CN101782769B - Quick prediction method of average flowing-through time on basis of index compensation - Google Patents

Abstract

Average flowing-through time is an important scheduling index to which enterprises pay attention. When a dispatching method based on soft computing and the like is used for optimizing dispatch, global simulation is required to be carried out on a dispatching strategy to obtain a corresponding average flowing-through time index; the process needs to be carried out several times; the process consumes longer time if used for building an accurate simulation model for a whole larger scale production line as well as used for global simulation on the dispatching strategy; thus, quick prediction of the average flowing-through time index has the important meaning for improving the performance of the dispatching algorithm. The invention discloses a quick prediction method of average flowing-through time on basis of index compensation, which divides a machine group into a bottleneck machine group and a non-bottleneck machine group so as to loosen the working capability of the non-bottleneck machine group to build a simplified dispatching model; then, an SVM (support vector machine) is used for obtaining the compensation relationship between the corresponding average flowing-through time indexes of the simplified dispatching model and a non-simplified dispatching model, thus realizing the quick prediction of the average flowing-through time index.

Description

A kind of quick prediction method of average flowing-through time based on index compensation

Technical field

The invention belongs to automatic control, infotech and advanced manufacturing field.Be specifically related in extensive, non-equilibrium production line Optimization Dispatching process a kind of quick prediction method of average flowing-through time based on index compensation.

Background technology

Average flowing-through time is an important scheduling index of enterprises pay attention, by the reasonable optimizing scheduling, can significantly improve this index.Utilization is optimized in the scheduling process based on the dispatching method of soft calculating etc., need carry out global simulation to obtain the average flowing-through time index to scheduling strategy, and These parameters computation process need repeatedly be carried out, if whole fairly large production line is set up accurate realistic model and scheduling strategy is carried out global simulation, consuming time longer, this has greatly limited the application of above-mentioned dispatching method in the scheduling of practical large-scale production run.Thereby, the average flowing-through time index of scheduling strategy correspondence is carried out fast prediction, significant to the performance that improves dispatching algorithm.

At present, existing average flowing-through time Forecasting Methodology mainly is to information such as length, goods in process inventory, machinery utilization rates according to the queuing before the moment each the machine group of whole process of production that feeds intake, adopt methods such as waiting line theory or neural network that average flowing-through time is predicted, these class methods can only be carried out macroscopic evaluation to the average flowing-through time index of production run in longer a period of time in future, be used to instruct the enterprise's whole decision and the production schedule, be difficult to embody the otherness of different scheduling schemes in the short time, thereby can't be applied in the scheduling process.

Summary of the invention

The present invention is directed to that a class is extensive, the above-mentioned average flowing-through time index prediction difficult problem in the Optimization Dispatching process of non-equilibrium production line (as semiconductor production line), a kind of quick prediction method of average flowing-through time based on index compensation is disclosed.This method is based on the non-equilibrium characteristics of production line, the machine group is divided into bottleneck and non-bottleneck machine group, and then lax non-bottleneck machine group working ability is set up the simplification scheduling model, utilize SVM (support vector machine) to simplify compensation relationship between the average flowing-through time index of scheduling model and non-simplification scheduling model correspondence then, thereby realize fast prediction the average flowing-through time index.This method can be used for the quick evaluation to the average flowing-through time index of scheduling strategy correspondence in dispatching algorithms such as soft calculating, to improve algorithm iteration optimizing efficient.

A kind of quick prediction method of average flowing-through time based on index compensation disclosed in this invention is realized on computers according to the following steps:

Step (1): initialization:

Based on the following information that from actual production process, obtains: the processing route of the machine quantity of machine group quantity, each machine group correspondence, workpiece kind to be scheduled and all kinds of quantity, all kinds of workpiece, the process time of each each operation of workpiece, form former scheduling problem in the whole production line;

Step (2): after initialization is finished, the scheduling rule of each machine group is made as the SRPT rule, wherein the SRPT rule is residue reckling priority rule process time, carries out the identification of bottleneck machine group according to the following steps:

Step (2.1): carry out the emulation of former scheduling problem, obtain each operation and arrive the time of machine group buffer zone and the simulation result data that this operation machines the time;

Step (2.2): determine the time of each operations flows through the machine group by following formula

