CN114326649B - Flow shop scheduling method based on combination of genetic algorithm and particle swarm optimization - Google Patents
Flow shop scheduling method based on combination of genetic algorithm and particle swarm optimization Download PDFInfo
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Abstract
The invention relates to a flow shop scheduling method based on combination of a genetic algorithm and a particle swarm algorithm. The method is suitable for the field of workshop scheduling, and the algorithm combines a particle swarm algorithm and a genetic algorithm aiming at the defects that the algorithm is easy to early ripen, has low convergence rate, has low later searching performance, has low individual optimizing capability and the like, so that the diversity of particles is increased, the possibility that the algorithm falls into local optimization due to too dense later population is reduced, the evolution process is accelerated, and the convergence efficiency and the population searching performance are improved.
Description
Technical Field
The invention relates to the field of path planning workshop scheduling, in particular to a flow workshop scheduling method based on combination of a genetic algorithm and a particle swarm algorithm.
Background
A flow shop refers to a production shop that is arranged in a flow line, comprising a number of processes and one or more parallel machines per process, also called a flexible flow shop. The workshop structure can effectively eliminate the influence of bottleneck machines on production continuity, and improve the efficiency of the whole production line, so that how to minimize the time consumption of a flow shop is a key point of research and a difficult point. The scheduling problem of flow shop is solved, mainly is two aspects: one is the choice of the code and the other algorithm.
Many algorithms and methods are available to address shop scheduling issues. The following categories are broadly classified: (1) mathematical programming; (2) linear programming, such as model-based optimization; (3) Fuzzy decision and multi-attribute decision approaches, such as Artificial Neural Networks (ANNs); (4) Optimization algorithms and artificial intelligence techniques, including Genetic Algorithm (GA), particle swarm algorithm (PSO), simulated Annealing (SA), ant colony Algorithm (AC), tabu Search (TS), and the like.
The particle swarm algorithm (Particle swarmoptimization, PSO) is an intelligent algorithm for global searching. The method has the advantages of simple principle, relatively easy algorithm realization and high operation efficiency. However, premature reaction tends to occur, trapping is locally extremely small, and the later search accuracy is not high.
Genetic algorithms (Genetic algorithm, GA) are a method of simulating the natural selection of darwinian bioelectrical evolutionary theory and the biological evolution process of genetic mechanisms, which can be well fused with other algorithms to accomplish the optimization. Genetic algorithms can improve convergence speed and population search performance.
Disclosure of Invention
The invention aims to overcome the steps of the prior art and provides a flow shop scheduling method based on the combination of a genetic algorithm and a particle swarm algorithm.
In order to achieve the above purpose, the technical scheme of the invention is as follows: a flow shop scheduling method based on the combination of genetic algorithm and particle swarm algorithm comprises the following steps:
step one: introducing a weight coefficient into a particle swarm algorithm;
step two: modeling a flow shop, namely in the flow machining process of n workpieces on m machines, the machining sequence of each part on each machine is the same, meanwhile, each workpiece is only machined once on each machine, each machine can only machine one workpiece at a time, the required machining time and the preparation time of each workpiece on each machine are known, and the machining completion time when a corresponding scheduling scheme is required to be obtained is the shortest;
step three: applying a particle swarm algorithm to a flow shop, and redefining the position and the speed of the particles;
step four: the speed of the particles is mutated, and meanwhile, a cross operation is carried out on the positions of the particles, and the genes of the individuals with excellent population of the previous generation are inherited to the next generation through the cross operation, so that the new population obtained by one-time evolution tends to be in a better and more diversified state;
step five: when the velocity of the particles approaches an extreme value, the particles move and inert, and the velocity of the inert particles, namely the particles with the velocity smaller than a threshold value, is changed;
step six: and the processing completion time required for obtaining the corresponding scheduling scheme result is shortest.
In one embodiment of the present invention, in the step one, in the particle swarm algorithm, the expressions of the speed and the position of the particles are as follows:
v id k+1 =w i v id k +c 1 r 1 (pbest id k -x id k )+c 2 r 2 (gbest id k -x id k )
x id k+1 =x id k +v id k+1
wherein w is i Inertial weight, c 1 And c 2 For acceleration constant r 1 And r 2 Is two in [ O,1 ]]Oral administration of random variable, individual extremum of pbest, global extremum of gbest, v id k Referring to the speed, x, of the individual named id in the kth iteration id k Refers to the position of the individual named id in the kth iteration.
