WO2016101181A1

WO2016101181A1 - Photoetching procedure dynamic scheduling method based on indicator forecasting and solution similarity analysis

Info

Publication number: WO2016101181A1
Application number: PCT/CN2014/094837
Authority: WO
Inventors: 刘民; 郝井华
Original assignee: 清华大学
Priority date: 2014-12-23
Filing date: 2014-12-24
Publication date: 2016-06-30
Also published as: CN104536412A; CN104536412B

Abstract

A photoetching procedure dynamic scheduling method based on indicator forecasting and solution similarity analysis, which relates to the fields of advanced manufacturing, automation and information. The dynamic scheduling method is provided for photoetching procedure dynamic scheduling on a semiconductor production line. The method comprises: firstly, dividing a photoetching procedure dynamic scheduling problem into a device selection scheduling sub-problem and a workpiece sequencing scheduling sub-problem; establishing, on line, a performance indicator forecasting model of the workpiece sequencing scheduling sub-problem; and then, solving an original scheduling problem by using a differential evolution algorithm based on solution similarity analysis. In the differential evolution algorithm, the performance indicator forecasting model of the workpiece sequencing scheduling sub-problem is used for performing quick rough evaluation on global scheduling performance of solutions of the device selection scheduling sub-problem. In the evaluation process on the scheduling solutions, a mode of combining precise evaluation and the rough evaluation is used to perform the performance evaluation on solutions in the differential evolution algorithm; by using the scheduling method, the efficiency and the effect of photoetching procedure production scheduling can be remarkably improved.

Description

Photolithography process dynamic scheduling method based on index prediction and solution similarity analysis

Technical field

The invention belongs to the fields of advanced manufacturing, automation and information, and particularly relates to a lithography process dynamic scheduling method for lithography process scheduling of semiconductor production lines, based on index prediction and solution similarity analysis.

Background technique

The lithography process scheduling problem for the semiconductor production line to which the present invention is directed is a single-process scheduling problem with the sum of the total weighted flow times as the optimization target, with machine suitability constraints and order related preparation time. The photolithography process is one of the key processes in the semiconductor production line, and its scheduling effect has a greater impact on the production performance indicators of the entire production line. For this kind of problem, the existing scheduling methods mainly include precise optimization methods, classical artificial intelligence methods, heuristic rules and intelligent optimization methods. However, the existing scheduling method is still not ideal when dealing with the above-mentioned scheduling problems of large scale. Therefore, it is important to propose a dynamic scheduling method for lithography processes with better performance.

Summary of the invention

In order to solve the scheduling problem of the semiconductor production line lithography process to minimize the total weighted flow time, the present invention proposes a lithography process dynamic scheduling method (hereinafter referred to as PASM) based on the index prediction and solution similarity analysis.

The lithography process scheduling problem for the semiconductor production line to which the present invention is directed is a single-process scheduling problem with a total weighted flow time sum as an optimization target, with machine suitability constraints and order related preparation time. In the present invention, The above scheduling problem is decomposed into the device selection scheduling sub-problem and the workpiece scheduling sub-problem. On this basis, the sub-problem scheduling problem is constructed and the performance index prediction model is constructed. The function of the above-mentioned scheduling sub-problem performance index prediction model is to predict the performance of the corresponding sub-problem problem by analyzing the characteristic information of the scheduling sub-problem without solving the scheduling sub-problem. Based on the above-mentioned scheduling sub-problem performance index prediction model, a differential evolution algorithm based on solution similarity analysis is proposed to solve the equipment selection scheduling sub-problem. The workpiece scheduling sub-problem performance index prediction model is used for the equipment. The solution of the scheduling sub-problem is selected to perform a quick evaluation of the global scheduling performance, thereby improving the global optimization performance.

(1) Description of the problem

The lithography process scheduling problem of the semiconductor production line can be specifically described as follows:

In the photolithography process, there are m lithography machines, and n workpieces to be scheduled are respectively recorded as M={1, 2, . . . , m} and N={1, 2, . . . , n}. Each workpiece needs to be processed on a lithography machine. The processing time, weight, and release time of the workpiece j (j∈N) on the machine l are recorded as p _{l, j} , w _j and r _j , and the workpiece j is also Corresponding to a machinable lithography machine set μ _j and lithography plate model b _j , only the lithography machine in the set can process the workpiece, and during processing, if the lithography plate corresponding to the previous processing task is the same as this time If the corresponding lithography plate is the same model, the required switching time is 0, otherwise a fixed reticle switching time is required. In addition, consider the following assumptions: the same machine can only process one workpiece at a time, the same workpiece can only be machined on one machine at a time, and once machining is started, it cannot be interrupted until the machining is completed. It is now necessary to arrange the workpiece to be machined on the lithography machine so that the total weighted flow time is the shortest.

