Civil aircraft distributed production scheduling method based on genetic algorithm

Abstract

The application discloses a kind of civil aircraft distributed production scheduling method based on genetic algorithm.The present application aims at the problem that the consideration of material inventory replenishment of existing civil aircraft distributed production scheduling method has limitation, proposes to use the resource-constrained project scheduling problem with inventory replenishment to describe civil aircraft distributed production scheduling problem, based on genetic algorithm, focuses on the complex constraint problem and local optimal problem caused by material inventory constraint, to solve the corresponding scheduling problem.The experimental results show that the present application can obtain approximate optimal solution with the objective of minimizing workstation completion time, and generate effective civil aircraft production scheduling strategy.

Description

Technical Field

[0001] This invention relates to the field of production scheduling and intelligent optimization algorithms, and in particular to a distributed production scheduling method for civil aircraft based on genetic algorithms that takes into account material inventory replenishment. Background Technology

[0002] Researching production scheduling methods is an important means of optimizing the production process. However, compared with other process manufacturing, civil aircraft production is a typical example of discrete manufacturing, where products are assembled from various materials through various production processes. Civil aircraft production is characterized by larger scale, higher technology intensity, and longer production cycles, and requires a wider variety of resources. These characteristics need to be analyzed to study solutions to its production scheduling problems.

[0003] In recent years, with the advancement of intelligent algorithms and the increasing demand for production optimization, new scheduling methods for civil aircraft production have been proposed. The constraints on civil aircraft production efficiency mainly stem from two aspects: the sequential constraints between processes and the resource constraints caused by limited production resources. Considering the existence of these two constraints and the distributed nature of civil aircraft manufacturing, the Resource Constrained Project Scheduling Problem (RCPSP) can be used to describe the production scheduling problem of each work package in aircraft production. Shan S, Hu Z, Liu Z, et al. (Shan S, Hu Z, Liu Z, et al. An adaptive genetic algorithm for demand-driven and resource-constrained projectscheduling in aircraft assembly[J]. Information Technology and Management,2017, 18: 41-53.) used RCPSP to describe the aircraft assembly scheduling problem and attempted to solve the problem using a demand-driven adaptive genetic algorithm with two different encoding methods. Lovato D, Guillaume R, Thierry C, et al. Managing disruptions in aircraft assembly lines with staircase criteria[J]. International Journal of Production Research, 2023, 61(2): 632-648. describe the aircraft assembly line rescheduling problem as RCPSP and propose a new optimization criterion suitable for the aircraft manufacturing environment. However, its main material resources are also non-replenishable.Lu Z, Ren Y, Wang L, et al. (Lu Z, Ren Y, Wang L, et al. A resource investment problem based on project splitting with time windows for aircraft moving assembly line[J]. Computers&Industrial Engineering, 2019, 135: 568-581.) proposed a variant of RCPSP for aircraft moving assembly lines where multiple workstations share resources. This variant describes the scheduling problem based on the resource investment problem (RIP) with time windows and uses a two-stage iterative loop algorithm to solve the optimization problem. It also considers the unpredictability of resource shortages.

[0004] However, the aforementioned aircraft production scheduling methods do not adequately consider resource availability. In the assumed methods, materials are considered non-replenishable due to the limitations of their application scenarios. In reality, material inventory fluctuates during production due to continuous supply from upstream suppliers. Coupled with inflexible scheduling strategies, civil aircraft manufacturers are prone to production delays caused by insufficient inventory in actual production. To improve the efficiency of scheduling methods, inventory replenishment should be taken into account, the complex constraints arising from inventory replenishment and consumption should be addressed, and appropriate and efficient methods should be used to solve these constraints. Summary of the Invention

[0005] In view of this, a distributed production scheduling method for civil aircraft based on genetic algorithms is proposed. First, by analyzing the civil aircraft production process, the civil aircraft production scheduling problem is transformed into a resource-constrained project scheduling problem model with inventory replenishment (RCPSP-IR), making it a mixed integer programming (MIP) problem. Based on this, a resource-constrained genetic algorithm is introduced to solve the problem, minimizing production time. Different constraint handling methods and local optimum prevention methods are considered to address complex constraints, including inventory constraints.

