CN104794322A - Multi-target batch scheduling method for solar cell module limited relief area based on second DNSGA - Google Patents

Abstract

The invention discloses a multi-target batch scheduling method for a solar cell module limited relief area based on a second DNSGA, and aims at efficiently and rapidly providing an optimal scheduling method which can be used for producing solar cells in a large scale to be selected by a manager. The scheduling method comprises the steps that 1 according to constraint conditions and optimized target functions in the actual producing process of solar cell modules, a mathematic model used for the problem of multi-target batch scheduling of the limited relief area of the solar cell modules is established; 2 according to the disperse character and the multi-target batch character of the problem, a variant curve fitting method is adopted to initialize a species; 3 based on the otherness between individuals of a parent species and non-dominated solution valuable information, a novel variant crossover operator is designed, and the global and local performances of a provided algorithm are balanced.

Description

Based on the solar module limited buffer multiple goal lot size scheduling method of DNSGA-II

Technical field

The present invention relates to the field such as artificial intelligence and production management, essentially disclose the solar module limited buffer multiple goal lot size scheduling method based on DNSGA-II, effectively can shorten the production cycle, enhance productivity.

Background technology

Sun power is the green energy resource that the mankind are inexhaustible, nexhaustible.The Appropriate application of sun power is to sustainable development, energy-saving and emission-reduction, the active response of protection of the environment and advocating.The production of solar cell is then the only way which must be passed making full use of sun power, occupies national economy critical role.Manufacture of solar cells is on batch production basis, under meeting technique, device constraints, determines processing sequence and the process time of different model battery component, whole product completion date is minimized.The formulation of the scheduling scheme of reasonable science, can ensure enterprise's the making full use of of device resource in whole production run, meet the delivery date of supplier, make whole production system smooth and easy, steady, run efficiently.

The production of solar cell is typical batch pipeline schedule (Lot Streaming Flow shop, LSFS) problem.General fluvial incision basic premise is, (a criticizing) workpiece is complete, indivisible, but in actual manufacture of solar cells environment, the battery component of same model, in each technological process stage, may be partitioned into some transfer batch, each transfer batch after completion of processing, can allow to enter on next stage apparatus and process on current generation equipment.Such batch machining mode, can accelerate production procedure, reduces production cost, has engineering background and important theoretical research widely and is worth.

In reality is produced, due to the restriction such as cost, resource, there is limited intermediate buffer (stock), even do not have intermediate buffer, the workpiece of part completion of processing or product are blocked on current processing equipment in a lot of production run.Life cycle of the product is caused to postpone.Therefore, according to intermediate buffer (stock) classification, batch streamline can be divided into: traditional batch streamline, limited buffer batch streamline and obstruction batch pipeline schedule (as shown in Figure 1).

In recent decades, the derivation algorithm of a lot of scholar to batch fluvial incision is studied.For example, genetic algorithm (Genetic Algorithm, GA), harmonic search algorithm (Harmony Search, HS), particle cluster algorithm (Particle Swarm Optimization, PSO), discrete artificial bee colony algorithm (DiscreteArtificial bee colony, DABC), Estimation of Distribution Algorithm (estimation of the distributionalgorithm, EDA) etc.Although there be the batch pipeline schedule of pertinent literature to limited buffer to be studied, as periodical " Journal of intelligent manufacturing " the 24th phase " A newgenetic algorithm for lot-streaming flow shop scheduling with limited capacitybuffers " of publication in 2013, but only consider single goal situation in literary composition.

Above-mentioned technological achievement is that solar cell limited buffer multiple goal batch production scheduling provides new solution, but, should be understood that, still there are the following problems for existing method: (1) current most manufacture of solar cells scheduling still adopts manually works out scheduling mode, the scheduling scheme of its extensive style and production scheduling inefficiency, poor accuracy, and in actual production engineering, enterprise often faces the order of extensive different model battery, increase scheduling problem difficulty, therefore only lean on some simple optimizing methods or manually work out scheduling mode, optimal scheduling scheme cannot be made, (2) existing method for optimizing scheduling, only considers single-object problem, and in solar cell actual production process, not only considers the completion date of product, also needs to consider multiple indexs such as supplier delivery date.For this situation, existing method is difficult to obtain desirable result; (3) the existing method solving multi-objective problem, usually compares individuality, sorts, the strategy such as selection improves, and do not provide further research for cross and variation operator crucial in algorithm.Traditional intersection, mutation operation has randomness, without purpose and non-directional, can not ensure that newly-generated individuality has higher quality, thus reduce search progress and speed of convergence, have impact on the efficiency of algorithm.

Summary of the invention

Technical matters to be solved by this invention overcomes the deficiencies in the prior art, discrete NSGA-II (DNSGA-II) is applied to solar module limited buffer batch production scheduling problem.Preferably Pareto forward position can be obtained for making algorithm, the present invention introduces the curve-fitting method initialization population of variation in DNSGA-II, utilize population at individual difference and non-domination solution excellent genes, propose new cross and variation operator, with the overall situation of balanced algorithm and local search ability, better serve the actual productions such as limited buffer multiple goal batch pipeline schedule.

