CN105785963B - A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm - Google Patents
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm Download PDFInfo
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Abstract
The invention discloses a kind of steel-making continuous casting dispatching methods being based on artificial bee colony algorithm (ABC), this method remains the frame (including employing bee stage, observation bee stage and investigation bee stage) of ABC, and is improved in conjunction with JADE algorithms.Wherein, it employs the bee stage to be updated to the individual in population using the search strategy of JADE, and population diversity is increased using the external archival mechanism of JADE；The bee stage is observed, is increased on the basis of ABC original search strategies and the update of difference solution and the formed archive of current population is operated；The investigation bee stage uses ABC original search strategies at this stage.This method can accelerate the convergence rate of population under the premise of ensureing population diversity, can generate ideal scheduling result within a short period of time, to realize the purpose saved parts waiting time during steel-making continuous casting, reduce processing cost.
Description
Technical field
It is the invention belongs to the job scheduling field during steel-making continuous casting, more particularly to a kind of based on artificial bee colony algorithm
Steel-making continuous casting dispatching method.
Background technology
Steel and iron industry is the basic industry of the industries such as many other buildings, automation, and weight is occupied in world economy
Want status.Steelmaking process (Steelmaking Process) refer to will the iron containing fixed mixing ratio chemical composition in hot environment
Under be smelt the process that steel is frozen into steel plate again, it can effectively help steel plant carry out Plate Production.Steelmaking process substantially divides
For ironmaking, steel-making continuous casting, hot rolling three phases, wherein the steel-making continuous casting stage plays to hold in entire steel manufacture process and open
Under effect, be the key link in steelmaking process.Its specific steps include：First, the former material of steel-making is added into smelting furnace
Expect iron block, obtains the iron of molten condition by the preliminary purification under refining and high temperature, then put it into purification furnace and add
Certain chemicals carries out further purification smelting and obtains the steel of melting state, and the last continuous casting stage cools down the steel of thawing
It is manufactured into solid steel plate.
Steel-making continuous casting scheduling problem can regard the hybrid flow shop scheduling of a final stage workpiece grouping production as
Problem refers to specifically the last stage produced in steel-making continuous casting, and workpiece is in the form of packets according to being set in advance
Priority orders carry out continuously casting.It has the characteristics that：
(1) all different workpieces will pass through same process stage successively, that is, make steel, refine, three process segments of continuous casting,
Corresponding processing machine of each stage is respectively to convert stove, purification furnace and conticaster；
(2) there are multiple parallel processing machines, the complete phase of parallel machine in each stage in each production and processing stage
Together, the base unit of the first two stage process and in processing is workpiece, and what each workpiece can be at this stage is any one
It is processed on platform machine；
(3) process three phases be processed as unit of casting, wherein each casting include which workpiece and
Each casting is processed on which conticaster to be set in advance；
(4) workpiece being processed in refining and continuous casting stage, waiting is had to when not having available machines used can until having
With machine, this can cause the workpiece temperature waited for decline, and will produce the cost heated again to workpiece；
(5) in the third process segment, the workpiece by serial number point at same group will continuously be cast on the same conticaster
It makes, these workpiece do not allow the situation for being interrupted or occurring the conticaster free time in the process of implementation.When necessary, the workpiece in casting
Beginning delay to ensure that the workpiece on the same casting is continuously processed, in other words, it is ensured that upper one in same casting
At the beginning of the deadline of workpiece is next workpiece；
(6) workpiece is shorter in the settling time of steel-making and refining stage, can be ignored, same casting on conticaster
Different workpieces before settling time is not present, but the settling time of a new casting is relatively long, this time will be from
It is separated in the execution time of workpiece；
(7) there is also a delivery times between two process segments for workpiece, but since capacity is huge, intermediate transportation
The configuration of crane, which is ignored, to be disregarded；
(8) delivery time between the processing time and crane of all workpiece is non-negative, known, determines；
(9) at a time a workpiece can only execute on a machine, and a machine can only also process a workpiece；
(10) casting should be performed in the predefined time started, and in advance or execution of delaying can bring library respectively
Deposit cost problem and delay steel rolling problem.
Fig. 1 gives the process flow chart of steel-making continuous casting process.
Finally, workpiece is exactly assigned in machinery equipment by the purpose of steel-making continuous casting scheduling, and to steel-making stage and refining
Workpiece on stage each machine is ranked up, at the same determine each workpiece at the beginning of all stages with the deadline,
To realize the optimization to optimization aim.
Since a series of process segments of smelting iron and steel are all to complete under high temperature environment, the time between any link drags
Prolonging can all cause to store in workpiece waiting process and maintain the cost needed for high temperature, therefore be ground to steel-making continuous casting scheduling problem
Studying carefully is particularly important.However, the existing method for steel-making continuous casting scheduling cannot obtain preferably in a relatively short period of time
Dispatching effect.
