Distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance

Abstract

The invention discloses a distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance, and the method comprises the steps: constructing a calculation model of distributed assembly line energy efficiency scheduling completion time and energy consumption considering equipment preventive maintenance through analyzing the influence of preventive maintenance operation on a production process; designing a coding and decoding rule to represent a mapping relationship between a search solution and a scheduling scheme, constructing an initial population by adopting a heuristic rule, and optimizing the quality of the population by adopting multiple search operations; and designing a selection mechanism based on feedback to realize population evolution, and evaluating a scheduling scheme through a scheduling target calculation model to realize distributed assembly line energy efficiency scheduling optimization considering equipment preventive maintenance. The heuristic rule and the search operator provided by the invention can optimize the performance of the solution, the designed selection mechanism based on feedback can accelerate the evolution of the solution, and the distributed assembly line energy efficiency scheduling problem considering the equipment preventive maintenance on a large scale is effectively and efficiently solved.

Description

Technical Field

[0001] The present invention relates to the technical field of complex production and machine maintenance scheduling and intelligent optimization, and in particular to a production energy efficiency scheduling optimization method in a distributed manufacturing environment, and belongs to the technical field of intelligent manufacturing, green manufacturing and operations optimization. Background Art

[0002] In order to promote the high-end, intelligent and green development of the manufacturing industry, combining information technology with artificial intelligence to achieve intelligent manufacturing and green manufacturing has become an important means to improve the economic benefits of the manufacturing industry, optimize resource allocation and reduce production costs. With the change of collaboration and consumption patterns among enterprises, distributed manufacturing has become a modern production model that can effectively respond to rapid changes in the market and reduce management risks. In order to cope with the fiercely competitive global market, effective and efficient supply management, planning and scheduling strategies are essential to ensure timely and efficient production. In particular, as the core of manufacturing management decisions, production scheduling is an effective means to reduce costs, increase production efficiency and meet customer needs. Effective operation optimization and efficient scheduling schemes can improve equipment utilization, while the availability and reliability of equipment directly affect the performance of scheduling methods. Most existing production scheduling assumes that machines are continuously available, but in actual scenarios, as machines continue to run, their maintainability and reliability will decrease, and machine failures are prone to occur, resulting in problems such as difficulty in stable operation, production interruptions, and order delays. Therefore, production scheduling considering machine preventive maintenance has attracted much attention, especially the coordinated scheduling of preventive maintenance and production. In the entire production process, machine preventive maintenance refers to specific operations to restore the production system to the desired state, including preventive maintenance and corrective maintenance, which refer to operations taken before or after machine failure. In order to extend machine life and reduce the risk of failure, preventive maintenance operations are widely used in industrial production. Its scheduling affects production efficiency and stability and has important engineering significance.

[0003] Distributed assembly line energy efficiency scheduling considering equipment preventive maintenance is more practical than traditional production scheduling problems, and requires coordinated scheduling of machine preventive operations and production processes. At the same time, distributed assembly line energy efficiency scheduling also needs to consider workpiece scheduling and machine speed settings. The sub-problems are coupled with each other, and the solution complexity is high, with multiple objectives, large scale, and complex constraints. There is currently a lack of effective and efficient scheduling methods. Therefore, there is an urgent need for a distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance to solve the above problems. Summary of the invention

[0004] The technical purpose of the present invention is to propose a distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance, to solve the problems of production and machine maintenance scheduling coupling, existing methods are difficult to directly solve, and lack of effective and efficient scheduling methods. The present invention establishes a distributed assembly line energy efficiency scheduling calculation model considering equipment preventive maintenance, provides a calculation method for total cost and total energy consumption, and designs an evolutionary optimization scheduling method based on feedback learning, so as to quickly obtain an effective scheduling scheme to collaboratively optimize production efficiency and energy consumption.