Technical solution of the present invention: set up solar cell limited buffer multiple goal batch fluvial incision mathematical model, then suitable initialization strategy is designed, cross and variation algorithm and elite's retention strategy, with speed convergence faster to the optimum forward position of Pareto.It is characterized in that step is as follows:

1, the production models that workpiece and machinery and equipment are made up of corresponding with solar module production procedure are built.

Solar module production procedure is a typical batch pipeline schedule process, when battery is after the completion of certain operation stage, keep in the buffer, when next process equipment is idle, continue processing, therefore, the production models set up, except meeting the constraint in process, also should by buffer zone number between each stage of technological process, as constraint condition, join in mathematical model, and set up 2 objective optimization functions:

$\begin{array}{cc}{f}_1=C\max \left(\mathrm{\π}\right)=D_{\mathrm{\τ}\left(e\right),m}& e=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_{\mathrm{\π}\left(n\right)}\end{array}$

$\begin{array}{cc}{f}_2=T\max \left(\mathrm{\π}\right)=\max (0,D_{\mathrm{\τ}\left(l_{\mathrm{\π}\left(j\right)}\right),m}-d_j)& j=\mathrm{1,2},\·\·\·,n\end{array}$

Wherein,

D _τ(1),1＝p _π(1),1

D _τ(1)，i＝D _τ(1)，i-1+p _π(1)，ii=2，3，...，m

$\begin{array}{cc}{D}_{\mathrm{\τ}\left(e\right),1}=D_{\mathrm{\τ}(e-1),1}+p_{\mathrm{\π}\left(j\right),1}& \begin{array}{c}e=\mathrm{2,3},\·\·\·,B_1+1\\ j=\mathrm{1,2},\·\·\·,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\τ}\left(e\right),1}=\max (D_{\mathrm{\τ}(e-1),1}+p_{\mathrm{\π}\left(j\right),1},D_{\mathrm{\τ}(e-B_1-1),2})& \begin{array}{c}e=B_1+2,B_1+3,\·\·\·,\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{l}_{\mathrm{\π}\left(k\right)}\\ j=1,2,\·\·\·,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\τ}\left(e\right),i}=\max (D_{\mathrm{\τ}(e-1),i},D_{\mathrm{\τ}\left(e\right),i-1})+p_{\mathrm{\π}\left(j\right),i}& \begin{array}{c}e=\mathrm{2,3},\·\·\·,B_i+1\\ j=1,2,\·\·\·,n\\ i=2,3,\·\·\·,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\τ}\left(e\right),i}=\max (\max (D_{\mathrm{\τ}(e-1),i},D_{\mathrm{\τ}\left(e\right),i-1})+p_{\mathrm{\π}\left(j\right),i},D_{\mathrm{\τ}(e-B_i-1),i+1})& \begin{array}{c}e=B_i+2,B_i+3,\·\·\·,\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{l}_{\mathrm{\π}\left(k\right)}\\ j=1,2,\·\·\·,n\\ i=2,3,\·\·\·,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\τ}\left(e\right),m}=\max (D_{\mathrm{\τ}(e-1),m},D_{\mathrm{\τ}\left(e\right),m-1})+p_{\mathrm{\π}\left(j\right),m}& \begin{array}{c}e=\mathrm{2,3},\·\·\·,\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{l}_{\mathrm{\π}\left(k\right)}\\ j=\mathrm{1,2},\·\·\·,n\end{array}\end{array}$

π is one and comprises n different model battery component (workpiece) sequence, that is, π=π (1), π (2) ..., π (j) ..., π (n) }; Each workpiece π (j) is split into some small batches, namely l _{π (j)}for the short run sum that workpiece π (j) comprises; τ is the short run set of all workpiece, wherein $\mathrm{\η}=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{l}_{\mathrm{\π}\left(j\right)};$ B _ifor buffer zone number between machine i and i+1; p _{π (j), i}for the process time of workpiece π (j) on machine i; D _{τ (e), i}for short run τ (e) leaves the time on machine i; d _jfor the delivery date of workpiece π (j); f ₁and f ₂maximal Makespan and postponement completion date respectively.

2, the NSGA-II algorithm optimization solar module limited buffer Multi-Objective Scheduling mathematical model of discrete.

The present invention is based on optimization problem characteristic, population at individual otherness and the valuable information of non-domination solution, and multi-objective Algorithm elite retention mechanism, propose new initialization strategy, variation crossover operator etc.Put forward the execution step following (as shown in Figure 3) of algorithm:

Step 1: initialization population.Due to the restriction of intermediate buffer, some short runs may be made to be blocked on machine, cause the short run of not dispatching to postpone to go into operation.Based on this problem characteristic, the present invention adopts curve-fitting method (Profile fitting, PF), attempt to find a sequence, make the blocking time of workpiece on machine and standby time sum minimum, therefore, in vPFE heuristic disclosed by the invention, first adopt PF heuristic to produce an initial solution; Then in conjunction with the NEH of variation is heuristic, neighborhood search is carried out to above-mentioned initial solution, based on the Relationship Comparison that is dominant, retain the solution of several better performances, finally, be maintain population diversity, adopt random function, generate residue in population and separate;