${\mathrm{\δ}}_{j_{k}l}=b_{j_{k}l}-a_{j_{k}l}$ j＝1，2，…，n；l＝1，2，…，m

Wherein,

Be respectively time and this operation that k operation that j workpiece process arrive machine group buffer zone and machine the time on machine group l; M is the quantity of machine group; N is the quantity of workpiece;

Step (2.3): the average flowing-through time that is calculated as follows all operations of the machine group l correspondence of flowing through is

${\stackrel{\‾}{\mathrm{\δ}}}_l=\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{l_j}{\mathrm{\Σ}}}{\mathrm{\δ}}_{j_{k}l}}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j}$

N is a workpiece quantity in the formula, l _jRepresent the operation amount that j workpiece processed on machine group l;

Step (2.4): the average flowing-through time that is calculated as follows all workpiece

$\stackrel{\‾}{f}=\frac{\underset{l=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j{\stackrel{\‾}{\mathrm{\δ}}}_l}{n}$

Step (2.5): according to

Order is from big to small carried out the ordering of machine group bottleneck degree, each the machine group after the note ordering Value sequence is { β ₁, β ₂..., β _m, determine bottleneck machine group quantity b by following formula:

$\underset{b}{\min }\frac{\underset{i=1}{\overset{b}{\mathrm{\Σ}}}{\mathrm{\β}}_i}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\β}}_i}\≥80\%$

Choose { β ₁, β ₂..., β _mIn before b the pairing machine group of value be bottleneck machine group;

Step (3): on bottleneck machine group identification basis, carry out scheduling model as follows and simplify:

Step (3.1): keep the relevant schedule constraints of bottleneck machine group correspondence constant, it is constant to comprise that maintenance can not be interrupted constraint, machine unique constraints and workpiece unique constraints;

Step (3.2): lax non-bottleneck machine group working ability is infinitely great, does not promptly consider to operate in the stand-by period on the non-bottleneck machine group, and the process time of directly using corresponding operating is as its flow time on this machine group;

Step (4): simplify on the basis in identification of bottleneck machine group and scheduling model, extract input feature vector attribute vector and the export target attribute data that training SVM needs according to following steps, and the SVM correlation parameter is trained, wherein SVM expresses support for vector machine:

Step (4.1): all operations to be scheduled to each machine group correspondence produces an ordering respectively at random, and ranking results as a scheduling strategy, is carried out emulation based on above-mentioned simplification scheduling model to production line, obtains each workpiece completion date sequence { sf ₁, sf ₂..., sf _n, wherein sequence satisfies sf ₁≤ sf ₂≤ ... ≤ sf _nRelation, and it is as follows to calculate its corresponding average flowing-through time:

$\stackrel{\‾}{\mathrm{sf}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{sf}}_i}{n}$

Step (4.2):, extract SVM input feature vector attribute vector as follows based on the workpiece completion date sequence of above-mentioned acquisition:

Step (4.2.1): the completion date of determining adjacent workpieces in the workpiece completion date sequence by following formula at interval forms workpiece completion date interval data sequence t ₁, t ₂..., t _N-1:

t _i＝sf _i+1-sf _i，i＝1，2，…，n-1

Step (4.2.2): according to following formula above-mentioned workpiece completion date interval data sequence is divided into the K group successively, note N=n-1, every group number is:

$b_k=\left\{\begin{array}{c}[N/K],k=\mathrm{1,2},\·\·\·,K-1\\ N-[N/K]\×(K-1),k=K\end{array}\right.$

Step (4.2.3): press the characteristic attribute vector that following formula extracts workpiece completion date interval data sequence:

X＝[m _m，m _σ，σ _m，σ _σ] ^T

Wherein: X represents the input feature vector attribute vector of current training sample

$m_{\mathrm{tk}}=\left\{\begin{array}{cc}\frac{\underset{i=(k-1)\×b_k+1}{\overset{k\×b_k}{\mathrm{\Σ}}}{t}_i}{b_k},& k=\mathrm{1,2},\·\·\·,K-1\\ \frac{\underset{i=(K-1)\×b_k+1}{\overset{N}{\mathrm{\Σ}}}{t}_i}{b_k},& k=K\end{array}\right.$