[0005] In view of the problems existing in the prior art, the present invention provides a distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance, constructs a distributed assembly line scheduling calculation model considering equipment preventive maintenance, constructs scheduling scheme encoding and decoding rules, uses heuristic rules to construct an initial population, and optimizes the quality of the population solution through a variety of search operations, and uses a selection operation based on a feedback mechanism to achieve population evolution, and finally obtains a local optimal solution for distributed assembly line energy efficiency scheduling considering equipment preventive maintenance;

[0006] It is characterized by comprising the following steps:

[0007] (1) Construct a distributed assembly line scheduling calculation model considering equipment preventive maintenance, including the optimization target calculation model of maximum completion time and total energy consumption and the relationship between their decision variables, specifically:

[0008] Construct the objective function calculation model of distributed flexible production and distribution joint scheduling, the objective function maximum completion time C max It refers to the maximum completion time of the last job of the last machine in all factories. It is calculated as shown in (1), where C(f) represents the completion time of factory f. represents the last job n on the last machine m in factory f f Completion time

[0009]

[0010] The calculation method for the completion time of the ,th job on machine i in factory f is shown in (2), where MT f，i represents the preventive maintenance time of the machine, t l，i represents the standard processing time of the lth workpiece, v f，i，l Indicates the machine processing speed

[0011] C f，i，l =max{C f，i-1，l , C f，i，l-1 +MT f，i，l}+t l，i / v f，i,l (2)

[0012] Preventive maintenance time MT for machine i in plant f f，i，l The maintenance level ML before the machine processes the first workpiece f，i,l The calculation method is shown in (3). When it is not enough to process the first workpiece, preventive maintenance operation is required, and the operation time is MT. f，i

[0013]

[0014] Maintenance level ML of machine i in factory f before processing the first workpiece f，i，l The calculation method is shown in (4). If the maintenance operation is performed, the maintenance level returns to the maximum value. Otherwise the maintenance level is inversely proportional to the processing time

[0015]

[0016] The total energy consumption TEC of the objective function consists of two parts: the energy consumption of the machine processing process PEC and the energy consumption of the machine idle process SEC. The calculation method is shown in (5), where PEC f，i and the SEC f，i Respectively represent the energy consumption of the i-th machine in factory f during processing and idle time

[0017]

[0018] Machine Process PEC f，i The calculation method is shown in (6), where PP f，i，v is the unit energy consumption of the i-th machine in factory f when processing a workpiece at speed v

[0019]

[0020] Machining ProcessSEC f，i The calculation method is shown in (7), where SP f，i，v is the unit energy consumption of the i-th machine in factory f when it is idle

[0021]

[0022] (2) Based on the distributed assembly line scheduling calculation model considering equipment preventive maintenance, the encoding and decoding rules of the scheduling scheme are constructed, specifically:

[0023] The encoding process uses the sequence string of F workpiece sequences Π={π1,...,π F} represents the factory allocation of workpieces and the order of workpieces within the factory, with a length of n, where each sequence π f Represents the workpiece sequence of factory f; using matrix V = (v j，i ) n×mRepresents the processing speed of each process, and the element v in the matrix j，i Indicates process O j，i Processing speed;

[0024] The decoding process allocates the workpieces to the corresponding factories in the order of Π according to the speed v j，i Before processing each process, the current machine maintenance level ML must be determined f，i，l Whether it can process the current workpiece, if it can, then ML f，i，l >t l，i / v f，i，l , then continue to process the workpiece; otherwise, perform preventive maintenance on the machine before processing the workpiece;

[0025] (3) Based on the encoding and decoding rules, the initial population is constructed using heuristic rules and evaluated through a distributed assembly line scheduling calculation model considering equipment preventive maintenance, specifically:

[0026] Generate a speed matrix randomly, and sort all workpieces in descending order according to the actual total processing time; insert workpieces into all positions of all factories in order, consider the impact of preventive maintenance operations on completion time, and select the position with the smallest completion time for insertion. If there are multiple positions with the same completion time, randomly select one position; repeat the above insertion process until all workpieces are assigned and sorted; by repeating the above steps, an initial population of size PS can be generated, and all non-dominated solutions in the initial population are selected to form a Pareto archive set;

[0027] (4) Based on the constructed initial population, a multi-search operator is used to optimize the population quality, specifically:

[0028] (a) Sort the population according to the normalized completion time and energy consumption ratio from small to large, and divide it into two populations. Pop1 corresponds to the population with a small completion time and high energy consumption, and Pop2 corresponds to the population with a large completion time and low energy consumption. The key factory of the two populations is defined as the factory with the largest energy consumption F t and the factory F with the largest completion time c ,The critical path is the uninterrupted workpiece path from the completion of the last process to the start of the process. The preventive maintenance operation is regarded as a general process. There is no idle time between any two processes on the critical path;

