CN110991056B

CN110991056B - Airplane assembly line operation scheduling method based on genetic variation neighborhood algorithm

Info

Publication number: CN110991056B
Application number: CN201911247383.1A
Authority: CN
Inventors: 张剑; 蔡玮; 陈浩杰; 袁铭晖; 江海凡; 付建林
Original assignee: Southwest Jiaotong University
Current assignee: Southwest Jiaotong University
Priority date: 2019-12-09
Filing date: 2019-12-09
Publication date: 2021-08-06
Anticipated expiration: 2039-12-09
Also published as: CN110991056A

Abstract

The invention discloses an aircraft assembly line operation scheduling method based on a genetic variation neighborhood algorithm, which comprises the steps of firstly establishing a resource-limited aircraft assembly line operation scheduling model, and converting an operation scheduling problem in actual production into a mathematical model problem for optimization solution; secondly, constructing a subsection operation scheduling model of the airplane assembly line by taking the total construction period of the minimized assembly operation as an optimization target and simultaneously considering the tight front and back constraint, the resource constraint and the space constraint; and finally, solving by adopting an improved genetic variation neighborhood algorithm. The invention designs a group initialization method combined with priority rules to reduce solution space, and adopts a variable neighborhood local search mode combined with an acceptance threshold value to construct three neighborhood structures considering the relationship between the front and the back to ensure that a legal solution is generated in the search process, so as to improve the search capability and avoid the traditional genetic algorithm from falling into local optimum; the scheduling scheme of the aircraft assembly line operation obtained by the method can effectively shorten the total construction period of the assembly operation.

Description

Airplane assembly line operation scheduling method based on genetic variation neighborhood algorithm

Technical Field

The invention belongs to the field of operation scheduling of an airplane assembly line operation workshop under the condition of limited resources and space, and particularly relates to an airplane assembly line operation scheduling method based on a genetic variation neighborhood algorithm.

Background

The aircraft assembly has the characteristics of large operation quantity, complex assembly relation and the like, and the space for accommodating resources in the section areas such as a cockpit is limited, so the operation Scheduling Problem of the aircraft assembly line can be regarded as a Resource Constrained Project Scheduling Problem (RCPSP) with special space constraint, and the Problem is proved to be a complex strong NP-hard Problem.

From the solution point of view, the algorithms for solving RCPSP and its extended problem can be divided into three major categories: precision algorithms, heuristics and meta-heuristics (smart algorithms), wherein precision algorithms, while yielding theoretically optimal solutions, are only suitable for small scale solutions, whereby approximation algorithms are beginning to be applied to solve large scale RCPSP problems. Since the 1963 scheduling generation scheme is proposed, various heuristic algorithms are successively applied to the problem, but the heuristic algorithms have no optimization capability and are often influenced by the problem and cannot obtain a satisfactory solution. The application of meta-heuristic algorithms and intelligent algorithms makes the problem solving new developments, such as introducing Simulated Annealing (SA) in local search to solve RCPSP, evolutionary algorithms (e.g. Genetic Algorithm, GA) and population intelligent algorithms (e.g. Ant Colony Optimization, ACO) are widely applied to solve RCPSP problems.

The scheduling problem of the airplane assembly line belongs to the expansion problem of the traditional RCPSP, wherein operation activities are restricted by the tight front and the tight back and resources, and in some sections of the airplane, a plurality of parallel activities meeting the resources can not be performed simultaneously due to space limitation, so that the complexity of problem space and calculation and solution is increased. Aiming at the complexity of the problems, the meta-heuristic algorithm is mixed to make up the defects of the respective algorithms, so that the method becomes a new method for solving the problems, the efficiency of solving the problems is improved through algorithm mixing, and meanwhile, a more accurate solution can be obtained in a global range.

Disclosure of Invention

In order to overcome the defects of the prior art in solving the problem of scheduling of the aircraft assembly line, the invention provides an aircraft assembly line operation scheduling method based on a genetic variation neighborhood algorithm.

