CN104122861A - Waiting time relaxation based conflict resolution method and optimization scheduling method - Google Patents

Abstract

The invention provides a waiting time relaxation based conflict resolution method. The waiting time relaxation based conflict resolution method comprises adjusting the waiting time length of the furnace number before the process which can be waited for through iterative relaxation to completely resolve the equipment conflict; ranking the beginning time of the furnace numbers in the converter process according to the time ascending order to obtain a beginning time sequence, setting an initial value of the waiting time of the furnace numbers in the buffering process to be zero and serving the furnace number which is corresponding to the last datum as the current furnace number; judging whether the equipment conflict occurs between the current furnace number and the closely previous furnace number in the converter process or not, serving the corresponding furnace number of the previous datum of the beginning time of the current furnace number as the new current furnace number and continuing if not and computing the equipment conflict time, checking the assigned waiting time of the closely previous furnace number in the buffering process after the converter process, computing the waiting time margin and adjusting the waiting time through the iterative relaxation to resolve the equipment conflict if yes. According to the waiting time relaxation based conflict resolution method and optimization scheduling method, the requirements of the optimization scheduling scheme under the busy and complex work conditions can be well met and the production efficiency of a converter steel mill is improved.

Description

Based on lax conflict resolution method of stand-by period and Optimization Scheduling

Technical field

The present invention is applied to steel-smelting-continuous casting manufacturing technique, is specially a kind of based on lax conflict resolution method of stand-by period and Optimization Scheduling.

Background technology

Steel smelting-continuous casting production run is the core link in the production procedure of modern steel associated enterprises, in this production run, first molten iron from blast furnace is converted into high-temperature molten steel through converter or electric furnace smelting, then carry out refining to meet chemical composition and the temperature requirement of molten steel through refining furnace, finally deliver to conticaster and be cast into slab or the square billet of different size.The raising of steel smelting-continuous casting production run production efficiency has material impact to whole iron and steel enterprise, and formulates rational production scheduling plan, is the key that ensures steel smelting-continuous casting production run high-efficiency operation.

With the visual angle of mathematical programming, steel-making continuous casting production run is that multistage is produced, multistage transport, multistage storage discrete and large high-temperature production run that external phase mixes, add the features such as discreteness, randomness, multiple goal and the multiple constraint of production run, make this production run itself just there is the complicacy of certain degree.In addition, in recent years, domestic most iron and steel enterprise is all carrying out or is completing structural adjustment and the production capacity upgrading of steel products, make the little enterprise of script rise to easily the scale of ten-million-ton scale, the several years ago iron and steel base of newly-built and new planning, as the scale of Shoudu Iron and Steel Co Cao Feidian, Baosteel Zhanjiang and Wuhan Iron and Steel Plant Port of Fangcheng all meets or exceeds the magnitude of ten million ton of production capacity substantially.The expansion of steel enterprise scale has further strengthened the difficulty of Steelmaking-Continuous Casting Production Scheduling.Thereby, how to design process scheme and production scheduling plan feasible, that optimize, ensure whole matching and the coordination of each process procedure (as desulfurization, converter, refining and continuous casting etc.), realize production logistics unimpeded, efficient, be to put at home and abroad engineering technical personnel and researchers' technical barrier in front always.

Steel-smelting-continuous casting manufacturing technique flow scheme or operation plan can be divided into two classes: a class is Production Lot Planning, and another kind of is production time plan.Production Lot Planning is taking client's contract dataset as raw data, according to process technology limit condition, different contract requirements is carried out to best of breed generates, and comprises heat plan and casting plan.Production time plan is on the basis of Production Lot Planning, taking heat as minimum planning unit, the special job-shop sequencing problem of a class in the situation that pursuing a certain evaluation function (as minimum latency, minimum are dragged phase expense, minimum main-process stream time in advance) the best, its net result is to determine with which kind of order, arranges each operation of the production run of molten steel from converter to conticaster when, on which kind of equipment.The present invention mainly realizes and forms production time plan taking Production Lot Planning as input, and clears up based on stand-by period relaxation method the device conflict that conventional method is not processed, particularly in the busy and complicated technological process of production.

Patent (the publication number " CN101303588A " of having applied for, a kind of automatic preparation method of steel smelting-continuous casting heat batch plan and system) according to the characteristic of the steel product of customer demand, build the mathematical model of describing heat batch plan problem, the mixing intelligent optimizing algorithm that has proposed the approximate dynamic programming of a class and Local Search obtains the optimization solution of model, and be translated into optimize produce heat batch plan, level and the quality of planning are improved thus, also greatly shortened the time of planning, but this is all for Production Lot Planning, for the preparation method of production time plan, this patent is not mentioned.

Patent (publication number " CN101770615A ", steel smelting-continuous casting production schedules based on mixing intelligent optimizing algorithm and Real-Time Scheduling optimization method and system) according to Production Lot Planning, go out production schedules and initial schedule scheme by mixing intelligent optimizing algorithmization, although this patent is addressed " in the time generating production schedules and scheduling scheme in summary, consider conflict possible between equipment and heat ", and the pre-defined rule having indicated on optional station collection in the 6th page, instructions (the 9th page of total page number) [0072]～[0076] paragraph comprises the minimum rule of device conflict ([0074] paragraph) etc., select the station of the start time of heat on station and the minimum of conflicting of the earliest available time of each station, but this rule can not ensure not occur device conflict, if generation device conflict, how to clear up conflict? this patent is not mentioned.

Document (Zheng Zhong, primary track flies, higher primary school is strong. the parallel backward inferring algorithm [J] of mixture length shop job scheduling. and computer integrated manufacturing system, 2008,14 (4): 749～756.) for the said equipment conflict situations, proposed rule-based conflict resolution method, its core concept is according to activity duration statistical law and randomness, in the zone of reasonableness of time distribution, clear up conflict by adjusting current task or its tight rear task generation or lasting time.This method has been utilized the statistical properties of activity duration distribution, although possible in theory, in practical application, there is following drawback: one, for ripe pneumatic steelmaking factory, taking converter smelting operation as example, the duration of blast of single stove molten steel is generally strict controlled in 28 minutes with interior (not comprising approximately 10 minutes non-cutting times), if utilize above rule-based conflict resolution method, for digesting equipment conflict, the processing time of converter smelting operation is shortened artificially or extended, to be all infeasible, because can causing smelting molten steel to guarantee the quality, completes in the shortening processing time on time, extend the operational use time that can cut down converter, affect the performance of converter production efficiency, and then affect efficiency and the benefit of whole pneumatic steelmaking factory, they are two years old, when by adjusting the generation of task or duration also cannot clear up conflict time, need to reset the beginning process time of station in the end operation of flow system, do like this, after all the method for still a kind of " examination is gathered ", lack specific aim as guide, not only increased amount of calculation, the success ratio of digesting equipment conflict also can not be guaranteed.