Invention content
As described above, existing steel-making continuous casting dispatching method cannot obtain ideal dispatching effect within a short period of time, it is
Overcome this technical problem, the present invention to save the time as much as possible during steel-making continuous casting, reduce cost as starting point,
Propose a kind of Memetic methods being based on artificial bee colony algorithm (Artificial Bee Colony Algorithm, ABC)
(abbreviation ABCMA), to solve steel-making continuous casting scheduling problem.
In order to achieve the above technical purposes, the technical scheme is that, a kind of steel-making based on artificial bee colony algorithm connects
Dispatching method is cast, is included the following steps：
The relevant parameter in steel-making continuous casting scheduling process is arranged in step 1)；
Step 2) analyzes actual steel-making continuous casting scheduling process comprising three processing ranks of steelmaking-refining-continuous casting
Section.Consider influence of the various boundary conditions to scheduling result, establish the object function for needing to optimize in steel-making continuous casting scheduling process,
According to object function and various constraintss, the mathematical model of steel-making continuous casting scheduling is established；
Step 3) initializes ABCMA parameters, and initialization population according to obtained mathematical model；
Step 4) uses ABCMA to generate offspring individual for the individual in population, and uses ranking value (ROV) by offspring individual
Carry out the sequence that discretization obtains including all workpiece number；The workpiece sequencing on every machine is determined, in conjunction with steel-making continuous casting tune
Constraints during degree determines each workpiece at the beginning of different phase, the deadline, and calculates target with this
Functional value；According to target function value, the individual in population is updated using greedy selection method；
Step 5) judges whether to meet stop condition, if satisfied, terminating to run and record with minimum target functional value
Individual and its corresponding target function value；Otherwise step 4) is gone to；
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 1), relevant parameter
Including need process whole number pieces, casting number, the machine number in each stage；The workpiece number that each casting includes
The conticaster number of mesh, casting belonging to the third process segment and the casting sequence on each conticaster；Workpiece is each
Process time in stage, workpiece are in the delivery time of different phase, the settling time of casting.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 2), the pact
Beam condition includes：Workpiece between different processing stages conversion time constraint, third process segment casting settling time
One all workpiece Continuous machings constraint in constraint, third process segment each casting, machine of a certain moment can only be processed
The constraint that one workpiece and a workpiece can only be processed on a machine；It is needed in the steel-making continuous casting scheduling process
The object function to be optimized includes：The punishment of workpiece residence time, third process segment casting start punishment in advance, third adds
Work stage casting, which is delayed, to start to punish.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, it is described in the step 4)
ABCMA includes the following steps：
4.1) NP individual is randomly choosed in decision spaceConstitute initial population, individualIndicate one
Include the sequence of all workpiece, xi,jIt isJ-th of workpiece number, initialization population maximum iteration maxcycle, nectar source
Give up parameter limit, JADE algorithm relevant parameter q, c, μF, μCRAnd archive setCurrent algebraically cycle=0；Its
In,
FiIt is individual in JADEZoom factor, CRiIt is individual in JADECross-over control parameter, q for determine kind
In group it is best before [q*NP] individual, q ∈ (0,1], [q*NP] is to carry out round to q*NP, and c is for controlling Fi
And CRiAdaptive degree, μFAnd μCRRespectively FiAnd CRiAuto-adaptive parameter；
4.2) individual in population is calculatedTarget function value
4.3) judge whether iterations reach maxcycle, stop iteration if having reached, output has minimum target
The individual and its corresponding target function value of functional value；Otherwise turn 4.4)；
4.4) according to formula (1) (2) more new individualCRiValue；
CRi=randni(μCR,0.1) (1)
μCR=(1-c) * μCR+c*meanA(SCR) (2)
Wherein, randni(μCR, 0.1) and it indicates with μCRFor mean value, with 0.1 for standard deviation normal distyribution function；SCRIt is to work as
All successful CR in former generationiSet, meanA() is arithmetic mean of instantaneous value；
4.5) according to formula (3) (4) more new individualFiValue；
Fi=randci(μF,0.1) (3)
μF=(1-c) * μF+c*meanL(SF) (4)
Wherein, randci(μF, 0.1) and it indicates with μFIt is Cauchy's distribution of scale parameter for location parameter, with 0.1；SFIt is to work as
All successful F in former generationiSet.meanL() is the silent average value of Lay, passes through formula (5) and obtains：
4.6) utilize formula (6) to the individual in populationMutation operation is carried out, variation vector is obtained
Wherein,Be from current population it is best before [q*NP] individual in a randomly selected individual, q ∈ (0,
