Equipment network comprehensive scheduling method based on improved Jaya algorithm

Abstract

The invention provides an equipment network comprehensive scheduling method based on an improved Jaya algorithm aiming at the condition that the migration time of working procedures between equipment is ignored in the existing flexible equipment network comprehensive scheduling method. The method is mainly divided into four parts. Wherein a double-chromosome coding method based on a process chain and an equipment chain is designed in the coding part, a coding method based on a quasi-schedulable process set and a random process coding method are designed in the process chain coding aspect, and the legality of a generated individual is ensured; in the aspect of the equipment chain, an equipment coding method based on short time and a random equipment coding method are designed to ensure that equipment distributed in the process is machinable equipment; a double-chain updating operation of updating a process chain first and then updating an equipment chain is designed in the updating part; in the decoding part, an equipment idle insertion decoding strategy considering migration time is designed; local search operation based on a critical path is designed in the local search part. The feasibility and superiority of the method are verified through experiments.

Description

Technical Field

[0001] The invention relates to a device network comprehensive scheduling method based on an improved Jaya algorithm. Background Art

[0002] Production scheduling is a typical NP problem, and there is no effective algorithm to ensure the optimal solution. In modern manufacturing, production scheduling is a key link to ensure production efficiency and cost-effectiveness. With the rise of Industry 4.0, the demand for intelligent and automated production processes is growing, and the problem of comprehensive scheduling of equipment networks has gradually become a hot topic of research. Traditional production scheduling methods often focus on a single-stage production process, but fail to fully consider the scheduling of products with complex process structures. In particular, the following problems still exist in the equipment network environment: 1. Because the traditional comprehensive scheduling method does not optimize the migration time of the process between equipment as an independent factor, the scheduling results deviate from the actual production, which in turn affects the production efficiency and the efficiency of equipment parallel operation; 2. Because the traditional equipment network method depends on the processing structure of a specific product, it has limited adaptability to different instances, resulting in the homogeneity of the scheduling strategy; 3. Due to defects in the coding design, the scheduling order of processes and equipment cannot be effectively represented; 4. Because the decoding and local search methods fail to effectively consider the migration time and reduce the idle time of the equipment, the overall production efficiency of the equipment network is affected. Summary of the invention

[0003] The purpose of the present invention is to solve the above-mentioned existing technical problems and propose a device network comprehensive scheduling method based on an improved Jaya algorithm.

[0004] The present invention is implemented by the following technical scheme. The present invention proposes a device network comprehensive scheduling method based on an improved Jaya algorithm. S1: Dual chromosome coding based on process chain and equipment chain A coding strategy of "determine the process chain first, and then select the equipment chain according to the process chain" is adopted; its purpose is to ensure that the equipment assigned to the process is a processable equipment; in terms of process chain coding, a coding method based on a quasi-schedulable process set and a random process coding method are adopted. By identifying the product process tree of complex products, the process set to be scheduled at the current moment is obtained, and a certain schedulable process is determined for processing according to the two coding methods, that is, the number on the gene position in the process chromosome after coding represents the process number of the complex product; in terms of equipment chain coding, a short-time-based equipment coding method and a random equipment coding method are used to encode the equipment chromosome. By identifying the coded process chain, according to the complex product process tree, the processable process set corresponding to the process at the current coding position is obtained, and a certain processing equipment is determined according to the two equipment coding methods, that is, the number on the gene position in the equipment chromosome after coding represents the processing equipment of the process chromosome corresponding to the process chromosome; S2: Dual-chain update operation A double-chain update operation of "updating the process chain first and then updating the equipment chain" is adopted to avoid the problem of unavailability of processing equipment due to mismatch between the process chain and the equipment chain; the newly generated process chromosome inherits the excellent characteristics of the optimal parent process chromosome and abandons the inferior characteristics of the worst parent chromosome, thereby ensuring that the new process chromosome satisfies the order constraint relationship; after the process chromosome is updated, the elements in the newly generated equipment chromosome correspond to the processable equipment of the new process chromosome; if the completion time of the updated individual exceeds the completion time before the update, whether to accept the updated individual is determined according to the preset acceptance criteria; S3: Decoding operation The device idle time decoding strategy takes into account the migration time; S4: Local search operation A local search operation based on the critical path.