Summary of the invention

The technical problem to be solved in the present invention is: provide a kind of based on lax conflict resolution method of stand-by period and Optimization Scheduling, improve pneumatic steelmaking factory production efficiency.

The present invention for solving the problems of the technologies described above taked technical scheme is: based on lax conflict resolution method of stand-by period, it is characterized in that: given opening of respectively watering time watered time arrow, realizes as follows:

Step 100, initialization: all heats were arranged by time ascending order in zero hour of converter operation, and each heat is set is 0 at the stand-by period initial value of buffering operation, obtain the sequence zero hour;

Step 200, from the end of above-mentioned zero hour of sequence, taking heat corresponding to last data as current heat;

Step 300, along the zero hour sequence review forward, find corresponding with current heat tight before zero hour of heat;

Step 400, judge current heat with tight before heat whether there is device conflict in converter operation, if without conflict, go to step 600, otherwise the computing equipment conflict time, and continue next step;

Step 500, check tight before the buffering operation of heat after converter operation stand-by period of having distributed, calculate stand-by period allowance, by iteration relax adjust tight before heat cushion the stand-by period digesting equipment conflict of operations at these;

Step 600, in zero hour sequence using heat corresponding to the previous data of current heat zero hour as new current heat, and judge whether these data are the N (k in the sequence zero hour _l)+1 data, if so, end loop, and record each heat in the stand-by period of waiting for operation, otherwise go to step 300;

Wherein N (k _l) number of devices that comprises for converter operation.

Press such scheme, described step 500 specifically comprises:

The first stand-by period allowance of step 501, calculating the 1st buffering operation after converter operation, if the device conflict time is less than or equal to this allowance value, continues next step, otherwise goes to step 504;

Step 502, reset tight before heat in the stand-by period of the 1st buffering operation, by wait digesting equipment conflict herein;

Step 503, by the zero hour of the operation between converter operation and the 1st buffering operation of heat before tight in advance, and go to step 507;

The second stand-by period allowance of step 504, calculating the 2nd buffering operation after converter operation, if the device conflict time is less than or equal to the first stand-by period allowance and the second stand-by period allowance sum, continue next step, otherwise record can not, by the lax device conflict duration of clearing up of the stand-by period of two buffering operations, finish;

Step 505, reset tight before heat in the stand-by period of the 1st and the 2nd buffering operation, by the wait digesting equipments conflict of two buffering operations;

Step 506, shifted to an earlier date the zero hour of the operation between converter operation and the 2nd buffering operation of heat before tight discriminatively;

Before step 507, tight after adjusting in advance the zero hour of heat the position in zero hour sequence, to maintain the ascending order order of the sequence zero hour;

Before step 508, judgement are tight, whether the position in zero hour sequence changes the zero hour of heat, if so, goes to step 300, otherwise goes to step 600.

An Optimization Scheduling for steel-making continuous casting producing process, is characterized in that: it comprises the following steps:

S1, set up Optimal Operation Model:

$\left\{\begin{array}{c}\min f_1\\ \min f_2\\ \min f_3\end{array}\right.---\left(1\right)$

s.t.x(i,j+1,K)＝x(i,j,K)+t _p(i,j,K),

i∈Θ,j∈Φ _i,j＝1,…,J _i-1； (2)

x(i,j,k+1)≥x(i,j,k)+t _p(i,j,k)+t _t(i,j,k),

i∈Θ,j∈Φ _i,k∈Ψ,k≤K-1； (3)

$x(i,j,k)\≥x(\hat{i},\hat{j},k)+t_p(\hat{i},\hat{j},k),\∀y(\hat{i},\hat{j},k)=y(i,j,k),$

$i,\hat{i}\∈\mathrm{\Θ},j,\hat{j}\∈{\mathrm{\Φ}}_i,k\∈\mathrm{\Ψ},k\≤K-1;---\left(4\right)$

$y(i,j,k)\≠0,\∀t_p(i,j,k)\≠0,i\∈\mathrm{\Θ},j\∈{\mathrm{\Φ}}_i,k\∈\mathrm{\Ψ};---\left(5\right)$

$0\≤t_w(i,j,k)\≤t_w^{\max }\left(k_r\right),k=k_r;---\left(6\right)$

$0\≤t_w(i,j,k)\≤t_w^{\max }\left(k_c\right),k=k_c;---\left(7\right)$

$f_1=T_{\mathrm{conf}}^{{\mathrm{can}}^{\′}t}\left(k_l\right)=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{j=1}{\overset{G_i}{\mathrm{\Σ}}}{t}_{\mathrm{conf}}^{{\mathrm{can}}^{\′}t}(i,j,k_l)$

Wherein, f ₂=makespan=max (x (i, j, K)+t _p(i, j, K))-min (x (i, j, 1))

$f_3=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{j=1}{\overset{G_i}{\mathrm{\Σ}}}(t_w(i,j,k_r)+t_w(i,j,k_c));$

In formula, the implication of each label is:

I is for watering time numbering, and total I is watered time, i=1, and 2 ..., I; J is heat numbering, and i the heat number comprising in watering time is J _i, i.e. j=1,2 ..., J _i; K is operation numbering, total K procedure, and definition desulfurization process is numbered k=1, and continuous casting working procedure is numbered k=K; Definition k _l, k _rand k _cbe respectively the numbering of converter, vacuum refining and continuous casting working procedure.

(i, j, k) is the combination of subscript or variable, waters the processing operation of j inferior heat at k procedure for unique identification i; for the combination of subscript or variable, operate its correspondence for the processing of unique identification and i j the heat watering time heat before k procedure uses same equipment tight in individual water time the individual heat; For continuous casting working procedure, the multiple heats in watering because same time are successively at same conticaster upper, so have: $\begin{array}{cc}(\hat{i},\hat{j},K)=(i,j-1,K)& \∀j\∈[2,J_i]\end{array}.$

X (i, j, k) is j heat during i the waters time zero hour at operation k; be j heat during i waters time operation k tightly before zero hour of heat; t _w(i, j, k) be j heat during i waters time in the stand-by period of operation k, before clear and definite, before vacuum and continuous casting working procedure processing start, be set the stand-by period, especially, the stand-by period that is defined in vacuum refining and continuous casting working procedure is respectively t _w(i, j, k _r) and t _w(i, j, k _c).

for heat is the 1st the stand-by period upper limit that can wait for operation (vacuum refining operation); for heat is the 2nd the stand-by period upper limit that can wait for operation (continuous casting working procedure).

T _p(i, j, k) is j heat during i the waters time processing time at operation k; t _t(i, j, k) is j heat during i the waters time haulage time between operation k and rear operation.