1], [q*NP] is to carry out round to q*NP,It is being different from of being selected at random from current populationIndividual,It is being different from of being selected at random from archive setWithIndividual；
4.7) rightWithTrial vector is generated using the crossover operator of JADECrossover operator used is shown in formula (7)
Binomial intersect；
Wherein, jrandIt is the randomly selected integer between [1, n], n is the total dimension of problem, and rand (0,1) is in [0,1]
Between equally distributed random number, due to jrandPresence can ensureIt is different from
4.8) trial vector is calculatedCorresponding target function valueUsing greedy selection method to individualIt carries out
Update：IfThenOtherwiseIt remains unchanged；
If 4.9)It is substitutedThen willIt stores to set A, by FiAnd CRiIt is stored respectively to SFAnd SCR, and
Limit is remained unchanged；Otherwise limit=limit+1；
If 4.10) number of individuals in set A (be denoted as | A |) is more than NP, a individual of random erasure (| A |-NP)；
4.11) formula (8) is utilized to calculate the corresponding Probability p of each individuali；
Wherein,It is individualTarget function value,The nectar amount of i-th of food source is represented, NP is
The number of food source and the individual amount in population；
4.12) according to Probability piSelection individual utilizes the individual that formula (9) is selectionGenerate offspring individual；
vi,j=xi,j+rand(-1,1)(xi,j-xk,j) (9)
Wherein, k indicates that any one individual number different from i, j ∈ [1, n] indicate j-th of dimension, and n is that problem is always tieed up
Degree, rand (- 1,1) indicate the equally distributed random number between [- 1,1]；
4.13) calculateTarget function valueUsing greedy selection method to individualIt is updated：IfThenOtherwiseIt remains unchanged；
4.14) ifIt is substitutedThen willIt stores to set A, and limit is remained unchanged, otherwise limit=
limit+1；
If 4.15) number of individuals in set A (be denoted as | A |) is more than NP, a individual of random erasure (| A |-NP)；
If 4.16) the limit values of some individual have reached the upper limit of setting, which is deleted (if reaching the upper limit
Individual have it is multiple, then random erasure one of them), and using formula (10) generate a new individual：
vi,j=xmin,j+rand(0,1)(xmax,j-xmin,j) (10)
Wherein, j ∈ [1, n] indicate j-th of dimension, and n is the total dimension of problem, xmax,jAnd xmin,jIt is the upper and lower of jth dimension respectively
Limit, rand (0,1) indicate the equally distributed random number between [0,1]；
4.17) individual and its corresponding target function value of the record with minimum target functional value, cycle=cycle+1,
And it goes to 4.3).
In above process, it is 4.4) -4.10) to employ the bee stage, 4.11) -4.15) it is to observe the bee stage, 4.16) it is to detect
Look into the bee stage.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 4), according to following
Method determines the workpiece sequencing on every machine：Machine choice, choosing are carried out according to comprising the workpiece that is ordered as that all workpiece are numbered
The machine of current idle is selected, when current idle machine is more than one, then arbitrarily specifies one.In conjunction on known conticaster
Casting composition and casting distribution, finally obtain the workpiece sequencing being processed on every machine.
The technical effects of the invention are that using this method, population can be accelerated under the premise of ensureing population diversity
Convergence rate, to achieve the purpose that shorten scheduling time, reduce scheduling cost.Method proposed by the present invention is in convergence effect
It is significantly better than that other common methods in terms of convergence rate.
The invention will be further described below in conjunction with the accompanying drawings.
Description of the drawings
Fig. 1 is the process flow chart during steel-making continuous casting；
Fig. 2 is the Job Scheduling schematic diagram of workpiece steel-making continuous casting process；
Fig. 3 is the scheduling gunter illustrated example of 7 workpiece in steel-making continuous casting scheduling, wherein the number of machines difference of three phases
It is 3,2,2, it is assumed here that by the optimal workpiece sequencing that some way obtains be π=[1,5,2,6,3,7,4]；
Fig. 4 is the flow chart of ABCMA；
1 corresponding scheduling convergence curve figure of example when Fig. 5 is NP=50, maxcycle=1000；
2 corresponding scheduling convergence curve figure of example when Fig. 6 is NP=50, maxcycle=2000；
3 corresponding scheduling convergence curve figure of example when Fig. 7 is NP=100, maxcycle=1000；
4 corresponding scheduling convergence curve figure of example when Fig. 8 is NP=100, maxcycle=2000；
Specific implementation mode
Steel-making continuous casting process includes three process segments of steelmaking-refining-continuous casting, its process flow chart is as shown in Figure 1.This
The problem of being solved the problems, such as in invention is the hybrid flow shop scheduling during steel-making continuous casting, and the Job Scheduling of problems shows
It is intended to as shown in Fig. 2, it can regard the hybrid flow shop scheduling problem of a final stage workpiece grouping production as.Except this
Except, the scheduling problem in actual production environment is solved, needs to consider a series of production constraints, as given in technical background
10 features of the steel-making scheduling problem gone out, they are this problem constraints needed to be considered simultaneously.
