CN114004008B - Airplane assembly line resource configuration optimization method based on neural network and genetic algorithm - Google Patents

Airplane assembly line resource configuration optimization method based on neural network and genetic algorithm Download PDF

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CN114004008B
CN114004008B CN202011366337.6A CN202011366337A CN114004008B CN 114004008 B CN114004008 B CN 114004008B CN 202011366337 A CN202011366337 A CN 202011366337A CN 114004008 B CN114004008 B CN 114004008B
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张�杰
蒋昌健
余剑峰
李原
敖瑞波
姚雅
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Northwestern Polytechnical University
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Abstract

The invention provides an aircraft assembly line resource allocation optimization method based on a neural network and a genetic algorithm, which is characterized in that a resource allocation scheme, a production target and resource constraint information are input into the method, autonomous optimization is carried out in an overall solution space through a rapid non-dominated sorting genetic algorithm, a population objective function is calculated by combining the neural network, and an optimal resource allocation scheme is output through iterative optimization. The neural network obtains training data through assembly line simulation, so that the trained neural network not only has approximate simulation evaluation precision, but also has higher response speed. The method can ensure that the airplane assembly line meets the actual production requirement and constraint, and performs multi-objective optimization on the resource allocation scheme.

Description

Airplane assembly line resource configuration optimization method based on neural network and genetic algorithm
Technical Field
The invention belongs to the field of optimization of airplane assembly line resources, and particularly relates to an optimization method for airplane assembly line resource allocation based on a neural network and a genetic algorithm.
Background
The resource cost of an assembly link in the general manufacturing industry is generally lower than 20%, while the resource cost of an airplane assembly line operation process is about 65%, and the method belongs to a resource-dependent production mode. Therefore, the resource allocation scheme needs to be adjusted accordingly as the production target and the actual site constraint change. Meanwhile, the optimal resource allocation scheme in the airplane assembly line not only needs to balance the workload of each station, but also needs to improve the production performance of the whole assembly line, so that the resource allocation optimization problem belongs to the sub-problem of the assembly line balance problem. Since the assembly line balancing problem is a typical NP-hard problem, it means that this type of problem cannot be solved by iterating through all possible solutions.
For the resource allocation optimization problem, a heuristic intelligent algorithm can be used, and in a solution space of the resource allocation optimization problem, the optimization solution is automatically carried out according to actual production requirements and constraints. In the optimization process, an evaluation model of the resource allocation scheme is needed to calculate the objective function. The discrete event simulation technology is widely applied to evaluation analysis of complex systems because the discrete event simulation technology can perform modeling analysis on all production elements in an assembly line while considering uncertainty factors in the production elements. However, the simulation model building and parameter modifying process has the problems of tedious operation, long time, easy error and the like, especially when the assembly system is complicated.
In this context, it is necessary to obtain training samples of the neural network by using discrete event simulation, so that the trained neural network can evaluate the resource allocation scheme with approximate simulation accuracy, and then combine the neural network with a heuristic intelligent algorithm to solve the problem of resource allocation optimization in the aircraft assembly line.
Disclosure of Invention
Aiming at solving the problems of complicated operation of model construction and parameter modification processes, incapability of realizing autonomous optimization of a simulation technology and the like in the conventional method for optimizing the resources of the airplane assembly line, the invention provides a method for optimizing the resource allocation of the airplane assembly line based on a neural network and a genetic algorithm. The neural network obtains training data through assembly line simulation, so that the trained neural network not only has approximate simulation evaluation precision, but also has higher response speed. The method can ensure that the airplane assembly line meets the actual production requirement and constraint, and performs multi-objective optimization on the resource allocation scheme.