Θ all waters inferior set, meets Θ={ i|i ∈ [1, I] }; Φ _ibe the heat set during i waters time, meet Φ _i={ j|j ∈ [1, J _i]; Ψ is the set of whole treatment process, meets Ψ={ k|k ∈ [1, K] }.

the conflict duration sum that can not clear up in converter operation for all heats.

In Optimal Operation Model, formula (1) is objective function collection, wherein:

F ₁represent that all heats can not be by the stand-by period converter processing apparatus conflict duration sum of clearing up that relaxes;

F ₂represent completion date, poor for the early start moment x (i, j, 1) that completes the latest moment and first operation of last procedure, the moment that completes the latest of last procedure is the x zero hour (i, j, K) and processing moment t _p(i, j, K) sum;

F ₃represent the stand-by period sum of all heats two buffering operations.

The technique meaning that above-mentioned objective function collection is set is: respectively water inferior opening the time of watering by optimizing, and rationally adjustment relaxes the stand-by period of each heat two buffering operations where necessary, make total device conflict duration minimum, completion date minimum, and total heat stand-by period minimum.Optimized variable is respectively to water the inferior zero hour.

Formula (2)～formula (5) is the constraint that must meet while working out conventional Steelmaking-Continuous Casting Production Scheduling plan, wherein: formula (2) represents to connect waters constraint, x (i, j, and x (i K), j+1, K) be respectively i water time in two adjacent heats water the moment opening of continuous casting working procedure, t _p(i, j, K) is duration of pouring of previous heat wherein; Formula (3) represents that, between the adjacent operation of same heat, a rear operation need be disposed and could start in last operation, also needs to consider the haulage time of adjacent inter process, x (i, j, k) and x (i, j, k+1) be respectively the zero hour of heat in adjacent operation; Formula (4) represents to use in same operation the adjacent heat of same equipment, need wait until tight before heat be disposed could next heat, y (i, j, k) and be respectively the equipment serial number of distributing to this pair of adjacent heat; Formula (5) represents need not to be that 0 operation is assigned on certain equipment of corresponding operation and processes by each processing time of heat.

Formula (6)～formula (7) represents stand-by period constraint, and each heat all can not exceed corresponding upper limit set value two stand-by period that can wait for process links.

S2, solve opening of respectively watering time and water time arrow:

S201, adopt natural number coding mode, chromosome waters time arrow by opening of watering time and forms;

S202, by f ₁as chromosome fitness, calculate every chromosomal f simultaneously ₂and f ₃, chromosomal being constructed as follows:

[x(1,1,K)?x(2,1,K)?…?x(I,1,K)?f ₃?f ₂?f ₁]

During superincumbent chromosome forms, x (1,1, K), x (2,1, K) and x (I, 1, K) philosophy be the 1st to I water time in the 1st heat water the moment opening of continuous casting working procedure, that is to say and water inferior 1 to I open and water the moment;

S203, one of structure have some chromosomal initial population, and chromosomal quantity is set as required;

S204, preserve when optimum individual in former generation population, if to make fitness be 0 chromosome when having in former generation population, or reach the maximum evolutionary generation setting in advance, stop calculating;

S205, select, crossover and mutation operation, and go to step S204.

S3, opening that S2 is obtained are watered time arrow and are watered time arrow as given opening of respectively watering time, clear up conflict according to above-mentioned based on lax conflict resolution method of stand-by period.

Beneficial effect of the present invention is:

1) overcome the drawback that shortens or extend artificially the converter smelting operation processing time in classic method for digesting equipment conflict, shortening the processing time can cause smelting molten steel to guarantee the quality completing on time, extend the operational use time that can cut down converter, affect the performance of converter production efficiency, and then affect efficiency and the benefit of whole pneumatic steelmaking factory, processing time based on the uncomfortable turn over stove of lax conflict resolution method of stand-by period smelting procedure and other any operations in the present invention, this is most important for the stability that keeps pneumatic steelmaking factory to produce, also agreed with the technique reality of ripe pneumatic steelmaking factory.

2) overcome " examination is gathered " feature in classic method, in the present invention based on lax conflict resolution method of stand-by period by specifying in advance the stand-by period upper limit of heat in buffering operation, allowance and the directivity adjusted are clear and definite, so not only simplify amount of calculation, contrast experiment's result shows, the success ratio of digesting equipment conflict has also had lifting by a relatively large margin.

3) overcome in classic method every group is opened and water time arrow execution " parallel retrodicting ", and attempt the numerous and diverse and reciprocal calculating that the device conflict for clearing up under every group of vector exists, and this reciprocal calculating is absorbed in the possibility of " endless loop ", the Multiobjective Optimal Operation model building by solving the present invention, can in calculating, single iteration identify fast when making respectively device conflict duration sum minimum and maximum optimum and the worst individual in former generation, be aided with " optimum individual preservation " principle in genetic algorithm simultaneously, not only simplify to optimize and calculated, also greatly accelerated convergence of algorithm process.

Brief description of the drawings

Fig. 1 is the corresponding relation schematic diagram of current heat and its tight front heat.

Fig. 2 is the position process flow diagram of the zero hour in sequence of adjusting the tight front heat after in advance.

Fig. 3 is the conflict resolution method processing flow chart lax based on the stand-by period.

Fig. 4 is the Optimized Operation result exemplary plot that application the present invention obtains.

Fig. 5 is another Optimized Operation result exemplary plot that application the present invention obtains.

Fig. 6 is conflict resolution method in the present invention and the comparison result of classic method.

Embodiment

Below in conjunction with instantiation and accompanying drawing, the present invention will be further described.

The process links that conventional pneumatic steelmaking factory comprises has: desulfurization (KR), converter smelting (LD), Argon (Ar), ladle furnace (LF), vacuum refining (RH) and continuous casting (CC) etc.Meet following technique precondition:

1) different steel grade correspondences different PROCESS FOR TREATMENT paths, can pass through successively above-mentioned all or part of process links, as KR → LD → Ar → CC, KR → LD → LF → RH → CC etc., but on processing route, there is not winding, can twice by same operation, melt down and within the situation that changes steel do not consider category herein.

2) molten steel several classes below the time of pneumatic steelmaking factory is divided into: the processing time (comprising non-cutting time) of operation, the haulage time of adjacent inter process, and stand-by period before operation.In the present invention, do not consider the flexibility of front two class times, and only have last class " stand-by period before operation " capable of regulating as required.

3) for requirement is watered by the company that meets conticaster, while is in conjunction with the actual conditions of steel-smelting-continuous casting manufacturing technique, allow molten steel to complete before conticaster cast starts and can wait for a period of time at converter smelting, but must meet the largest interval time-constrain of maximum latency constraint or adjacent inter process.