In one embodiment of the present invention, in step two, the completion time of the flow shop scheduling problem for m machines, n workpieces may be expressed as c (j) i ,1)=t ji1 The method comprises the steps of carrying out a first treatment on the surface of the Let c (j) i K) represents a workpiece j i Time of completion of the process on machine k, { j 1 ,j 2 ,j 3 ,…,j n And } represents the scheduling of the workpiece.
In the present inventionIn one embodiment, the method combines the habit that species in the biological kingdom find that the living density is too high and automatically separate home and migrate to provide a self-adaptive escape particle swarm algorithm; based on the self-adaptive escape particle swarm algorithm thought, a mixed PSO algorithm which can not only improve the convergence rate, but also increase the population diversity and improve the population evolution quality is provided by combining with the biological evolution characteristics; the speed variation operation is improved in the hybrid PSO algorithm, and a cross operation on the position is introduced; the cross operation can enable the hybrid PSO algorithm to get rid of local extreme points better, and improves the convergence speed and global convergence of the algorithm; the specific description of the hybrid PSO algorithm is as follows: randomly picking m particles from the updated population, and collecting the current positions X of the m particles i With its current individual extremum p i And the first m extremum (sp i ) Crossing to obtain m new particle positions X i 'A'; if the adaptation value f (X i ') is superior to the historical optimal adaptation value f (sp) of the corresponding individual extremum after sequencing i ) Then f (X) i ' substitution of f (X) i ) At the same time use X i ' substituted X i 。
Compared with the prior art, the invention has the following beneficial effects:
1. the convergence speed is increased, and the convergence time is shortened.
2. The diversity of particles is increased, the population evolution quality is increased, and the probability of searching the optimal solution is improved.
3. And combining the crossover and mutation operations of the genetic algorithm, and improving the convergence speed to generate a global optimal solution.
Drawings
Fig. 1 illustrates a first example of a solution using a hybrid PSO algorithm.
Fig. 2 illustrates a second example of a solution using the hybrid PSO algorithm.
Fig. 3 is a sample three of a solution using the hybrid PSO algorithm.
Fig. 4 shows the adaptation of the first example of the hybrid PSO algorithm.
Fig. 5 shows the adaptation of sample two under the hybrid PSO algorithm.
Fig. 6 shows the adaptation of sample three under the hybrid PSO algorithm.
Fig. 7 is a comparison of fitness trends of a standard PSO algorithm and a hybrid PSO algorithm in sample one.
Fig. 8 is a comparison of fitness trends of the standard PSO algorithm and the hybrid PSO algorithm in sample two.
Fig. 9 is a comparison of fitness trends of the standard PSO algorithm and the hybrid PSO algorithm in sample three.
FIG. 10 is a flowchart of the combination of the genetic algorithm and particle swarm algorithm of the present invention.
Fig. 11 is a flow chart of a particle swarm algorithm.
FIG. 12 is a flowchart of a genetic algorithm.
Detailed Description
The technical scheme of the invention is specifically described below with reference to the accompanying drawings.
The invention discloses a flow shop scheduling method based on combination of a genetic algorithm and a particle swarm algorithm, which comprises the following steps:
step one: introducing a weight coefficient into a particle swarm algorithm;
step two: modeling a flow shop, namely in the flow machining process of n workpieces on m machines, the machining sequence of each part on each machine is the same, meanwhile, each workpiece is only machined once on each machine, each machine can only machine one workpiece at a time, the required machining time and the preparation time of each workpiece on each machine are known, and the machining completion time when a corresponding scheduling scheme is required to be obtained is the shortest;
step three: applying a particle swarm algorithm to a flow shop, and redefining the position and the speed of the particles;
step four: the speed of the particles is mutated, and meanwhile, a cross operation is carried out on the positions of the particles, and the genes of the individuals with excellent population of the previous generation are inherited to the next generation through the cross operation, so that the new population obtained by one-time evolution tends to be in a better and more diversified state;
step five: when the velocity of the particles approaches an extreme value, the particles move and inert, and the velocity of the inert particles, namely the particles with the velocity smaller than a threshold value, is changed;
step six: and the processing completion time required for obtaining the corresponding scheduling scheme result is shortest.
The following is a specific embodiment of the present invention.
The invention aims to minimize the processing time of a flow shop and stabilize the obtained result, so the invention utilizes the genetic algorithm to have the advantages of jumping out of local optimum and improving convergence speed and group searching performance, combines the genetic algorithm and the particle swarm algorithm, not only increases the diversity of particles, but also increases the efficiency of searching for the optimum solution, and the algorithm after mixing can improve convergence speed and group searching performance, thereby shortening searching time.