${\mathrm{\σ}}_{\mathrm{tk}}=\left\{\begin{array}{cc}\frac{1}{b_k}\underset{i=(k-1)\×b_k+1}{\overset{k\×b_k}{\mathrm{\Σ}}}{(t_i-m_{\mathrm{tk}})}^2,& k=\mathrm{1,2},\·\·\·,K-1\\ \frac{1}{b_k}\underset{i=(K-1)\×b_k+1}{\overset{N}{\mathrm{\Σ}}}{(t_i-m_{\mathrm{tk}})}^2,& k=K\end{array}\right.$

$m_m=\frac{\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{m}_{\mathrm{tk}}}{K},$ $m_{\mathrm{\σ}}=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{(m_{\mathrm{tk}}-m_m)}^2$

${\mathrm{\σ}}_m=\frac{\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\σ}}_{\mathrm{tk}}}{K},$ ${\mathrm{\σ}}_{\mathrm{\σ}}=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{({\mathrm{\σ}}_{\mathrm{tk}}-{\mathrm{\σ}}_m)}^2$

Step (4.3): based on resulting scheduling strategy in the step (4.1), former scheduling problem is carried out emulation based on non-simplified model, utilize the computing formula of step (2.4), obtain the average flowing-through time of all workpiece Determine objective attribute target attribute value in the current training sample according to following formula:

$\mathrm{\Δf}=\stackrel{\‾}{f}-\stackrel{\‾}{\mathrm{sf}}$

Step (4.4): repeating step (4.1)～step (4.3) is pressed following formula and is formed training sample set until satisfying the training sample quantity S requirement of setting:

Input feature vector attribute vector collection: XX=[X ₁, X ₂..., X _S]

Export target property set: ff=[Δ f ₁, Δ f ₂..., Δ f _S]

Step (4.5): the input feature vector attribute vector collection and the export target property set that utilize training sample set to provide, SVM is trained as follows:

Utilize the quadratic programming algorithm, find the solution optimization problem:

$\underset{\mathrm{\α},{\mathrm{\α}}^{*}}{\max }\{-\mathrm{\ϵ}\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({{\mathrm{\α}}_i}^{*}+{\mathrm{\α}}_i)+\underset{i=1}{\overset{S}{\mathrm{\Σ}}}\mathrm{\Δ}{f}_i({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)-\frac{1}{2}\underset{i=1}{\overset{S}{\mathrm{\Σ}}}\underset{j=1}{\overset{S}{\mathrm{\Σ}}}{({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)}^{T}K(X_i,X_j)({{\mathrm{\α}}_j}^{*}-{\mathrm{\α}}_j)\}$

s.t.

$\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({\mathrm{\α}}_i-{{\mathrm{\α}}_i}^{*})=\mathrm{0,0}\≤{\mathrm{\α}}_i,{{\mathrm{\α}}_i}^{*}\≤C,i=\mathrm{1,2},\·\·\·,S$

Wherein, ε is a given parameter value, Δ f _iBe the target output value of training set, K (X _i, X _j) be the radial basis function kernel function, form is:

$K(X_i,X_j)=\exp (-\frac{{\left|\right|X_i-X_j\left|\right|}^2}{2{\mathrm{\γ}}^2})$

X _iBe the characteristic attribute vector of input, γ is the gaussian kernel function width parameter.

After training is finished, set up the SVM regression function and be:

$\mathrm{\Δ}{f}_y\left(X\right)=\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)K(X_i,X)+b$

Wherein: the threshold value that b obtains for training, Δ f _y(X) be predicted value, i.e. the compensation rate of average flowing-through time, α to X _i ^*, α _iThe parameter of asking for for training;

Step (5):, in the optimizing process of dispatching algorithm,, determine average flowing-through time index prediction value according to following steps to given scheduling strategy at the simplification scheduling model that obtains former scheduling problem and after being used to calculate the SVM of average flowing-through time offset:

Step (5.1):, extract the input feature vector attribute vector X that SVM needs according to scheduling strategy given in the Optimization Dispatching process;

Step (5.2): the SVM regression function that utilizes training to obtain, calculate the average flowing-through time offset:

$\mathrm{\Δ}{f}_y=\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)K(X_i,X)+b$

Step (5.3): the average flowing-through time index prediction value that is calculated as follows above-mentioned scheduling strategy correspondence:

${\stackrel{\‾}{f}}_y=\stackrel{\‾}{\mathrm{sf}}+\mathrm{\Δ}{f}_y=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{sf}}_i}{n}+\mathrm{\Δ}{f}_y$

Wherein:

Be average flowing-through time index prediction value.