In providing the present invention before dispatching method more detailed description, steel-making continuous casting scheduling to be solved is first provided
The model of problem, as shown in table 1.
Object function (1) is that workpiece residence time, casting shift to an earlier date/delay and punish caused by execution and be multiplied by after penalty coefficient
Summation；Constraints (2) indicates that each workpiece must successively pass through three process segments, and a sometime workpiece
It can only be processed on a certain machine in a certain stage；Constraints (3) is technological constraint, indicates the same workpiece three
In the process of a successive stages, the latter process operation has to wait for previous process operation and is finished and workpiece quilt
It is transferred to after the machine needed for the latter process operation and just starts to execute；Constraints (4) indicated in the third process segment
The Starting Executing Time for first casting processed on machine (conticaster) constrains；Constraints (5) is specified in same casting
On be processed workpiece continuity requirement；Constraints (6) indicates two be processed on same conticaster continuously
Setup time constraint between casting.
1 problem model of table
Wherein,
Φ1Indicate workpiece residence time penalty term；
Φ2Indicate that casting shifts to an earlier date time started penalty term；
Φ3Indicate that casting is delayed time started penalty term；
N indicates workpiece total number；
CP1Indicate workpiece residence time penalty coefficient；
CP2Indicate that casting shifts to an earlier date time started penalty coefficient；
CP3Indicate that casting is delayed time started penalty coefficient；
J indicates that any one workpiece, J are the set of all workpiece；
S indicates that process segment, s ∈ { 1,2,3 }, 3 stages are respectively to make steel, refine, continuous casting；
MsIndicate the collection of machines in s stages；
fs,j,kCharacterize whether j-th of workpiece is assigned in the s stages on k-th of machine, it is yes that value, which takes 1, and it is no that value, which takes 0,；
Ss,jIndicate j-th of workpiece at the beginning of the s stages；
Ps,jIndicate j-th of workpiece the s stages the execution time；
Ts,s+1Indicate the delivery time between two stages, s ∈ { 1,2 }；
R3,mIndicate the release time of third process segment machine m；
Indicate the settling time of first casting on m-th of conticaster；
Indicate the unit one on first casting on m-th of conticaster；
CN indicates conticaster set；
Indicate the casting number on m-th of conticaster；
It is the scheduling gunter illustrated example of 7 workpiece shown in attached drawing 3, relevant workpiece residence time, work is given in figure
The nouns paraphrase such as part conversion time and casting settling time.Assuming that by some way obtained workpiece sequencing be π=[1,5,
2,6,3,7,4], then the Gantt chart means that the Job Scheduling effect obtained according to this workpiece sequencing.
The present invention is exactly under the premise of considering relevant constraint limitation, to the workpiece residence time described in table 1, casting
Part shifts to an earlier date the time started, casting is delayed object functions such as time started, using a kind of side Memetic based on artificial bee colony algorithm
Method, i.e. ABCMA optimize, and are as follows described：
The relevant parameter in steel-making continuous casting scheduling process is arranged in step 1)；
Step 2) analyzes actual steel-making continuous casting scheduling process comprising three processing ranks of steelmaking-refining-continuous casting
Section.Consider influence of the various boundary conditions to scheduling result, establish the object function for needing to optimize in steel-making continuous casting scheduling process,
According to object function and various constraintss, the mathematical model of steel-making continuous casting scheduling is established；
Step 3) initializes ABCMA parameters, and initialization population according to obtained mathematical model；
Step 4) uses ABCMA to generate offspring individual for the individual in population, and uses ranking value (ROV) by offspring individual
Carry out the sequence that discretization obtains including all workpiece number；The workpiece sequencing on every machine is determined, in conjunction with steel-making continuous casting tune
Constraints during degree determines each workpiece at the beginning of different phase, the deadline, and calculates target with this
Functional value；According to target function value, the individual in population is updated using greedy selection method；
Step 5) judges whether to meet stop condition, if satisfied, terminating to run and record with minimum target functional value
Individual and its corresponding target function value；Otherwise step 4) is gone to；
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 1), relevant parameter
Including need process whole number pieces, casting number, the machine number in each stage；The workpiece number that each casting includes
The conticaster number of mesh, casting belonging to the third process segment and the casting sequence on each conticaster；Workpiece is each
Process time in stage, workpiece are in the delivery time of different phase, the settling time of casting.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 2), the pact