[0005] Furthermore, the encoding method based on the quasi-schedulable process set comprises the following specific steps: Step 1.1: For each schedulable process, calculate its quasi-schedulable process set, and perform a quantitative evaluation of the cardinality (i.e., the number of elements in the set) of each quasi-schedulable process set; Step 1.2: Use the roulette wheel selection mechanism to screen the schedulable processes; processes with larger cardinality have a higher probability of being selected; Step 1.3: Repeat step 1.1 to determine whether the length of the schedulable process set obtained at this moment is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.2.

[0006] Furthermore, the random process coding method comprises the following specific steps: Step 1.4: Obtain the schedulable process set based on the product process tree; Step 1.5: Under the condition that the constraints of the process tree are satisfied, randomly select a schedulable process from the schedulable process set; Step 1.6: Repeat step 1.4 to determine whether the length of the schedulable process set obtained at this time is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.5; Furthermore, the device encoding method based on short-duration comprises the following specific steps: Step 1.7: Obtain the processable equipment set of each process in the process chain from left to right; Step 1.8: For each processable device, calculate the processing time of the process on the device; use the roulette wheel selection strategy to determine the device; the device with a shorter processing time has a higher probability of being selected.

[0007] Furthermore, the random device encoding method comprises the following specific steps: Step 1.9: Obtain the processable equipment set of each process in the process chain from left to right; Step 1.10: Randomly select a device from the device set corresponding to the process; Furthermore, the process chain update operation comprises the following specific steps: Step 2.1: Randomly select the worst individual V worst For a process in the process chain, loop to obtain its descendant nodes and add them to the process set to be updated S b ; Step 2.2: Determine the updated individual V i Middle and V worst Between b The location of the intermediate process; Step 2.3: From V i Delete the S b The same position of the process, and copy the remaining process to the newly generated individual V new middle; Step 2.4: According to the optimal individual V best Adjust S b The order of the processes in the process is adjusted and the adjusted order is used as S a , fill in V new The corresponding empty element position.

[0008] Furthermore, the device chain update operation comprises the following specific steps: Step 2.5: Identify the updated individual V i , the worst individual V worst The process set S to be updated b Processing equipment in the same position equipment chain; Step 2.6: From V i Delete the S b The processing equipment in the same equipment chain and copy the remaining equipment chains to V new In the device chain; Step 2.7: Based on the adjusted process set S a From the optimal individual V best Get the processing equipment corresponding to its equipment chain, and then copy it to V in sequence new The corresponding empty element position in; Furthermore, the device idle interpolation decoding strategy operation considering the migration time comprises the following specific steps: Step 3.1: Analyze the process chain and related equipment chain in the processing plan, and determine the corresponding processing equipment for each process to be executed; Step 3.2: Dynamic evaluation of equipment idle time periods and process scheduling; obtain each process O in the process chain from left to righti , and identify the corresponding processing equipment from the equipment chain; for each equipment, execute the process insertion strategy.

[0009] Furthermore, the step 3.2 is specifically as follows: Check the equipment has processed process set S mk , determine the current working status of the equipment, including the processed processes and their schedules; calculate the equipment idle time period TP mk , evaluate the target equipment M for the processing step k Has it been used for at least one process before? i ; If the equipment has not completed any process, it is considered that the equipment currently has no idle time period, so it is not suitable for the current process to be inserted, and it will directly turn to the next process. Otherwise, for each process completed on the equipment, calculate the difference between its start time and the end time of the immediately preceding process, that is, the idle time period of the equipment between the corresponding processes; if the process under consideration is the first process processed by the equipment, the end time of the immediately preceding process is defined as 0; calculate the total time P of the process to be processed and the migration time period oi , add the processing time of the process to be scheduled and the migration time from the immediately preceding process to the current equipment; evaluate the equipment idle time and the total process time. If TP mk ≥P oi , then further verify whether the start time of the process meets the dependency constraints of the process tree, that is, determine whether the start time of the process is later than the end time of the immediate predecessor process; if the constraints are met, the process is scheduled to a suitable position in the set of processes to be executed by the equipment; otherwise, it is determined that the current equipment has no suitable idle time period.