Average flowing-through time indicator quick prediction method disclosed in this invention can be used for the average flowing-through time of scheduling strategy correspondence is carried out fast prediction in the dispatching method based on soft calculating etc., and the performance that improves above-mentioned dispatching algorithm is had vital role.

Description of drawings

Fig. 1: average flowing-through time prognoses system structural drawing, the SVM training computer is realized the study of SVM correlation parameter according to simplifying scheduling model and non-simplification scheduling model simulation result among the figure, and correlation parameter passed to the average flowing-through time predictive computer, in the Optimization Dispatching process, the average flowing-through time predictive computer receives simplifies the completion date sequence that scheduling model emulation obtains, by extracting corresponding characteristic attribute vector, obtain the average flowing-through time desired value of the required input feature vector attribute vector of SVM and this simplification scheduling model correspondence, then the average flowing-through time predictive computer utilizes SVM to calculate the offset of average flowing-through time, and add the average flowing-through time desired value of simplifying the scheduling model correspondence, thereby obtain the average flowing-through time predicted value of above-mentioned optimisation strategy correspondence.

Fig. 2: the process flow diagram of in the Optimization Dispatching process, using for algorithm, on bottleneck machine group identification basis, in the Optimization Dispatching process, at first given scheduling strategy is carried out emulation based on simplifying scheduling model, obtain simplifying the completion date sequence of scheduling model correspondence, then, the average flowing-through time Forecasting Methodology of utilizing the present invention to provide, average flow time desired value prediction, according to predicting the outcome, given scheduling strategy is estimated and selected.

(b) (c) (d) for Fig. 3 (a): it is under 100 conditions that Fig. 3 (a) has provided in the workpiece scale, utilize the graph of errors between average flowing-through time predicted value that the present invention provides and the average flowing-through time actual value that emulation obtains based on non-simplification scheduling model, Fig. 3 (b) has provided the relative percentage of error, the i.e. number percent of the relative actual value of error amount; Fig. 3 (c) is the average flowing-through time actual value that emulation obtains based on non-simplification scheduling model; The average flowing-through time predicted value that Fig. 3 (d) provides for the present invention.

Embodiment

Workpiece quick prediction method of average flowing-through time of the present invention is realized by scheduling index prediction software.System forms (structural drawing is seen Fig. 1) by SVM training computer, average flowing-through time predictive computer.Training computer can be trained the SVM correlation parameter according to emulated data, obtains the SVM related parameter values.The flow time predictive computer receives SVM related parameter values and workpiece completion date sequence information, calculates the average flowing-through time predicted value.

Below above-mentioned quick prediction method of average flowing-through time specific embodiments that the present invention is proposed based on index compensation describe:

The first step: carry out the SVM training

At first determine machine group quantity, the machine quantity of each machine group correspondence, workpiece kind to be scheduled and all kinds of quantity, the processing route of all kinds of workpiece, information process time of each each operation of workpiece in the whole production line, form former scheduling problem, simultaneously, the better scheduling strategy of given each machine group correspondence is the SRPT rule; According to given initiation parameter information, middle to specifications step (2) is carried out the identification of bottleneck machine group then; On definite bottleneck machine group basis, carry out scheduling model according to step (3) and simplify; On bottleneck machine group identification and scheduling model simplification basis, utilize the method in the instructions of the present invention, according to step (4) SVM that is used to calculate average flowing-through time index compensation value is trained; Based on simplifying scheduling model and non-simplification scheduling model production line is carried out repeatedly emulation, generate the SVM training data that is used to calculate average flowing-through time index compensation value, and SVM is trained;

Second step: utilize the scheduling model and the SVM that simplify to average the prediction of flow time desired value

In scheduling process, for the corresponding scheduling strategy of given each machine group, at first adopt the simplification scheduling model of being set up to carry out emulation, obtain the average flowing-through time desired value of the required input feature vector attribute vector of SVM and this simplification scheduling model correspondence, utilize SVM to calculate average flowing-through time index compensation value then, to simplify the average flowing-through time desired value of scheduling model correspondence and the two addition of average flowing-through time index compensation value of calculating gained at last, obtain the average flowing-through time predicted value of this given scheduling strategy correspondence by SVM.