Step 2: algorithm evolution iterations t=1 is set;

Step 3: arrange progeny population size PS, arranges offspring individual counter w=1;

Step 4: perform mutation operation (as shown in Figure 4);

Step 4.1: from current population, 3 different workpiece sequences in Stochastic choice population, π _a, π _b, π _c;

Step 4.2: each new workpiece sequence is made up of n workpiece, that is, π=π (1), π (2) ..., π (i) ..., π (n) }, Number of Jobs counter i=1 is set;

Step 4.3: by following formula, obtains the value of each workpiece of new workpiece sequence:

π(i)＝(π _b(i)-π _c(i))*flagοπ _a(i)

Wherein, a, b, c represent the location label of workpiece sequence in population, and its span is [1, PS], and PS is Population Size; π (i) is i-th workpiece of workpiece sequence π; Flag is Boolean variable, and its value is 0 or 1; Sign of operation " * " is multiplication sign, and sign of operation " o " is complementation symbol, that is, (π _b(i)-π _c(i)) * flag ο π _a(i)=((π _b(i)-π _c(i)) * flag+ π _a(i)+n) %n+1;

Step 4.4:i=i+1; If i<=n, perform step 4.3, otherwise, export new explanation π, perform step 5;

Step 5: perform interlace operation (as shown in Figure 4):

Step 5.1: the workpiece repeated in the π obtained by above-mentioned mutation operation is deleted, and obtains new part workpiece sequence π _p, separate as the reference guided for the overall situation, note π _pthe total number of middle workpiece is k;

Step 5.2: from non-domination solution concentrate, Stochastic choice 1 workpiece sequence, π ', and will wherein with π _pidentical workpiece is deleted, and obtains new part workpiece sequence π _new, object is, utilizes the valuable information of non-domination solution, guides Evolution of Population;

Step 5.3: the number of times s=1 performing following update is set;

Step 5.4: from π _pin, take out s workpiece, i.e. π _pt (), is inserted into π _newmiddle different position, obtains n-k+s different workpieces sequence, the workpiece sequence that choice function value is minimum, and assignment is to π again _new;

Step 5.5:s=s+1; If s<=k; Perform step 5.4, otherwise, perform step 5.6;

Step 5.6: evaluate the complete workpiece sequence π obtained _new, and put it in progeny population.

Step 6: if w<=PS, then perform step 4; Otherwise perform step 7;

Step 7: environmental selection.Merge parent population and progeny population, to be dominant relation based on Pareto, the population of merging to be carried out grade classification, obtains the non-dominant disaggregation of different brackets, for the individuality of same grade, then adopt crowding distance method, select.By said method, PS individual weight new work is selected to be that parent is individual.

Step 8: dynamically update external store collection, to retain the good non-domination solution that each iteration produces.

Step 9:t=t+1; If t< maximum iteration time, then perform step 3, otherwise algorithm terminates, export Pareto optimal solution set.

The present invention's advantage is compared with prior art:

(1) in processing solar panel process, needed for each stage, process time is different, causes in the complete workpiece temporary storage buffer region of a certain stage process.Due to the restriction of cost, the buffer zone that each stage is arranged can not be too much, causes workpiece to block like this.And the mathematical model of existing batch fluvial incision does not consider that this actual production retrains.Therefore, the present invention is directed to solar module production procedure and actual production constraint, establish solar module limited buffer multiple goal lot size scheduling problem mathematical model, can be more reasonable, more fully reflect actual production process.

(2) the existing method (NSGA-II) solving multi-objective problem, does not provide further research for cross and variation operator crucial in algorithm.Traditional intersection, mutation operation has randomness, without purpose and non-directional, can not ensure that newly-generated individuality has higher quality.Therefore, the present invention, according to problem characteristic, makes full use of species information and non-domination solution information, propose new initialization strategy and cross and variation operator, can the overall situation of balanced algorithm and Local Property, accelerate search progress and speed of convergence, find the more excellent scheduling scheme that some are selected for decision maker.

Accompanying drawing explanation

Fig. 1 general batch fluvial incision, limited buffer batch fluvial incision, blocks batch fluvial incision Gantt chart

The transition diagram that Fig. 2 solar module and production procedure are represented by workpiece and machine

Fig. 3 carries algorithm flow chart

Fig. 4 makes a variation crossover process figure

Fig. 5 DNSGA-II, NSGA-II and DABC algorithm evolution curve map in time

Embodiment

Below in conjunction with concrete accompanying drawing and example, the embodiment to institute of the present invention extracting method is described in detail.