[0010] Furthermore, the local search operation based on the critical path comprises the following specific steps: Step 4.1: Establish a directed acyclic graph (DAG). Establish a set of nodes of the DAG through the scheduling sequence. Each node represents a process. The node contains the following attributes: start time, end time, processing time, and processing equipment. Add an edge relationship between each node and its predecessor node. The weight of the edge is the migration time from the equipment of the predecessor process to the equipment of the current process. Step 4.2: Use the topological sorting method to sort the DAG to determine the processing order of the nodes; Step 4.3: Create a dynamic programming array to store the longest path time from the starting point to each node; update the longest path time of each node in turn according to the result of topological sorting; the longest path time is the longest path time of its predecessor node plus the processing time and migration time of the current node; finally, starting from the end node, reversely trace the update process of the longest path time to determine the critical path of the scheduling sequence; Step 4.4: Local search optimization; determine the key nodes in the critical path, replace the processing equipment from the set of processable equipment at the key nodes in turn, and try to find a better equipment combination; evaluate the scheduling plan after replacing the equipment, calculate the new scheduling time and cost, and compare whether it is better than the current plan.

[0011] Compared with the prior art, the present invention has the following advantages: The method described in the present invention takes into account the migration time of the process between devices in the equipment network, which can more accurately reflect the time consumption in the actual production process, thereby improving the accuracy and efficiency of the scheduling scheme; the designed process encoding method based on the quasi-schedulable process set and the equipment encoding operation based on short time are easy to operate, ensuring the legitimacy of the generated individuals and balancing the diversity of the population solutions; an update mechanism based on the process descendant nodes is introduced, so that the solution to be updated can be far away from the worst solution and gradually approach the optimal solution; this mechanism helps to optimize the scheduling scheme and improve the quality of the solution. A device idle slot decoding considering the migration time is given. Compared with the traditional decoding method, this method significantly improves the actual production efficiency in the equipment network production environment. A local search strategy for the critical path based on the migration time is designed to achieve the local optimal solution of the individual. The experimental results show the feasibility and superiority of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a schematic diagram of the process tree for product A; Figure 2 This is a schematic diagram of the equipment migration time for product A; Figure 3 It is a schematic diagram of the double-stranded chromosome coding; Figure 4 This is a schematic diagram of the process chromosome update; Figure 5 Update the schematic diagram for the device chromosome; Figure 6 Gantt chart for scheduling product A; Figure 7 Another Gantt chart for scheduling product A; Figure 8 This is the optimal solution for product A and the average completion time change curve. DETAILED DESCRIPTION

[0013] The technical scheme in the embodiment of the present invention will be described in detail below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the present invention, not all of it. Based on these embodiments, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0014] Related definitions: Complex product: The product must meet the following two conditions at the same time: first, the product is assembled from a group of workpieces with constraints according to a tree-like process diagram; second, the workpiece is composed of a series of processes with forward and backward constraints. Such a product is defined as a complex product.

[0015] Product process tree: In the process tree, each process is represented by a node. Each node consists of three parts, representing the process name, equipment name and processing time respectively. The direction of the arrow on the edge represents the priority constraint relationship between processes.

[0016] Device network: refers to a cross-enterprise, distributed shared device resource network. In this network, device resources in different geographical locations are integrated together to form a virtual device pool for multiple enterprises or users to share and use.

[0017] The set of quasi-schedulable processes: includes all subsequent processes that meet the conditions and can be included in the scheduling plan after the current process is successfully scheduled.