The technical scheme of the invention is as follows:
the aircraft assembly line resource configuration optimization method based on the neural network and the genetic algorithm comprises the following steps:
step 1: selecting the configuration quantity of key resources as a design variable and determining an optimization target
Step 1.1: selecting design variables: selecting n kinds of key resources in an aircraft assembly line as an object for configuration optimization, wherein the distribution quantity of the n kinds of resources in m assembly work station positions is used as a design variable, so that a resource configuration scheme (RL) in the method can be expressed as (RL ═ w ═ in i,j 1,2, …, m, j 1,2, …, n }), wherein w i,j The allocation quantity of the jth resource at the ith station position is represented;
step 1.2: determining an optimization objective: the method takes the minimized production takt (CT) of the airplane assembly line, the balanced delay rate (Bd) among stations and the total number (Y) of resources as the target of resource allocation optimization;
step 1.3: establishing a multi-objective optimization mathematical model: using the three optimization objectives as the objective function, and setting the production cycle time requirement (CT) pre ) And the maximum total number of resources available (Y) up ) As a constraint condition, the optimized mathematical model is as follows:
Figure BDA0002805531370000021
wherein X is a design variable, f 1 ,f 2 ,f 3 Is an objective function, X min And X max Upper and lower limits for design variables;
and 2, step: obtaining a training sample:
step 2.1: generating a plurality of groups of resource allocation schemes between the upper limit and the lower limit of the design variable; for example, a random design method can be adopted, and a plurality of groups of resource allocation schemes are randomly generated between the upper limit and the lower limit of design variables;
step 2.2: establishing a simulation model of the airplane assembly line by using a discrete event simulation technology, inputting the resource configuration scheme generated in the step 2.1 into the simulation model, and acquiring the production beat and the station balance delay rate of the airplane assembly line under each resource configuration scheme as sample labels through simulation operation;
step 2.3: 2.1, forming a sample library by the plurality of groups of resource allocation schemes generated in the step 2.1 and the corresponding sample labels obtained in the step 2.2, and dividing samples in the sample library into a training set and a test set according to a certain proportion;
each sample in the sample library contains a resource configuration scheme and two label data, which can be expressed as:
sample＝{w 1,1 ,w 1,2 ,...,w 1,n ,...,w m,1 ,w m,2 ,...,w m,n |CT,Bd} (2)
and step 3: constructing a neural network and training the neural network by using a training set:
the design variable X is used as the neural network input layer. In order to improve the prediction accuracy of CT and Bd, it is preferable to design a neural network with the same two input nodes to output CT and Bd respectively. Thus, two neural networks are constructed, wherein each neural network has an input layer containing m × n neurons and an output layer containing one neuron. The number of the middle hidden layers and the number of the neurons in each layer are determined through experiments, and the specific experimental method is to design neural network models with various structures, wherein the neural network models have different hidden layer numbers and neuron numbers, the prediction accuracy of the neural network models on the same group of test sets is tested respectively, and the neural network with the highest prediction accuracy is selected according to the experimental results. A BP neural network is preferably employed here.
In the neural network, all neurons use a ReLU function as an activation function, and the specific expression is as follows:
f(x)＝max(0,w Τ x+b) (3)
where w represents a weight matrix and b represents a bias matrix.
And using a mean square error function as a loss function for evaluating the prediction accuracy of the neural network, wherein the specific expression is as follows:
Figure BDA0002805531370000031
wherein, Target t Represents the expected output value, i.e., the sample tag value; output t Representing the actual predicted output value of the neural network and K representing the total number of samples.
And 4, step 4: optimized solution using fast non-dominated sorting genetic algorithm
Step 4.1: determining the size (N) of the initial population, randomly generating the initial population based on the upper limit and the lower limit of design variables, wherein each individual in the population represents a resource allocation scheme;
step 4.2: and calculating three objective function values of all individuals in the population by using two neural networks and a resource total calculation formula, and performing quick non-dominated sorting and congestion degree calculation on each individual based on the calculation result of the objective function. Thus each individual in the current population has two attribute values: the branch is assigned a ranking level and a congestion degree.
Step 4.3: comparing every two individuals of the population by adopting a rapid non-dominated sorting genetic algorithm according to the two attribute values, and when the two individuals belong to different non-dominated sorting levels, regarding the individuals with lower sorting levels as more excellent; when two individuals belong to the same non-dominant ranking level, the crowdedness is compared, and the individual with the larger crowdedness value is considered to be better. Therefore, all individuals in the population are subjected to the priority sorting, then the current population is subjected to the crossing and mutation operation, for example, the current population can be subjected to the crossing and mutation operation by adopting an imitation binary crossing operator and a polynomial mutation operator, and thus the offspring populations with the same population size are obtained. And then combining the parent and child population to execute an elite reservation strategy. And then adding one to the population algebra, and turning to the step 4.2 to repeat the steps for iterative optimization until the population algebra reaches a preset maximum algebra (Genmax), and outputting the population at the moment as a group of pareto optimal resource allocation scheme sets.