[0006] The technical solution to be protected by this invention is characterized as follows: A distributed production scheduling method for civil aircraft based on genetic algorithms includes: The data platform is used to obtain the sequential constraints of various production activities at a certain workstation in the aircraft production process, the required time and materials, as well as the replenishment cycle and replenishment quantity of various materials. Based on the information obtained from the data platform, a resource-constrained project scheduling problem model with inventory replenishment is used to model the mixed integer programming problem corresponding to the production scheduling problem of this workstation. Based on a genetic algorithm that takes into account material inventory constraints, this mixed integer programming problem is solved to obtain the theoretically approximately optimal shortest total production time, and the scheduling scheme is presented in the form of the start time of each production activity.

[0007] Furthermore, for the resource-constrained project scheduling problem with inventory replenishment, the objective is to minimize the maximum completion time of each workstation: in It is the end time of production activities.

[0008] Furthermore, the resource-constrained project scheduling problem model with inventory replenishment includes the following inventory constraints and sequence constraints: Taking time 0 as the starting point of the entire production process, therefore for each production activity... Its start time With end time They should all be at least non-negative, and their relationship is as follows: Production activities obtained from the data platform Execution time and various production activities Start time With end time There exists an equality relationship, as follows: There are sequential constraints among production activities; a production process can only begin after all its preceding activities are completed. The relationships are as follows: After incorporating sequence constraints, the relationship between the start times of each production activity is as follows: Each material At any moment Inventory There should be a lower bound, and it should not be negative. If a safety stock needs to be set, the lower bound can be fixed to other values, as follows: There are actually many types of materials, which can be divided into structural components. Standard parts , raw materials This is only based on For example.

[0009] Current inventory depends on supplier deliveries and consumption from production activities, affecting materials. Every moment Inventory There is a recursive relationship, as follows: in It is a material The amount of inventory replenished in a single transaction. Production activities Materials required for execution The amount of these materials in It is taken from the inventory at the start of execution, therefore it will be It immediately causes a reduction in inventory at the start.

[0010] and and These are Boolean values, each describing a specific moment. Are there any materials? Restocking, timing Has production started? Boolean functions. It depends on the manufacturer's ordering strategy. And for... The relationship is as follows: Furthermore, the genetic algorithm considering inventory constraints includes the following constraint handling methods: To reduce constraint complexity and minimize the feasible region, the scheduling scheme of the genetic algorithm for individuals... Coded into various production activities Start time and all its predecessors The difference in the latest end time The relationship is as follows: To address the complex constraints introduced by inventory replenishment, a penalty function method is needed to modify the fitness function of the genetic algorithm. For a specific scheduling scheme... Its fitness function The previous shortest time objective An additional penalty item needs to be added. ,Right now: Penalty items Defined as in the current solution Below, every moment The degree to which the inventory of each type of material is below the preset lower limit . Structural components For example: Penalty items There are several specific calculation methods. Based on actual comparative experiments, the following adaptive penalty was adopted: Furthermore, the specific steps of the genetic algorithm considering inventory constraints are as follows: Step 1: Define the basic parameters of the genetic algorithm, including the population selection mechanism (tournament selection), crossover mechanism (two-point crossover), and mutation mechanism (uniform mutation), as well as the number of iteration rounds that allow the objective function of the optimal feasible solution to not produce improvements. Maximum number of iteration rounds.

[0011] Step 2: Define the population encoding method for the genetic algorithm according to the method described in the constraint handling section, and generate a random initial population. .

[0012] Step 3: Population Each scheduling scheme in The fitness function is calculated according to the constraint handling method described above. .

[0013] Step 4: Population A new population is generated according to the mechanism defined in step 1. .

[0014] Step 5: Selecting the Population The optimal feasible solution in [the algorithm]. To avoid the method getting trapped in local optima, if the algorithm goes through continuous [various steps]... Rounds of iterations, the objective function value of the optimal feasible solution All remain unchanged, then from Remove all currently optimal feasible solutions and replace them with randomly generated new individuals.

[0015] Step 6: Recalculate each scheduling scheme in population P according to the constraint handling method. fitness function ,use replace .

[0016] Step 7: Repeat steps 4 through 6 until the maximum number of iterations is reached.

[0017] Step 8: Select the population The optimal feasible scheduling scheme is taken as the output of the algorithm.