Suppose that am _j (am _j ∈M) is the processing machine assigned to workpiece j, f _j is the machining completion time of workpiece j, and S is the switching time matrix between workpieces, S={s _pq } _n×n , where s _pq The switching time required for the workpiece p to be adjacent to the workpiece q on the same lithography machine. In the dynamic scheduling problem of the photolithography process for the present invention, if two workpieces use the same reticle, the switching time between the two is zero, otherwise a certain switching time is required. The above lithography process scheduling problem can be described by a mixed integer programming model, as follows:

S.t.

St _j ≥r _j ,j=1,2,...,n (2)

Am _j ∈μ _j ,j=1,2,...,n (3)

_{_{st l, j -st l, i}} ≥p l, i + s ij ∪st l, i -st l, j ≥p l, j + s ji

k=1,2,...,m,i,j=1,2,...,n,i≠j (4)

Among them, (1) represents the optimization goal, (2) represents the workpiece release time constraint, (3) represents the machine fit constraint, and (4) represents the device uniqueness constraint and the workpiece switching time constraint.

(2) Problem decomposition

In order to solve the above scheduling model, the present invention first decomposes the above scheduling problem, and decomposes the original scheduling problem into a device selection scheduling sub-problem and an artifact scheduling sub-problem. The two scheduling sub-problems can be described as follows:

(1) device selection scheduling subproblem

Let Θ _k be the set of all the workpieces assigned to the lithography machine k, and f(Θ _k ) is the total weighted flow time corresponding to the workpieces in the set Θ _k . The mathematical model of the device selection scheduling sub-problem is described as follows:

S.t.

Am _j ∈μ _j ,j=1,2,...,n (6)

Equation (5) is the objective function corresponding to the model, and Equation (6) indicates that the device allocation scheme of the workpiece should satisfy the device suitability constraint. It can be seen that the search space of the model is greatly reduced compared with the original problem, because there is no need to give a specific workpiece sorting scheme.

(2) Workpiece scheduling scheduling subproblem

Given the solution of the device selection scheduling subproblem, ie Θ _k (k=1,2,...,m), the workpiece scheduling subproblem can be regarded as m independent suboptimization problems, where k The suboptimization problem can be described as follows:

S.t.

St _j ≥r _j ,j∈Θ _k (8)

_{_{st l, j -st l, i}} ≥p l, i + s ij ∪st l, i -st l, j ≥p l, j + s ji

i,j∈Θ _k ,i≠j (9)

Equation (7) corresponds to the objective function of device k (ie, total weighted transit time), equation (8) represents the release time constraint of the workpiece, and equation (9) represents the device uniqueness constraint and the preparation time constraint.

(III) Construction of forecasting model for performance indicators of dispatching subproblems

After the above problem decomposition is completed, in the present invention, a performance index prediction model of the workpiece sorting scheduling sub-problem will be established. It should be noted that, in the present invention, the performance indicator prediction model is not based on the solution of the given workpiece scheduling sub-problem, but directly uses the key features corresponding to the workpiece scheduling sub-question as input to perform scheduling. Sub-problem performance indicator forecast.

The present invention employs a minimum norm extreme learning machine (MN-ELM) to establish a performance indicator prediction model for the above-described scheduling sub-problem.

The input feature extraction is first performed. After analyzing the characteristics of the above-mentioned workpiece sorting scheduling sub-problem, combined with a large number of numerical calculation experiments, we determined the following problem feature quantity as the input of the performance index of the workpiece sorting scheduling sub-problem for forecasting a given machine:

The total weighted processing time of the workpieces assigned to the machine l:

● Number of reticle categories: NB

● The concentration of the workpiece release time assigned to the current lithography machine: Cr

● The objective function value obtained by the minimum weighted processing time rule: TWFT _swpt

● The interval i corresponds to the total number of workpieces: | Ω _i |, i = 1, 2, ..., I.