[0018] If we take the process tree of complex product A as an example, Figure 1 As shown, the device network diagram of product A is as follows Figure 2 As shown, Indicates process O i Processing from M1 to M2 can only be completed after migration.

[0019] The present invention proposes a device network comprehensive scheduling method based on an improved Jaya algorithm. S1: Double chromosome encoding based on product process tree A To ensure that the equipment assigned to the process is processable equipment, a coding strategy of "first determine the process chain, then select the equipment chain based on the process chain" is adopted; The process chromosome is encoded by using the coding method based on the quasi-schedulable process set and the random process coding method. By identifying the product process tree of the complex product, the process set to be scheduled at the current moment is obtained. According to the two coding methods, a certain schedulable process is determined for processing, that is, the number on the gene position in the process chromosome after encoding represents the process number of the complex product; the selection probability of the coding method based on the quasi-schedulable process set is 20%, and the selection probability of the random process coding method is 80%; The equipment chromosome is encoded by using the equipment encoding method based on short time and the random equipment encoding method. By identifying the process chain after encoding, the process set corresponding to the process at the current encoding position is obtained according to the process tree of the complex product. A certain processing equipment is determined according to the two equipment encoding methods, that is, the number on the gene position in the equipment chromosome after encoding represents the processing equipment of the process chromosome corresponding to the process; the selection probability of the equipment encoding method based on short time is 20%, and the probability of the random equipment encoding method is 80%; The encoding method based on the quasi-schedulable process set is specifically: Step 1.1: For each schedulable process in the product process tree, calculate its quasi-schedulable process set, and perform a quantitative evaluation of the cardinality (i.e., the number of elements in the set) of each quasi-schedulable process set; Step 1.2: Use the roulette wheel selection mechanism to screen the schedulable processes. Processes with a larger cardinality have a higher probability of being selected; Step 1.3: Repeat step 1.1 to determine whether the length of the schedulable process set obtained at this time is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.2.

[0020] The random process coding method is specifically as follows: Step 1.4: Obtain the set of schedulable processes based on the product process tree.

[0021] Step 1.5: Under the condition that the process tree constraint relationship is satisfied, randomly select a schedulable process from the schedulable process set; Step 1.6: Repeat step 1.4 to determine whether the length of the schedulable process set obtained at this time is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.5; The device encoding method based on short-time usage is specifically as follows: Step 1.7: Obtain the processable equipment set of each process in the coded process chain from left to right; Step 1.8: For each processable device, calculate the processing time of the process on the device; use the roulette wheel selection strategy to determine the device; the device with a shorter processing time has a higher probability of being selected; Furthermore, the random device encoding method comprises the following specific steps: Step 1.9: Obtain the processable equipment set of each process in the process chain from left to right; Step 1.10: Randomly select a device from the device set corresponding to the process; Through the above-mentioned process chromosome encoding method: the encoding method based on the quasi-schedulable process set, the random process encoding method and the equipment chromosome encoding method: the equipment encoding method based on short time and the random equipment encoding method, a double chromosome individual that fully meets the product process priority constraints can be obtained. Figure 3 This is a schematic diagram of chromosome encoding obtained by applying the above encoding method to complex product A.

[0022] S2: Dual-chain update operation In order to avoid the problem of unavailability of processing equipment due to mismatch between process chain and equipment chain, a double-chain update operation of "updating process chain first, then updating equipment chain" is adopted. The core idea of ​​the update operation is "stay away from the worst chromosome and get close to the best chromosome". The newly generated process chromosome inherits the good characteristics of the best parent process chromosome and abandons the poor characteristics of the worst parent chromosome, so as to ensure that the new process chromosome satisfies the order constraint relationship. After the process chromosome is updated, the elements in the newly generated equipment chromosome correspond to the processable equipment of the new process chromosome. If the completion time of the updated individual exceeds the completion time before the update, the acceptance of the updated individual is determined according to the preset acceptance criteria.