[0018] By adopting the above solution, the beneficial effects of the present invention are: 1. This invention improves the intelligence of civil aircraft production scheduling by using resource-constrained project scheduling modeling with inventory replenishment and a genetic algorithm that considers material inventory constraints. 2. This invention proposes a resource-constrained project scheduling modeling method with inventory replenishment, which takes into account the inventory factors in civil aircraft production scheduling and is more in line with actual production scenarios; 3. This invention proposes a distributed production scheduling method for civil aircraft based on genetic algorithms that takes into account material inventory replenishment. Based on the optimal time and processing scheme given by the model, the process can be arranged more flexibly, providing a decision basis for actual production scheduling. Attached Figure Description

[0019] Figure 1 This is a basic flowchart of the distributed production scheduling method for civil aircraft based on genetic algorithms, which takes into account material inventory replenishment, according to the present invention.

[0020] Figure 2 This is a basic flowchart of the genetic algorithm considering material inventory constraints in the implementation example.

[0021] Figure 3 This is a graph showing the convergence of the objective value of the optimal feasible solution obtained by the genetic algorithm considering material inventory constraints with the number of iterations.

[0022] Figure 4 The embodiment depicts the civil aircraft production scheduling scheme in the form of a Gantt chart that includes each production activity. Detailed Implementation

[0023] Figure 1 A distributed production scheduling method for civil aircraft based on genetic algorithms includes: Step 1: Obtain from the data platform the sequential constraints of each production activity at a certain workstation during the aircraft production process, the required time and materials, as well as the replenishment cycle and replenishment quantity of various materials. Step 2: Based on the information obtained from the data platform, a resource-constrained project scheduling problem model with inventory replenishment is used to model the mixed integer programming problem corresponding to the production scheduling problem of this workstation. Step 3: Based on the genetic algorithm that takes into account material inventory constraints, solve the mixed integer programming problem to obtain the theoretically approximately optimal shortest total production time, and present the scheduling scheme in the form of the start time of each production activity.

[0024] The technical solution of the present invention will be further described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments.

[0025] First, the sequential constraints, required time and materials, and replenishment cycles and quantities of various materials for each production activity at a specific workstation in the aircraft production process are obtained from the data platform and used as inputs for the method proposed in this invention. The mathematical constraints are described using a resource-constrained project scheduling problem model that considers inventory replenishment. Then, a genetic algorithm considering material inventory constraints is used to solve the problem.

[0026] Figure 2 The flowchart shown: Step 1: Define the basic parameters of the genetic algorithm, including the population selection mechanism (tournament selection, tournament format 2), crossover mechanism (two-point crossover, crossover probability 0.3), and mutation mechanism (uniform mutation, mutation rate 0.3), allowing the objective function of the optimal feasible solution to not generate an improved number of iteration rounds. =1500, the maximum number of iterations. Generally, approximately optimal results can be found after 2000 iterations. To increase the search range, the maximum number of iterations can be set to 15000~30000.

[0027] Step 2: Define the population encoding method for the genetic algorithm according to the method described in the constraint handling section, and generate a random initial population. The scale is 300. Its specific coding object is production activities. Start time and all its predecessors The difference in the latest end time The relationship is as follows: Step 3: Population Each scheduling scheme in Calculate its fitness function The specific calculation method is as follows: Based on the following relations, and the above... The definition can be used to define the scheduling scheme. Every moment Production activities Whether it is executed Then combine with a certain material exist Is the stock being replenished at any time? Replenishment quantity Based on inventory Given the existing recursive relationships, calculate the current scheduling scheme. The current inventory levels of various materials are as follows: Due to the existence of inventory constraints, each time step is defined as follows: The degree to which the inventory of each type of material is below the preset lower limit .

[0028] Then, by combining the various scheduling schemes in the current genetic algorithm population, the scheduling scheme for each scheme is calculated. The value of the fitness function Step 4: Population A new population is generated according to the mechanism defined in step 1. .

[0029] Step 5: Selecting the Population The optimal feasible solution in [the algorithm]. To avoid the method getting trapped in local optima, if the algorithm goes through continuous [various steps]... Rounds of iterations, the objective function value of the optimal feasible solution All remain unchanged, then from Remove all currently optimal feasible solutions and replace them with randomly generated new individuals.

[0030] Step 6: Recalculate each scheduling scheme in population P according to the fitness function calculation method described in Step 3. fitness function ,use replace .

[0031] Step 7: Repeat steps 4 through 6 until the maximum number of iterations is reached. Step 8: Select the population The optimal feasible scheduling scheme is output.