4) according to the situation from domestic certain typical pneumatic steelmaking factory investigation, in whole STEELMAKING PRODUCTION flow process, the flexible adjustable time is mainly two sections below: 1. handle from converter the time interval that vacuum starts to process and be no more than for example 25min; 2. handling conticaster from vacuum (if without vacuum, referring to a upper procedure of continuous casting) opens the time interval of watering and is no more than for example 30min.Note, in two kinds of situations, all will comprise the haulage time of molten steel at inter process.In addition, the 25min here and 30min are only examples, can be in conjunction with the actual time span arbitrarily of being arranged to.

5) stand-by period before specific to vacuum and continuous casting working procedure by the time adjustable above-mentioned flexibility, clear up contingent device conflict by the stand-by period at lax this two place.

In all process steps that pneumatic steelmaking factory comprises, although may there is device conflict in each operation in the time working out a production plan, but the bottleneck place of the general Shi Quan of converter smelting operation factory productive capacity, the possibility maximum clashing in this operation, clear up this operation conflict the most difficult, method is also the most complicated.Based on this, the basic ideas of explaination based on lax conflict resolution method of stand-by period as an example of converter smelting operation example below.

Water time arrow for every group of given inferior opening of watering, according to " parallel backward algorithm ", (this algorithm is referring to document (Zheng Zhong, primary track flies, higher primary school is strong. the parallel backward inferring algorithm [J] of mixture length shop job scheduling. and computer integrated manufacturing system, 2008,14 (4): 749～756.)), can know each heat by inference at x (the i zero hour of converter operation, j, k _l), all heats were arranged by time ascending order in the zero hour of converter operation.

J the heat that definition and i water time is arranged on same block converter equipment, and the heat of processing processing sequence before it be tight before heat, be the zero hour of tightly front heat if suppose, each processing time of watering time in converter operation equates, is t _p(i, j, k _l), each heat and its tight before the condition of heat processing time in converter operation below must meeting, just unlikely generation device conflict,

$x(i,j,k_l)-x(\hat{i},\hat{j},k_l)\≥t_p(i,j,k_l)$

Below from sorted all heats the end of sequence of the composition zero hour of converter operation, taking last heat as current heat, calculate current heat and its tight before interval between heat zero hour, before tight, need review forward the zero hour of heat along sequence, is the current heat zero hour of N (k before _l) individual data, wherein, N (k _l) number of devices that comprises for converter operation.

Taking Fig. 1 as example explanation.As shown in Figure 1, if definition heat m is current heat, be x (i, j, k its zero hour _l),, under converter quantity is the prerequisite of 3, before it is tight, heat is m-3, tight before zero hour of heat be

If the interval between the two is less than t _p(i, j, k _l), definition:

$t_{\mathrm{conf}}(i,j,k_l)=t_p(i,j,k_l)-[x(i,j,k_l)-x(\hat{i},\hat{j},k_l)]$

Wherein, t _conf(i, j, k _l) be the duration of current heat and its tight front heat generation device conflict, for eliminating this conflict, need the zero hour of tight front heat in advance.Because retrodict and obtain prior to converter operation the zero hour of converter subsequent handling, so need the link waited for after converter be set the stand-by period.Because except part high-quality steel, in the process route of not all steel grade, all comprise the 1st and can wait for link (being vacuum refining operation), so whether be divided into two kinds of situations through vacuum refining operation by heat before tight below describe.

Situation 1: through vacuum refining operation

Check tight before after converter operation the 1st of heat can wait for the stand-by period that link has been distributed if be less than explanation wait herein not yet reaches the upper limit, can be used in addition clearing up the argin of converter processing apparatus conflict.That is:

If

$t_{\mathrm{conf}}(i,j,k_l)\≤t_w^{\max }\left(k_r\right)-t_w^{\′}(\hat{i},\hat{j},k_r)$

Order

$t_w(\hat{i},\hat{j},k_r)=t_w^{\′}(\hat{i},\hat{j},k_r)+t_{\mathrm{conf}}(i,j,k_l)$

Wherein, for heat before tight after lax adjustment is in the stand-by period of vacuum refining operation.

Now, if heat also has other operations between converter operation and vacuum refining operation before tight, need shift to an earlier date in the lump the zero hour of other operations and converter operation, that is:

$x(\hat{i},\hat{j},k)=x^{\&prime;}(\hat{i},\hat{j},k)-t_{\mathrm{conf}}(i,j,k_l),\&ForAll;k_l\&le;k<k_r$

Wherein, with being respectively before and after lax adjustment the zero hour of i j the heat watering time at operation k.

If

$t_{\mathrm{conf}}(i,j,k_l)>t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)$

Also need to check tight before after converter operation the 2nd of heat can wait for the stand-by period that link has been distributed with the 1st can wait for that the processing logic of link is similar,

If

$t_{\mathrm{conf}}(i,j,k_l)>t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)\mathrm{and}$

$t_{\mathrm{conf}}(i,j,k_l)\&le;[t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)]+[t_w^{\max }\left(k_c\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_c)]$

Order

$t_w(\hat{i},\hat{j},k_r)=t_w^{\max }\left(k_r\right)$

$t_w(\hat{i},\hat{j},k_c)=t_w^{\&prime;}(\hat{i},\hat{j},k_c)+\{t_{\mathrm{conf}}(i,j,k_l)-[t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)\left]\right\}$

Wherein, with be respectively the lax stand-by period of rear tight front heat at vacuum refining operation and continuous casting working procedure of adjusting.

It should be noted that, if in this lax adjustment, before tight, heat all changed in the stand-by period of vacuum refining and continuous casting working procedure, needed shift to an earlier date in the lump with converter operation the zero hour of other operations between converter and continuous casting working procedure by it, and the algorithm shifting to an earlier date is:

$x(\hat{i},\hat{j},k)=x^{\&prime;}(\hat{i},\hat{j},k)-t_{\mathrm{conf}}(i,j,k_l),\&ForAll;k_l\&le;k<k_r$

$x(\hat{i},\hat{j},k)=x^{\&prime;}(\hat{i},\hat{j},k)-\{t_{\mathrm{conf}}(i,j,k_l)-[t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)\left]\right\},\&ForAll;k_r\&le;k<k_c$

Wherein, with implication with reference to above.

If two the argin sums that can wait for link are less than conflict duration, the device conflict duration that record now can not be cleared up is meet:

$t_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}(i,j,k_l)=t_{\mathrm{conf}}(i,j,k_l)-\left\{\right[t_w^{\max }\left(k_r\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_r)]+[t_w^{\max }\left(k_c\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_c)\left]\right\}$

Situation 2: without vacuum refining operation

Because heat before tight can be waited for link without the 1st, the argin that obviously can be used for clearing up the conflict of converter processing apparatus in this operation is 0, need check tight before after converter operation the 2nd of heat can wait for the stand-by period that link has been distributed processing logic is also similar with situation 1.