And 5: according to actual production requirements and constraints, inputting constraint conditions CT pre And Y up Screening an optimal resource allocation scheme in the pareto optimal resource allocation scheme set by the following steps:
step 5.1: eliminating resource allocation scheme with unqualified production tempo (CT > CT) pre )；
Step 5.2: resource allocation scheme with total eliminated resources exceeding maximum limit (Y > Y) up )；
Step 5.3: if a plurality of residual schemes exist in the current resource allocation scheme set, the residual schemes can be directly output and selected by specific operators, and of course, the scheme with the minimum Bd value can be preferably selected as the optimal resource allocation scheme to be output; and if no residual solution exists in the current resource allocation solution set, outputting a resource allocation solution which is not feasible under the current production requirement and constraint conditions.
We can then verify the resource allocation scheme using discrete event simulation techniques:
according to the optimization process, a resource allocation scheme with an optimal effect can be obtained, simulation solving analysis is carried out on the production beat and the balance delay rate under the scheme, if the production beat output by the simulation analysis cannot meet the preset beat requirement, the resource allocation scheme is proved to be not feasible, overfitting exists in the existing neural network model, the existing neural network model is proved to have good accuracy only on a test set, and the construction of the neural network and the optimization solving of the genetic algorithm need to be carried out again.
Advantageous effects
Compared with the prior art, the invention has the following beneficial effects:
the invention provides an aircraft assembly line resource allocation optimization method based on a neural network and a genetic algorithm, which can quickly and effectively carry out multi-target optimization solution on the allocation scheme of the aircraft assembly line key resources through the combination of a simulation technology, the neural network and the genetic algorithm, can effectively improve the balance of an assembly line on the premise of ensuring that the assembly line meets production requirements and constraint conditions, and is favorable for optimizing and improving the overall performance of the aircraft assembly line.
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.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of the steps of the present invention;
FIG. 2 is a diagram of operational logic according to an embodiment of the present invention;
FIG. 3 is a flow chart of an embodiment of the present invention;
FIG. 4 is a diagram of upper limits of design variables in an embodiment of the present invention.
FIG. 5 is a lower limit diagram of design variables in an embodiment of the present invention.
Fig. 6 is a diagram of different hyper-parameter configurations of a neural network for predicting production beats, which is designed in the embodiment of the invention.
Fig. 7 is a comparison graph of prediction accuracy of a neural network for predicting a production cycle under different hyper-parameter configurations in the embodiment of the present invention.
FIG. 8 is a diagram of different hyper-parameter configurations of a neural network for predicting equilibrium delay rates as designed in an embodiment of the present invention.
FIG. 9 is a comparison graph of prediction accuracy of a neural network for predicting a balance delay rate under different hyper-parameter configurations in an embodiment of the present invention.
Fig. 10 is a comparison graph of the predicted values and the tag values of the neural network for predicting the tact in the embodiment of the present invention.
FIG. 11 is a graph comparing predicted values and tag values of a neural network predicting a balance delay rate in an embodiment of the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein, and it will be appreciated by those skilled in the art that the present invention may be practiced without departing from the spirit and scope of the present invention and that the present invention is not limited by the specific embodiments disclosed below.
In the preferred embodiment of the invention, an overall assembly line of an aircraft is selected as the example object, and 95 operations contained in the assembly line are distributed to 5 discrete stations according to the logic relationship diagram shown in fig. 2. The invention is implemented according to the detailed flow chart shown in fig. 3 in the concrete application of the embodiment.
Step 1: in the aircraft assembly line, 10 key resources are selected as design variables, wherein the key resources comprise tooling equipment resources and operating personnel resources with special professional skills, and the resources are respectively an automatic hole making robot, a laser tracker, an electric adjustable jack, a pressure checking device, an oxygen airtight pressurization device, a hydraulic professional operator, a fuel professional operator, an electronic professional operator, a sheet metal professional operator and a ordnance professional operator, so in the preferred embodiment of the invention, the resource allocation scheme is expressed as follows: RL ═ w 1,1 ,w 1,2 ,…,w 1,10 ,w 2,1 ,w 2,2 ,…,w 5,10 }. The upper limit and the lower limit of the design variable are counted according to the actual situation of the production field, the upper limit of the design variable in the embodiment of the invention is shown in fig. 4, and the lower limit of the design variable is shown in fig. 5.