[0023] The process chain update operation is specifically as follows: Step 2.1: Randomly select the worst individual V worst For a process in the process chain, loop to obtain its descendant nodes and add them to the process set to be updated S b ; Step 2.2: Determine the updated individual V i Middle and V worst Between b The location of the intermediate process; Step 2.3: From V i Delete the S b The same position of the process, and copy the remaining process to the newly generated individual V new middle; Step 2.4: According to the optimal individual V best Adjust S b The order of the processes in the process is adjusted and the adjusted order is used as S a , fill in V new The corresponding empty element position.

[0024] Updated process chromosome V new The generation process is as follows Figure 4 shown.

[0025] The device chain update operation is specifically as follows: Step 2.5: Identify the updated individual V i , the worst individual V worst The process set S to be updated b Processing equipment in the same position equipment chain; Step 2.6: From V i Delete the S bThe processing equipment in the same equipment chain and copy the remaining equipment chains to V new In the device chain; Step 2.7: Based on the adjusted process set S a From the optimal individual V best Get the processing equipment corresponding to its equipment chain, and then copy it to V in sequence new The corresponding empty element position in .

[0026] Updated device chromosome V new The generation process is as follows Figure 5 shown.

[0027] The legitimacy of the process chain and equipment chain update operation is based on the following logic: In the process chain update operation, step 2.1 ensures that the process set S to be updated b From a legitimate individual V worst , steps 2.2 to 2.4 by switching from V i Delete the same position of the process and copy the remaining process to the new individual V new In the meantime, according to the optimal individual V best Adjust S b The order of the new individual V new The process sequence in still satisfies the original sequence constraints; similarly, in the equipment chain update operation, step 2.5 identifies the processing equipment at the corresponding position, and steps 2.6 and 2.7 delete V i devices in the same position and according to V best The device chain sequentially fills in new individuals V new , ensuring that the new individual V new , the device chain sequence in meets the constraints; in summary, all update operation steps ensure the legitimacy of the newly generated individuals, that is, no infeasible solution will be generated.

[0028] S3: Decoding operation The device idle time interpolation decoding strategy takes migration time into consideration.

[0029] The device idle interpolation decoding strategy operation considering the migration time is specifically as follows: Step 3.1: Analyze the process chain and related equipment chain in the processing plan, and determine the corresponding processing equipment for each process to be executed Step 3.2: Dynamic evaluation of equipment idle time periods and process scheduling; obtain each process O in the process chain from left to right i , and identify the corresponding processing equipment from the equipment chain; for each equipment, perform the following steps: Furthermore, the step 3.2 is specifically as follows: Check the equipment has processed process set S mk, determine the current working status of the equipment, including the processed processes and their schedules; calculate the equipment idle time period TP mk , evaluate the target equipment M for the processing step k Has it been used for at least one process before? i ; If the equipment has not completed any process, it is considered that the equipment currently has no idle time period, so it is not suitable for the current process to be inserted, and it will directly turn to the next process. Otherwise, for each process completed on the equipment, calculate the difference between its start time and the end time of the immediately preceding process, that is, the idle time period of the equipment between the corresponding processes; if the process under consideration is the first process processed by the equipment, the end time of its immediately preceding process is defined as 0; calculate the total time P of the process to be processed and the migration time period oi , add the processing time of the process to be scheduled and the migration time from the immediately preceding process to the current equipment; evaluate the equipment idle time and the total process time. If TP mk ≥P oi , then further verify whether the start time of the process meets the dependency constraints of the process tree, that is, determine whether the start time of the process is later than the end time of the immediate predecessor process; if the constraints are met, the process is scheduled to a suitable position in the set of processes to be executed by the equipment; otherwise, it is determined that the current equipment has no suitable idle time period.

[0030] S4: Local search operation A local search operation based on the critical path.

