Aero-engine pulse assembly line scheduling method based on improved genetic algorithm

Abstract

The invention provides an aero-engine pulse assembly line scheduling method based on an improved genetic algorithm, and the method comprises the steps: constructing a three-section type coding structure which comprises the number of station assembly people, the distribution of process stations and a process execution sequence, and designing an algorithm decoding mechanism and a feasibility restoration strategy; cooperative optimization of station worker allocation, process allocation and assembly priority is realized, so that the parallel assembly capacity is fully excavated on the premise of meeting station capacity limitation and process constraint, and the purpose of shortening the overall assembly rhythm is achieved.

Description

Technical Field

[0001] This invention relates to the field of aircraft engine pulse assembly line scheduling, specifically to an aircraft engine pulse assembly line scheduling method based on an improved genetic algorithm. Background Technology

[0002] The final assembly process of aero-engines typically employs a pulsed assembly line structure, using a multi-station sequential approach to complete highly complex assembly procedures. This pulsed assembly mode requires each station to complete its assigned tasks within a uniform assembly cycle time, and then move the entire product to the next station after the cycle ends. Due to the complex dependencies between aero-engine processes and the high degree of human involvement, the allocation of assembly resources and the sequence of process execution directly impact cycle time stability and assembly efficiency. Therefore, under constraints of limited station capacity and worker resources, developing an efficient scheduling scheme becomes a key issue in improving the assembly efficiency of aero-engines.

[0003] In existing technologies, such as the Chinese patent application "Joint Optimization Method for Production Scheduling and Worker Allocation for Aircraft Pulsating Assembly Lines" (Publication No. CN119809259A), a method is proposed to construct a lexicographically ordered bi-objective integer programming model and combine it with resource-time mapping and genetic algorithms to optimize the allocation of worker resources among different workstations and the scheduling of multi-mode assembly tasks, thereby improving assembly cycle coordination while taking resource consumption into account. However, existing technologies still have the following shortcomings in dealing with the complexity of aero-engine pulsed assembly lines:

[0004] 1. Insufficient characterization of worker capacity constraints at workstations: Existing methods often adopt the method of allocating worker resources as a whole at workstations, without fully considering the impact of the spatial constraint of "maximum number of workers that a workstation can accommodate" on scheduling feasibility. This may result in scheduling schemes that cannot be implemented when the assembly capacity of a workstation is limited.

[0005] 2. The potential of parallel assembly has not been fully explored: The existing scheduling strategy treats the processes at the same station as strictly sequential execution objects, which fails to make full use of the parallel assembly capabilities that can be achieved under the condition of satisfying process dependence, thus limiting the space for cycle time compression.

[0006] 3. Lack of collaborative optimization between worker allocation and process scheduling: Traditional algorithms generally solve the worker resource allocation and process scheduling processes separately, lacking a unified coding framework to achieve collaborative optimization between station allocation, process station assignment and assembly execution order, making it difficult to balance the coupling relationship between resource constraints and the goal of minimizing cycle time from a global perspective.

[0007] Therefore, there is an urgent need for a systematic scheduling method that can simultaneously consider the capacity limitations of workers at each workstation and the characteristics of parallel assembly processes in the pulsed assembly line of aero-engines, and achieve integrated and collaborative optimization of worker allocation, process stationing decisions and assembly sequence, so as to improve the overall assembly cycle efficiency and enhance the feasibility and stability of the scheduling solution. Summary of the Invention

[0008] To address the shortcomings of existing scheduling methods for aero-engine pulse assembly lines, such as insufficient characterization of station worker capacity constraints, inadequate utilization of parallel assembly potential, and lack of collaborative optimization mechanisms for worker allocation and process scheduling, this invention proposes an aero-engine pulse assembly line scheduling method based on an improved genetic algorithm. By constructing a three-segment encoding structure that includes the number of assembly workers at each station, station allocation for processes, and process execution order, and designing an algorithm decoding mechanism and feasibility repair strategy, the method achieves collaborative optimization of station worker allocation, process allocation, and assembly priority. This fully leverages the parallel assembly capability while meeting station capacity limitations and process constraints, thereby shortening the overall assembly cycle time.