1, solar module limited buffer multiple goal lot size scheduling problem mathematical model is built:

Solar module technological process is typical production line balance pattern, and process is successively through 11 stages: (1) battery detecting; (2) front welding, inspection; (3) back serial connection, inspection; (4) lay (glass cleaning, cut material, cleaning glass window, cleared of debris); (5) lamination; (6) burr removing (trimming, cleaning); (7) rim frame (gluing, dress angle key, punching, frame up, clean remaining glue); (8) Welding junction box; (9) Hi-pot test; (10) module testing, visual testing; (11) packaging warehouse-in.A processing batch regarded as by same size battery plate, and a namely processing work, the different phase of technological process is considered as different processing machine (as shown in Figure 2).According to cell voltage and production equipment performance, be divided into some short runs by each batch, agreement each stage of technological process process sequence of upper each short run is identical, different in the process time of different phase.Process meets the following conditions:

(1) in same process stage same model battery completion of processing after, just can process the battery of different model, that is, on the identical production phase, after all short run completion of processing of same batch, the short run of next batch just can be processed;

(2) operation stages can only process one batch, and a small batch can only be processed on an operation stage;

(3) stand-by period is had between adjacent two batches of same operation stage;

(4) machine ready time and short run haulage time are ignored;

Above-mentioned about intrafascicular, implied condition is, at least exists and is more than or equal to n-1 buffer zone, after a short run completion of processing, can keep in the buffer, can not get clogged on a current machine between machine.If but between adjacent two machines, when there is limited intermediate buffer, now, when a short run is on machine i after completion of processing, if downstream machine i+1 is just occupied, now, by the workpiece of completion on machine i, put into buffer zone, such machine i is in idle condition, for next short run.If buffer zone is full, then the workpiece completed gets clogged on a current machine, until downstream machine or buffer zone can be used.Like this, above-mentioned batch fluvial incision is just converted into the batch fluvial incision of limited buffer.If the objective function number optimized is greater than 1, then the problems referred to above are converted into again the multiple goal batch fluvial incision of limited buffer.Due to the restriction of buffer zone, make original conventional batch fluvial incision mathematical model unavailable, need to re-establish corresponding number model.Therefore, describe and constraint condition according to the problems referred to above, set up following solar module limited buffer multiple goal batch production scheduling mathematic model.

Suppose, have n (π=π (1), π (2) ..., π (j) ..., π (n) }) individual processing batch, process at m operation stage according to identical process route.Each work-piece batch π (j) comprises the transfer batch of some quantity, namely τ is the short run set of all workpiece, $\mathrm{\&tau;}=\{\mathrm{\&tau;}\left(1\right),\mathrm{\&tau;}\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&tau;}\left(l_{\mathrm{\&pi;}\left(1\right)}\right),\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&tau;}(\underset{k=1}{\overset{j=1}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}+1),\mathrm{\&tau;}(\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}+2),\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&tau;}(\underset{k=1}{\overset{j=1}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}+l_{\mathrm{\&pi;}\left(j\right)}),\&CenterDot;\&CenterDot;\&CenterDot;,\mathrm{\&tau;}\left(\mathrm{\&eta;}\right)\}=$ $\{{\mathrm{\&pi;}\left(1\right)}_1,{\mathrm{\&pi;}\left(1\right)}_2,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&pi;}\left(1\right)}_{l_{\mathrm{\&pi;}\left(1\right)}},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&pi;}\left(j\right)}_1,{\mathrm{\&pi;}\left(j\right)}_2,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&pi;}\left(j\right)}_{l_{\mathrm{\&pi;}\left(j\right)}},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&pi;}\left(n\right)}_{l_{\mathrm{\&pi;}\left(n\right)}}\},$ Wherein $\mathrm{\&eta;}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(j\right)}.$

The objective function optimized

$\begin{array}{cc}{f}_1=C\max \left(\mathrm{\&pi;}\right)=D_{\mathrm{\&tau;}\left(e\right),m}& e=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(n\right)}\end{array}$

$\begin{array}{cc}{f}_2=T\max \left(\mathrm{\&pi;}\right)=\max (0,D_{\mathrm{\&tau;}\left(l_{\mathrm{\&pi;}\left(j\right)}\right),m}-d_j)& j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}$

Wherein,

D _τ(1),1＝p _π(1),1

D _τ(1),i＝D _τ(1),i-1+p _π(1),ii＝2,3,...,m

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),1}=D_{\mathrm{\&tau;}(e-1),1}+p_{\mathrm{\&pi;}\left(j\right),1}& \begin{array}{c}e=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;,B_1+1\\ j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),1}=\max (D_{\mathrm{\&tau;}(e-1),1}+p_{\mathrm{\&pi;}\left(j\right),1},D_{\mathrm{\&tau;}(e-B_1-1),2})& \begin{array}{c}e=B_1+2,B_1+3,\&CenterDot;\&CenterDot;\&CenterDot;,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=1,2,\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),i}=\max (D_{\mathrm{\&tau;}(e-1),i},D_{\mathrm{\&tau;}\left(e\right),i-1})+p_{\mathrm{\&pi;}\left(j\right),i}& \begin{array}{c}e=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;,B_i+1\\ j=1,2,\&CenterDot;\&CenterDot;\&CenterDot;,n\\ i=2,3,\&CenterDot;\&CenterDot;\&CenterDot;,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),i}=\max (\max (D_{\mathrm{\&tau;}(e-1),i},D_{\mathrm{\&tau;}\left(e\right),i-1})+p_{\mathrm{\&pi;}\left(j\right),i},D_{\mathrm{\&tau;}(e-B_i-1),i+1})& \begin{array}{c}e=B_i+2,B_i+3,\&CenterDot;\&CenterDot;\&CenterDot;,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=1,2,\&CenterDot;\&CenterDot;\&CenterDot;,n\\ i=2,3,\&CenterDot;\&CenterDot;\&CenterDot;,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),m}=\max (D_{\mathrm{\&tau;}(e-1),m},D_{\mathrm{\&tau;}\left(e\right),m-1})+p_{\mathrm{\&pi;}\left(j\right),m}& \begin{array}{c}e=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n\end{array}\end{array}$