[0031] The local search operation based on the critical path is specifically as follows: Step 4.1: Establish a directed acyclic graph (DAG). Establish a set of nodes of the DAG through the scheduling sequence. Each node represents a process. The node contains the following attributes: start time, end time, processing time, and processing equipment. Add an edge relationship between each node and its predecessor node. The weight of the edge is the migration time from the equipment of the predecessor process to the equipment of the current process. Step 4.2: Use the topological sorting method to sort the DAG to determine the processing order of the nodes; Step 4.3: Create a dynamic programming array to store the longest path time from the starting point to each node; update the longest path time of each node in turn according to the result of topological sorting; the longest path time is the longest path time of its predecessor node plus the processing time and migration time of the current node; finally, starting from the end node, reversely trace the update process of the longest path time to determine the critical path of the scheduling sequence; Step 4.4: Local search optimization; determine the key nodes in the critical path, replace the processing equipment from the set of processable equipment at the key nodes in turn, and try to find a better equipment combination; evaluate the scheduling plan after replacing the equipment, calculate the new scheduling time and cost, and compare whether it is better than the current plan.

[0032] The core of the design of a comprehensive scheduling method for complex product equipment networks lies in how to deal with the migration time of processes between equipment. The dual-chromosome encoding method designed by the present invention generates an initial solution set with a wide range of characteristics to improve the exploration ability of the search method in different areas of the solution space, thereby increasing the chance of finding a global optimal solution or a better solution and avoiding the premature convergence problem of falling into a local optimal solution. In order to avoid the problem of unavailable equipment chains, the designed dual-chain update operation adopts a strategy of "updating the process chain first, then updating the equipment chain". The feasibility, convergence and superiority of the present invention are demonstrated below through specific experimental data and results. The device idle interpolation decoding strategy considering the migration time considers the migration time of the process between equipment separately during decoding, and interpolates during the idle time period of the equipment. Finally, the proposed local search method based on the critical path identifies bottleneck tasks in the equipment network to improve production capacity and efficiency. The feasibility, convergence and superiority of the present invention are demonstrated below through specific experimental data and results.

[0033] The core of the design of a comprehensive scheduling method for complex product equipment networks lies in how to deal with the migration time of processes between equipment. The present invention designs a dual-chromosome encoding method to generate an initial solution set with a wide range of characteristics, thereby improving the exploration ability of the search method in different areas of the solution space. This design increases the chance of finding a global optimal solution or a better solution and avoids the premature convergence problem of falling into a local optimal solution. In order to avoid the problem of equipment chain unavailability, the designed dual-chain update operation adopts the strategy of "updating the process chain first, then updating the equipment chain". The experimental data and results show the feasibility, convergence and superiority of the present invention. In terms of decoding, the present invention considers the device idle interpolation decoding strategy of the migration time. When decoding, the migration time of the process between equipment is considered separately, and the interpolation operation is performed during the equipment idle time period. Finally, a local search method based on the critical path is proposed, which identifies the bottleneck tasks in the equipment network to improve production capacity and efficiency. The experimental data and results further prove the feasibility, convergence and superiority of the present invention.

[0034] feasibility by Figure 1Taking the process tree of complex product A shown in the figure as an example, the parameters in the experiment are set as follows: the initial population size is 50, the local search probability is 0.9, the number of iterations is 40, and the method is implemented by Python language and independently run for 30 times. During the 30 times of running the method, the average completion time of the solution is 170, which is the theoretical optimal solution to the scheduling problem of complex product A. Figure 7 and Figure 8 They are respectively partial scheduling Gantt charts obtained by the method of the present invention. Figure 7 The scheduling order shown is A8, A1, A5, A10, A13, A2, A3, A7, A12, A4, A6, A16, A9, A11, A14, A17, A15, A19, A18, A20, and the corresponding processing equipment numbers are 4, 4, 2, 2, 2, 1, 3, 3, 1, 1, 3, 1, 1, 4, 4, 4, 3, 2, 1, 2, and the total processing time is 175 working hours. Figure 8 The scheduling order shown is: A5, A1, A2, A4, A8, A3, A6, A10, A11, A13, A15, A9, A14, A7, A12, A16, A17, A18, A19, A20. The corresponding processing equipment numbers are 2, 4, 1, 1, 4, 3, 3, 2, 4, 2, 3, 1, 4, 3, 3, 1, 4, 3, 2, 2. The total processing time is 175 working hours.