[0009] The technical solution of this invention is as follows:

[0010] A scheduling method for aero-engine pulsed assembly line based on an improved genetic algorithm includes the following steps:

[0011] Step 1: Initialize the scheduling problem of the aircraft engine pulse assembly line;

[0012] The aircraft engine pulse assembly line includes individual station and There are assembly workers, Assembly process Requires execution;

[0013] The scheduling constraints of the aero-engine pulse assembly line include: station capacity constraints, process constraints, and process attribute constraints.

[0014] The ultimate scheduling objective is to minimize the assembly cycle time of the aircraft engine pulse assembly line;

[0015] Step 2: Construct an improved genetic algorithm to solve the scheduling problem of the aircraft engine pulsed assembly line:

[0016] Step 2.1: Initialize the parameters of the improved genetic algorithm, including: population size. Maximum number of iterations Cross rate Variation rate Number of elites Penalty coefficient upper limit of beat ;

[0017] Step 2.2: Generate the initial population single chromosome It contains three sections; Assemble the number of chromosomes for each station. For the position Number of workers assigned, segment Assign chromosome positions to each process step. Indicates the first The station positions assigned to each process, and the sections Chromosomes representing process priority Indicates the first The priority of each process;

[0018] Step 2.3: Initialize the algorithm state: Let the number of iterations be... Global Optimum No improvement in count ;

[0019] Step 2.4: Analyze the chromosomes in the population separately. Perform decoding operations and calculate the assembly cycle time of the corresponding pulsating production line for the chromosome. ;

[0020] Step 2.5: Update the global optimum based on the population fitness value: If the best chromosome in this generation is better than the global optimum, then update... ;

[0021] Step 2.6: Termination condition judgment: If Output If the algorithm fails, terminate the algorithm; otherwise, proceed to step 2.7.

[0022] Step 2.7: Elite Preservation: Sort by fitness and select the top-performing individuals in the population. A chromosome enters Proceed to step 2.8;

[0023] Step 2.8: For Crossover, mutation, and repair processes are performed to generate offspring populations;

[0024] Step 2.9: Generate a new population , Proceed to step 2.4 and continue iterating.

[0025] In a further preferred embodiment, the scheduling constraints of the aero-engine pulse assembly line in step 1 are specifically as follows:

[0026] The station capacity constraint is: each station The maximum number of workers allowed at any given time is , Furthermore, assembly workers do not move between stations after being assigned to them; assume that the number of workers assigned to each station is... , ;

[0027] The process constraint is: any process The processing time is The required number of workers is , The start date is Any two processes , The process constraints are derived from the directed acyclic graph. Decide, Indicate process Prior to process Assembly is carried out; when processes without process constraints are assigned to the same station, they are assembled in parallel, but the number of workers required at any given time must not exceed the station capacity.

[0028] Process attribute constraints are as follows: Let the process... Assigned to a station process Assigned to a station , , Meet process constraints Process , The positional constraints that are satisfied are ,like Then the start time constraint is , For process Processing time.

[0029] A further preferred embodiment, in step 2, is a single chromosome. Each segment is initialized as follows:

[0030] part The number of assembly workers at each station is randomly generated using the Stars and Bars algorithm. In the generated chromosome, each gene locus... satisfy ;

[0031] part The generation uses relative displacement encoding and the current process. Pre-process Add a non-negative integer increment to the last station position. The encoding scheme, The calculation method is as follows:

[0032]

[0033] When the process When there is no preceding process, The value is set to 1; when hour, ;

[0034] part Generation using Random number encoding between.