In formula, B _ifor buffer zone number between machine i and i+1; p _{π (j), i}for the process time of workpiece π (j) on machine i; D _{τ (e), i}for short run τ (e) leaves the time on machine i; d _jfor the delivery date of workpiece π (j); f ₁and f ₂maximal Makespan and postponement completion date respectively.

2, the NSGA-II algorithm of discrete

By reference to the accompanying drawings, carried algorithm is illustrated further.

(1) coded system of algorithm: based in summary of the invention, the description of solar module limited buffer multiple goal lot size scheduling problem, algorithm disclosed by the invention adopts the coded system based on discrete workpieces sequence, carries out whole algorithm design.A complete workpiece sequence represents a solution in population, and the dimension of solution is identical with Number of Jobs in workpiece sequence (shown in Fig. 2).

(2) initialization strategy

Based on initialization strategy in summary of the invention, followingly provide concrete initialization procedure:

Make π be the sequence comprising k scheduled workpiece, U is the set of waiting to dispatch workpiece containing μ.First PF heuristic is adopted to produce an initial solution; Then in conjunction with the NEH (vNEH) of variation is heuristic, neighborhood search is carried out to above-mentioned initial solution, based on the Relationship Comparison that is dominant, retain β performance and separate preferably, finally, be maintain population diversity, adopt random function, generate residue in population and separate.Concrete steps are as follows:

Step 1: perform PF heuristic:

Step 1.1: select the minimum workpiece of total elapsed time as the unit one of π, i.e. π={ π (1) };

Step 1.2: make U=U-{ π (1) }, k=1;

Step 1.3: the time departure D calculating last workpiece in π _{w (e), i}, i=1,2 ..., m,

Step 1.4: from treating to take out workpiece j collating sequence U, add the last of π to, become kth+1 workpiece of π.Calculate the time departure D' of workpiece j _{w (e'), i}, i=1,2 ..., m, then according to following formula, calculate standby time caused by workpiece j and blocking time sum;

$t_{j,\left[k\right]}={\mathrm{\&Sigma;}}_{i=1}^m({D^{\&prime;}}_{w\left(e^{\&prime;}\right),i}-D_{w\left(e\right),i}-\underset{k^{\&prime;}=1}{\overset{l_{\mathrm{\&pi;}\left(j\right)}}{\mathrm{\&Sigma;}}}{p}_{\mathrm{\&pi;}\left(j\right),i})$

Step 1.5: repeat step 1.4, until each workpiece is considered complete in U.Select t _{j, [k]}minimum workpiece is as kth+1 workpiece π (k+1) of π;

Step 1.6: make U=U-{ π (k+1) }, k=k+1, performs step 1.4, until the initiation sequence π that output PF produces=and π (1), π (2) ..., π (n) };

Step 2: perform vNEH heuristic:

Step 2.1: take out the first two workpiece π (1) from π, π (2) carries out permutation and combination, obtain two partial ordered { π (1), π (2) } and { π (2), π (1) }, evaluate these two partial ordered objective function f ₁, select f ₁a minimum sequence, as current portions sequence π *, makes k=2;

Step 2.2: kth+1 workpiece π (k+1) of taking out π, is inserted into k+1 the diverse location of π * respectively by it, the raw k+1 of common property is individual partial ordered.Selection makes desired value f ₁minimum partial ordered be π *;

Step 2.3: make k=k+1.If k < is n, then go to step 2.2; Otherwise k=n performs step 2.4;

Step 2.4:k=n, takes out n-th workpiece π (n) of π, it is inserted into respectively n the diverse location of π (k+1), raw n the complete sequence of common property.Evaluate these workpiece sequences, and utilize the Pareto relation of being dominant to compare, select β Pareto optimum solution.Perform step 3;

Step 3: random generation remains workpiece:

Step 3.1: counter i=PS-β is set;

Step 3.2: adopt following random function, produces workpiece sequence,

π _i＝random_shuffle(π'.begin(),π'.end())

Wherein, π ' is known workpiece sequence, and first parameter points to the iterator of sequence π ' header element, and second parameter then points to the next position of last element of sequence π ';

Step 3.3: if the solution π produced _iexist in population, then cast out, perform step 3.2.Otherwise, after it is evaluated, perform step 3.4;

Step 3.4: make i=i+1, if i is <=PS, performs step 3.2, otherwise termination algorithm.Export initial population.