Step 2: 11000 groups of resource allocation schemes are randomly generated between the upper limit and the lower limit of the design variable, 1000 groups of the resource allocation schemes are randomly selected to serve as a test set, and the remaining 10000 groups of the resource allocation schemes serve as a training set.
And step 3: 12 network structures are respectively designed for the two neural networks, and prediction precision under various network structures is obtained through continuous debugging of hyper-parameters. The configuration of neural network parameters for predicting the production beat is shown in fig. 6, and the experimental result is shown in fig. 7; the configuration of relevant parameters of the neural network for predicting the equilibrium delay rate is shown in fig. 8, and the experimental result is shown in fig. 9. The hierarchical structure of two neural networks can be determined according to the experimental result, wherein the neural network for predicting the production beat adopts a 5-layer network structure, and the number of neurons is distributed to 50/64/32/16/1; the neural network for predicting the equilibrium delay rate adopts a 6-layer network structure, and the number of neurons is distributed as 50/32/16/8/4/1. 15 groups of samples are selected from the training set to perform the demonstration of the prediction effect of two neural networks, as shown in fig. 10 and 11, which proves that the neural network constructed in the embodiment can predict the production beat and the balance delay rate with the precision similar to that of discrete event simulation.
And 4, step 4: in this embodiment, it is found through debugging experiments that the pareto optimal solution set can be sufficiently searched in the solution space of the resource allocation optimization problem by setting the initial population size of the fast non-dominated sorting genetic algorithm to 300 and the maximum iteration algebra to 2000.
And 5: according to the production site requirement and the maximum available personnel total limit, the CT is adopted in the embodiment pre Is set to 18, Y up Set to 320.
Through the solution of the method, a resource allocation scheme with optimal effect can be obtained, which can be expressed as:
Figure BDA0002805531370000071
the scheme is brought into a discrete event simulation model for verification, and the verification result shows that under the scheme, the aircraft assembly line can meet the preset production requirement and the total number of personnel limit, and has a better balance delay rate, so the resource allocation scheme can be used as a feasible optimization scheme of the aircraft assembly line.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (8)

1. An aircraft assembly line resource allocation optimization method based on a neural network and a genetic algorithm is characterized in that: the method comprises the following steps:
step 1: selecting the configuration quantity of the key resources as a design variable, and simultaneously determining an optimization target:
step 1.1: selecting design variables: selecting n key resources in an aircraft assembly line as an object for configuration optimization, wherein the distribution quantity of the n resources in m assembly work stations is used as a design variable, and the obtained resource configuration scheme RL is expressed as RL ═ w i,j 1,2, …, m, j 1,2, …, n }, where w i,j The allocation quantity of the jth resource at the ith station position is represented;
step 1.2: determining an optimization objective: the method comprises the following steps of taking a minimized production beat CT of an airplane assembly line, a balanced delay rate Bd between stations and a total resource number Y as a target for optimizing resource allocation;
step 1.3: establishing a multi-objective optimization mathematical model: minimizing three optimization targets into an objective function, and meeting the preset production beat requirement CT pre And the maximum total number of resources available Y up As a constraint condition, the optimized mathematical model is as follows:
Figure FDA0002805531360000011
wherein X is a design variable, f 1 ,f 2 ,f 3 Is an objective function, X min And X max Upper and lower limits for design variables;
step 2: obtaining a training sample:
step 2.1: generating a plurality of groups of resource allocation schemes between the upper limit and the lower limit of the design variable;
step 2.2: establishing a simulation model of the airplane assembly line by using a discrete event simulation technology, inputting the resource configuration scheme generated in the step 2.1 into the simulation model, and acquiring the production beat and the station balance delay rate of the airplane assembly line under each group of resource configuration scheme as sample labels through simulation operation;
step 2.3: 2.1, forming a sample library by the plurality of groups of resource allocation schemes generated in the step 2.1 and the corresponding sample labels obtained in the step 2.2, and dividing samples in the sample library into a training set and a test set according to a certain proportion;
and step 3: constructing a neural network and training the neural network by using a training set:
taking a design variable X as a neural network input layer; constructing two neural networks with the same input node to respectively output CT and Bd; both neural networks have an input layer containing m × n neurons and an output layer containing one neuron, and an intermediate hidden layer; training two neural networks by adopting the training set obtained in the step 2.3;