Beam condition includes：Workpiece between different processing stages conversion time constraint, third process segment casting settling time
One all workpiece Continuous machings constraint in constraint, third process segment each casting, machine of a certain moment can only be processed
The constraint that one workpiece and a workpiece can only be processed on a machine；It is needed in the steel-making continuous casting scheduling process
The object function to be optimized includes：The punishment of workpiece residence time, third process segment casting start punishment and third in advance
A process segment casting, which is delayed, to start to punish.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, it is described in the step 4)
ABCMA includes the following steps：
4.1) NP individual is randomly choosed in decision spaceConstitute initial population, individualIndicate one
Include the sequence of all workpiece, xi,jIt isJ-th of workpiece number, initialization population maximum iteration maxcycle, nectar source
Give up parameter limit, JADE algorithm relevant parameter q, c, μF, μCRAnd archive setCurrent algebraically cycle=0；Its
In,
FiIt is individual in JADEZoom factor, CRiIt is individual in JADECross-over control parameter, q for determine kind
In group it is best before [q*NP] individual, q ∈ (0,1], [q*NP] is to carry out round to q*NP, and c is for controlling Fi
And CRiAdaptive degree, μFAnd μCRRespectively FiAnd CRiAuto-adaptive parameter；
4.2) individual in population is calculatedTarget function value
4.3) judge whether iterations reach maxcycle, stop iteration if having reached, output has minimum target
The individual and its corresponding target function value of functional value；Otherwise turn 4.4)；
4.4) according to formula (1) (2) more new individualCRiValue；
CRi=randni(μCR,0.1) (1)
μCR=(1-c) * μCR+c*meanA(SCR) (2)
Wherein, randni(μCR, 0.1) and it indicates with μCRFor mean value, with 0.1 for standard deviation normal distyribution function；SCRIt is to work as
All successful CR in former generationiSet, meanA() is arithmetic mean of instantaneous value；
4.5) according to formula (3) (4) more new individualFiValue；
Fi=randci(μF,0.1) (3)
μF=(1-c) * μF+c*meanL(SF) (4)
Wherein, randci(μF, 0.1) and it indicates with μFIt is Cauchy's distribution of scale parameter for location parameter, with 0.1；SFIt is to work as
All successful F in former generationiSet.meanL() is the silent average value of Lay, passes through formula (5) and obtains：
4.6) utilize formula (6) to the individual in populationMutation operation is carried out, variation vector is obtained
Wherein,Be from current population it is best before [q*NP] individual in a randomly selected individual, q ∈ (0,
1], [q*NP] is to carry out round to q*NP,It is being different from of being selected at random from current populationIndividual,It is being different from of being selected at random from archive setWithIndividual；
4.7) rightWithTrial vector is generated using the crossover operator of JADECrossover operator used is shown in formula (7)
Binomial intersect；
Wherein, jrandIt is the randomly selected integer between [1, n], n is the total dimension of problem, and rand (0,1) is in [0,1]
Between equally distributed random number, due to jrandPresence can ensureIt is different from
4.8) trial vector is calculatedCorresponding target function valueUsing greedy selection method to individualIt carries out
Update：IfThenOtherwiseIt remains unchanged；
If 4.9)It is substitutedThen willIt stores to set A, by FiAnd CRiIt is stored respectively to SFAnd SCR, and
Limit is remained unchanged；Otherwise limit=limit+1；
If 4.10) number of individuals in set A (be denoted as | A |) is more than NP, a individual of random erasure (| A |-NP)；
4.11) formula (8) is utilized to calculate the corresponding Probability p of each individuali；
Wherein,It is individualTarget function value,Represent the nectar amount of i-th of food source, NP
The number for being food source and the individual amount in population；
4.12) according to Probability piSelection individual utilizes the individual that formula (9) is selectionGenerate offspring individual；
vi,j=xi,j+rand(-1,1)(xi,j-xk,j) (9)
Wherein, k indicates that any one individual number different from i, j ∈ [1, n] indicate j-th of dimension, and n is that problem is always tieed up
Degree, rand (- 1,1) indicate the equally distributed random number between [- 1,1]；
4.13) calculateTarget function valueUsing greedy selection method to individualIt is updated：IfThenOtherwiseIt remains unchanged；
4.14) ifIt is substitutedThen willIt stores to set A, and limit is remained unchanged, otherwise limit=
limit+1；
If 4.15) number of individuals in set A (be denoted as | A |) is more than NP, a individual of random erasure (| A |-NP)；
If 4.16) the limit values of some individual have reached the upper limit of setting, which is deleted (if reaching the upper limit
Individual have it is multiple, then random erasure one of them), and using formula (10) generate a new individual：
vi,j=xmin,j+rand(0,1)(xmax,j-xmin,j) (10)
Wherein, j ∈ [1, n] indicate j-th of dimension, and n is the total dimension of problem, xmax,jAnd xmin,jIt is the upper and lower of jth dimension respectively
Limit, rand (0,1) indicate the equally distributed random number between [0,1]；
4.17) individual and its corresponding target function value of the record with minimum target functional value, cycle=cycle+1,
And it goes to 4.3).