The scheduling problem of the flow shop can be described as a flow machining process of n workpieces on m machines, wherein the machining sequence of each part on each machine is the same, each workpiece is only machined once on each machine, each machine can only machine one workpiece at a time, the required machining time and the preparation time of each workpiece on each machine are known, and certain index is optimal when a certain scheduling scheme is required to be obtained. The completion time of a flow shop scheduling problem for n workpieces, m machines may be expressed as c (j) i ,1)=t ji1 The method comprises the steps of carrying out a first treatment on the surface of the Let c (j) i K) represents a workpiece j i Time of completion of the process on machine k, { j 1 ,j 2 ,j 3 ,…,j n And indicates the scheduling of the workpiece, then,
c(j i ,k)=c(j i ,k-1)+t jik ,k=2,…,m
c(j i ,1)=c(j i-1 ,1)+t ji1 ,i=2,…,m
c(j i ,k)=mαx{c(j i-1 ,k),c(j i ,k-1)}+t jik ,k=2,…,m,i=2,…,m
then the maximum flow time is c max =c(j n M). The scheduling goal is to determine { j } 1 ,j 2 ,j 3 ,…,j n } to make c max Minimum.
As shown in fig. 10-12, the flow shop scheduling method based on the combination of genetic hybridization and particle swarm algorithm comprises the following specific steps:
step 1, initializing algorithm parameters including information such as the number, the position and the speed of particles. The method comprises the steps of evolution times, individual number and population information, wherein the evolution times are set to 2500, and the individual number is set to 150;
initializing:
numofItemerations; number of evolutions
numOfIndinvivisual; number of individuals
individual = zeros (numOfIndivisual, numOfJobs); population information
fori=1:numOfIndivisual
Differential (i,:) = randperm (numOfJobs); generating random sequences using random permutation functions
end
Step 2, when v i 1 And x i 1 When generated, the location and velocity information is initialized.
And step 3, determining the iteration times.
And 4, executing a particle swarm algorithm and updating the position and speed transfer formula of the particles.
Step 5, generating [0,1 ]]Is subjected to t times of iterative updating v i t And x i t At this time, the fitness values of the particles are evaluated and ranked.
And (5) calculating a fitness value:
fitofindivisual=fitness (inventdual, timeOfJobs); calculating population fitness
Value, index ] = min (fitOfIndivisual); recording optimal subscript
flowpbest=index; current individual optimization
flowgbest=index; current global optimum
recordpbest=inf_ons (1, numofindivisual); individual optimal records
recordgbest= fitOfIndivisual (index); group optimal recording
newIndivisual = indivisual; creating a backup of population information to update
And 6, randomly selecting m particles, and executing a genetic algorithm to update particle information.
And 7, determining the evolution times and the number of individuals of the genetic algorithm.
Step 8, performing cross operation to obtain the current positions X of m particles i With its current individual extremum p i And the first m extremum (sp i ) Crossing to obtain m new particle positions X i '. If the adaptation value f (X i ') is superior to the historical optimal adaptation value f (sp) of the corresponding individual extremum after sequencing i ) Then f (X) i ' substitution of f (X) i )
Crossover operation:
crossing with individual optima:
numofjobs=size (data, 1); the size function is the number of read tasks
c1 =unidrnd (numOfJobs-1); % generate cross bit
c2 =unidrnd (numOfJobs-1); % generate cross bit
while c1==c2
c1=round(rand*(numOfJobs-2))+1;
c2=round(rand*(numOfJobs-2))+1;
end
chb1=min(c1,c2);
chb2=max(c1,c2);
cros=flowPbest(i,chb1:chb2);
ncros=size(cros,2);
Cross with the overall optimization
c1 =round (rand x (numofjob-2)) +1; generating crossing bits
c2 =round (rand x (numofjob-2)) +1; generating crossing bits
while c1==c2
c1=round(rand*(numOfJobs-2))+1;
c2=round(rand*(numOfJobs-2))+1;
end
chb1=min(c1,c2);
chb2=max(c1,c2);
cros=flowGbest/flowPbest(chb1:chb2);
ncros=size(cros,2);
And 9, evaluating the fitness value of the particle, if the fitness value of the particle is improved, updating the fitness value and the speed and position information of the particle, otherwise, retaining the fitness value, the speed and the position information of the particle before crossing.
And step 10, performing mutation operation, and performing mutation on the speed of the inert particles.