The invention discloses an aircraft assembly line operation scheduling method based on a genetic variation neighborhood algorithm, which comprises the following specific steps of:

step 1: setting relevant parameters of airplane assembly line operation scheduling

Setting an aircraft assembly operation project as a activity set J; j ═ 0,1,2, …, n +1, where activities 0 and n +1 are virtual activities, representing only the beginning and end of the item, and not taking up time and resources; for immediate preceding action set P of Activity j_jJ ∈ J denotes a set of operations immediately after J is set with S_jRepresents; t is t_jIndicates the duration of the activity j, st_jRepresents the job start time of activity j; define M as a set of segments, M ═ {1,2, …, z }, M ∈ M as a segment number, z is a positive integer, C_mRepresenting the active set in section m, e_jRepresenting the space occupation of the job activity j, the maximum space capacity of each section being N_m；R＝{r₁,r₂,…,r_q,…,r_kDenotes the set of k resources in the assembly process, denoted by r_jqRepresenting the demand of activity j for the qth resource unit time, b_qIs the maximum supply of the resource q per unit time; discretizing time, wherein d is a discrete time node, T represents the total construction period of the assembly work, and A_d＝{j|st_j<d≤st_j+t_jThe set of job activities being executed at time d.

Step 2: establishing a mathematical model for optimizing the operation scheduling target of the airplane assembly line, wherein the target function is as follows:

minT＝st_n+1 (1)

namely solving the total construction period of the minimum assembly operation, the constraint is as follows:

t₀＝t_n+1＝0 (5)

r_0q＝r_(n+1)q＝0,q＝1,2,...,k (6)

wherein, the formula (2) is a decision variable; equation (3) indicates that each job activity must be completed for its specified duration; equation (4) indicates that activity j, once started, cannot be interrupted until completion; equations (5) and (6) indicate that the duration and resource demand of virtual activities 0 and n +1 are both 0; equation (7) is a constraint that immediately precedes and follows the activity, and activity j must begin only after all activities immediately precede and follow it; equation (8) is a resource constraint, and the demand of all activities being executed at time d on a certain resource is not more than the maximum supply of the resource per unit time; equation (9) is the space constraint for each segment, and the demand for space for all activities being performed in segment m at time d is not greater than the maximum space capacity of segment m.

And step 3: the genetic variable neighborhood algorithm is optimized and solved, because the genetic algorithm has the defect of being easy to fall into local optimum, the method designs a variable neighborhood algorithm combined with a receiving threshold value to carry out local search, and designs a cross strategy, a variation strategy and three neighborhood structures generating legal solutions to ensure the algorithm to carry out and improve the search capability, a specific algorithm flow chart is shown in figure 1, and the method comprises the following steps:

3.1 setting parameters: setting the maximum generation times as maxGen; population size popSize; cross probability of P_c(ii) a The mutation probability is P_m。

3.2 population initialization: the popSize chromosomes are generated by integer coding, and the immediate before and after relationship of each activity is considered, for example, the chromosome a ═ (0,1,2, …, n +1) contains n +2 activities together, where 0 and n +1 represent the virtual activities of beginning and end, and 1,2, …, n represents the scheduling order of the activities and satisfies the immediate before and after relationship. Considering that the solution target is the minimized project construction period, a priority rule (the adopted priority rule is EDDF or MINLFT, so that the quality of the initial solution is improved, and the solution space is reduced) is firstly adopted to initialize part of individuals, and the other individuals are randomly initialized to improve the diversity of the initial population.

3.3 calculating an individual Fitness value, selecting a coefficient C multiplied by the reciprocal 1/T of the target function as a Fitness function, namely Fitness ═ C/T, judging whether the current iteration frequency gen reaches the maximum iteration frequency maxGen, and outputting an optimal solution if the current iteration frequency gen reaches the maximum iteration frequency; otherwise go to step 3.4.

3.4 selecting: and selecting individuals by adopting a tournament selection strategy, randomly selecting a certain number of individuals from the population each time, selecting the optimal individual from the population to enter a new population according to the fitness function value of the individual, and repeating the operation until the size of the selected new population reaches 90% of that of the initial population.

3.5, crossing: according to cross probability p_cPerforming cross operation, improving on the basis of single-point cross, and forming a cross strategy considering the relation between the front and the back; taking two individuals from the parent to cross, wherein the two individuals are respectively M₁And M₂Taking a random integer m as a breakpoint, wherein m is more than or equal to 1<n, then obtainTwo offspring C₁And C₂(ii) a Offspring C₁In the active sequence of (1), …, M is derived from the parent M₁And i is M +1, …, part of n being from parent M₂But in this part of the sequence, already from the parent M₁The selected activities are not considered any more, so that the operation ensures that the priority of the activities in the parent is preserved, each activity only appears once, the generated child individuals do not appear illegal individuals, and the child C does not appear₂The same can be obtained by the generation of the method, so that two new filial individuals are obtained.