In above process, it is 4.4) -4.10) to employ the bee stage, 4.11) -4.15) it is to observe the bee stage, 4.16) it is to detect
Look into the bee stage.
A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, in the step 4), according to following
Method determines the workpiece sequencing on every machine：Machine choice, choosing are carried out according to comprising the workpiece that is ordered as that all workpiece are numbered
The machine of current idle is selected, when current idle machine is more than one, then arbitrarily specifies one.In conjunction on known conticaster
Casting composition and casting distribution, finally obtain the workpiece sequencing being processed on every machine.
In order to more truly reflect effect of the present invention in steel-making continuous casting scheduling problem, it is necessary to assure the input of experiment
Situation is close to actual production environment.Therefore, the narration in conjunction with other related articles to experimental situation, reference of the present invention
The practical condition of Shanghai Baoshan steel plant produces 20 production instances to simulate true steel-making continuous casting scheduling process.
In 20 all examples, each example, which contains, needs the number pieces processed, casting number, the continuous casting belonging to casting
Machine, workpiece are believed in the process time in each stage, workpiece in inputs such as the delivery time of different phase, the settling times of casting
Breath.In addition, in order to liberally compare the effect of distinct methods, now unify the relevant parameter that given distinct methods are related to：Limit=
100, q=0.05, c=0.01, NP=50 or 100.Moreover, after the experimental result of each example is independent operating same number
Obtained average value.All experiments all carry out under identical software and hardware environment.
It is found by Experimental comparison, the ABCMA proposed in the present invention is apparent excellent in terms of convergence effect and convergence rate
In other common methods.Carry out the validity of comprehensive verification this method in terms of two below.
1) ABCMA of discrete version is used to solve the problems, such as the hybrid flow shop scheduling during steel-making continuous casting
Due to when solving practical steel-making continuous casting scheduling problem, the individual of ABCMA uses discrete codes, thus be referred to as from
Dissipate the ABCMA of version.The emphasis that scheduling performances of the ABCMA of discrete version during steel-making continuous casting is the present invention is verified, is
The validity of verification this method, has chosen a variety of different stopping criterions to be compared, and specifically includes following groups experiment：
(1) Population Size NP=50, CPU time t=30s；
(2) Population Size NP=50, iterations maxcycle=1000；
(3) Population Size NP=50, iterations maxcycle=2000；
(4) Population Size NP=100, iterations maxcycle=1000；
(5) Population Size NP=100, iterations maxcycle=2000.
The method compared in the present invention includes：The artificial bee colony algorithm (referred to as DABC) of classical discrete version, from
Dissipate proposed in the artificial bee colony algorithm (be referred to as DABC_heu) and the present invention with heuristic of version based on people
The Memetic methods (referred to as ABCMA) of work ant colony algorithm.All experimental results in the part are mixed during steel-making continuous casting
The average value obtained after being run 5 times on 20 examples of Flow Shop Scheduling is closed, obtained target function value is smaller, table
Show that the performance of method is better.For each example, the best result in three kinds of methods is indicated with runic.Table 2 gives reality
Test (1) corresponding experimental result.
The scheduling result of steel-making continuous casting problem when table 2 deadline t=30s
As shown in table 2, when using t=30s as criterion is terminated, on 20 examples, the result that ABCMA is obtained is all bright
The aobvious result obtained better than DABC and DABC_heu.Specifically, compared with DABC, the whole result that ABCMA is obtained is in performance
On improve 76.73%；Compared with DABC_heu, the whole result that ABCMA is obtained improves 42.06% in performance.Thus
As it can be seen that relative to existing other two methods, ABCMA is identical in deadline, and dispatching effect, which has, significantly to be carried
Height, this illustrates that ABCMA has faster convergence rate.
Experiment (2)~(5) are the restrictive conditions that the present invention casts aside t=30s in Practical Project, respectively to maximum iteration
The research of method performance when maxcycle=1000 and maxcycle=2000.Due to relative to DABC_heu and ABCMA, DABC
Performance it is poor, therefore in further experiment, performance only has been carried out to DABC_heu and ABCMA and has been compared.
Table 3 gives in NP=50 and NP=100, maxcycle=1000, the experiment knot of DABC_heu and ABCMA
Fruit, best result of the two methods in different instances are indicated with runic.As NP=50 and maxcycle=1000, from table
As can be seen that the result that ABCMA is obtained on all 20 examples is all substantially better than DABC_heu in 3.Moreover, ABCMA is obtained
The obtained whole results of whole result ratio DABC_heu 67.73% is improved in performance.When NP from 50 variation for 100 when,
The performance of DABC_heu is not obviously improved, and the overall performance of ABCMA improves 29.18%.This is because ABCMA be by
The new Memetic methods that ABC and JADE is constituted, [q*NP] a best individual is to other in population before JADE is used in population
Individual guides, and NP=100 can ensure the selection space bigger of defect individual in population, restrained so as to avoid population
It is absorbed in local optimum in the process.