The heuristic combination didactic with NEH of PF, can be civilian see " A note on constructive heuristicsfor the flowshop problem with blocking " in the 87th phase in 2004 " InternationalJournal of Production Economics ".It should be noted that, existing PFE heuristic, perform once, an initial solution can only be produced, and the vPFE heuristic of variation that the present invention proposes, due to the multiple goal characteristic of problem, having incorporated Pareto is dominant relation, perform and once can produce multiple non-domination solution, make initialization population have better convergence like this.Concrete Pareto is dominant contextual definition, can see " A fast and elitist multiobjective genetic algorithm:NSGA-II.Evolutionary Computation " in the 6th phase in 2002 " IEEE Transactions on EvolutionaryComputation ", the present invention does not explain.

(3) crossover and mutation operation is the key component of NSGA-II algorithm, the present invention carries in operator, utilizes interindividual otherness and external store in population to concentrate the individual effective information of elite, produces every height in progeny population individual, composition graphs 4, provides concrete steps below:

Step 1: mutation process:

Step 1.1: from current population, the individuality that Stochastic choice 3 is different, π _a, π _b, π _c;

Step 1.2: Number of Jobs counter j=1 in workpiece sequence is set;

Step 1.3: in workpiece sequence π, each workpiece is by formula acquisition below

π(j)＝(π _b(j)-π _c(j))*flagοπ _a(j)

Wherein a, b, c are the random numbers between 1 to PS, represent individual label in population; π (j) is a jth workpiece of workpiece sequence π; Flag is Boolean variable, and value is 0 or 1; Sign of operation " * " is multiplication sign, and sign of operation " o " is complementation symbol, that is, (π _b(j)-π _c(j)) * flag ο π _a(j)=((π _b(j)-π _c(j)) * flag+ π _a(j)+n) %n+1;

Step 1.4:j=j+1; If j<=n, perform step 1.3, no person, export new explanation π, then, perform step 2;

Step 2: crossover process:

Step 2.1: delete the workpiece repeated in the π that above-mentioned variation obtains, obtain new part workpiece sequence π _p, and by π _pmiddle Number of Jobs is designated as k.

Step 2.2: concentrate from non-domination solution, the individual π ' of Stochastic choice 1 elite, object is, utilizes the valuable information of non-domination solution, guides Evolution of Population;

Step 2.3: from π ', deletes and π _pidentical workpiece, obtains part workpiece sequence π _new, remain the valuable information of non-domination solution part like this, neighborhood search carried out to it, guide population Fast Convergent;

Step 2.4: counter t=1 is set;

Step 2.5: from π _pin, take out t workpiece, i.e. π _pt (), is inserted into π _newmiddle different position, obtains n-k+t different workpieces sequence, selects to make functional value f ₁minimum workpiece sequence, assignment is to π again _new;

Step 2.6:t=t+1; If t<=k; Perform step 2.5, otherwise, perform step 2.7;

Step 2.7: obtain complete workpiece sequence π _new, after it is evaluated, put into progeny population.

(4) environmental selection and external store collection upgrade

By variation interlace operation, obtain the progeny population O of PS size.Merge current parent for population P and progeny population O, generate the population PO with PS+PS individuality, adopt the Pareto relation that is dominant to carry out grade classification to individuality in population PO, then individual in conjunction with crowding distance method choice PS, upgrade parent population.

Each time in iterative process, all produce the limited non-domination solution of some, in order to avoid the non-domination solution of each grey iterative generation is lost, in the algorithm that the present invention proposes, the solution that a limited external store collection retains the Pareto forward position that per generation searches is set, and dynamically updates deposit collection.

Individual grade classification and crowding distance method, can see " A fast and elitist multiobjective geneticalgorithm:NSGA-II.Evolutionary Computation " in the 6th phase in 2002 " IEEE Transactionson Evolutionary Computation ", the present invention does not explain.

As can be seen from said process, in the discrete NSGA-II algorithm that the present invention proposes, mutation process make use of the difference in population between Different Individual, ensure that the overall performance of new explanation, in crossover process, have selected elite's individuality and carry out neighborhood search, and elite's individual relative position remains unchanged, take full advantage of the good gene information of non-domination solution, ensure that the convergence of new explanation.By testing 13 different model solar module limited buffer multiple goal lot size scheduling problems, demonstrate the present invention put forward validity and the feasibility of algorithm, and multiple good scheduling scheme can be produced, select for decision maker.

Application example

All algorithm simulating environment are: the processor of 3.0GHz CPU, 2G internal memory and Intel (R) Core (TM).Contemplated by the invention the solar module of 13 different models, be respectively: QX6060-4/80, QX6060-4/120, QX6060-4/70, QX5555-4/40, QX6060-8/100, QX6060-8/80, QX6060-8/60, QX6060-5/100, QX6060-5/80, QX5555-6/50, QX7070-8/50, QX8060-8/100.Each model produced at random respectively in the process time in 11 production technology stages in following span: [30s, 40s], [30s, 40s], [30s, 40s], [120s, 160s], [1500s, 2000s], [300s, 400s], [180s, 240s], [120s, 160s], [60s, 80s], [180s, 240s], [60s, 80s].Emulation experiment optimum configurations is respectively: Population Size is 20, crossover probability 0.9, mutation probability 0.1, and external store collection size is 100, and the algorithm termination time is set to 4290s.Often kind of algorithm independent operating 30 times.