[0029] (b) For each individual in the population, a search operation is randomly selected to be performed, including: randomly selecting a workpiece from the key factory and inserting it into another factory, randomly selecting two workpieces from the key factory to exchange, randomly selecting a workpiece to insert into another position in the key factory, randomly selecting two workpieces in the key factory to exchange, randomly selecting workpieces between two positions in the key factory to reverse the order, and randomly improving the key operation O on the key path in the key factory. j，i Reduce the processing speed of all non-critical operations on non-critical paths in critical factories without extending the workpiece completion time;

[0030] (5) Generate a new population through the above search operation, and use the selection operation based on the feedback mechanism to achieve population evolution, specifically:

[0031] ①Uniformly initialize PS weight vectors in the target space to satisfy For each individual x a Associate a recent weight, let in is the normalized reference point, i.e., the minimum target value obtained during the search process;

[0032] ② Establish a candidate solution pool of size PS. At the same time, the solutions in the Pareto archive are also considered as candidate solutions. The potential value index (PVI) of the solution is defined as in and Respectively represent the solution x a Normalized makespan and TEC values, g a and g(t) represent x a The number of generations generated and the current generation, iter a Represents x a The number of iterations in the evolutionary process;

[0033] ③ Determine each individual x a and the newly generated individual x′ a Each neighborhood solution x b Does it satisfy g(x b |λ a , z * )≤g(x′ a |λ a , z * ), if it satisfies, then x′ a Replace x b ; Otherwise, randomly select a solution from the candidate solution pool and compare the PVI value. If it is greater than x b PVI value, then replace x b ; if x′ aWithout updating any solution, determine whether the candidate solution pool size reaches PS. If not, directly update x′ a Add to the pool; otherwise, it will compete with the smallest solution in the pool, the solution with a larger value wins and enters the candidate solution pool, and each new individual is used to update the Pareto archive set;

[0034] (6) By iterating the population optimization of (4) and the population evolution of (5), the optimal Pareto solution set is obtained, and the decoding rule is used to generate the scheduling solution set. The optimization target value is calculated by the distributed assembly line scheduling calculation model considering the equipment preventive maintenance. According to the given optimal scheduling solution set, the distributed assembly line energy efficiency scheduling considering the equipment preventive maintenance can be realized.

[0035] The characteristics and beneficial effects of the present invention are:

[0036] 1. The present invention establishes a distributed assembly line energy efficiency scheduling method that takes into account equipment preventive maintenance. By considering the preventive maintenance operation of the machine, a fast calculation model for two scheduling objectives, namely, completion time and energy consumption, is provided;

[0037] 2. The encoding method proposed in the present invention can effectively characterize the factory allocation of workpieces, the sorting of workpieces in the factory, and the running speed of the machine in the distributed assembly line energy efficiency scheduling. A decoding method is proposed to effectively consider the preventive maintenance scheduling plan of the machine, and based on the scheduling calculation model, the performance of the scheduling plan can be effectively improved;

[0038] 3. The evolutionary optimization scheduling method based on feedback learning proposed in the present invention can quickly construct an efficient scheduling scheme population through heuristic rules, optimize the population quality through multiple search operations, and adopt a feedback-based selection strategy to realize the evolution of the population, thereby improving the quality of the scheduling scheme. The scheduling method has a clear and simple structure and is easy to implement. It can effectively and efficiently solve the distributed assembly line energy efficiency scheduling problem considering equipment preventive maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A distributed assembly line energy efficiency scheduling Gantt chart considering equipment preventive maintenance is provided in an embodiment of the present invention.

[0040] Figure 2 A schematic flow chart of an evolutionary optimization scheduling method based on feedback learning provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] Assembly line scheduling is the most common type of scheduling in the manufacturing industry. Distributed assembly line problems in a distributed manufacturing environment are more complicated, requiring coordinated scheduling of workpiece allocation between distributed production lines and workpiece sorting on each assembly line. At the same time, since the machine can set the processing speed and thus affect the production energy consumption, the distributed assembly line energy efficiency scheduling considering equipment preventive maintenance needs to consider workpiece scheduling, machine speed and preventive maintenance scheduling at the same time. Traditional production scheduling methods are difficult to efficiently solve the distributed assembly line energy efficiency scheduling problem considering equipment preventive maintenance, and existing scheduling methods are difficult to achieve production and preventive maintenance coordinated scheduling to optimize completion time and energy consumption. Since workpiece allocation, workpiece sorting, machine speed and preventive maintenance scheduling are coupled with each other, scheduling optimization is difficult. Designing an effective and efficient scheduling method to achieve distributed assembly line energy efficiency scheduling considering equipment preventive maintenance is of great significance to the development of intelligent manufacturing and green manufacturing.