● The interval i corresponds to the total weighted processing time of the workpiece:

i=1,2,...,I.

Wherein, p _l,j , w _j and r _j are the processing time, weight and release time of the workpiece j on the lithography machine 1, respectively, j=1, 2, . . . , n, Ω _i is the workpiece assigned to the interval i The method of dividing the interval is to divide the entire scheduling time axis into I intervals, I is an integer, and the length of each interval is u=(r _i,max +p _i,max -r _i,min )/I, p _i,max is the maximum processing time in all workpieces, r _i,max and r _i,min are

The maximum and minimum values of all workpiece release times, the starting time of the interval is r _i,min ;

According to the above feature selection method, the sub-sequence problem of the workpiece sorting for a given machine is used to construct the performance index prediction model of the sub-problem problem. There are 2I+4 features, wherein the value of I is [4] according to the problem scale. , 8] interval prediction effect is better. Cr is an indicator reflecting whether there is congestion in front of the machine. The larger the value, the greater the possibility of congestion.

The calculation steps for Cr are as follows:

1) Let L _i (i = 1, 2, ..., I) represent the total load of the i-th interval, and L _i,j be the contribution of the workpiece j to L _i .

2) For the workpiece j(j∈Ω _i ), let st _j =r _j , then c _j =r _j +p _l,j , calculate L _i,j by the formula (10):

3) Calculate the total negative of the i-th interval

4) Calculate Cr by equation (11):

Two interval-related properties, |Ω _i | and

It is calculated as follows.

1) Sort all the workpieces in order of their release time from small to large, without loss of generality, remember j' ₁ , j' ₂ , ..., j' _n for each workpiece after sorting, r' ₁ , r' ₂ ,...,r' _n is the corresponding release time.

2) For the workpiece j' _k (i = 1, 2, ..., n), if iu ≤ r' _k < (i +1) u holds, where i is the sequence number of the time window, then j' _k belongs to the ith The collection of artifacts corresponding to the time window.

3) For each time window, |Ω _i | is the number of workpieces corresponding to the time window,

The sum of the weighted processing times of the workpiece corresponding to the time window.

Based on the above input feature attributes, based on the Extreme Learning Machine (ELM) model framework, the following steps are used to establish a scheduling sub-problem performance indicator prediction model. It should be noted that the training data required for the training process of the scheduling sub-problem performance indicator prediction model is gradually obtained with the operation of the algorithm. Therefore, the extreme learning machine used should be based on the online learning framework.

Step (1): Model parameter initialization

For a given N samples, the input is recorded as

Where x _i represents a vector consisting of 2I + 4 dimensional data per i samples; the corresponding output of the N sample inputs is recorded as

y _i is the performance indicator value of the corresponding scheduling sub-problem;

Given the number L of hidden layer nodes of the extreme learning machine based on structural risk minimization, the radial basis function is used as the feature transformation function, and the function form is

i = 1, 2, ..., L, where a _i , b _i are the parameters of the radial basis function, the a _i dimension is 2I + 3 dimensions, the value is randomly selected from [-1 1], b _i is 1 Dimension, the value is from

Random selection; according to the approximation theory of the extreme learning machine algorithm, as long as the number of hidden layer nodes is large enough, the algorithm can approximate any function with arbitrary precision. Therefore, in the present invention, the number of hidden layer nodes can be selected as a relatively large value, such as L. >20.

Thus, the generated extreme learning machine feature mapping matrix H(X) is:

Step (2): Algorithm initialization

For the time t, the weighting parameter W _{t of the} extreme learning machine ELM is initialized to:

among them:

X _t represents the sample that has been obtained at time t, and the number of samples is N, so the resulting extreme learning machine mapping matrix is:

ν is the penalty coefficient;

Step (3): Online learning process

For the t+1 time, it is assumed that the number of newly arrived samples is k, and the input corresponding to the newly arrived sample is

Output is

The extreme learning machine mapping matrix formed by the newly arrived sample data is then:

The t+1 time limit learning machine weight parameter W _t+1 is updated as follows:

W _t+1 =K _t W _t +K _t A _t ^-1 H(X _IC ) ^T Y _IC

among them:

K _t =IA _t ^-1 H(X _IC ) ^T [H(X _IC )A _t ^-1 H(X _IC ) ^T +I _k×k ] ^-1 H(X _IC )

A _t+1 ^-1 =K _t A _t ^-1

I _{k × k} is an identity matrix with a diagonal of 1;

K _t and A _t ^-1 are introduced intermediate variables, thereby simplifying the expression of the updated weight parameter W _t+1 ;

Step (4): termination of the training process

When all the training data are involved in the training, the training process is terminated, and the limit learning machine weight parameter W after the training is completed is output;

(4) Differential evolution algorithm based on performance indicator prediction model and solution similarity analysis

The invention proposes a differential evolution algorithm based on the performance index prediction model and the solution similarity analysis, which is used to solve the dynamic scheduling problem of the original lithography process, and dynamically gives a scheduling scheme. The proposed differential evolution algorithm is performed on the computer by the following steps:

Step (1): Algorithm initialization

The solution for each device selection scheduling subproblem can be expressed as:

A=[r ₁ ,r ₂ ,...,r _n ]

Where r _j is a real number indicating that the workpiece j corresponds to the processing machine, r _j ∈(0, |μ _j |].

In the algorithm initialization, the solution of the NP device selection scheduling sub-problems is first generated to form an initial solution set (also referred to as an initial population), which is generated for each workpiece from its corresponding optional device set μ _j . Select a device as its processing device. At the same time, several parameters in the differential evolution algorithm (DE) are set, including the crossover rate CR and the scaling factor F. In the present invention, CR ∈ [0, 1], F ∈ [0.5, 1]. The stopping condition of the algorithm is that the running time of the algorithm reaches the running time limit.

In the algorithm initialization, it is also necessary to train to generate an initial scheduling sub-problem performance indicator prediction model. In the problem addressed by the present invention, once the solution of the device selection scheduling sub-problem in the solution set is given, then each parameter in the ordering sub-question is also determined. The present invention employs a branch and bound algorithm (B&B) (Rabia Nessah, Imed Kacem. Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates. Computers & Operations research, 2012, 39: 471-478 ) to solve each sorting sub-problem separately, so as to obtain the corresponding performance index value of each device selection scheduling sub-problem solution. After the above solution process is completed, the obtained data can be used, and the initial scheduling sub-problem performance index prediction model is generated by the method of the foregoing third section. In the algorithm initialization phase, the number of solutions that are accurately evaluated is N ₀ , and in the present invention, N ₀ = NP/2 is selected.

Step (2): Differential variation

For each solution in a given set of solutions, the similarity matrix of the solution is first calculated:

among them,

Indicates the distance between solution i and solution j,

Represents the ith solution in the g-th set of solutions. Further, the example is defined as:

Where 1 (·) is the indication function, if

Established

otherwise

The smaller the distance, the higher the similarity between the two solutions.

Based on the above solution similarity matrix M _d , the selection probability matrix M _{p is} calculated:

Where i, j = 1, 2, ..., NP. Randomly select a solution from the current solution set, denoted as

Selection probability matrix select probability vector obtained M _p M _p (r _1, ·) (i.e., the probability of selecting _a r-th row of the matrix M _p), for the selection probability vector, roulette embodiment of the method, selecting based on two mutually The same solution (ie, the probability of selection is approximately inversely proportional to its distance). Without loss of generality, remember that the other two solutions selected are

Use the following formula to obtain the modified solution:

Step (3): Cross operation

In the present invention, the crossover operation of the solution is performed by the following method: the post-variation solution for the step (2)

For each element, a real number r∈[0,1] is randomly generated. If r≤CR, the element replaces the element in the corresponding position in the target solution, otherwise the element in the corresponding position in the target solution is retained.

Step (4): Evaluation and selection

After the above optimization operation is completed, the present invention needs to evaluate all target solutions in the solution set. The evaluation process is divided into two phases, first with a rough evaluation and second with an accurate evaluation. In the rough evaluation stage, the performance evaluation model of the scheduling sub-problem established above is used to evaluate the performance of each device selection scheduling sub-problem in the solution set (and also each solution in the differential evolution algorithm solution set). On the top, the better solution of the pre-p is selected (that is, the corresponding total weighted solution with a smaller time), and the branching and delimiting algorithm is used to accurately evaluate it. The data obtained by the accurate evaluation is also used for the online training of the performance evaluation model of the sub-problem, and the online training method is as described in the third section. After the evaluation process is completed, a new next-generation solution set is selected from the solution set using the standard roulette method.