[0035] Convergence The variation curve of the average completion time of each generation and the value of the optimal solution during the execution of the method of the present invention is as follows: Figure 8 As shown in the figure. From the change curve, it can be seen that for the scheduling problem of complex product A, as the number of iterations increases, the change of data gradually decreases, especially from the 24th iteration, the data tends to stabilize between 175. Therefore, the device network comprehensive scheduling method based on improved Jaya designed by the method of the present invention has a faster convergence speed.

[0036] The above is a detailed introduction to a device network comprehensive scheduling method based on an improved Jaya algorithm provided by the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A device network comprehensive scheduling method based on improved Jaya algorithm, characterized by: S1: Dual chromosome coding based on process chain and equipment chain Adopt a coding strategy of "determine the process chain first, and then select the equipment chain based on the process chain"; Its purpose is to ensure that the equipment assigned to the process is processable equipment; in terms of process chain coding, the coding method based on the quasi-schedulable process set and the random process coding method are adopted. By identifying the product process tree of complex products, the process set to be scheduled at the current moment is obtained, and a certain schedulable process is determined for processing according to the two coding methods, that is, the number on the gene position in the process chromosome after coding represents the process number of the complex product; in terms of equipment chain coding, the equipment chromosome is encoded by the equipment coding method based on short time and the random equipment coding method. By identifying the coded process chain, according to the complex product process tree, the processable process set corresponding to the process at the current coding position is obtained, and a certain processing equipment is determined according to the two equipment coding methods, that is, the number on the gene position in the equipment chromosome after coding represents the processing equipment of the process chromosome corresponding to the process; S2: Dual-chain update operation A double-chain update operation of "updating the process chain first and then updating the equipment chain" is adopted to avoid the problem of unavailability of processing equipment due to mismatch between the process chain and the equipment chain; the newly generated process chromosome inherits the excellent characteristics of the optimal parent process chromosome and abandons the inferior characteristics of the worst parent chromosome, thereby ensuring that the new process chromosome satisfies the order constraint relationship; after the process chromosome is updated, the elements in the newly generated equipment chromosome correspond to the processable equipment of the new process chromosome; if the completion time of the updated individual exceeds the completion time before the update, whether to accept the updated individual is determined according to the preset acceptance criteria; S3: Decoding operation The device idle time decoding strategy takes into account the migration time; S4: Local search operation A local search operation based on the critical path.

2. The method according to claim 1, characterized in that: The encoding method based on the quasi-schedulable process set comprises the following specific steps: Step 1.1: For each schedulable process, calculate its quasi-schedulable process set, and perform a quantitative evaluation of the cardinality (i.e., the number of elements in the set) of each quasi-schedulable process set; Step 1.2: Use the roulette selection mechanism to screen the schedulable processes; the processes with a larger cardinality have a higher probability of being selected; Step 1.3: Repeat step 1.1 to determine whether the length of the schedulable process set obtained at this time is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.

2.

3. The method according to claim 1, characterized in that: The random process coding method comprises the following specific steps: Step 1.4: Obtain the schedulable process set based on the product process tree; Step 1.5: Under the condition that the constraints of the process tree are satisfied, randomly select a schedulable process from the schedulable process set; Step 1.6: Repeat step 1.4 to determine whether the length of the schedulable process set obtained at this time is empty. If it is an empty set, the encoding process of the process chromosome ends, otherwise jump to step 1.

5.

4. The method according to claim 1, characterized in that: The device encoding method based on short-time usage comprises the following specific steps: Step 1.7: Obtain the processable equipment set of each process in the process chain from left to right; Step 1.8: For each processable device, calculate the processing time of the process on the device; use the roulette wheel selection strategy to determine the device; the device with a shorter processing time has a higher probability of being selected.