[0032] The above description is merely a description of preferred embodiments of this application and is not intended to limit the scope of this application in any way. Any changes or modifications made by those skilled in the art based on the above-disclosed technical content should be considered as equivalent and valid embodiments and fall within the scope of protection of the technical solution of this application.

Claims

1. A distributed production scheduling method for civil aircraft based on genetic algorithms, characterized in that, include: Step 1: Obtain from the data platform the sequential constraints of each production activity at a certain workstation during the aircraft production process, the required time and materials, as well as the replenishment cycle and replenishment quantity of various materials. Step 2: Based on the information obtained from the data platform, a resource-constrained project scheduling problem model with inventory replenishment is used to model the mixed integer programming problem corresponding to the production scheduling problem of this workstation. Step 3: Based on a genetic algorithm that considers material inventory constraints, solve the mixed integer programming problem to obtain the theoretically near-optimal shortest total production time, and present the scheduling scheme in the form of the start time of each production activity; The resource-constrained project scheduling problem model with inventory replenishment includes the following inventory constraints and sequence constraints; Using time 0 as the starting point of the entire production process, for each production activity... Its start time With end time Both are non-negative, and their relationship is as follows: Production activities obtained from the data platform Execution time and various production activities Start time With end time There exists an equality relationship, as follows: There are sequential constraints among production activities; a production process can only begin after all its preceding activities are completed. The relationships are as follows: After incorporating sequence constraints, the relationship between the start times of each production activity is as follows: Each material At any moment Inventory All have a lower bound and are not negative. If a safety stock needs to be set, the lower bound should be fixed to another value, as follows: There are actually various materials, categorized into structural components. Standard parts , raw materials ; by For example, then Current inventory depends on supplier deliveries and consumption from production activities, affecting materials. Every moment Inventory There is a recursive relationship, as follows: in It is a material The amount of inventory replenished in a single transaction. Production activities Materials required for execution The amount of these materials in It is taken from the inventory at the start of execution. This immediately reduces inventory at the outset; and and These are Boolean values, each describing a specific moment. Are there any materials? Restocking, timing Has production started? Boolean functions; It depends on the manufacturer's ordering strategy; for The relationship is as follows: Standard parts , raw materials The situation is the same as above; In step 3, the genetic algorithm considering material inventory constraints includes the following constraint handling methods: To reduce constraint complexity and minimize the feasible region, the solution individuals in the genetic algorithm, i.e., the scheduling scheme, are... Encoded into various production activities Start time and all its predecessors The difference between the latest end times The relationship is as follows: The fitness function of the genetic algorithm is modified using the penalty function method; for a specific scheduling scheme Its fitness function The previous shortest time objective An additional penalty item needs to be added. ,Right now: Penalty items Defined in the current scheduling scheme Below, every moment The degree to which the inventory of each type of material is below the preset lower limit ; Structural components For example: Penalty items There are several specific calculation methods; based on actual comparative experiments, the following adaptive penalty is adopted: Finally, the value of its fitness function should be: 。 2. The method according to claim 1, characterized in that, In step 2, the objective of the resource-constrained project scheduling problem with inventory replenishment is to minimize the maximum completion time of each workstation. in It is the end time of production activities.

3. The method according to claim 1, characterized in that, In step 3, the genetic algorithm considering inventory constraints includes the following steps: Step 31: Define the population selection mechanism, crossover mechanism, and mutation mechanism of the genetic algorithm, as well as the number of iteration rounds that allow the objective function of the optimal feasible solution to not produce improvements. ; Step 32: Define the population encoding method of the genetic algorithm according to the method described above, and generate a random initial population. ; Step 33: Population Each scheduling scheme in Based on the calculation of its fitness function ; Step 34: Population A new population is generated according to the mechanism defined in step 31. ; Step 35: Selecting the Population The optimal feasible solution in; Step 36: Based on the recalculated scheduling schemes in population P fitness function ,use replace ; Step 37: Repeat steps 34 to 36 until the maximum number of iterations is reached; Step 38: Selecting a Population The optimal feasible scheduling scheme is taken as the output of the algorithm.

4. The method according to claim 3, characterized in that, In step 35, to minimize the risk of the method getting trapped in local optima, if the algorithm goes through continuous... Rounds of iterations, the objective function value of the optimal feasible solution All remain unchanged, then from Remove all currently optimal feasible solutions and replace them with randomly generated new individuals.

Images