3.6 mutation: according to the probability of variation p_mChanging the genotype of a genetic operator, adopting a right shift mutation strategy, considering that an activity sequence lambda of a certain individual is {1, 2., i, …, n }, wherein i is randomly selected activity, right shifting a position of i to a certain position to generate a new generation of individual, and in order to ensure that the activity sequence of the new individual still accords with the priority sequence of the activity without generating illegal solution, judging the right-shifted position with the minimum activity before right shifting, namely not destroying the original close-behind relationship, but because the activity is right shifted, the activity immediately before is still effective, thereby obtaining a new individual lambda' {1, …, i-1, i +1, …, h-1, i, h, …, n }, wherein the position of h is the right-shifted position with the minimum i; after the mutation operation a new population newPop is generated.

3.7 variable neighborhood operation: and selecting individuals with the first 20% of the fitness value from the newPop as an initial solution set S of variable neighborhood operation, and generating a local optimal solution set after the variable neighborhood operation.

Here, 3 kinds of neighborhood structures that do not generate illegal solutions are designed, specifically as follows:

randomly selecting a certain point in the individual genes, and recording the maximum subscript position of all immediately preceding activities of the corresponding activities on the point in the item list and the minimum subscript position of all immediately following activities of the activities in the item list according to the relationship between immediately preceding activities and immediately following activities. (1) The gene is inserted into the position one bit before the minimum subscript position of the activity after the gene is moved right to form a first neighborhood structure; (2) the gene is left-shifted and inserted to a position behind the maximum lower mark position of the activity immediately before to form a second neighborhood structure; (3) the gene is randomly inserted between the minimum subscript position and the maximum subscript position to form a third neighborhood structure.

Three specific examples of neighborhood structures are shown in fig. 2. Randomly selecting a gene locus G in chromosome F, wherein G corresponds to the maximum subscript position G in all pre-close activities of activity 5₁The maximum subscript position of all the activities after tightening is G₂Then neighborhood structure 1 inserts activity 5 into P₁Location finding of New Individual F₁Neighborhood Structure 2 inserts Activity 5 into P₂Location finding of New Individual F₂Neighborhood structure 3 randomly inserts activity 5 into P₁And P₂Intermediate position P of₃Or P₄To obtain a new individual F₃Or F₃’。

In addition to the design of the neighborhood structure, considering that the strategy of neighborhood search based on elite reservation still has the risk of falling into local optimum, a calculation method of an acceptance threshold is provided, namely whether the optimal solution obtained by variable neighborhood search is accepted or not is considered in the acceptance threshold, the initial solution of the variable neighborhood search is set as s, the objective function value is f(s), the new solution obtained after the neighborhood search is set as s ', and the objective function value is f (s'). When the obtained new solution is better than the initial solution, namely f (s ') -f(s) <0, accepting the new solution with the probability p ═ 1, and enabling s ═ s' to enter the next iteration; when the obtained new solution is inferior to the initial solution, namely f (s ') -f(s) >0, accepting inferior solution by using the probability p ═ exp { - [ f (s ') -f (s)) ]/f (s)) }, and leading s ═ s ' to enter the next iteration.

3.8, reinserting the local optimal solution set into the original population, and turning to the step 3.3.

Compared with the prior art, the invention has the following technical effects:

(1) the invention takes the practical situation that the assembly of certain sections of the airplane is limited by space constraints in the process of assembling the final assembly of the airplane into consideration. In the process of aircraft assembly, a plurality of parallel operation activities exist, and due to the fact that space of certain sections (such as an aircraft cockpit) of an aircraft is narrow, personnel and equipment required by the activities of the parallel operation in the sections cannot meet the requirement of start-up at the same time, and in the process of modeling of the scheduling problem of the existing aircraft assembly line, the problem is often ignored, and the scheduling result is inconsistent with the actual field situation. The invention fully considers the actual influence of space constraint on the scheduling of the airplane assembly line and establishes a multi-constraint airplane assembly line operation scheduling mathematical model, so that the scheduling solution is more accurate and effective.

(2) The invention solves the scheduling model of the airplane assembly line operation by adopting an improved genetic variation neighborhood algorithm. A population initialization method combined with priority rules is designed to modify the initial population of the genetic algorithm, so that the quality of the solution is improved, and the solution space is reduced; searching the population after genetic operation by adopting a variable neighborhood searching method to improve the local searching capability of the algorithm, and designing a calculation method of an acceptance threshold value in the searching process to avoid the searching process from falling into local optimum; in the process of constructing the crossing, mutation and neighborhood structure, the operation method which can not generate illegal solutions is considered, and the arithmetic performance of the algorithm is improved.