5. The method according to claim 1, characterized in that: The random device encoding method comprises the following specific steps: Step 1.9: Obtain the processable equipment set of each process in the process chain from left to right; Step 1.10: Randomly select a device from the device set corresponding to the process.

6. The method according to claim 1, characterized in that: The double chain update operation specifically includes the following steps: Step 2.1: Randomly select the worst individual For a process in the process chain, loop to obtain its descendant nodes and add them to the set of processes to be updated ; Step 2.2: Determine the individual to be updated Zhongyu between The location of the intermediate process; Step 2.3: From Delete the The same process in the same position in the process, and copy the remaining process to the newly generated individual middle; Step 2.4: According to the optimal individual Adjustment The order of the processes in the , fill in The corresponding empty element position.

7. The method according to claim 1, characterized in that: The device chain update operation includes the following specific steps: Step 2.5: Identify the updated individuals , the worst individual Process Sets in Progress and to be Updated Processing equipment in the same position equipment chain; Step 2.6: From Delete the The processing equipment in the same equipment chain and copy the remaining equipment chains to In the device chain; Step 2.7: Based on the adjusted process set From the best individual Get the processing equipment corresponding to its equipment chain, and then copy it to The corresponding empty element position in .

8. The method according to claim 1, characterized in that: The device idle interpolation decoding strategy operation considering the migration time specifically comprises the following steps: Step 3.1: Analyze the process chain and related equipment chain in the processing plan, and determine the corresponding processing equipment for each process to be executed; Step 3.2: Dynamic evaluation and process scheduling of equipment idle time periods, obtaining each process in the process chain from left to right , and identify the corresponding processing equipment from the equipment chain; for each equipment, execute the process insertion strategy.

9. The method according to claim 8, characterized in that: The step 3.2 is specifically as follows: Check the equipment's processing process set , determine the current working status of the equipment, including the processed operations and their schedule; Calculate device idle time , evaluate the target equipment for the process to be processed Has it been used for at least one process before? ; If the equipment has not completed any process, it is considered that the equipment currently has no idle time period, so it is not suitable for the current process to be inserted, and it will directly turn to the next process. Otherwise, for each process completed on the equipment, calculate the difference between its start time and the end time of the immediately preceding process, that is, the idle time period of the equipment between the corresponding processes; if the process under consideration is the first process processed by the equipment, the end time of the immediately preceding process is defined as 0; calculate the total time of the process to be processed and the migration time period , add the processing time of the process to be scheduled and the migration time from the immediately preceding process to the current equipment; evaluate the equipment idle time and the total process time. If , then further verify whether the start time of the process meets the dependency constraints of the process tree, that is, determine whether the start time of the process is later than the end time of the immediate predecessor process; if the constraints are met, the process is scheduled to a suitable position in the set of processes to be executed by the equipment; otherwise, it is determined that the current equipment has no suitable idle time period.

10. The method according to claim 1, characterized in that: The local search operation based on the critical path includes the following specific steps: Step 4.1: Create a directed acyclic graph (DAG). Create a set of nodes of the DAG through the scheduling sequence. Each node represents a process. The node contains the following attributes: start time, end time, processing time, and processing equipment. Add an edge relationship between each node and its predecessor node. The weight of the edge is the migration time from the equipment of the predecessor process to the equipment of the current process. Step 4.2: Use the topological sorting method to sort the DAG to determine the processing order of the nodes; Step 4.3: Create a dynamic programming array to store the longest path time from the starting point to each node; update the longest path time of each node in turn according to the result of topological sorting; the longest path time is the longest path time of its predecessor node plus the processing time and migration time of the current node; finally, starting from the end node, reversely trace the update process of the longest path time to determine the critical path of the scheduling sequence; Step 4.4: Local search optimization; determine the key nodes in the critical path, replace the processing equipment from the set of processable equipment at the key nodes in turn, and try to find a better equipment combination; evaluate the scheduling plan after replacing the equipment, calculate the new scheduling time and cost, and compare whether it is better than the current plan.

Images