If

$t_{\mathrm{conf}}(i,j,k_l)\&le;t_w^{\max }\left(k_c\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_c)$

Order

$t_w(\hat{i},\hat{j},k_c)=t_w^{\&prime;}(\hat{i},\hat{j},k_c)+t_{\mathrm{conf}}(i,j,k_l)$

Wherein, for heat before tight after lax adjustment is in the stand-by period of continuous casting working procedure.

Except adjusting tight front heat in the stand-by period of continuous casting working procedure, also need the zero hour of every other operation between converter and continuous casting working procedure by it in advance, algorithm is as follows:

$x(\hat{i},\hat{j},k)=x^{\&prime;}(\hat{i},\hat{j},k)-t_{\mathrm{conf}}(i,j,k_l),\&ForAll;k_l\&le;k<k_c$

Wherein, with implication with reference to above.

If

$t_{\mathrm{conf}}(i,j,k_l)>t_w^{\max }\left(k_c\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_c)$

The device conflict duration that record now can not be cleared up is meet:

$t_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}(i,j,k_l)=t_{\mathrm{conf}}(i,j,k_l)-[t_w^{\max }\left(k_c\right)-t_w^{\&prime;}(\hat{i},\hat{j},k_c)]$

Before address, in the case of device conflict duration can be cleared up by the wait of buffering operation, need by heat before tight zero hour of converter operation in advance.In addition, may also need to adjust tight before zero hour of heat the position in whole zero hour sequence, to maintain the ascending order rule of this sequence.The flow process that sequence is adjusted as shown in Figure 2, comprises the steps: 1) before tight after relatively in advance heat tight in zero hour of converter operation and sequence before the sequencing of the zero hour of previous heat of heat, before the correspondence that value is less occurs in; 2) if the zero hour that is less than its previous heat the zero hour of tight front heat, the tight front heat of exchange and the sequencing of its previous heat in sequence.Step 1) and 2) also need iteration to carry out, until the sequence zero hour of all heats keeps ascending order to arrange.

If before tight after rearrangement there is variation in the position of heat zero hour, need to be with N (k before current heat zero hour _l) individual data are as zero hour of heat before tight, again carry out treatment scheme above.

Current heat is disposed, along the zero hour sequence move forward, using the previous data of current heat as the new current heat zero hour, above-mentioned treatment scheme is carried out in circulation, until the N (k of sequence _l)+1 data stop cycling.

Finally, check all heats, determining whether can not be by waiting for the device conflict of clearing up, if having, illustrates that the method can not be cleared up allly to water by given opening the device conflict that time arrow is retrodicted the converter operation drawing.Now, defining the conflict duration sum that all heats can not clear up in converter operation is meet:

$T_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}\left(k_l\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{J_i}{\mathrm{\&Sigma;}}}{t}_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}(i,j,k_l)$

In above formula, J _ifor watering the heat number comprising in time i, I is for watering sub-quantity.

If all device conflicts can be cleared up, illustrate that the method is effectively, now, need record each heat in the stand-by period that can wait for link.

Based on above-mentioned theory, the present embodiment provide based on lax conflict resolution method of stand-by period, given opening of respectively watering time watered time arrow, realizes as follows:

Step 100, initialization: all heats were arranged by time ascending order in zero hour of converter operation, and each heat is set is 0 at the stand-by period initial value of buffering operation, obtain the sequence zero hour;

Step 200, from the end of above-mentioned zero hour of sequence, taking heat corresponding to last data as current heat;

Step 300, along the zero hour sequence review forward, find corresponding with current heat tight before zero hour of heat;

Step 400, judge current heat with tight before heat whether there is device conflict in converter operation, if without conflict, go to step 600, otherwise the computing equipment conflict time, and continue next step;

Step 500, check tight before the buffering operation of heat after converter operation stand-by period of having distributed, calculate stand-by period allowance, by iteration relax adjust tight before heat cushion the stand-by period digesting equipment conflict of operations at these;

Step 500 specifically comprises:

The first stand-by period allowance of step 501, calculating the 1st buffering operation (being vacuum refining) after converter operation, if the device conflict time is less than or equal to this allowance value, continues next step, otherwise goes to step 504;

Step 502, reset tight before heat in the stand-by period of the 1st buffering operation, by wait digesting equipment conflict herein;

Step 503, will be tight before zero hour of heat operation between converter operation (comprising) and the 1st buffering operation (not comprising) shift to an earlier date, and go to step 507;

The second stand-by period allowance of step 504, calculating the 2nd buffering operation (continuous casting) after converter operation, if the device conflict time is less than or equal to the first stand-by period allowance and the second stand-by period allowance sum, continue next step, otherwise record can not, by the lax device conflict duration of clearing up of the stand-by period of two buffering operations, finish;

Step 505, reset tight before heat in the stand-by period of the 1st and the 2nd buffering operation, by the wait digesting equipments conflict of two buffering operations;

Step 506, heat before tight is shifted to an earlier date discriminatively in converter operation (comprising) and the 2nd zero hour of cushioning operation between operation (not comprising);

Before step 507, tight after adjusting in advance the zero hour of heat the position in zero hour sequence, to maintain the ascending order order of the sequence zero hour;

Before step 508, judgement are tight, whether the position in zero hour sequence changes the zero hour of heat, if so, goes to step 300, otherwise goes to step 600.

Step 600, in zero hour sequence using heat corresponding to the previous data of current heat zero hour as new current heat, and judge whether these data are the N (k in the sequence zero hour _l)+1 data, if so, end loop, and record each heat in the stand-by period of waiting for operation, otherwise go to step 300;

Wherein N (k _l) number of devices that comprises for converter operation.

Above-mentioned is all given opening to water under time arrow and applying of respectively watering time based on lax conflict resolution method of stand-by period.Water time arrow in order to obtain suitable opening, need to set up corresponding Optimal Operation Model and solve and obtain, therefore the invention provides a kind of Optimization Scheduling of steel-making continuous casting producing process, it comprises the following steps:

S1, set up Optimal Operation Model:

$\left\{\begin{array}{c}\min f_1\\ \min f_2\\ \min f_3\end{array}\right.---\left(1\right)$

s.t.x(i,j+1,K)＝x(i,j,K)+t _p(i,j,K),

i∈Θ,j∈Φ _i,j＝1,…,J _i-1； (2)

x(i,j,k+1)≥x(i,j,k)+t _p(i,j,k)+t _t(i,j,k),

i∈Θ,j∈Φ _i,k∈Ψ,k≤K-1； (3)

$x(i,j,k)\&GreaterEqual;x(\hat{i},\hat{j},k)+t_p(\hat{i},\hat{j},k),\&ForAll;y(\hat{i},\hat{j},k)=y(i,j,k),$