3 distinct methods of table are in maxcycle=1000 to the scheduling result of steel-making continuous casting problem
In NP=50, maxcycle=2000, as shown in table 4, the result that ABCMA is obtained maintains essentially in 10000 left sides
It is right.However, the result that DABC_heu is obtained in different instances differs larger (between 20000-60000), at 20
The whole result obtained on example is 4.01 times of ABCMA.In NP=100, when result and NP=50 that DABC_heu is obtained
Variation is little, and the result that ABCMA is obtained improves 20.83%.Generally speaking, compared with DABC_heu, with further
The result of iteration, ABCMA has been always maintained at downward trend.
The result explanation for testing (2)~(5), under identical experiment condition, ABCMA has preferably convergence effect.And
And results of the ABCMA after 1000 iteration is even substantially better than results of the DABC_heu after 2000 iteration.
4 distinct methods of table are in maxcycle=2000 to the scheduling result of steel-making continuous casting problem
In order to more intuitively compare the performance difference of two methods during evolution, NP=50 is set forth in the present invention
With convergence curve of population when NP=100 in 1000 generations and 2000 generations.As shown in Figure 5-Figure 8, regardless of NP=50 or NP=
100, ABCMA illustrate better performance, however the result decrease speed of DABC_heu is slow.
In summary, when solving steel-making continuous casting scheduling problem, ABCMA ratio DABC and DABC_heu tool proposed by the present invention
There are better convergence rate and convergence effect.
2) Numerical Optimization is solved with the ABCMA of continuous version
In the experiment of this part, the present invention has chosen 5 from IEEE evolutionary computation conferences in 2005 has representative
The test function (being shown in Table 5) of property, these test functions include single mode (F1-F4) and multimode (F5) feature, their optimal value is equal
It is 0.Since when solving these Numerical Optimizations, the individual of ABCMA uses continuous real coding, therefore referred to as continuous version
This ABCMA.The common methods such as ABCMA and ABC, JADE, CLPSO have carried out performance comparison.For the sake of justice, to all
5 test functions when being tested, the Population Size of these methods is NP=100, individual dimension n=30.In general, this
End condition is used as using 300000 object function evaluations in invention.For some test cases, in 300000 target letters
After number evaluation cannot differentiating method well performance difference, use 150000 object functions evaluations as terminating item at this time
Part.
The 5 test function situations used in 5 Numerical Optimization of table
Experimental result is given in Table 6, and wherein each experimental result is the average value obtained after independent operating 25 times,
And 2 significant digits are remained using scientific notation.As shown in table 6, compared to other 3 kinds of methods, the globality of ABCMA
There can be absolute predominance.Specifically, ABCMA is in test function F2-F5On be substantially better than other 3 kinds of methods.For test function
F1, after 150000 object functions are evaluated, only ABCMA and JADE have found optimal solution.Above the experiment results show that ABCMA
The successful fusion respective advantage of ABC and JADE, and better overall performance is shown, this also absolutely proves knot of the present invention
It is successful to close ABC and JADE and design new Memetic methods.
Experimental result comparison of 6 distinct methods of table on different test functions
In summary the experimental result under the conditions of two broad aspects, various different comparisons, can fully find out in the present invention and carry
The validity of the ABCMA gone out, it has when solving discrete steel-making continuous casting scheduling problem and continuous Numerical Optimization
Performance, future can be applied to other practical problems and Numerical Optimization well.