[0042] The embodiment of the present invention provides a distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance, constructs a distributed assembly line scheduling calculation model considering equipment preventive maintenance, constructs scheduling scheme encoding and decoding rules, uses heuristic rules to construct the initial population, and optimizes the quality of the population solution through multiple search operations, uses a selection operation based on a feedback mechanism to achieve population evolution, and quickly obtains a scheduling scheme with low completion time and low energy consumption, so as to effectively and efficiently solve the distributed assembly line energy efficiency scheduling problem considering equipment preventive maintenance. The specific implementation steps are as follows:

[0043] (1) Construct a distributed assembly line scheduling calculation model considering equipment preventive maintenance, including the optimization target calculation model of maximum completion time and total energy consumption and the relationship between their decision variables, specifically:

[0044] Construct the objective function calculation model of distributed flexible production and distribution joint scheduling, the objective function maximum completion time C max It refers to the maximum completion time of the last job of the last machine in all factories. It is calculated as shown in (1), where C(f) represents the completion time of factory f. represents the last job n on the last machine m in factory f f Completion time

[0045]

[0046] The calculation method for the completion time of the ,th job on machine i in factory f is shown in (2), where MT f，i represents the preventive maintenance time of the machine, t l，i represents the standard processing time of the lth workpiece, v f，i，l Indicates the machine processing speed

[0047] C f，i，l =max{C f，i-1，l , C f，i，l-1 +MT f，i，l}+t l，i / v f，i，l (2)

[0048] Preventive maintenance time MT for machine i in plant f f，i，l The maintenance level ML before the machine processes the first workpiece f，i，l The calculation method is shown in (3). When it is not enough to process the first workpiece, preventive maintenance operation is required, and the operation time is MT. f，i

[0049]

[0050] Maintenance level ML of machine i in factory f before processing the first workpiece f，i，l The calculation method is shown in (4). If the maintenance operation is performed, the maintenance level returns to the maximum value. Otherwise the maintenance level is inversely proportional to the processing time

[0051]

[0052] The total energy consumption TEC of the objective function consists of two parts: the energy consumption of the machine processing process PEC and the energy consumption of the machine idle process SEC. The calculation method is shown in (5), where PEC f，i and the SEC f，i Respectively represent the energy consumption of the i-th machine in factory f during processing and idle time

[0053]

[0054] Machine Process PEC f，i The calculation method is shown in (6), where PP f，i，v is the unit energy consumption of the i-th machine in factory f when processing a workpiece at speed v

[0055]

[0056] Machining ProcessSEC f，i The calculation method is shown in (7), where SP f，i，v is the unit energy consumption of the i-th machine in factory f when it is idle

[0057]

[0058] The energy efficiency scheduling target of distributed assembly line considering equipment preventive maintenance is the completion time and total energy consumption of all workpieces. Through the above calculation model, the target value of the scheduling plan can be obtained.

[0059] Specifically, there are n workpieces to be processed in F heterogeneous flow shops, and each workpiece j (j = 1, ..., n) contains m operations (O j，1 ...,O j，i , ..., O j,m} need to be processed on m machines in sequence, and the order of the workpieces on each machine is consistent. f，i ) has s (v=1, ..., 5) adjustable processing speeds. The higher the speed, the shorter the processing time and the greater the power consumption. j，i The actual processing time is t j，i =p j,i / V v , where p j，i O j，i Standard processing time, V v is the actual processing speed. Total energy consumption refers to the energy consumption of all machines in all factories in both operating and standby modes. Since equipment will fail over time, considering preventive maintenance (PM) of machines can improve the reliability of the production system. The maintenance level (ML) of a machine represents its health status and decreases linearly with the use of the machine. When the ML of machine i in factory f is not enough to process the next workpiece, a PM operation will be performed to restore it to the maximum ML value The workpiece processing or PM operation of the machine cannot be interrupted. Considering the heterogeneity of the distributed factory, each factory contains m machines with different maintenance time MT f，i and maintenance level

[0060] In the distributed assembly line energy efficiency scheduling model considering equipment preventive maintenance, formulas (1-4) are used to calculate the completion time target, where (3-4) represents the impact of machine preventive maintenance operations on the completion time; formulas (5-6) are used to calculate the total energy consumption of the scheduling process, including machine processing energy consumption and idle energy consumption.