and 4, step 4: and (3) carrying out optimization solution by using a rapid non-dominated sorting genetic algorithm:
step 4.1: determining the scale of the initial population; generating an initial population based on the upper and lower limits of the design variables, each individual in the population representing a resource allocation scheme;
step 4.2: and calculating three objective function values of all individuals in the population by using two neural networks and a resource total calculation formula, and performing quick non-dominated sorting and congestion degree calculation on each individual based on the calculation result of the objective function. Thus each individual in the current population has two attribute values: the branch is matched with the ranking grade and the crowding degree;
step 4.3: comparing every two individuals in the population according to the two attribute values by adopting a rapid non-dominated sorting genetic algorithm, and when the two individuals belong to different non-dominated sorting levels, regarding the individuals with lower sorting levels as more excellent; when the two individuals belong to the same non-dominated sorting level, the crowdedness is compared, and the individual with the larger crowdedness value is considered to be better; all individuals in the population are subjected to priority sorting, and then the current population is subjected to crossover and variation operation to obtain offspring populations with the same population size; combining the parent and child population to execute an elite retention strategy; then adding one to the population algebra, returning to the step 4.2, repeating the steps for iterative optimization until the population algebra reaches a preset maximum algebra, and outputting the population at the moment as a group of pareto optimal resource allocation scheme sets;
and 5: according to constraint CT pre And Y up Screening an optimal resource allocation scheme in a pareto optimal resource allocation scheme set through the following steps:
eliminating resource allocation schemes with production beats not reaching the standard, and eliminating resource allocation schemes with the total number of eliminated resources exceeding the maximum limit; then if the resource allocation scheme set has no residual scheme, outputting a resource allocation scheme which is not feasible under the current production requirement and constraint conditions; if the resource configuration scheme set still has a single residual scheme, directly outputting the scheme; and if a plurality of residual schemes still exist in the resource allocation scheme set, selecting the scheme with the minimum Bd value from the plurality of residual schemes as the optimal resource allocation scheme to be output.
2. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 1, is characterized in that: in step 2.1, a random design method is adopted, and a plurality of groups of resource allocation schemes are randomly generated between the upper limit and the lower limit of the design variable.
3. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 1, is characterized in that: in step 3, the neural network adopts a BP neural network.
4. The aircraft assembly line resource configuration optimization method based on the neural network and the genetic algorithm is characterized in that: in step 3, the number of the middle hidden layers of the neural network and the number of the neurons in each layer are determined through experiments, the specific experimental method is to design neural network models with various structures, the neural network models respectively have different numbers of the hidden layers and the neurons, the prediction accuracy of the neural network models on the same group of test sets is respectively tested, and the neural network with the highest prediction accuracy is selected according to the experimental result.
5. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 4, is characterized in that: in step 3, the ReLU function is used as the activation function.
6. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 4, is characterized in that: in step 3, the mean square error function is used as a loss function for evaluating the prediction accuracy of the neural network.
7. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 1, is characterized in that: and 4.3, carrying out crossing and mutation operations on the current population by adopting an imitation binary crossing operator and a polynomial mutation operator to obtain the offspring populations with the same population size.
8. The method for optimizing the resource allocation of the aircraft assembly line based on the neural network and the genetic algorithm, according to claim 1, is characterized in that: and 5, after the optimal resource allocation scheme is obtained, carrying out simulation solving analysis on the production tempo and the balance delay rate under the scheme, if the production tempo output by the simulation analysis cannot meet the preset tempo requirement, showing that the resource allocation scheme is not feasible, and showing that the existing neural network model has overfitting and only shows good accuracy on a test set, and needing to carry out construction of the neural network and optimization solution of the genetic algorithm again.
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