$i,\hat{i}\&Element;\mathrm{\&Theta;},j,\hat{j}\&Element;{\mathrm{\&Phi;}}_i,k\&Element;\mathrm{\&Psi;},k\&le;K-1;---\left(4\right)$

$y(i,j,k)\&NotEqual;0,\&ForAll;t_p(i,j,k)\&NotEqual;0,i\&Element;\mathrm{\&Theta;},j\&Element;{\mathrm{\&Phi;}}_i,k\&Element;\mathrm{\&Psi;};---\left(5\right)$

$0\&le;t_w(i,j,k)\&le;t_w^{\max }\left(k_r\right),k=k_r;---\left(6\right)$

$0\&le;t_w(i,j,k)\&le;t_w^{\max }\left(k_c\right),k=k_c;---\left(7\right)$

$f_1=T_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}\left(k_l\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{G_i}{\mathrm{\&Sigma;}}}{t}_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}(i,j,k_l)$

Wherein, f ₂=makespan=max (x (i, j, K)+t _p(i, j, K))-min (x (i, j, 1))

$f_3=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{G_i}{\mathrm{\&Sigma;}}}(t_w(i,j,k_r)+t_w(i,j,k_c));$

In formula, the implication of each label is:

I is for watering time numbering, and total I is watered time, i=1, and 2 ..., I; J is heat numbering, and i the heat number comprising in watering time is J _i, i.e. j=1,2 ..., J _i; K is operation numbering, total K procedure, and definition desulfurization process is numbered k=1, and continuous casting working procedure is numbered k=K; Definition k _l, k _rand k _cbe respectively the numbering of converter, vacuum refining and continuous casting working procedure.

(i, j, k) is the combination of subscript or variable, waters the processing operation of j inferior heat at k procedure for unique identification i; for the combination of subscript or variable, operate its correspondence for the processing of unique identification and i j the heat watering time heat before k procedure uses same equipment tight in individual water time the individual heat; For continuous casting working procedure, the multiple heats in watering because same time are successively at same conticaster upper, so have: $\begin{array}{cc}(\hat{i},\hat{j},K)=(i,j-1,K)& \&ForAll;j\&Element;[2,J_i]\end{array}.$

X (i, j, k) is j heat during i the waters time zero hour at operation k; be j heat during i waters time operation k tightly before zero hour of heat; t _w(i, j, k) be j heat during i waters time in the stand-by period of operation k, before clear and definite, before vacuum and continuous casting working procedure processing start, be set the stand-by period, especially, the stand-by period that is defined in vacuum refining and continuous casting working procedure is respectively t _w(i, j, k _r) and t _w(i, j, k _c).

for heat is the 1st the stand-by period upper limit that can wait for operation (vacuum refining operation); for heat is the 2nd the stand-by period upper limit that can wait for operation (continuous casting working procedure).

T _p(i, j, k) is j heat during i the waters time processing time at operation k; t _t(i, j, k) is j heat during i the waters time haulage time between operation k and rear operation.

Θ all waters inferior set, meets Θ={ i|i ∈ [1, I] }; Φ _ibe the heat set during i waters time, meet Φ _i={ j|j ∈ [1, J _i]; Ψ is the set of whole treatment process, meets Ψ={ k|k ∈ [1, K] }.

the conflict duration sum that can not clear up in converter operation for all heats.

In Optimal Operation Model, formula (1) is objective function collection, wherein:

F ₁represent that all heats can not be by the stand-by period converter processing apparatus conflict duration sum of clearing up that relaxes;

F ₂represent completion date, poor for the early start moment x (i, j, 1) that completes the latest moment and first operation of last procedure, the moment that completes the latest of last procedure is the x zero hour (i, j, K) and processing moment t _p(i, j, K) sum;

F ₃represent the stand-by period sum of all heats two buffering operations.

The technique meaning that above-mentioned objective function collection is set is: respectively water inferior opening the time of watering by optimizing, and rationally adjustment relaxes the stand-by period of each heat two buffering operations where necessary, make total device conflict duration minimum, completion date minimum, and total heat stand-by period minimum.Optimized variable is respectively to water the inferior zero hour.

Formula (2)～formula (5) is the constraint that must meet while working out conventional Steelmaking-Continuous Casting Production Scheduling plan, wherein: formula (2) represents to connect waters constraint, x (i, j, and x (i K), j+1, K) be respectively i water time in two adjacent heats water the moment opening of continuous casting working procedure, t _p(i, j, K) is duration of pouring of previous heat wherein; Formula (3) represents that, between the adjacent operation of same heat, a rear operation need be disposed and could start in last operation, also needs to consider the haulage time of adjacent inter process, x (i, j, k) and x (i, j, k+1) be respectively the zero hour of heat in adjacent operation; Formula (4) represents to use in same operation the adjacent heat of same equipment, need wait until tight before heat be disposed could next heat, y (i, j, k) and be respectively the equipment serial number of distributing to this pair of adjacent heat; Formula (5) represents need not to be that 0 operation is assigned on certain equipment of corresponding operation and processes by each processing time of heat.

Formula (6)～formula (7) represents stand-by period constraint, and each heat all can not exceed corresponding upper limit set value two stand-by period that can wait for process links.

S2, solve opening of respectively watering time and water time arrow: while specifically solving, adopt the optimizing of genetic algorithm iterative computation.Because genetic algorithm is as conventional intelligent algorithm, wherein basic selection, crossover and mutation operation etc. have been known by people, form and the relevant key link such as fitness is definite so only address below to chromosome.

S201, adopt natural number coding mode, chromosome waters time arrow by opening of watering time and forms;

S202, by f ₁as chromosome fitness, calculate every chromosomal f simultaneously ₂and f ₃, chromosomal being constructed as follows:

[x(1,1,K)?x(2,1,K)?…?x(I,1,K)?f ₃?f ₂?f ₁]

During superincumbent chromosome forms, x (1,1, K), x (2,1, K) and x (I, 1, K) philosophy be the 1st to I water time in the 1st heat water the moment opening of continuous casting working procedure, that is to say and water inferior 1 to I open and water the moment;

S203, one of structure have some chromosomal initial population, and chromosomal quantity is set as required, generally gets more than 200, and the present embodiment selects 300;

S204, preserve when optimum individual in former generation population, if to make fitness be 0 chromosome when having in former generation population, or reach the maximum evolutionary generation setting in advance, stop calculating;

S205, select, crossover and mutation operation, and go to step S204.

S3, opening that S2 is obtained are watered time arrow and are watered time arrow as given opening of respectively watering time, clear up conflict according to above-mentioned based on lax conflict resolution method of stand-by period.