Variation:
numofjobs=size (data, 1); where the size function is the number of read tasks
c1 =round (rand x (numOfJobs-1)) +1; producing a variant
c2 =round (rand x (numOfJobs-1)) +1; producing a variant
while c1==c2
c1=round(rand*(numOfJobs-2))+1;
c2=round(rand*(numOfJobs-2))+1;
end
swap(newIndivisual(i,c1),newIndivisual
And step 11, judging whether the global optimal solution is changed after mutation, if so, updating the fitness value, the speed and the position information of the particles, otherwise, keeping the fitness value, the speed and the position information of the particles before mutation.
And outputting the optimal fitness value and the particle information.
Particle swarm algorithm, the specific particle velocity and position expression is as follows
v id k+1 =w i v id k +c 1 r 1 (pbest id k -x id k )+c 2 r 2 (gbest id k -x id k )
x id k+1 =x id k +v id k+1
Wherein w is i Inertial weight, c 1 And c 2 For acceleration constant r 1 And r 2 Is two in [ O,1 ]]Oral administration of random variable, individual extremum of pbest, global extremum of gbest, v id k Referring to the speed, x, of the individual named id in the kth iteration id k Refers to the position of the individual named id in the kth iteration.
Because this is a particle swarm algorithm that works in a flow shop, redefinition of the location and velocity of the particles is required. A total of n workpieces are provided, and a certain position X= (X) 1 ,x 2 ,x 3 ,…,x n ) The velocity at this position is v= (V) 1 ,v 2 ,v 3 ,…,v n ). The position of each particle is the machining sequence of the batch of workpieces and the speed is the number of corrections to the machining sequence. P= (P) 1 ,p 2 ,p 3 ,…,p n ),P i The best location experienced by particle i, i.e., the location experienced by particle i that has the best fitness value, is the individual best location. P (P) g Refers to the best location experienced by all particles in the population of particles, being the global best location. Wherein c i =(c 1 ,c 2 ,c 3 ,…,c n ) Is constant, r i =(r 1 ,r 2 ,r 3 ,…,r n ) To be generated by a random function, define c i r i =(c 1 r 1 ,c 2 r 2 ,c 3 r 3 ,…,c n r n )。
Later in the iteration, when the position x of some particles i And its speed update is determined by wv when its pbest approaches the gbest of the population. Because w is<1, the running speed of the particles will quickly tend to a certain value V, at which time the particles are inert in operation. As the iteration proceeds, other particles will quickly aggregate around these inert particles, causing the particles to prematurely converge to gbest, which is the best point the population currently finds, and cannot guarantee a globally optimal solution that must be an optimization problem. Therefore, the speed of the particles with the speed smaller than a certain threshold value is mutated, so that the possibility of the algorithm falling into local optimum is reduced.
The self-adaptive escape particle swarm algorithm is provided by combining the habit that the species in the biological kingdom can automatically separate home and migrate when the survival density is too high. Based on the algorithm thought, the mixed PSO algorithm which can not only improve the convergence rate, but also increase the population diversity and improve the population evolution quality is provided by combining with the biological evolution characteristics. The speed variation operation in the algorithm is improved and a cross operation on the position is introduced. The cross operation can enable the PSO algorithm to get rid of local extreme points better, and improves the convergence speed and global convergence of the algorithm. The idea of this interleaving operation is as follows: randomly picking m particles from the updated population, and collecting the current positions X of the m particles i With its current individual extremum p i And the first m extremum (sp i ) Crossing to obtain m new particle positions X i '. If the adaptation value f (X i ') is superior to the historical optimal adaptation value f (sp) of the corresponding individual extremum after sequencing i ) Then f (X) i ' substitution of f (X) i ) At the same time use X i ' substituted X i . Obviously, the intersection not only makes use of historical experience information of the particles in one evolution, but also makes use of experience information of excellent individuals in the population, so that the diversity of the particles is increased, the evolution quality of the population is increased, and the possibility that the particles find global optimum is increased.
The written program was run to give the following results in table 1. Wherein, the Chinese number indicates the number of bits of the work piece arranged in the scheduling sequence.
From the flow shop schedule that has been obtained for both examples, the following Gantt chart (as shown in FIGS. 1-3) can be made. Wherein the abscissa represents the processing time of the workpiece, and the ordinate is the machine sequence of M1, M2, M3, M4, … and Mm from top to bottom, which is the reverse direction in the figure.
TABLE 1
In order to fully understand the change condition of the total delay of the objective function in the training process of the iterative annealing of the simulated annealing algorithm, a training process diagram of single machine scheduling is required. The simulated annealing training process for each example is shown in fig. 4-6.