[0061] Figure 1 A distributed assembly line energy efficiency scheduling Gantt chart considering equipment preventive maintenance is provided in an embodiment of the present invention. Figure 1 There are two factories, each with three machines and 10 workpieces to be processed. Workpieces 2, 8, 4, 7, and 6 are processed in factory 1, while the remaining workpieces are processed in factory 2. Assume that machine M 1，1 The maximum ML is Then when the workpiece 7 is in the machine M 1,1 Upper completion time ML 11 =1, so the PM operation should be performed before processing workpiece 6. The figure shows the ML trend of each machine in Factory 1. The PM operation can restore the machine to the maximum ML value, and the ML remains unchanged when the machine is in idle mode.

[0062] Based on the above distributed assembly line scheduling calculation model considering equipment preventive maintenance, Figure 2 The flowchart of the scheduling method provided by the embodiment of the present invention is as follows: constructing an initial population according to a heuristic method, optimizing the initial population through multiple search operations, and realizing population evolution by adopting a feedback selection strategy of a candidate solution pool, and finally obtaining a distributed assembly line scheduling scheme considering equipment preventive maintenance. The specific steps include:

[0063] (2) Based on the distributed assembly line scheduling calculation model considering equipment preventive maintenance, the encoding and decoding rules of the scheduling scheme are constructed, specifically:

[0064] The encoding process uses the sequence string of F workpiece sequences Π={π1,...,π F} represents the factory allocation of workpieces and the order of workpieces within the factory, with a length of n, where each sequence π f Represents the workpiece sequence of factory f; using matrix V = (v j，i ) n×m Represents the processing speed of each process, and the element v in the matrix j，i Indicates process O j，i Processing speed;

[0065] The decoding process allocates the workpieces to the corresponding factories in the order of Π according to the speed v j，i Before processing each process, the current machine maintenance level ML must be determined f，i，l Whether it can process the current workpiece, if it can, then ML f，i，l >t l，i / v f，i，l , then continue to process the workpiece; otherwise, perform preventive maintenance on the machine before processing the workpiece;

[0066] (3) Based on the encoding and decoding rules, the initial population is constructed using heuristic rules and evaluated through a distributed assembly line scheduling calculation model considering equipment preventive maintenance, specifically:

[0067] Generate a speed matrix randomly, and sort all workpieces in descending order according to the actual total processing time; insert workpieces into all positions of all factories in order, consider the impact of preventive maintenance operations on completion time, and select the position with the smallest completion time for insertion. If there are multiple positions with the same completion time, randomly select one position; repeat the above insertion process until all workpieces are assigned and sorted; by repeating the above steps, an initial population of size PS can be generated, and all non-dominated solutions in the initial population are selected to form a Pareto archive set;

[0068] (4) Based on the constructed initial population, a multi-search operator is used to optimize the population quality, specifically:

[0069] (a) Sort the population according to the normalized completion time and energy consumption ratio from small to large, and divide it into two populations. Pop1 corresponds to the population with a small completion time and high energy consumption, and Pop2 corresponds to the population with a large completion time and low energy consumption. The key factory of the two populations is defined as the factory with the largest energy consumption F t and the factory F with the largest completion time c ,The critical path is the uninterrupted workpiece path from the completion of the last process to the start of the process. The preventive maintenance operation is regarded as a general process. There is no idle time between any two processes on the critical path;

[0070] (b) For each individual in the population, a search operation is randomly selected to be performed, including: randomly selecting a workpiece from the key factory and inserting it into another factory, randomly selecting two workpieces from the key factory to exchange, randomly selecting a workpiece to insert into another position in the key factory, randomly selecting two workpieces in the key factory to exchange, randomly selecting workpieces between two positions in the key factory to reverse the order, and randomly improving the key operation O on the key path in the key factory. j，i Reduce the processing speed of all non-critical operations on non-critical paths in critical factories without extending the workpiece completion time;

[0071] (5) Generate a new population through the above search operation, and use the selection operation based on the feedback mechanism to achieve population evolution, specifically:

[0072] ①Uniformly initialize PS weight vectors in the target space to satisfy For each individual x a Associate a recent weight, let in is the normalized reference point, i.e., the minimum target value obtained during the search process;