In the time of actual solving, find as long as the scale of initial population arranges properly, even do not need to carry out selection, the crossover and mutation operation of genetic algorithm, in initial population, just having comprised many, to make fitness be 0 chromosome.Only need in these chromosomes, select to make successively completion date f ₂minimum and total waiting time f ₃minimum is just passable.But it should be noted that, this without heredity and mutation operation, directly in initial population, find the method for feasible solution to there is uncertainty, when population scale is adjusted enough greatly, when still not occur making fitness be 0 chromosome, should stop increasing population scale, and carry out optimizing by genetic manipulation.

Method in the present invention and model can meet the demand of Optimized Operation solution formulation under busy and complex working condition preferably, and plan scheduling and organization of production are played to good directive function, finally reach the object that improves pneumatic steelmaking factory production efficiency.

Embodiments of the invention are the pneumatic steelmaking factory of a large-scale iron and steel enterprise.This steelworks has 3 desulfurization stations, 3 block converters, 3 Argon stations, 2 RH vacuum refining furnaces, and 4 conticasters.The heat size of converter is 70 tons, and the day productive capacity of single seat converter is 90 stove left and right.Due to this converter heat size, relatively other newly-built converters are less, organization of production is comparatively flexible, thus bear high standard and short run contract for future delivery nearly all in iron and steel enterprise, and the development work of multiple new steel grades; In addition, because converter and the conticaster quantity of this steelworks are unequal, traditional " stove machine coupling " rule is inapplicable at this, coordinates converter and conticaster more difficult.Just because of above-mentioned 2 reasons cause this steelworks having relatively high expectations to plan scheduling and organization of production.Inventor has selected so representational pneumatic steelmaking factory, verifies validity of the present invention.

Taking the production schedule of this steelworks day shift on February 13rd, 2012 (8 hours dutys) as example, total stove number in the works on duty reaches 31 stoves, and steel grade quantity is 6 kinds, is to be that typical multi-varieties and small-batch contract is produced, thereby having relatively high expectations to scheduling.The concrete production schedule is as shown in table 1 below.

Table 1 production schedule example

Particularly, the processing route of each steel grade and the processing time of each operation are as shown in table 2 below.In table, the unit in operation processing time is minute, if certain steel grade does not have numerical value in concrete operation, to illustrate that it is without this operation.

The processing route of table 2 steel grade and each operation processing time

By application the present invention propose based on lax conflict resolution method of stand-by period and Optimal Operation Model and algorithm, the Optimized Operation result obtaining is as shown in Figure 4.Wherein, the stand-by period upper limit before vacuum refining and continuous casting working procedure is all set to 15 minutes.In Fig. 4, a lot of heats have a little rectangle on the upper left side of the processing time of vacuum refining and continuous casting working procedure square, and this just represents the stand-by period optimal value of heat before these operations, the length of the width corresponding waiting time of little rectangle.

Fig. 5 is another Optimized Operation result of above-mentioned example.The Optimized Operation result that Fig. 4 and Fig. 5 are corresponding is indiscriminate from the objective function collection of scheduling model, both f ₁be 0, namely device conflict is cleared up completely, without conflict, completion date f ₂be 519 minutes, at the stand-by period sum f of buffering operation ₃be 90 minutes.Can see, both difference have 2 points: one, and the 5th heat (code name 6.5 in figure) that the 5th the 2nd heat (code name 5.2 in figure) watering time and the 6th water time is in the difference of converter processing apparatus appointment; Its two, each heat is the stand-by period difference before operation in buffering.

In order to verify the conflict resolution method validity in the present invention, we have done three groups of experiments altogether, experiment number in every group is respectively 30,40 and 50 times, with comparing based on lax conflict resolution method of stand-by period in classic method and the present invention, two kinds of diverse ways of record application can obtain the number of times without the scheduling result of device conflict respectively.The comparison result of three groups of experiments as shown in Figure 6, can be found out, applies the number of times of the complete digesting equipment conflict of conflict resolution method of the present invention apparently higher than classic method.

Above embodiment is only for calculating thought of the present invention and feature are described, its object is to make those skilled in the art can understand content of the present invention and implement according to this, and protection scope of the present invention is not limited to above-described embodiment.So the disclosed principle of all foundations, equivalent variations or the modification that mentality of designing is done, all within protection scope of the present invention.

Claims (3)

1. based on lax conflict resolution method of stand-by period, it is characterized in that: given opening of respectively watering time watered time arrow, realizes as follows:

Step 100, initialization: all heats were arranged by time ascending order in zero hour of converter operation, and each heat is set is 0 at the stand-by period initial value of buffering operation, obtain the sequence zero hour;

Step 200, from the end of above-mentioned zero hour of sequence, taking heat corresponding to last data as current heat;

Step 300, along the zero hour sequence review forward, find corresponding with current heat tight before zero hour of heat;

Step 400, judge current heat with tight before heat whether there is device conflict in converter operation, if without conflict, go to step 600, otherwise the computing equipment conflict time, and continue next step;

Step 500, check tight before the buffering operation of heat after converter operation stand-by period of having distributed, calculate stand-by period allowance, by iteration relax adjust tight before heat cushion the stand-by period digesting equipment conflict of operations at these;

Step 600, in zero hour sequence using heat corresponding to the previous data of current heat zero hour as new current heat, and judge whether these data are the N (k in the sequence zero hour _l)+1 data, if so, end loop, and record each heat in the stand-by period of waiting for operation, otherwise go to step 300;

Wherein N (k _l) number of devices that comprises for converter operation.

2. according to claim 1 based on lax conflict resolution method of stand-by period, it is characterized in that: described step 500 specifically comprises:

The first stand-by period allowance of step 501, calculating the 1st buffering operation after converter operation, if the device conflict time is less than or equal to this allowance value, continues next step, otherwise goes to step 504;

Step 502, reset tight before heat in the stand-by period of the 1st buffering operation, by wait digesting equipment conflict herein;

Step 503, by the zero hour of the operation between converter operation and the 1st buffering operation of heat before tight in advance, and go to step 507;

The second stand-by period allowance of step 504, calculating the 2nd buffering operation after converter operation, if the device conflict time is less than or equal to the first stand-by period allowance and the second stand-by period allowance sum, continue next step, otherwise record can not, by the lax device conflict duration of clearing up of the stand-by period of two buffering operations, finish;

Step 505, reset tight before heat in the stand-by period of the 1st and the 2nd buffering operation, by the wait digesting equipments conflict of two buffering operations;

Step 506, shifted to an earlier date the zero hour of the operation between converter operation and the 2nd buffering operation of heat before tight discriminatively;

Before step 507, tight after adjusting in advance the zero hour of heat the position in zero hour sequence, to maintain the ascending order order of the sequence zero hour;

Before step 508, judgement are tight, whether the position in zero hour sequence changes the zero hour of heat, if so, goes to step 300, otherwise goes to step 600.