DRAWINGS

Figure 1: Schematic diagram of hardware system structure of dynamic scheduling method for lithography process based on index prediction and solution similarity analysis.

Figure 2: Schematic diagram of the lithography process dynamic scheduling method based on indicator prediction and solution similarity analysis.

Detailed ways

The dynamic scheduling method proposed by the invention relies on a related data acquisition system, and is implemented by a scheduling system client and a scheduling server. A schematic diagram of a software and hardware architecture for applying the present invention to dynamic scheduling of a lithography area of an actual semiconductor production line is shown in FIG. 1, and an embodiment of the present invention is as follows.

Step (1): Obtain data corresponding to the dynamic scheduling problem of the lithography area of the above semiconductor production line.

Including the number of devices, the release time of each device, the release time of the workpiece to be processed / processing time / priority / processable machine group information, and stored in the scheduling database, and the method of the first section of the "invention content" is used to form An example of a dynamic scheduling problem in a lithography area of a semiconductor production line to be solved.

Step (2): Decomposition of dynamic scheduling problem in lithography area

For the obtained lithography zone dynamic scheduling problem instance, the method is decomposed into the device selection scheduling sub-problem and the workpiece scheduling scheduling sub-problem by the method of the second section of the "Summary of the Invention". In the subsequent steps, the above two sub-problems are iteratively solved to form a final lithography zone dynamic scheduling scheme.

Step (3): Solving the dynamic scheduling problem in the lithography zone

For the above example of the dynamic scheduling problem of the lithography zone, the methods of the third section and the fourth section of the "invention content" are used to solve the above problem, and a dynamic scheduling scheme is formed.

Step (3.1): Initialization of differential evolution algorithm

Set the parameters related to the differential evolution algorithm and the scheduling sub-problem performance indicator prediction model:

The solution set size in the differential evolution algorithm: NP=30;

Scaling factor in differential evolution algorithm: F=0.95;

Crossover rate in differential evolution algorithm: CR=0.5;

Accurate evaluation ratio in differential evolution algorithm: p=20%;

Stop conditions in differential evolution algorithms: different algorithms need to be set according to different problem scenarios. Line time limit, see the description of the results of subsequent experiments;

Step (3.2): Scheduling subproblem performance indicator prediction model initialization

Interval division parameter in the performance index prediction model of the scheduling sub-problem: I=6;

The parameters of the radial basis function in the performance index prediction model of the scheduling sub-problem: a _i dimension is 2I+3 dimensions, and the value of each dimension is randomly selected from [-1 1], b _i is 1 dimension, Value from

choose randomly;

The number of hidden layer nodes in the performance model of the scheduling sub-problem performance indicator: L=20;

The penalty factor ν in the performance model of the scheduling sub-problem performance indicator is 2 ^-15 according to experience;

Based on the above parameter setting, using the method of the fourth step (2) of the "Summary of the Invention" of the present invention, the NP initial solutions of the device selection scheduling sub-problem are generated to form an initial solution set, and then NP/2 solutions are randomly selected. The branch and bound algorithm is used for accurate evaluation, and the scheduling objective function value corresponding to each solution (ie, the total weighted transit time) is obtained. On this basis, using the prediction model learning method in the third section of "Invention Content", using the obtained scheduling sub-problem and its corresponding objective function value data, the initial scheduling sub-problem performance index prediction model is obtained.

Step (3.3): Differential Variation and Crossover

Using the method of step (3) and step (4) of the fourth section of the "Summary of the Invention", the solution in the solution set is first subjected to a differential mutation operation, and then the cross operation is performed. After the operation is completed, a new solution set is formed.

Step (3.4): Evaluation and selection

Using the method of the fourth section of the "Summary of the Invention" (5), the solution in the solution set is firstly evaluated by the scheduling sub-problem performance indicator prediction model. On this basis, the better solution of the pre-p% is selected to be accurate. Evaluation, then, using standard roulette methods to select, forming a new generation of solution sets.