[0035] The further optimized solution, step 2.4, is as follows:

[0036] Step 2.4.1: Chromosome analysis The meaning of each gene within each segment; segment Each gene represents, in turn, the number of assembly workers assigned to each station. Each gene sequentially represents the station index assigned to each process step, segment Each gene represents the assembly priority of each process in turn;

[0037] Step 2.4.2: Take out the segments one by one Gene Take out the segment The number of assembly workers configured at the corresponding station ; satisfy all process Add to queue Proceed to step 2.4.3; if all processes meet the requirements... Then proceed to step 2.4.4;

[0038] Step 2.4.3: When the queue If necessary, repeat steps 2.4.3.1 through 2.4.3.3:

[0039] Step 2.4.3.1: Removal Process ,like and This indicates that the chromosome is an illegal solution. Let Proceed to step 2.4.5; otherwise, proceed with the process. Position Shift one position to the right, that is Proceed to step 2.4.3.2;

[0040] Step 2.4.3.2: For the process Each subsequent process ,like Then let and the process Add to queue ;

[0041] Step 2.4.3.3: If shifted to the right Still satisfied Then the process Add to queue ;

[0042] Step 2.4.4: For the segment An event-driven decoding method is used;

[0043] Step 2.4.5: Calculate the fitness value: For a feasible solution, calculate the assembly cycle time. fitness value For illegal solutions, the fitness value .

[0044] A further preferred solution, in step 2.4.4, is to optimize the segment... The specific process of using the event-driven decoding method is as follows:

[0045] For each station ,make For process Release time, For the ready process set, For the position The set of processes that have not yet been scheduled. This is the set of event moments. Repeat steps 2.4.4.1 through 2.4.4.6:

[0046] Step 2.4.4.1: Initialize the set of unscheduled procedures Event time set ;

[0047] Step 2.4.4.2: Obtain the set of ready processes ,like Proceed to step 2.4.4.6; otherwise, proceed to step 2.4.4.3. This is the preceding process;

[0048] Step 2.4.4.3: Select middle The process with the highest value Let the scan start point be Proceed to step 2.4.4.4, where... for Release time;

[0049] Step 2.4.4.4: Search for the earliest feasible starting point. From the set of event times... Not less than Starting from the specified moment, scan to the right along the event sequence to find the first segment that can continuously accommodate a length of... And the remaining capacity is greater than or equal to If the interval is found, proceed to step 2.4.4.5; otherwise, schedule the process at the end of the timeline. Proceed to step 2.4.4.5; where... For process Processing time, For process Number of workers required;

[0050] Step 2.4.4.5: [The process is described in the original text.] Arranged in [ t * , t * + p i * ] ,renew And update the occupancy curve. For subsequent processes renew Proceed to step 2.4.4.2;

[0051] Step 2.4.4.6: Let ,renew To update to the latest release time. If Position Scheduling complete; otherwise, proceed to step 2.4.4.2.

[0052] A further preferred option, in step 2.8, is... The specific process of generating offspring populations through crossover, mutation, and repair is as follows:

[0053] Repeat steps 2.8.1 through 2.8.4 until... The number of offspring reached :

[0054] Step 2.8.1: Obtain parent chromosomes using tournament selection operator. , ;

[0055] Step 2.8.2: Using probability Crossover operation is performed on the chromosomes of the two parents to obtain segments. ,part He Duan ;

[0056] Step 2.8.3: Using probability To perform mutation operations on chromosomes;

[0057] Step 2.8.4: Repair the obtained offspring chromosomes: For segments ,when season ,like Before reaching Add 1 evenly to each position until it is full; if Before reaching Reduce the number of positions by 1 evenly until the total is reached; and ensure that... , For the segment Recalculate according to the process constraint sequence For the segment ,Will Cut off to [0,1] Inside.

[0058] A further preferred solution, in step 2.8.2, is segment... Using the single-point crossover operator to obtain ,part Using the multi-point crossover operator to obtain ,part Using the arithmetic crossover operator to obtain .