Drawings

FIG. 1 is a flowchart of a genetic variation neighborhood algorithm.

FIG. 2 is a neighborhood operation example.

Examples

5 groups of initial input data are randomly selected under 3 working conditions with the activity numbers of 30, 60 and 90 by using the examples in the standard example library PSPLIB. Work items on each scale share 4 resources, each resource having a maximum supply per unit time, and each activity requires one or more resources. Randomly selecting a certain resource as space demand, and randomly generating the number of sections [1, z ] for each working condition]And randomly distributing the activities into the segments, the maximum space capacity N of the segments_mIs a random integer between the maximum value of the demand amount for space and the maximum supply amount per unit time of the resource as the demand amount for space in the activity performed by the section. Numerical experiments are carried out through a Matlab2014b platform, IGA-VNS is compared with a traditional Genetic Algorithm (GA), a variable neighborhood algorithm (VNS) and a genetic simulated annealing algorithm (GASA), operation is carried out for 5 times under each working condition, and obtained experimental results are shown in table 1, wherein Duration represents the average value of the total construction period of assembly, and GAP is the percentage of difference.

In the formula (10), T₁Total time limit mean, T, for other algorithms₂Is the average of the total time limit of the IGA-VNS algorithm. And (4) analyzing results: the results of the numerical experiments are shown in table 1.

Table 13 experimental results at scale

Experimental results show that under different operation scales, the results of the airplane assembly line scheduling problem solved based on the IGA-VNS algorithm are superior to those of the other three algorithms, and under the scale that the activity number is 30, the target value of the IGA-VNS is improved by 4.69% on average in precision compared with that of the other algorithms. The advantage of the IGA-VNS is also expanded as the campaign size increases, with the IGA-VNS improving on average 4.89% of the accuracy with respect to the target value of the other algorithm at a campaign size of 60 and 9.84% of the accuracy with respect to the target value of the other algorithm at a campaign size of 90. And the IGA-VNS has obvious advantages compared with the solving capability of GA and VNS, and has certain advantages for GASA with global and local searching capability. It can be seen comprehensively that the aircraft assembly line operation scheduling solving method provided by the invention is superior to the prior art.

Claims

1. An aircraft assembly line operation scheduling method based on a genetic variation neighborhood algorithm is characterized by comprising the following steps:

step 1: setting relevant parameters of airplane assembly line operation scheduling;

setting an aircraft assembly operation project as a activity set J; j ═ 0,1,2, …, n +1, where activities 0 and n +1 are virtual activities, representing only the beginning and end of the item, and not taking up time and resources; for immediate preceding action set P of Activity j_jJ ∈ J denotes a set of operations immediately after J is set with S_jRepresents; t is t_jIndicating the duration of activity j，st_jRepresents the job start time of activity j; define M as a set of segments, M ═ {1,2, …, z }, M ∈ M as a segment number, z is a positive integer, C_mRepresenting the active set in section m, e_jRepresenting the space occupation of the job activity j, the maximum space capacity of each section being N_m(ii) a By r_jqRepresenting the demand of the activity j on the qth resource unit time, wherein q is 1,2, …, k, k is an integer; b_qIs the maximum supply of the resource q per unit time; discretizing time, wherein d is a discrete time node, T represents the total construction period of the assembly work, and A_d＝{j|st_j＜d≤st_j+t_jThe j is the set of job activities being executed at time d;

minT＝st_n+1 (1)

t₀＝t_n+1＝0 (5)

r0_q＝r(n+1)_q＝0，q＝1，2，...，k (6)

wherein, the formula (2) is a decision variable; equation (3) indicates that each job activity must be completed for its specified duration; equation (4) indicates that activity j, once started, cannot be interrupted until completion; equations (5) and (6) indicate that the duration and resource demand of virtual activities 0 and n +1 are both 0; equation (7) is a constraint that immediately precedes and follows the activity, and activity j must begin only after all activities immediately precede and follow it; equation (8) is a resource constraint, and the demand of all activities being executed at time d on a certain resource is not more than the maximum supply of the resource per unit time; equation (9) is the space constraint of each segment, and the demand of all activities being executed in segment m at time d is not greater than the maximum space capacity of segment m;

and step 3: the genetic variation neighborhood algorithm optimization solution comprises the following steps:

3.1 setting parameters: setting the maximum generation times as maxGen; population size popSize; cross probability of P_c(ii) a The mutation probability is P_m；

3.2 population initialization: generating popSize chromosomes in an integer coding mode, initializing partial individuals by adopting a priority rule in consideration of the problem that the solution target is the minimized project construction period, and randomly initializing the rest individuals to improve the diversity of an initial population;

the priority rule adopted in the step 3.2 is EDDF or MINLFT, so that the quality of the initial solution is improved, and the solution space is reduced;

3.3 calculating an individual Fitness value, selecting a coefficient C multiplied by the reciprocal 1/T of the target function as a Fitness function, namely Fitness ═ C/T, judging whether the current iteration frequency gen reaches the maximum iteration frequency maxGen, and outputting an optimal solution if the current iteration frequency gen reaches the maximum iteration frequency; otherwise, turning to the step 3.4;

3.4 selecting: selecting individuals by adopting a championship selection strategy, randomly selecting a certain number of individuals from the population each time, selecting the optimal individual from the population to enter a new population according to the fitness function value of the individual, and repeating the operation until the size of the selected new population reaches 90% of that of the initial population;

3.5, crossing: according to cross probability p_cPerforming cross operation, improving on the basis of single-point cross, and forming a cross strategy considering the relation between the front and the back; taking two individuals from the parent to cross, wherein the two individuals are respectively M₁And M₂Taking a random integer m 'as a breakpoint, wherein m is not less than 1 ≦ m'<n and n are integers, two filial generations C are obtained₁And C₂(ii) a Offspring C₁In the active sequence of (1), …, M' is derived from the parent M₁And i ═ M' +1, …, n, n are integers, the part coming from the parent M₂But in this part of the sequence, already from the parent M₁The selected activities are not considered any more, so that the operation ensures that the priority of the activities in the parent is preserved, each activity only appears once, the generated child individuals do not appear illegal individuals, and the child C does not appear₂The same principle can be obtained by the generation of the two new filial generation individuals;

3.6 mutation: according to the probability of variation p_mChanging the genotype of a genetic operator, adopting a right shift mutation strategy, considering that an activity sequence lambda of an individual is {1,2, i, …, n }, n is an integer, i is randomly selected activity, shifting the position of i to the right to generate a new generation of individual, in order to ensure that the activity sequence of the new individual still accords with the priority sequence of the activity without generating illegal solution, judging the right shift position with the minimum activity before the right shift, namely not destroying the original close-after relationship, but moving the activity to the right so that the activity immediately before the activity is still effective, thereby obtaining the new individual

λ' {1, …, i-1, i +1, …, h-1, i, h, …, n }, where n is an integer and h is the smallest right-shiftable position of i; generating a new population newPop after mutation operation;

3.7 variable neighborhood operation: selecting individuals with the first 20% of fitness value from newPop as an initial solution set S of variable neighborhood operation, and generating a local optimal solution set after the variable neighborhood operation;

3 kinds of neighborhood structures which can not generate illegal solutions are designed in the step 3.7, and the method specifically comprises the following steps:

randomly selecting a certain site in the individual genes, and recording the maximum subscript positions of all immediately preceding activities of all the activities corresponding to the site in the item list and the minimum subscript positions of all immediately following activities of the activities in the item list according to the relationship between immediately preceding activities and immediately following activities; the gene is inserted into the position one bit before the minimum subscript position of the activity after the gene is moved right to form a first neighborhood structure; the gene is left-shifted and inserted to a position behind the maximum lower mark position of the activity immediately before to form a second neighborhood structure; randomly inserting the gene between the minimum subscript position and the maximum subscript position to form a third neighborhood structure;

step 3.7 also provides a method for calculating an acceptance threshold, namely, whether the optimal solution obtained by variable neighborhood search is accepted or not is considered in the acceptance threshold, the initial solution of the variable neighborhood search is set to be s, the objective function value is f(s), the new solution obtained after neighborhood search is set to be s ', and the objective function value is f (s'); when the obtained new solution is better than the initial solution, namely f (s ') -f(s) <0, accepting the new solution with the probability p ═ 1, and enabling s ═ s' to enter the next iteration; when the obtained new solution is inferior to the initial solution, namely f (s ') -f(s) >0, accepting inferior solution by using the probability p ═ exp{ - [ f (s ') -f (s)) ]/f (s)) }, and leading s ═ s ' to enter the next iteration;