The present invention propose based on the quick prediction method of average flowing-through time process flow diagram of index compensation as shown in Figure 2.

According to the above-mentioned quick prediction method of average flowing-through time that proposes based on index compensation, the present invention has done a large amount of l-G simulation tests, because length is limit, and only provides the performance verification result who carries out method proposed by the invention at the semiconductor production process scheduling problem with 100 workpiece here.Wherein, totally 33 of machine groups, bottleneck machine group quantity by specification step (2.5) is determined, three class workpiece, quantity are respectively 30,30,40, and machine configuration set and associated workpiece experiment parameter see Table 1～4, the SVM parameter value is C=20, ε=0.1, γ=0.6.

The workpiece processing time in the configuration of table 1 workshop and each machine group

Table 2 processing route 1

ENTER-1-2-3-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-1-2-3-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-16-17-1-2-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-16-17-16-18-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-19-16-20-21-22-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-1-2-15-16-17-21-1-18-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-23-24-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-25-26-9-15-16-27-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-25-9-28-EXIT

Table 3 processing route 2

ENTER-1-2-3-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-1-2-3-1-2-3-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-16-17-21-1-2-3-26-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-16-17-16-18-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-29-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-29-16-20-21-1-2-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-1-2-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-23-24-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-25-30-9-15-5-7-5-31-9-9-15-32-27-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-26-9-33-24-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-26-9-15-28-EXIT

Table 4 processing route 3

ENTER-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-16-17-16-18-15-1-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-19-16-20-21-22-2-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-1-2-15-16-17-21-1-18-15-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-9-23-24-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-25-26-9-15-16-27-4，5，6-7，8-5，13，14，6-9-10-10-11-9-12-10-11-9-26-9-33-24-9-26-9-15-28-EXIT。

Workpiece average flowing-through time predicted value that the present invention provides and the comparison between the actual value are shown in Fig. 3 (a) and (b), (c), (d).It is under 100 conditions that Fig. 3 (a) has provided in the workpiece scale, utilize the graph of errors between average flowing-through time predicted value that the present invention provides and the average flowing-through time actual value that emulation obtains based on non-simplification scheduling model, Fig. 3 (b) has provided the relative percentage of error, the i.e. number percent of the relative actual value of error amount; Fig. 3 (c) is the average flowing-through time actual value that emulation obtains based on non-simplification scheduling model; The average flowing-through time predicted value that Fig. 3 (d) provides for the present invention.As seen in 2%, the absolute error maximal value is in 10 hours substantially for precision of prediction of the present invention; Simultaneously, be about 2s when finish a subline emulation based on non-simplification scheduling model to calculate the average flowing-through time required time, and adopt the present invention to finish the about 1.2s of average flowing-through time predicted time one time, the time has improved 40%.To adopt differential evolution algorithm to be solved to example, suppose that per generation population number is 30, iteration algebraically is 30, then finish whole scheduling process and need 900 subline emulation, need 1800s altogether, and the algorithm that adopts the present invention to provide, need and simplify scheduling model and carry out 20 subline emulation respectively based on non-simplification scheduling model, be total to 64s, about 1s of SVM training time, and then the index prediction method that adopts the present invention to propose is carried out 900 subline emulation, the about 1080s of required time, whole algorithm needs 1145s (the used time of other links of dispatching algorithm is identical) in the SVM training altogether with production line emulation link, with adopt non-simplified model to carry out production line emulation to compare, the used time has shortened about 36%, visible the present invention can be under the condition of guaranteeing the higher forecasting precision, significantly shortened the average flowing-through time index prediction time, created conditions towards the counting yield of the dispatching algorithm of fairly large production line thereby can be raising.