Step (3.5): Online training updates the prediction model parameters to form a new scheduling sub-problem performance indicator prediction model

Using the method of Section III of the "Invention", combined with the accurate evaluation data of the pre-p% better solution obtained in step (3.4), online training, updating the original forecast model parameters, forming a new scheduling sub-problem performance index forecasting model .

Step (3.6): Algorithm termination condition discrimination

If the running time of the algorithm has reached the set value, stop; otherwise, go to step (3.3) for iterative optimization.

According to the above-mentioned lithography process dynamic scheduling method based on index prediction and solution similarity analysis, the present invention performs a large number of simulation experiments, and the running hardware environment is: P4 2.8 GHz CPU, 4 G RAM, and operating system is Windows 7. Due to space limitations, only some of the experimental results are listed. First, based on the production data of the actual lithography area, several examples of dynamic scheduling problems are randomly generated, wherein the processing time, weight, and release time of the workpiece are generated as follows:

p _l,j ～U[1,20]

w _j ~U[1,10]

Among them, δ(δ∈R ⁺ ) is the blocking coefficient, which reflects the intensity of the workpiece release interval in this problem; n is the number of workpieces, m is the number of machines, U[·,·] represents the uniform distribution of the given range, avg (p _l,j ) is the average of all processing times. In order to verify the effectiveness of the method of the present invention, random disturbances are applied to the processing time and release time parameters of the workpiece based on the above-mentioned problem examples. Table 1 lists the scheduling method proposed by the present invention (abbreviated as SM-DE) and the typical differential evolution optimization algorithm in the literature (MGEpitropakis, DKTasoulis, NGPavlidis, VPPlagianakos, MNVrahatis. Enhance differential evolution utilizing proximity-based mutation operators. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 99-119, abbreviated as Pro-DE) Application comparison on instances of randomly generated scheduling problems.

Table 1 Comparison of experimental results

In Table 1, avg _TFT and std _TFT are respectively the average value and variance of the total weighted transit time obtained by solving the problem with the corresponding algorithm for 20 times. The algorithm allows the running time to be 100 seconds. Marked as "blackened". It can be seen that SM-DE is superior to Pro-DE algorithm in most cases under the condition that the algorithm allows the same running time.

Claims

A lithography process dynamic scheduling method based on index prediction and solution similarity analysis, characterized in that the method is an iterative optimization process based on solution similarity analysis, and the workpiece obtained by accurate evaluation is continuously utilized. Sorting the scheduling sub-problem instance and the scheduling solution performance index data, and performing on-line learning on the workpiece ranking scheduling sub-problem performance index prediction model to improve the prediction accuracy of the prediction model, thereby improving the optimization efficiency and effect of the differential evolution algorithm; On the computer, follow the steps below to achieve:

Step (1): obtaining data corresponding to a dynamic scheduling problem of a lithography area of a semiconductor production line;

Obtaining data related to the dynamic scheduling problem of the lithography area based on the manufacturing execution system or other data acquisition system on the semiconductor production line, specifically including the number of available devices in the lithography area, the release time of each device, the type and number of lithography plates, and the to-be-processed The release time/processing time/priority/processable device information of each workpiece is stored in the scheduling database to form an example of the dynamic scheduling problem of the lithography area of the semiconductor production line to be solved;

Step (2): Decomposition of dynamic scheduling problem in lithography area

For the obtained lithography zone dynamic scheduling problem instance, the instance is decomposed into a device selection scheduling sub-problem and an artifact scheduling sub-problem;

Step (3): Solving the dynamic scheduling problem in the lithography zone

Step (3.1): Initialization of differential evolution algorithm

Set the parameters related to the differential evolution algorithm and the scheduling sub-problem performance indicator prediction model:

The solution set size NP in the differential evolution algorithm is between the intervals [20, 1000];

The scaling factor F in the differential evolution algorithm, between intervals [0.5, 1];

The crossover rate CR in the differential evolution algorithm is between the intervals [0, 1];

The exact ratio p in the differential evolution algorithm is between the intervals [10%, 30%];

Stop conditions in the differential evolution algorithm: different algorithm runtime limits need to be set according to different needs, between intervals [5 seconds, 2000 seconds];

Step (3.2): Scheduling subproblem performance indicator prediction model initialization

Interval division parameter I in the sub-problem performance indicator prediction model, between intervals [4, 8];

