. Step 423) repeats step 422) until all workpieces are allocated and a batch list is created.

7. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: In step 4), for the batch sorting sub-problem, the completion time of the workpiece processing is determined, and the optimal batch sorting rule is designed to minimize the completion time of the workpiece processing as the heuristic rule for batch sorting, wherein: For any machine, the completion time of workpiece processing is: Among them, b i is the number of batches on machine i, u is the number of batches between two consecutive maintenance sessions, r ig is the number of locations in the g-th block on machine i, d l is the machine degradation rate, r is the position index, P igr For B igr Normal processing time, B igr For G ig The batch at block position r, G ig is the g-th block on machine i, T sum and C d Represents the total maintenance time and the total setup time respectively; The optimal batch sorting rule is implemented through the following steps: Step 431) All batches are sorted in non-decreasing order according to processing time to form a batch list, and r=1; Step 432) If Select the first one in the batch list batches, assigning the batches to the rth position of each block and deleting the batches from the list, otherwise, executing step 434); Step 433) r = r + 1, go to step 432); Step 434) Select the top of the list batches and assign the batches to the previous The r-th position of the blocks and delete these batches from the list; Step 435) r = r + 1, if r>u, then end; otherwise, go to step 434).

8. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1 is characterized in that: The step 5) comprises the following steps: Step 51) Artifact division based on coding: For the parallel batch scheduling problem involving n workpieces and m machines, a chromosome consisting of n+m-1 genes is used for encoding, where the chromosome consists of two main parts: workpiece genes and split genes. Workpiece genes represent workpieces numbered from 1 to n, and split genes consist of integer arrays from n+1 to n+m-1. Split genes are used to achieve workpiece partitioning. In the encoding process, the segmentation genes are first randomly generated, and it is ensured that the segmentation genes are not located at the beginning or end of the chromosome and are not adjacent to each other; then, the artifact genes are randomly generated in the remaining vacancies of the chromosome to complete the encoding process; after the encoding is completed, all artifacts are divided into m parts; Step 52) Decode and calculate the target function: Step 521) using a heuristic rule for assigning workpieces to assign each part of the workpiece to a machine; Step 522) using the heuristic rules for batch formation to group the workpieces on each machine into batches; Step 523) sorting the batches using the heuristic rule for batch sorting; Step 524) Calculate three target values ​​corresponding to the chromosome; Step 53) Aggregation function: using a normalized Chebyshev aggregation function to guide the evolution of the group by comparing the quality of individuals; Step 54) Evolution operation: Step 541) Crossover operator: use uniform crossover method, that is, the genes of the offspring individuals are randomly selected from the genes at the corresponding positions of the parent individuals to determine; Step 542) Mutation operator: randomly select two working genes or one working gene and one segmentation gene, and exchange their positions in the new individuals generated by the crossover operation; Step 55) Use MOEA / D-VNS algorithm to solve: The solution is searched by combining the MOEA / D algorithm and the VNS algorithm, and the optimal solution is obtained as a multi-objective unrelated parallel batch scheduling scheme that comprehensively considers the collaborative optimization of degradation and maintenance.

9. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 8, characterized in that: The normalized Chebyshev aggregation function is expressed as: Where x represents the solution to the problem; λ is the weight vector; f a (x) represents the a-th objective function value of solution x; represents an ideal point; for any a=1,…,L, Where Ω is the variable space; L is the number of objective functions.

10. The multi-objective unrelated parallel batch scheduling method considering degradation and maintenance collaborative optimization according to claim 1, characterized in that: The MOEA / D-VNS algorithm selects individuals in the external population and individuals in the neighborhood that have not been selected more than three times as objects, and performs the following operations on the objects: Machine exchange: Randomly select two machines and exchange all batches on these two machines to reduce the maximum completion time; Batch exchange: randomly select a machine and randomly select two batches at the same position in different blocks to exchange to reduce the maximum completion time; Job swapping: randomly select a batch in a machine and remove the last job, trying to insert it into the last position of another batch in the same machine, in the attempt to choose a position that minimizes the maximum completion time.

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