[0073] ② Establish a candidate solution pool of size PS. At the same time, the solutions in the Pareto archive are also considered as candidate solutions. The potential value index (PVI) of the solution is defined as in and Respectively represent the solution x a Normalized makespan and TEC values, g a and g(t) represent x a The number of generations generated and the current generation, iter a Represents x a The number of iterations in the evolutionary process;

[0074] ③ Determine each individual x a and the newly generated individual x′ a Each neighborhood solution x b Does it satisfy g(x b |λ a , z * )≤g(x′ a |λ a , z * ), if it satisfies, then x′ a Replace x b ; Otherwise, randomly select a solution from the candidate solution pool and compare the PVI value. If it is greater than x b PVI value, then replace x b ; if x′ a Without updating any solution, determine whether the candidate solution pool size reaches PS. If not, directly update x′ a Add to the pool; otherwise, it will compete with the smallest solution in the pool, the solution with a larger value wins and enters the candidate solution pool, and each new individual is used to update the Pareto archive set;

[0075] (6) By iterating the population optimization of (4) and the population evolution of (5), the optimal Pareto solution set is obtained, and the decoding rule is used to generate the scheduling solution set. The optimization target value is calculated by the distributed assembly line scheduling calculation model considering the equipment preventive maintenance. According to the given optimal scheduling solution set, the distributed assembly line energy efficiency scheduling considering the equipment preventive maintenance can be realized.

[0076] The evolutionary optimization scheduling method based on feedback learning proposed in the embodiment of the present invention can construct an initial scheduling population with better performance through a heuristic method, and optimize the population through various local search operations, effectively improving the performance of the scheduling scheme, and adopts a selection strategy based on feedback learning to realize the evolution of the population, and finally obtain a more satisfactory set of scheduling schemes in a shorter time, effectively and efficiently solving the distributed assembly line energy efficiency scheduling considering equipment preventive maintenance.