The parameters of the radial basis function in the performance index prediction model of the scheduling sub-problem: a i dimension is 2I+3 dimensions, and the value of each dimension is randomly selected from [-11], b i is 1 dimension, and the value is For
Random selection; the number of hidden layer nodes L in the performance model of the scheduling sub-problem performance indicator is between the intervals [5, 100];

The penalty factor ν in the performance model of the scheduling sub-problem performance indicator is 2 -15 according to experience;

On the basis of the above parameter settings, the NP initial solutions of the device selection scheduling sub-problem are randomly generated to form an initial solution set, and then 1 to NP solutions are randomly selected, and the branch and bound algorithm is used for accurate evaluation, and the corresponding scheduling is obtained. The objective function value; on this basis, using the online learning method of the extreme learning machine, using the obtained scheduling sub-problem and its corresponding objective function value data, the initial scheduling sub-problem performance index prediction model is obtained;

Step (3.3): Differential Variation and Crossover

For the solution in the solution set, the distance matrix is first calculated. On this basis, the differential mutation operation based on the solution similarity analysis is performed, and finally the cross operation is performed; after the operation is completed, a new solution set is formed;

Step (3.4): Evaluation and selection based on the combination of rough evaluation and accurate evaluation

For the solution in the solution set, the scheduling sub-problem performance indicator prediction model is firstly used for rough evaluation. On this basis, the 1 to NP better solution is selected from the current solution set for accurate evaluation, and then the standard roulette method is used. Select to form a new generation of solution sets;

Step (3.5): using the online learning method of the extreme learning machine, online learning to update the scheduling sub-problem performance index prediction model parameters, and forming a new scheduling sub-problem performance index prediction model;

Step (3.6): Algorithm termination condition discrimination

If the running time of the algorithm has reached the set value, stop; otherwise, go to step (3.3) for iterative optimization.
The lithography process dynamic scheduling method based on the indicator prediction and the solution similarity analysis according to claim 2,

The input of the scheduling sub-problem performance indicator prediction model includes the following attributes:

The total weighted processing time of the workpieces assigned to the machine l:

● Number of reticle categories: NB

● The concentration of the workpiece release time assigned to the current lithography machine: Gr

● The objective function value obtained by the minimum weighted processing time rule: TWFT swpt

● The interval i corresponds to the total number of workpieces: | Ω i |, i = 1, 2, ..., I.

● The interval i corresponds to the total weighted processing time of the workpiece:

Where p l, j , w j and r j are the processing time, weight, and release time of the workpiece j on the lithography machine 1, respectively, j=1, 2, ..., n, Ω i are the workpieces assigned to the interval i The method of dividing the interval is to divide the entire scheduling time axis into I intervals, I is an integer, and the length of each interval is u=(r i,max +p i,max -r i,min )/I, p i,max is the maximum processing time in all workpieces, r i,max and r i,min are the maximum and minimum values of the release time of all workpieces, and the starting time of the interval is r i,min ;

The calculation steps for Cr are as follows:

1) Let L i (i = 1, 2, ..., I) represent the total load of the i-th interval, and L i,j be the contribution of the workpiece j to L i ;

2) For the workpiece j(j∈Ω i ), let st j =r j , then c j =r j +p l,j , calculate L i,j by the following formula:

3) Calculate the total load of the i-th interval

4) Calculate Cr by the following formula:

Among the above attributes, two attributes related to the scheduling time interval, |Ω i | and
The calculation steps are as follows:

1) All the workpieces on the lithography machine are sorted in order of their release time, without loss of generality, and j' 1 , j' 2 , ..., j' n are sorted workpieces, r' 1 , r′ 2 ,...,r′ n is the corresponding release time;

2) For the workpiece j' k (k = 1, 2, ..., n), if iu ≤ r' k < (i +1) u holds, where i is the number of the time window, then j' k belongs to the ith a collection of artifacts corresponding to the time window;

3) For each time window, |Ω i | is the number of workpieces corresponding to the time window,
The sum of the weighted processing times of the workpiece corresponding to the time window;

According to the above input attribute selection method, the sub-question scheduling sub-problem for a given single device has 2I+4 features for constructing the prediction model. According to the problem scale, the value of I is in the interval [4,8]. ]between.