[0059] Further optimization, in step 2.8.3, uses probability... Perform mutation operations on chromosomes; the mutation operation is: segment Two stations are randomly selected from the middle. ,make , , ;part Multiple genes are randomly selected from the data, and... , ;part Multiple genes are randomly selected from the data, and... .

[0060] Furthermore, the present invention also proposes an electronic device and a readable storage medium:

[0061] An electronic device includes a processor and a memory, the memory being used to store one or more programs;

[0062] The above method is implemented when the one or more programs are executed by the processor.

[0063] A readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0064] Beneficial effects

[0065] Compared with the prior art, the beneficial effects of the present invention are:

[0066] 1. To address the problem of insufficient characterization of worker capacity constraints in existing technologies, this invention adopts a three-segment chromosome structure to uniformly encode worker allocation, work station, and work priority, thereby achieving collaborative optimization of resource allocation and assembly sequence under station capacity constraints, and improving the feasibility and overall performance of the scheduling scheme.

[0067] 2. To address the problem that the potential of parallel assembly in existing technologies has not been fully explored, this invention designs a relative displacement encoding method to generate process station allocation. During the decoding process, it combines the directed acyclic graph of the process with the station capacity limit to automatically correct infeasible solutions. This can simultaneously satisfy process constraints and the maximum worker capacity constraint of the station, fully explore the potential of parallel assembly, and significantly improve the feasibility and applicability of the method in complex pulsating assembly environments.

[0068] 3. To address the lack of collaborative optimization in worker allocation and process scheduling in existing technologies, this invention uses an event-driven decoding mechanism to determine the earliest feasible start time based on process priority and remaining station capacity. With minimizing assembly cycle time as the fitness objective, it achieves global optimization of the overall assembly cycle, which can significantly shorten the pulsating assembly cycle time and improve assembly efficiency and equipment utilization.

[0069] 4. To further improve the algorithm performance, this invention adopts an elite retention strategy, a segmented crossover method, and a multi-layer mutation mechanism to improve the global search capability and accelerate the convergence speed. After mutation, capacity and process constraints are introduced to correct for invalid solutions, thereby improving the stability and search quality of the algorithm and preventing it from getting trapped in local optima.

[0070] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0071] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0072] Figure 1 This is a flowchart of the method of the present invention.

[0073] Figure 2 This is a schematic diagram of the chromosomes in this invention. Detailed Implementation

[0074] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0075] This embodiment addresses the problems in existing scheduling methods for aero-engine pulsed assembly lines, such as insufficient characterization of worker capacity constraints at workstations, inadequate utilization of the potential for parallel assembly processes, and a lack of collaborative optimization mechanisms between worker allocation and process scheduling. It proposes a scheduling method for aero-engine pulsed assembly lines based on an improved genetic algorithm. This method can achieve a unified solution for scheduling optimization schemes under the combined effects of spatial constraints, process dependencies, and assembly cycle time targets. Specifically, it includes the following steps:

[0076] Step 1: Initialize the scheduling problem of the aircraft engine pulse assembly line.

[0077] Consider a line containing individual station and A pulsed production line for aircraft engines with a single assembly worker. Assembly process It needs to be executed.

[0078] The scheduling constraints of the aircraft engine pulse assembly line include:

[0079] Station capacity constraints: Due to the limited station space on the pulsed assembly line, each station... The maximum number of workers allowed at any given time is Furthermore, assembly workers do not move between stations after being assigned to them. Assume the number of workers assigned to each station is... Then the constraints it needs to satisfy are: .

[0080] Process constraints: any process The processing time is The required number of workers is The start date is Any two processes , The process constraints are derived from the directed acyclic graph. Decide, Indicate process Prior to process Assembly can proceed. When processes without process constraints are assigned to the same station, parallel assembly can be performed, but the number of workers required at any given time must not exceed the station's capacity.