3. an Optimization Scheduling for steel-making continuous casting producing process, is characterized in that: it comprises the following steps:

S1, set up Optimal Operation Model:

$\left\{\begin{array}{c}\min f_1\\ \min f_2\\ \min f_3\end{array}\right.---\left(1\right)$

s.t.x(i,j+1,K)＝x(i,j,K)+t _p(i,j,K),

i∈Θ,j∈Φ _i,j＝1,…,J _i-1； (2)

x(i,j,k+1)≥x(i,j,k)+t _p(i,j,k)+t _t(i,j,k),

i∈Θ,j∈Φ _i,k∈Ψ,k≤K-1； (3)

$x(i,j,k)\&GreaterEqual;x(\hat{i},\hat{j},k)+t_p(\hat{i},\hat{j},k),\&ForAll;y(\hat{i},\hat{j},k)=y(i,j,k),$

$i,\hat{i}\&Element;\mathrm{\&Theta;},j,\hat{j}\&Element;{\mathrm{\&Phi;}}_i,k\&Element;\mathrm{\&Psi;},k\&le;K-1;---\left(4\right)$

$y(i,j,k)\&NotEqual;0,\&ForAll;t_p(i,j,k)\&NotEqual;0,i\&Element;\mathrm{\&Theta;},j\&Element;{\mathrm{\&Phi;}}_i,k\&Element;\mathrm{\&Psi;};---\left(5\right)$

$0\&le;t_w(i,j,k)\&le;t_w^{\max }\left(k_r\right),k=k_r;---\left(6\right)$

$0\&le;t_w(i,j,k)\&le;t_w^{\max }\left(k_c\right),k=k_c;---\left(7\right)$

$f_1=T_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}\left(k_l\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{G_i}{\mathrm{\&Sigma;}}}{t}_{\mathrm{conf}}^{{\mathrm{can}}^{\&prime;}t}(i,j,k_l)$

Wherein, f ₂=makespan=max (x (i, j, K)+t _p(i, j, K))-min (x (i, j, 1))

$f_3=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{G_i}{\mathrm{\&Sigma;}}}(t_w(i,j,k_r)+t_w(i,j,k_c));$

In formula, the implication of each label is:

I is for watering time numbering, and total I is watered time, i=1, and 2 ..., I; J is heat numbering, and i the heat number comprising in watering time is J _i, i.e. j=1,2 ..., J _i; K is operation numbering, total K procedure, and definition desulfurization process is numbered k=1, and continuous casting working procedure is numbered k=K; Definition k _l, k _rand k _cbe respectively the numbering of converter, vacuum refining and continuous casting working procedure;

(i, j, k) is the combination of subscript or variable, waters the processing operation of j inferior heat at k procedure for unique identification i; for the combination of subscript or variable, operate its correspondence for the processing of unique identification and i j the heat watering time heat before k procedure uses same equipment tight in individual water time the individual heat; For continuous casting working procedure, $\begin{array}{cc}(\hat{i},\hat{j},K)=(i,j-1,K)& \&ForAll;j\&Element;[2,J_i]\end{array};$

X (i, j, k) is j heat during i the waters time zero hour at operation k; be j heat during i waters time operation k tightly before zero hour of heat; t _w(i, j, k) be j heat during i waters time in the stand-by period of operation k, before clear and definite, before vacuum and continuous casting working procedure processing start, be set the stand-by period, especially, the stand-by period that is defined in vacuum refining and continuous casting working procedure is respectively t _w(i, j, k _r) and t _w(i, j, k _c);

for heat is the 1st the stand-by period upper limit that can wait for operation; for heat is the 2nd the stand-by period upper limit that can wait for operation; Can wait for that operation is vacuum refining operation for the 1st; Can wait for that operation is continuous casting working procedure for the 2nd;

T _p(i, j, k) is j heat during i the waters time processing time at operation k; t _t(i, j, k) is j heat during i the waters time haulage time between operation k and rear operation;

Θ all waters inferior set, meets Θ={ i|i ∈ [1, I] }; Φ _ibe the heat set during i waters time, meet Φ _i={ j|j ∈ [1, J _i]; Ψ is the set of whole treatment process, meets Ψ={ k|k ∈ [1, K] };

the conflict duration sum that can not clear up in converter operation for all heats;

In Optimal Operation Model, formula (1) is objective function collection, wherein:

F ₁represent that all heats can not be by the stand-by period converter processing apparatus conflict duration sum of clearing up that relaxes;

F ₂represent completion date, poor for the early start moment x (i, j, 1) that completes the latest moment and first operation of last procedure, the moment that completes the latest of last procedure is the x zero hour (i, j, K) and processing moment t _p(i, j, K) sum;

F ₃represent the stand-by period sum of all heats two buffering operations;

The constraint that formula (2)～formula (5) must meet while being Steelmaking-Continuous Casting Production Scheduling plan, wherein: formula (2) represents to connect waters constraint, x (i, j, and x (i K), j+1, K) be respectively i water time in two adjacent heats water the moment opening of continuous casting working procedure, t _p(i, j, K) is duration of pouring of previous heat wherein; Formula (3) represents that, between the adjacent operation of same heat, a rear operation need be disposed and could start in last operation, also needs to consider the haulage time of adjacent inter process, x (i, j, k) and x (i, j, k+1) be respectively the zero hour of heat in adjacent operation; Formula (4) represents to use in same operation the adjacent heat of same equipment, need wait until tight before heat be disposed could next heat, y (i, j, k) and be respectively the equipment serial number of distributing to this pair of adjacent heat; Formula (5) represents need not to be that 0 operation is assigned on certain equipment of corresponding operation and processes by each processing time of heat;

Formula (6)～formula (7) represents stand-by period constraint, and each heat all can not exceed corresponding upper limit set value two stand-by period that can wait for process links;

S2, solve opening of respectively watering time and water time arrow:

S201, adopt natural number coding mode, chromosome waters time arrow by opening of watering time and forms;

S202, by f ₁as chromosome fitness, calculate every chromosomal f simultaneously ₂and f ₃, chromosomal being constructed as follows:

[x(1,1,K)?x(2,1,K)?…?x(I,1,K)?f ₃?f ₂?f ₁]

During superincumbent chromosome forms, x (1,1, K), x (2,1, K) and x (I, 1, K) philosophy be the 1st to I water time in the 1st heat water the moment opening of continuous casting working procedure, that is to say and water inferior 1 to I open and water the moment;

S203, one of structure have some chromosomal initial population, and chromosomal quantity is set as required;

S204, preserve when optimum individual in former generation population, if to make fitness be 0 chromosome when having in former generation population, or reach the maximum evolutionary generation setting in advance, stop calculating;

S205, select, crossover and mutation operation, and go to step S204;

S3, opening that S2 is obtained are watered time arrow and are watered time arrow as given opening of respectively watering time, according to clearing up conflict based on lax conflict resolution method of stand-by period described in claim 1 or 2.