The inventive method is produced 13 kinds of different model solar modules and is emulated, and analyzes its performance for acquired results.

(1) initialization strategy validity is verified

Existing PFE heuritic approach, execution once can only produce one and initially dissolve, and slow down the speed of convergence of population like this, for this reason, the present invention proposes vPFE heuristic, perform and once can produce β the good initial solution of performance, in experiment, β=8 are set.For the validity of checking institute extracting method, table 1 gives, and adopts PFE respectively, vPFE and random device initialization population, the optimum Pareto optimal solution set obtained.As shown in Table 1, the inventive method obtains 4 non-domination solution, and be dominant respectively PFE and the non-domination solution that obtains at random 2 of concentrating separate and 1 solution, illustrate that the vPFE heuristic that the present invention carries can produce high-quality initial population.

(2) validity utilizing non-domination solution information in crossover process is verified

When performing crossover operator, the inventive method utilizes the valuable information of non-domination solution as local channeling direction, guides using the partial solution that mutation process obtains as the overall situation, produces new individual.For checking non-domination solution is to the convergence of population, play guiding function, table 2 gives, and utilizes non-domination solution information (DNAGA-II_ND) and without non-domination solution information (DNAGA-II_PO) in crossover process, the optimum Pareto optimal solution set obtained.As shown in Table 2, the open method of the present invention, utilizes non-domination solution information as neighborhood search object, can obtain 2 Pareto optimum solutions, and 2 non-domination solution that the DNAGA-II_PO that is dominant produces.This illustrates, in crossover process, the valuable information of non-domination solution can guide population Fast Convergent.

(3) DNAGA-II method validity is put forward in checking

The inventive method and existing NSGA-II and the DABC algorithm intersected based on single-point, produce 13 kinds of different model solar modules and emulate.Table 3 obtains respective optimal solution set after giving 3 kinds of algorithms operation 4290s respectively.As shown in Table 3, although NSGA-II algorithm obtains 4 non-domination solution, 3 non-domination solution that the optimum solution domination NSGA-II that the inventive method obtains obtains, and 2 non-domination solution that the DABC that is all dominant obtains.From interpretation of result, the inventive method is obviously better than 2 control methodss.

In addition, Fig. 5 with reference to the distance between disaggregation and Pareto disaggregation for index (range index specifically can see " the A novel differentialevolution algorithm for bi-criteria no-wait flow shop scheduling problems " in the 36th phase in 2009 " Computers and Operations Research ") gives the evolution curve that 3 kinds of algorithms increase in time.As seen from Figure 5, along with the time increases, the evolution curve of the inventive method is starkly lower than the evolution curve of contrast algorithm, illustrates that the convergence of the inventive method is very good, can with speed of convergence faster, close to true Pareto forward position.

Claims (4)

1., based on a solar module limited buffer multiple goal lot size scheduling method of DNSGA-II, it is characterized in that, the method comprises:

(1) solar module production scheduling modeling: the solar module of different model is regarded as a workpiece to be processed, the different phase of technological process regards a machine as, according to actual production flow process and satisfied working condition, build the production models that workpiece and machinery and equipment are made up of corresponding with solar module production procedure;

(2) according to discrete feature and the multiple goal characteristic of problem, the DNSGA-II algorithm optimization solar module scheduling model based on workpiece sequential coding mode is adopted.

2. the solar module limited buffer multiple goal lot size scheduling method based on DNSGA-II according to claim 1, it is characterized in that, solar module production procedure is a typical batch pipeline schedule process, when battery is after the completion of certain operation stage, keep in the buffer, when next process equipment is idle, continue processing, therefore, the production models set up, except meeting the constraint in process, also should by buffer zone number between each stage of technological process, as constraint condition, join in mathematical model, and set up 2 objective optimization functions:

$\begin{array}{cc}{f}_1=C\max \left(\mathrm{\&pi;}\right)=D_{\mathrm{\&tau;}\left(e\right),m}& e=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(n\right)}\end{array}$

$\begin{array}{cc}{f}_2=T\max \left(\mathrm{\&pi;}\right)=\max (0,D_{\mathrm{\&tau;}\left(l_{\mathrm{\&pi;}\left(j\right)}\right),m}-d_j)& j=\mathrm{1,2},...,n\end{array}$