[0081] Process attribute constraints: Set process Assigned to a station process Assigned to a station , , Meet process constraints Process , The required station constraints are as follows: ,like Then the start time constraint is , For process Processing time.

[0082] The final scheduling objective is:

[0083] Minimize the assembly cycle time of the aircraft engine pulse assembly line, i.e. .

[0084] like Figure 2 As shown, in this embodiment, an aircraft engine pulse assembly line is set up including... Each station, represented as a set. The entire production line is equipped with There are assembly workers, totaling [number] people. There are a set of assembly processes that need to be performed, represented as follows: .

[0085] Each station is limited by space and can accommodate a maximum number of workers. Assembly workers are assigned to specific stations and remain stationary, not moving between stations. Stations are defined. The number of workers allocated is The constraints that need to be satisfied are: The example worker allocation scheme is as follows: .

[0086] The processing time, number of workers required, and process constraints for each step are shown in Table 1 below:

[0087] Table 1: Processing time, number of workers required, and process constraints for each step

[0088]

[0089] The final generated directed acyclic graph for The scheduling problem is to minimize the overall assembly cycle time:

[0090]

[0091] Step 2: Construct an improved genetic algorithm to solve the scheduling problem of the aero-engine pulse assembly line.

[0092] Step 2.1: Initialize the parameters of the improved genetic algorithm, including: population size. The maximum number of iterations is Crossover rate The mutation rate is The number of elites is The penalty coefficient is The upper bound of the beat is In this embodiment, the population size is set as follows: Maximum number of iterations Cross rate Variation rate Number of elites Penalty coefficient upper limit of beat .

[0093] Step 2.2: Generate the initial population single chromosome It contains three sections. Assemble the number of chromosomes for each station, segment Assign chromosome positions to each process step. Indicates the first The station positions assigned to each process, and the sections Chromosomes representing process priority Indicates the first Prioritization of each process step.

[0094] part The number of assembly workers at each station is randomly generated using the Stars and Bars algorithm. To generate the best possible individuals, each gene locus in the generated chromosome is... The following constraints must be met. .

[0095] part The generation uses relative displacement encoding, that is, according to the current process. Pre-process Add a non-negative integer increment to the last station position. The encoding scheme is calculated as follows:

[0096]

[0097] When the process When there is no preceding process, The value is set to 1; when hour, .

[0098] part The generation uses random number encoding, that is , The value indicates the process. The assembly priority is indicated by a higher value, with higher priority indicating higher priority.

[0099] like Figure 2 As shown, an example of chromosome coding in a pulsed assembly line for an aero-engine is as follows:

[0100] part Each gene locus The following constraints must be met.

[0101]

[0102] Get an example .

[0103] part For process No preceding process. ,set up , For the process No preceding process. ,set up , For the process The preceding process is , The last station position is 1. ,set up , For the process The preceding process is , The last station position is 2. ,set up , For the process The preceding process is and , , ,set up , Get an example .

[0104] part : .

[0105] Step 2.3: Initialize the algorithm state: Let the number of iterations be... Global Optimum No improvement in count .

[0106] Step 2.4: Population Fitness Assessment. This involves assessing the chromosomes within the population. Perform decoding operations and calculate the assembly cycle time of the corresponding pulsating production line for the chromosome. .

[0107] Step 2.4.1: Chromosome analysis The meaning of each gene within each segment; segment Each gene represents, in turn, the number of assembly workers assigned to each station. Each gene sequentially represents the station index assigned to each process step, segment Each gene represents the assembly priority of each process in turn.

[0108] Step 2.4.2: Take out the segments one by one Gene Take out the segment The number of assembly workers configured at the corresponding station To satisfy all process Add to queue Proceed to step 2.4.3; if all processes meet the requirements... Then proceed to step 2.4.4.

[0109] Step 2.4.3: When the queue When this happens, repeat steps 2.4.3.1 to 2.4.3.3.