Claims (1)

1. the quick prediction method of average flowing-through time based on index compensation is characterized in that, described method is to realize according to the following steps successively on computers:

Step (1): initialization:

Based on the following information that from actual production process, obtains: the processing route of the machine quantity of machine group quantity, each machine group correspondence, workpiece kind to be scheduled and all kinds of quantity, all kinds of workpiece, the process time of each each operation of workpiece, form former scheduling problem in the whole production line;

Step (2): after initialization is finished, the scheduling rule of each machine group is made as the SRPT rule, wherein the SRPT rule is residue reckling priority rule process time, carries out the identification of bottleneck machine group according to the following steps:

Step (2.1): carry out the emulation of former scheduling problem, obtain each operation and arrive the time of machine group buffer zone and the simulation result data that this operation machines the time;

Step (2.2): determine the time of each operations flows through the machine group by following formula

${\mathrm{\δ}}_{j_{k}l}=b_{j_{k}l}-a_{j_{k}l}$ j＝1，2，…，n；l＝1，2，…，m

Wherein,

Be respectively time and this operation that k operation that j workpiece process arrive machine group buffer zone and machine the time on machine group l; M is the quantity of machine group; N is the quantity of workpiece;

Step (2.3): the average flowing-through time that is calculated as follows all operations of the machine group l correspondence of flowing through is

${\stackrel{\‾}{\mathrm{\δ}}}_l=\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{l_j}{\mathrm{\Σ}}}{\mathrm{\δ}}_{j_{k}l}}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j}$

N is a workpiece quantity in the formula, l _jRepresent the operation amount that j workpiece processed on machine group l;

Step (2.4): the average flowing-through time that is calculated as follows all workpiece

$\stackrel{\‾}{f}=\frac{\underset{l=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_j{\stackrel{\‾}{\mathrm{\δ}}}_l}{n}$

Step (2.5): according to

Order is from big to small carried out the ordering of machine group bottleneck degree, each the machine group after the note ordering

Value sequence is { β ₁, β ₂..., β _m, determine bottleneck machine group quantity b by following formula:

$\underset{b}{\min }\frac{\underset{i=1}{\overset{b}{\mathrm{\Σ}}}{\mathrm{\β}}_i}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\β}}_i}\≥80\%$

Choose { β ₁, β ₂..., β _mIn before b the pairing machine group of value be bottleneck machine group;

Step (3): on bottleneck machine group identification basis, carry out scheduling model as follows and simplify:

Step (3.1): keep the relevant schedule constraints of bottleneck machine group correspondence constant, it is constant to comprise that maintenance can not be interrupted constraint, machine unique constraints and workpiece unique constraints;

Step (3.2): lax non-bottleneck machine group working ability is infinitely great, does not promptly consider to operate in the stand-by period on the non-bottleneck machine group, and the process time of directly using corresponding operating is as its flow time on this machine group;

Step (4): simplify on the basis in identification of bottleneck machine group and scheduling model, extract input feature vector attribute vector and the export target attribute data that training SVM needs according to following steps, and the SVM correlation parameter is trained, wherein SVM expresses support for vector machine:

Step (4.1): all operations to be scheduled to each machine group correspondence produces an ordering respectively at random, and ranking results as a scheduling strategy, is carried out emulation based on above-mentioned simplification scheduling model to production line, obtains each workpiece completion date sequence { sf ₁, sf ₂..., sf _n, wherein sequence satisfies sf ₁≤ sf ₂≤ ... ≤ sf _nRelation, and it is as follows to calculate its corresponding average flowing-through time:

$\stackrel{\‾}{\mathrm{sf}}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{sf}}_i}{n}$

Step (4.2):, extract SVM input feature vector attribute vector as follows based on the workpiece completion date sequence of above-mentioned acquisition:

Step (4.2.1): the completion date of determining adjacent workpieces in the workpiece completion date sequence by following formula at interval forms workpiece completion date interval data sequence t ₁, t ₂..., t _N-1:

t _i＝sf _i+1-sf _i，i＝1，2，…，n-1

Step (4.2.2): according to following formula above-mentioned workpiece completion date interval data sequence is divided into the K group successively, note N=n-1, every group number is:

$b_k=\left\{\begin{array}{c}[N/K],k=\mathrm{1,2},\·\·\·,K-1\\ N-[N/K]\×(K-1),k=K\end{array}\right.$