Claims

1. A distributed assembly line energy efficiency scheduling method considering equipment preventive maintenance, constructing a distributed assembly line scheduling calculation model considering equipment preventive maintenance, constructing scheduling scheme encoding and decoding rules, using heuristic rules to construct the initial population, and optimizing the quality of the population solution through multiple search operations, using a selection operation based on a feedback mechanism to achieve population evolution, and finally obtaining a local optimal solution for distributed assembly line energy efficiency scheduling considering equipment preventive maintenance; It is characterized in that The steps include: Step (1) constructs a distributed assembly line scheduling calculation model considering equipment preventive maintenance, including the optimization target calculation model of maximum completion time and total energy consumption and the relationship between their decision variables, specifically: Construct the objective function calculation model of distributed flexible production and distribution joint scheduling, the objective function maximum completion time C max It refers to the maximum completion time of the last job of the last machine in all factories. It is calculated as shown in (1), where C(f) represents the completion time of factory f. represents the last job n on the last machine m in factory f f Completion time The completion time of the lth job on machine i in factory f is calculated as shown in (2), where MT f,i represents the preventive maintenance time of the machine, t l,i represents the standard processing time of the lth workpiece, v f,i,l Indicates the machine processing speed C f,i,l =max{C f,i-1,l ,C f,i,l-1 +MT f,i,l }+t l,i / v f,i,l (2) Preventive maintenance time MT for machine i in plant f f,i,l The maintenance level ML before the machine processes the first workpiece f,i,l The calculation method is shown in (3). When it is not enough to process the first workpiece, preventive maintenance operation is required, and the operation time is MT. f,i Maintenance level ML before machine i processes the lth workpiece in factory f f,i,l The calculation method is shown in (4). If the maintenance operation is performed, the maintenance level returns to the maximum value. Otherwise the maintenance level is inversely proportional to the processing time The total energy consumption TEC of the objective function consists of two parts: the energy consumption of the machine processing process PEC and the energy consumption of the machine idle process SEC. The calculation method is shown in (5), where PEC f,i and the SEC f,i Respectively represent the energy consumption of the i-th machine in factory f during processing and idle time Machine Process PEC f,i The calculation method is shown in (6), where PP f,i,b is the unit energy consumption of the i-th machine in factory f when processing workpieces at speed v: Machining ProcessSEC f,i The calculation method is shown in (7), where SP f,i,v is the unit energy consumption of the i-th machine in factory f when it is idle: Step (2) is to construct the encoding and decoding rules of the scheduling scheme based on the distributed assembly line scheduling calculation model considering equipment preventive maintenance, which are as follows: The encoding process uses the sequence of F workpiece sequences Π={π1,…,π F } represents the factory allocation of workpieces and the order of workpieces within the factory, with a length of n, where each sequence π f Represents the workpiece sequence of factory f; using matrix V = (v j,i ) n×m Represents the processing speed of each process, and the element v in the matrix j,i Indicates process O j,i Processing speed; The decoding process allocates the workpieces to the corresponding factories in the order of Π according to the speed v j,i Before processing each process, the current machine maintenance level ML must be determined f,i,l Whether it can process the current workpiece, if it can, then ML f,i,l >t l,i / v f,i,l , then continue to process the workpiece; otherwise, perform preventive maintenance on the machine before processing the workpiece; Step (3), based on the encoding and decoding rules, the initial population is constructed using heuristic rules and evaluated through a distributed assembly line scheduling calculation model considering equipment preventive maintenance; specifically: Generate a speed matrix randomly, and sort all workpieces in descending order according to the actual total processing time; insert workpieces into all positions of all factories in order, consider the impact of preventive maintenance operations on completion time, and select the position with the smallest completion time for insertion. If there are multiple positions with the same completion time, randomly select one position; repeat the above insertion process until all workpieces are assigned and sorted; by repeating the above steps, an initial population of size PS can be generated, and all non-dominated solutions in the initial population are selected to form a Pareto archive set; Step (4), based on the constructed initial population, a multi-search operator is used to optimize the population quality; specifically: (a) Sort the population according to the normalized completion time and energy consumption ratio from small to large, and divide it into two populations. Pop1 corresponds to the population with a small completion time and high energy consumption, and Pop2 corresponds to the population with a large completion time and low energy consumption. The key factory of the two populations is defined as the factory with the largest energy consumption F t and the factory F with the largest completion time c ,The critical path is the uninterrupted workpiece path from the completion of the last process to the start of the process. The preventive maintenance operation is regarded as a general process. There is no idle time between any two processes on the critical path; (b) For each individual in the population, a search operation is randomly selected to be performed, including: randomly selecting a workpiece from the key factory and inserting it into another factory, randomly selecting two workpieces from the key factory to exchange, randomly selecting a workpiece to insert into another position in the key factory, randomly selecting two workpieces in the key factory to exchange, randomly selecting workpieces between two positions in the key factory to reverse the order, and randomly improving the key operation O on the key path in the key factory. j,i Reduce the processing speed of all non-critical operations on non-critical paths in critical factories without extending the workpiece completion time; Step (5) generates a new population through the above search operation, and uses a selection operation based on a feedback mechanism to achieve population evolution, specifically: ①Uniformly initialize PS weight vectors in the target space to satisfy For each individual x a Associate a recent weight, let in is the normalized reference point, i.e., the minimum target value obtained during the search process; ② Establish a candidate solution pool of size PS. At the same time, the solutions in the Pareto archive are also considered as candidate solutions. The potential value index PVI of the solution is defined as in and Respectively represent the solution x a Normalized makespan and TEC values, g a and g(t) represent x a The number of generations generated and the current generation, iter a Represents x a The number of iterations in the evolutionary process; ③ Determine each individual x a and the newly generated individual x′ a Each neighborhood solution x b Does it satisfy g(x b |λ a ,z * )≤g(x′ a |λ a ,z * ), if it satisfies, then x′ a Replace x b ; Otherwise, randomly select a solution from the candidate solution pool and compare the PVI value. If it is greater than x b PVI value, then replace x b ; if x′ a Without updating any solution, determine whether the candidate solution pool size reaches PS. If not, directly update x′ a Add to the pool; otherwise, it will compete with the smallest solution in the pool, the solution with a larger value wins and enters the candidate solution pool, and each new individual is used to update the Pareto archive set; Step (6), through iterative optimization, the population of step (4) and the population of step (5) are evolved to obtain the optimal Pareto solution set, and the scheduling solution set is generated by using the decoding rule. The optimization target value is calculated by the distributed assembly line scheduling calculation model considering the equipment preventive maintenance, and according to the given optimal scheduling solution set, the distributed assembly line energy efficiency scheduling considering the equipment preventive maintenance can be realized.

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