As can be seen from fig. 4-6, the mixed PSO algorithm tends to be smaller and smaller with increasing iteration number, and gradually stabilizes within a certain threshold. The speed of the search will be faster when the population size is increased. Therefore, the application of the mixed PSO algorithm in the Flow-Shop scheduling problem achieves a good effect, and the feasibility of the mixed PSO algorithm in the running water workshop scheduling is shown.
From fig. 7-9, it is clear that the standard PSO algorithm is inferior to the hybrid PSO algorithm in that the tendency for the degree of inadequacy to decrease is slower than that of the hybrid PSO, and in some cases the solution obtained by the standard PSO algorithm is significantly worse than that obtained by the hybrid PSO algorithm. For the problem of flow shop, the search direction is difficult to distinguish, and the single experimental result of the standard PSO algorithm has large difference. The secondary experimental result of the mixed PSO algorithm is stable, the data difference is relatively small, and the mixed PSO algorithm has better stability and practicability on the problem of a flow shop.
The above is a preferred embodiment of the present invention, and all changes made according to the technical solution of the present invention belong to the protection scope of the present invention when the generated functional effects do not exceed the scope of the technical solution of the present invention.
Claims (4)
1. A flow shop scheduling method based on the combination of a genetic algorithm and a particle swarm algorithm is characterized by comprising the following steps:
step one: introducing a weight coefficient into a particle swarm algorithm;
step two: modeling a flow shop, namely in the flow machining process of n workpieces on m machines, the machining sequence of each part on each machine is the same, meanwhile, each workpiece is only machined once on each machine, each machine can only machine one workpiece at a time, the required machining time and the preparation time of each workpiece on each machine are known, and the machining completion time when a corresponding scheduling scheme is required to be obtained is the shortest;
step three: applying a particle swarm algorithm to a flow shop, and redefining the position and the speed of the particles;
step four: the speed of the particles is mutated, and meanwhile, a cross operation is carried out on the positions of the particles, and the genes of the individuals with excellent population of the previous generation are inherited to the next generation through the cross operation, so that the new population obtained by one-time evolution tends to be in a better and more diversified state;
step five: when the velocity of the particles approaches an extreme value, the particles move and inert, and the velocity of the inert particles, namely the particles with the velocity smaller than a threshold value, is changed;
step six: and the processing completion time required for obtaining the corresponding scheduling scheme result is shortest.
2. The flow shop scheduling method according to claim 1, wherein in the first step, the expression of the speed and position of the particles in the particle swarm algorithm is as follows:
v id k+1 =w i v id k +c 1 r 1 (pbest id k —x id k )+c 2 r 2 (gbest id k -x id k )
x id k+1 =x id k +v id k+1
wherein w is i Inertial weight, c 1 And c 2 For acceleration constant r 1 And r 2 Is two in [ O,1 ]]Oral administration of random variable, individual extremum of pbest, global extremum of gbest, v id k Referring to the speed, x, of the individual named id in the kth iteration id k Refers to the position of the individual named id in the kth iteration.
3. The flow shop scheduling method according to claim 1, wherein in the second step, the completion time of the flow shop scheduling problem of m machines and n workpieces can be expressed asLet c (j) i K) represents a workpiece j i Time of completion of the process on machine k, { j 1 ,j 2 ,j 3 ,...,j n And } represents the scheduling of the workpiece.
4. The flow shop scheduling method based on the combination of genetic algorithm and particle swarm algorithm according to claim 1, wherein the method combines the habit that species in the biological kingdom can automatically separate home and migrate when the survival density is found to be too high, and provides a self-adaptive escape particle swarm algorithm; based on the self-adaptive escape particle swarm algorithm thought, a mixed PSO algorithm which can not only improve the convergence rate, but also increase the population diversity and improve the population evolution quality is provided by combining with the biological evolution characteristics; the speed variation operation is improved in the hybrid PSO algorithm, and a cross operation on the position is introduced; the cross operation can enable the hybrid PSO algorithm to get rid of local extreme points better, and improves the convergence speed and global convergence of the algorithm; the specific description of the hybrid PSO algorithm is as follows: randomly picking m particles from the updated population, and collecting the current positions X of the m particles i With its current individual extremum p i And the first m extremum (sp i ) Crossing to obtain m new particle positions X i 'A'; if the adaptation value f (X i ') is superior to the historical optimal adaptation value f (sp) of the corresponding individual extremum after sequencing i ) Then f (X) i ' substitution of f (X) i ) At the same time use X i ' substituted X i 。
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