[0110] Step 2.4.3.1: Removal Process ,like and This indicates that the chromosome is an illegal solution. Let Proceed to step 2.4.5; otherwise, proceed with the process. Position Shift one position to the right, that is Proceed to step 2.4.3.2; where... The penalty coefficient forms the penalty function for illegal solutions, making illegal solutions inferior to any feasible solution;

[0111] Step 2.4.3.2: For the process Each subsequent process ,like Then let and the process Add to queue ; For the set of subsequent processes;

[0112] Step 2.4.3.3: If shifted to the right Still satisfied Then the process Add to queue .

[0113] Step 2.4.4: For the segment An event-driven decoding method is used. For each station... ,make For process Release time, For the ready process set, For the position The set of processes that have not yet been scheduled. This is the set of event moments. Repeat steps 2.4.4.1 through 2.4.4.6.

[0114] Step 2.4.4.1: Initialize the set of unscheduled procedures Event time set ;

[0115] Step 2.4.4.2: Obtain the set of ready processes ,like Proceed to step 2.4.4.6; otherwise, proceed to step 2.4.4.3. This is the preceding process;

[0116] Step 2.4.4.3: Select middle The process with the highest value Let the scan start point be Proceed to step 2.4.4.4, where... for Release time.

[0117] Step 2.4.4.4: Search for the earliest feasible starting point. From the set of event times... Not less than Starting from the specified moment, scan to the right along the event sequence to find the first segment that can continuously accommodate a length of... And the remaining capacity is greater than or equal to If the interval is found, proceed to step 2.4.4.5; otherwise, schedule the process at the end of the timeline. Proceed to step 2.4.4.5; where... For process Processing time, For process Number of workers required;

[0118] Step 2.4.4.5: [The process is described in the original text.] Arranged in [ t * , t * + p i * ] ,renew And update the occupancy curve. That is to and Perform a difference operation on the subsequent processes. renew Proceed to step 2.4.4.2.

[0119] Step 2.4.4.6: Let ,renew To update to the latest release time. If Position Scheduling complete; otherwise, proceed to step 2.4.4.2.

[0120] Step 2.4.5: Calculate the fitness value: For a feasible solution, calculate the assembly cycle time. fitness value For illegal solutions, the fitness value .

[0121] Step 2.5: Update the global optimum based on the population fitness value: If the best chromosome in this generation is better than the global optimum, then update... .

[0122] Step 2.6: Termination condition determination. If Output If the algorithm terminates, proceed to step 2.7; otherwise, proceed to step 2.7.

[0123] Step 2.7: Elite Preservation. Sort by fitness and select the top-performing individuals from the population. A chromosome enters Proceed to step 2.8. This embodiment takes... .

[0124] Step 2.8: Generate the offspring population. Repeat steps 2.8.1-2.8.4 until... The number of offspring reached .

[0125] Step 2.8.1: Obtain parent chromosomes using tournament selection operator. , .

[0126] Step 2.8.2: Using probability Crossover is performed on the chromosomes of both parents. Using the single-point crossover operator to obtain ,part Using the multi-point crossover operator to obtain ,part Using the arithmetic crossover operator to obtain In this embodiment, we take... .

[0127] Step 2.8.3: Using probability Perform mutation operations on chromosomes. Two stations are randomly selected from the middle. ,make , , ;part Multiple genes are randomly selected from the data, and... , ;part Multiple genes are randomly selected from the data, and... In this embodiment, we take... .

[0128] Step 2.8.4: Repair the obtained offspring chromosomes. For segments... ,when season ,like Before reaching Add 1 evenly to each position until it is full; if Before reaching The number of positions is reduced by 1 evenly until it is filled. In addition, it is necessary to ensure... , For the segment Recalculate according to the process constraint sequence For the segment ,Will Cut off to [0,1] Inside.

[0129] Step 2.9: Generate a new population , Proceed to step 2.4 and continue iterating.