Step (4.2.3): press the characteristic attribute vector that following formula extracts workpiece completion date interval data sequence:

X＝[m _m，m _σ，σ _m，σ _σ] ^T

Wherein: X represents the input feature vector attribute vector of current training sample

$m_{\mathrm{tk}}=\left\{\begin{array}{cc}\frac{\underset{i=(k-1)\×b_k+1}{\overset{k\×b_k}{\mathrm{\Σ}}}{t}_i}{b_k},& k=\mathrm{1,2},\·\·\·,K-1\\ \frac{\underset{i=(K-1)\×b_k+1}{\overset{N}{\mathrm{\Σ}}}{t}_i}{b_k},& k=K\end{array}\right.$

${\mathrm{\σ}}_{\mathrm{tk}}=\left\{\begin{array}{cc}\frac{1}{b_k}\underset{i=(k-1)\×b_k+1}{\overset{k\×b_k}{\mathrm{\Σ}}}{(t_i-m_{\mathrm{tk}})}^2,& k=\mathrm{1,2},\·\·\·,K-1\\ \frac{1}{b_k}\underset{i=(K-1)\×b_k+1}{\overset{N}{\mathrm{\Σ}}}{(t_i-m_{\mathrm{tk}})}^2,& k=K\end{array}\right.$

$m_m=\frac{\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{m}_{\mathrm{tk}}}{K},$ $m_{\mathrm{\σ}}=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{(m_{\mathrm{tk}}-m_m)}^2$

${\mathrm{\σ}}_m=\frac{\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\σ}}_{\mathrm{tk}}}{K},$ ${\mathrm{\σ}}_{\mathrm{\σ}}=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{({\mathrm{\σ}}_{\mathrm{tk}}-{\mathrm{\σ}}_m)}^2$

Step (4.3): based on resulting scheduling strategy in the step (4.1), former scheduling problem is carried out emulation based on non-simplified model, utilize the computing formula of step (2.4), obtain the average flowing-through time of all workpiece

Determine objective attribute target attribute value in the current training sample according to following formula:

$\mathrm{\Δf}=\stackrel{\‾}{f}-\stackrel{\‾}{\mathrm{sf}}$

Step (4.4): repeating step (4.1)～step (4.3) is pressed following formula and is formed training sample set until satisfying the training sample quantity S requirement of setting:

Input feature vector attribute vector collection: XX=[X ₁, X ₂..., X _S]

Export target property set: ff=[Δ f ₁, Δ f ₂..., Δ f _S]

Step (4.5): the input feature vector attribute vector collection and the export target property set that utilize training sample set to provide, SVM is trained; After training is finished, set up the SVM regression function and be:

$\mathrm{\Δ}{f}_y\left(X\right)=\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)K(X_i,X)+b$

Wherein:

Be gaussian kernel function, γ is the gaussian kernel function width parameter, the threshold value that b obtains for training, Δ f _y(X) be predicted value, i.e. the compensation rate of average flowing-through time, α to input feature vector attribute vector X _i ^*, α _iThe parameter that obtains after finishing for training;

Step (5):, in the optimizing process of dispatching algorithm,, determine average flowing-through time index prediction value according to following steps to given scheduling strategy at the simplification scheduling model that obtains former scheduling problem and after being used to calculate the SVM of average flowing-through time offset:

Step (5.1):, extract the input feature vector attribute vector X that SVM needs according to scheduling strategy given in the Optimization Dispatching process;

Step (5.2): the SVM regression function that utilizes training to obtain, calculate the average flowing-through time offset:

$\mathrm{\Δ}{f}_y=\underset{i=1}{\overset{S}{\mathrm{\Σ}}}({{\mathrm{\α}}_i}^{*}-{\mathrm{\α}}_i)K(X_i,X)+b$

Step (5.3): the average flowing-through time index prediction value that is calculated as follows above-mentioned scheduling strategy correspondence:

${\stackrel{\‾}{f}}_y=\stackrel{\‾}{\mathrm{sf}}+\mathrm{\Δ}{f}_y=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{sf}}_i}{n}+\mathrm{\Δ}{f}_y$

Wherein:

Be average flowing-through time index prediction value.

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