Wherein,

D _τ(1),1＝p _π(1),1

D _τ(1),i＝D _τ(1),i-1+p _π(1),ii＝2,3,...,m

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),1}=D_{\mathrm{\&tau;}(e-1),1}+p_{\mathrm{\&pi;}\left(j\right),1}& \begin{array}{c}e=\mathrm{2,3},...,B_1+1\\ j=\mathrm{1,2},...,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),1}=\max (D_{\mathrm{\&tau;}(e-1),1}+p_{\mathrm{\&pi;}\left(j\right),1},D_{\mathrm{\&tau;}(e-B_1-1),2})& \begin{array}{c}e=B_1+2,B_2+3,...,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=\mathrm{1,2},...,n\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),i}=\max (D_{\mathrm{\&tau;}(e-1),i},D_{\mathrm{\&tau;}\left(e\right),i-1})+p_{\mathrm{\&pi;}\left(j\right),i}& \begin{array}{c}e=\mathrm{2,3},...,B_i+1\\ j=\mathrm{1,2},...,n\\ i=\mathrm{2,3},...,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),i}=\max (\max (D_{\mathrm{\&tau;}(e-1),i},D_{\mathrm{\&tau;}\left(e\right),i-1})+p_{\mathrm{\&pi;}\left(j\right),i},D_{\mathrm{\&tau;}(e-B_i-1),i+1})& \begin{array}{c}e=B_i+2,B_i+3,...,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=\mathrm{1,2},...,n\\ i=\mathrm{2,3},...,m-1\end{array}\end{array}$

$\begin{array}{cc}{D}_{\mathrm{\&tau;}\left(e\right),m}=\max (D_{\mathrm{\&tau;}(e-1),m},D_{\mathrm{\&tau;}\left(e\right),m-1})+p_{\mathrm{\&pi;}\left(j\right),m}& \begin{array}{c}e=\mathrm{2,3},...,\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(k\right)}\\ j=\mathrm{1,2},...,n\end{array}\end{array}$

π is one and comprises n different model battery component (workpiece) sequence, that is, π=π (1), π (2) ..., π (j) ..., π (n) }; Each workpiece π (j) is split into some small batches, namely l _{π (j)}for the short run sum that workpiece π (j) comprises; τ is the short run set of all workpiece, wherein $\mathrm{\&eta;}=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{l}_{\mathrm{\&pi;}\left(j\right)};$ B _ifor buffer zone number between machine i and i+1; p _{π (j), i}for the process time of workpiece π (j) on machine i; D _{τ (e), i}for short run τ (e) leaves the time on machine i; d _jfor the delivery date of workpiece π (j); f ₁and f ₂maximal Makespan and postponement completion date respectively.

3. the solar module limited buffer multiple goal lot size scheduling method based on DNSGA-II according to claim 1, it is characterized in that, in view of this problem contains restrictive and multiple goal characteristic, when initialization population, have employed the curve-fitting method of variation, produce the initial solution of several better performances; In addition, in order to ensure initial population diversity, remaining initial solution, is produced by random function.

4. the solar module limited buffer multiple goal lot size scheduling method based on DNSGA-II according to claim 1, it is characterized in that, based on the excellent genes of individual difference and non-domination solution in parent population, design new variation crossover operator, produce distributivity and the good offspring individual of convergence, generate offspring individual step as follows:

Step 1: perform mutation operation;

Step 1.1: from current population, 3 different workpiece sequences in Stochastic choice population, π _a, π _b, π _c;

Step 1.2: each new workpiece sequence is made up of n workpiece, that is, π=π (1), π (2) ..., π (i) ..., π (n) }, Number of Jobs counter i=1 is set;

Step 1.3: by following formula, obtains the value of each workpiece of new workpiece sequence:

π(i)＝(π _b(i)-π _c(i))*flagоπ _a(i)

Wherein, a, b, c represent the location label of workpiece sequence in population, and its span is [1, PS], and PS is Population Size; π (i) is i-th workpiece of workpiece sequence π; Flag is Boolean variable, and its value is 0 or 1; Sign of operation " * " is multiplication sign, and sign of operation " o " is complementation symbol, that is, (π _b(i)-π _c(i)) * flag o π _a(i)=((π _b(i)-π _c(i)) * flag+ π _a(i)+n) %n+1;

Step 1.4:i=i+1; If i<=n, perform step 1.3, otherwise, export new explanation π, perform step 2;

Step 2: perform interlace operation:

Step 2.1: the workpiece repeated in the π obtained by above-mentioned mutation operation is deleted, and obtains new part workpiece sequence π _p, separate as the reference guided for the overall situation, note π _pthe total number of middle workpiece is k;

Step 2.2: from non-domination solution concentrate, Stochastic choice 1 workpiece sequence, π ', and will wherein with π _pidentical workpiece is deleted, and obtains new part workpiece sequence π _new, object is, utilizes the valuable information of non-domination solution, guides Evolution of Population;

Step 2.3: the number of times t=1 performing following update is set;

Step 2.4: from π _pin, take out t workpiece, i.e. π _pt (), is inserted into π _newmiddle different position, obtains n-k+t different workpieces sequence, the workpiece sequence that choice function value is minimum, and assignment is to π again _new;

Step 2.5:t=t+1; If t<=k; Perform step 2.4, otherwise, perform step 2.6;

Step 2.6: evaluate the complete workpiece sequence π obtained _new, and put it in progeny population.