[0130] Through the complete process described above, the method proposed in this embodiment, under the premise of satisfying the capacity and process constraints of all workstations, collaboratively optimizes worker allocation, process workstations and assembly sequence, and finally obtains an optimized scheduling scheme that minimizes the assembly cycle time.

[0131] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A scheduling method for aero-engine pulsed assembly line based on an improved genetic algorithm, characterized in that: Includes the following steps: Step 1: Initialize the scheduling problem of the aircraft engine pulse assembly line; The aircraft engine pulse assembly line includes individual station and There are assembly workers, Assembly process Requires execution; The scheduling constraints of the aero-engine pulse assembly line include: station capacity constraints, process constraints, and process attribute constraints. The ultimate scheduling objective is to minimize the assembly cycle time of the aircraft engine pulse assembly line; Step 2: Construct an improved genetic algorithm to solve the scheduling problem of the aircraft engine pulsed assembly line: Step 2.1: Initialize the parameters of the improved genetic algorithm, including: population size. Maximum number of iterations Cross rate Variation rate Number of elites Penalty coefficient upper limit of beat ; Step 2.2: Generate the initial population single chromosome It contains three sections; Assemble the number of chromosomes for each station. For the position Number of workers assigned, segment Assign chromosome positions to each process step. Indicates the first The station positions assigned to each process, and the sections Chromosomes representing process priority Indicates the first The priority of each process; Step 2.3: Initialize the algorithm state: Let the number of iterations be... Global Optimum No improvement in count ; Step 2.4: Analyze the chromosomes in the population separately. Perform decoding operations and calculate the assembly cycle time of the corresponding pulsating production line for the chromosome. ; Step 2.5: Update the global optimum based on the population fitness value: If the best chromosome in this generation is better than the global optimum, then update... ; Step 2.6: Termination condition judgment: If Output If the algorithm fails, terminate the algorithm; otherwise, proceed to step 2.

7. Step 2.7: Elite Preservation: Sort by fitness and select the top-performing individuals in the population. A chromosome enters Proceed to step 2.8; Step 2.8: For Crossover, mutation, and repair processes are performed to generate offspring populations; Step 2.9: Generate a new population , Proceed to step 2.4 and continue iterating.

2. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 1, characterized in that: In step 1, the scheduling constraints of the aero-engine pulse assembly line are specifically as follows: The station capacity constraint is: each station The maximum number of workers allowed at any given time is , Furthermore, assembly workers do not move between stations after being assigned to them; assume that the number of workers assigned to each station is... , ; The process constraint is: any process The processing time is The required number of workers is , The start date is Any two processes , The process constraints are derived from the directed acyclic graph. Decide, Indicate process Prior to process Assembly is carried out; when processes without process constraints are assigned to the same station, they are assembled in parallel, but the number of workers required at any given time must not exceed the station capacity. Process attribute constraints are as follows: Let the process... Assigned to a station process Assigned to a station , , Meet process constraints Process , The positional constraints that are satisfied are ,like Then the start time constraint is , For process Processing time.

3. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 2, characterized in that: In step 2, a single chromosome Each segment is initialized as follows: part The number of assembly workers at each station is randomly generated using the Stars and Bars algorithm. In the generated chromosome, each gene locus... satisfy ; part The generation uses relative displacement encoding and the current process. Pre-process Add a non-negative integer increment to the last station position. The encoding scheme, The calculation method is as follows: When the process When there is no preceding process, The value is set to 1; when hour, ; part Generation using Random number encoding between.

4. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 2, characterized in that: The specific process of step 2.4 is as follows: Step 2.4.1: Chromosome analysis The meaning of each gene within each segment; segment Each gene represents, in turn, the number of assembly workers assigned to each station. Each gene sequentially represents the station index assigned to each process step, segment Each gene represents the assembly priority of each process in turn; Step 2.4.2: Take out the segments one by one Gene Take out the segment The number of assembly workers configured at the corresponding station ; satisfy all process Add to queue Proceed to step 2.4.3; if all processes meet the requirements... Then proceed to step 2.4.4; Step 2.4.3: When the queue If necessary, repeat steps 2.4.3.1 through 2.4.3.3: Step 2.4.3.1: Removal Process ,like and This indicates that the chromosome is an illegal solution. Let Proceed to step 2.4.5; otherwise, proceed with the process. Position Shift one position to the right, that is Proceed to step 2.4.3.2; Step 2.4.3.2: For the process Each subsequent process ,like Then let and the process Add to queue ; Step 2.4.3.3: If shifted to the right Still satisfied Then the process Add to queue ; Step 2.4.4: For the segment An event-driven decoding method is used; Step 2.4.5: Calculate the fitness value: For a feasible solution, calculate the assembly cycle time. fitness value For illegal solutions, the fitness value .

5. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 4, characterized in that: In step 2.4.4, for segment The specific process of using the event-driven decoding method is as follows: For each station ,make For process Release time, For the ready process set, For the position The set of processes that have not yet been scheduled. For the set of event moments, repeat steps 2.4.4.1 to 2.4.4.6: Step 2.4.4.1: Initialize the set of unscheduled procedures Event time set ; Step 2.4.4.2: Obtain the set of ready processes ,like Proceed to step 2.4.4.6; otherwise, proceed to step 2.4.4.

3. This is the preceding process; Step 2.4.4.3: Select middle The process with the highest value Let the scan start point be Proceed to step 2.4.4.4, where... for Release time; Step 2.4.4.4: Search for the earliest feasible starting point from the set of event times. Not less than Starting from the specified moment, scan to the right along the event sequence to find the first segment that can continuously accommodate a length of... And the remaining capacity is greater than or equal to If the interval is found, proceed to step 2.4.4.5; otherwise, schedule the process at the end of the timeline. Proceed to step 2.4.4.5; where... For process Processing time, For process Number of workers required; Step 2.4.4.5: [The process is described in the original text.] Arranged in ,renew And update the occupancy curve, For subsequent processes renew Proceed to step 2.4.4.2; Step 2.4.4.6: Let ,renew To update the latest release time, if Position Scheduling complete; otherwise, proceed to step 2.4.4.

2.

6. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 2, characterized in that: In step 2.8, for The specific process of generating offspring populations through crossover, mutation, and repair is as follows: Repeat steps 2.8.1 through 2.8.4 until... The number of offspring reached : Step 2.8.1: Obtain parent chromosomes using tournament selection operator. , ; Step 2.8.2: Using probability Crossover operation is performed on the chromosomes of the two parents to obtain segments. ,part He Duan ; Step 2.8.3: Using probability To perform mutation operations on chromosomes; Step 2.8.4: Repair the obtained offspring chromosomes: For segments ,when season ,like Before reaching Add 1 evenly to each position until it is full; if Before reaching Reduce the number of positions by 1 evenly until the total is reached; and ensure that... , For the segment Recalculate according to the process constraint sequence For the segment ,Will Cut off to Inside.

7. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 6, characterized in that: In step 2.8.2, segment Using the single-point crossover operator to obtain ,part Using the multi-point crossover operator to obtain ,part Using the arithmetic crossover operator to obtain .

8. The method for scheduling aero-engine pulsed assembly lines based on an improved genetic algorithm according to claim 6, characterized in that: In step 2.8.3, using probability Perform mutation operations on chromosomes; the mutation operation is: segment Two stations are randomly selected from the middle. ,make , , ;part Multiple genes are randomly selected from the data, and... , ;part Multiple genes are randomly selected from the data, and... .

9. An electronic device comprising a processor and a memory, the memory being used to store one or more programs; characterized in that: When the one or more programs are executed by the processor, the method of any one of claims 1 to 8 is implemented.

10. A readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the method described in any one of claims 1 to 8.

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