Claims (3)
1. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, referred to as ABCMA, which is characterized in that ensureing kind
The convergence rate that population is accelerated under the premise of group is multifarious generates ideal workpiece row within a short period of time to realize
Sequence, and then the hybrid flow shop scheduling during steel-making continuous casting is instructed, include the following steps：
The relevant parameter in steel-making continuous casting scheduling process is arranged in step 1)；
The relevant parameter includes the whole number pieces for needing to process, casting number, the machine number in each stage；Each
The conticaster number of number pieces, casting belonging to the third process segment and the casting on each conticaster that casting includes
Sequence；Workpiece is in process time in each stage, workpiece in the delivery time of different phase, the settling time of casting；
Step 2) analyzes actual steel-making continuous casting scheduling process comprising three process segments of steelmaking-refining-continuous casting；
Consider influence of the various boundary conditions to scheduling result, establishes the object function for needing to optimize in steel-making continuous casting scheduling process, according to
According to object function and various constraintss, the mathematical model of steel-making continuous casting scheduling is established；
The object function optimized is needed to include in the steel-making continuous casting scheduling process：The punishment of workpiece residence time, third add
Work stage casting starts punishment in advance, third process segment casting delays and starts to punish；
Obtained by the mathematical model, that is, integrated objective function and constraints of the steel-making continuous casting scheduling, object function is funny for workpiece
Stay time, casting shift to an earlier date/delay execute caused by punishment be multiplied by summation after penalty coefficient；The constraints includes：
Conversion time constraint of the workpiece between different processing stages, the setup time constraint of third process segment casting, third
On process segment each casting all workpiece Continuous maching constraint, one machine of a certain moment can only process a workpiece and
The constraint that one workpiece can only be processed on a machine；
Step 3) initializes ABCMA parameters, and initialization population according to obtained mathematical model；
Step 4) uses ABCMA to generate offspring individual for the individual in population, and it is discrete to use ranking value to carry out offspring individual
Change the sequence for obtaining including all workpiece number；The workpiece sequencing on every machine is determined, in conjunction in steel-making continuous casting scheduling process
Constraints, determine each workpiece at the beginning of different phase, the deadline, and calculating target function value is come with this；
According to target function value, the individual in population is updated using greedy selection method；
The ABCMA includes the following steps：
4.1) NP individual is randomly choosed in decision spaceConstitute initial population, individualIndicating one includes
The sequence of all workpiece, xI, jIt isJ-th of workpiece number, initialization population maximum iteration maxcycle, nectar source is given up
Parameter limit, JADE algorithm relevant parameter q, c, μF, μCRAnd archive setCurrent algebraically cycle=0；Wherein,
FiIt is individual in JADEZoom factor, CRiIt is individual in JADECross-over control parameter, q is for determining in population
[q*NP] individual before best, and q ∈ (0,1], [q*NP] is to carry out round to q*NP, and c is for controlling FiAnd CRi
Adaptive degree, μFAnd μCRRespectively FiAnd CRiAuto-adaptive parameter；
4.2) individual in population is calculatedTarget function value
4.3) judge whether iterations reach maxcycle, stop iteration if having reached, output has minimum target function
The individual and its corresponding target function value of value；Otherwise turn 4.4)；
4.4) according to formula (1) (2) more new individualCRiValue；
CRi=randni(μCR,0.1) (1)
μCR=(1-c) * μCR+c*meanA(SCR) (2)
Wherein, randni(μCR, 0.1) and it indicates with μCRFor mean value, with 0.1 for standard deviation normal distyribution function；SCRIt is to work as former generation
In all successful CRiSet, meanA() is arithmetic mean of instantaneous value；
4.5) according to formula (3) (4) more new individualFiValue；
Fi=randci(μF,0.1) (3)
μF=(1-c) * μF+c*meanL(SF) (4)
Wherein, randci(μF, 0.1) and it indicates with μFIt is Cauchy's distribution of scale parameter for location parameter, with 0.1；SFIt is to work as former generation
In all successful FiSet；meanL() is the silent average value of Lay, passes through formula (5) and obtains：
4.6) utilize formula (6) to the individual in populationMutation operation is carried out, variation vector is obtained
Wherein,Be from current population it is best before [q*NP] individual in a randomly selected individual, q ∈ (0,1], [q*
NP] it is that round is carried out to q*NP,It is being different from of being selected at random from current populationIndividual,Be from
That is selected at random in archive set is different fromWithIndividual；
4.7) rightWithTrial vector is generated using the crossover operator of JADECrossover operator used is two shown in formula (7)
Item formula is intersected；
Wherein, jrandIt is the randomly selected integer between [1, n], n is the total dimension of problem, and rand (0,1) is between [0,1]
Equally distributed random number, due to jrandPresence can ensureIt is different from
4.8) trial vector is calculatedCorresponding target function valueUsing greedy selection method to individualIt is updated：
IfThenOtherwiseIt remains unchanged；
If 4.9)It is substitutedThen willIt stores to set A, by FiAnd CRiIt is stored respectively to SFAnd SCR, and limit is protected
It holds constant；Otherwise limit=limit+1；
If 4.10) number of individuals in set A is more than NP, number of individuals is denoted as | A |, then a individual of random erasure (| A |-NP)；
4.11) formula (8) is utilized to calculate the corresponding Probability p of each individuali；
Wherein,It is individualTarget function value,The nectar amount of i-th of food source is represented, NP is food
The number in source and the individual amount in population；
4.12) according to Probability piSelection individual utilizes the individual that formula (9) is selectionGenerate offspring individual；
vi,j=xi,j+rand(-1,1)(xi,j-xk,j) (9)
Wherein, k indicates that any one individual number different from i, j ∈ [1, n] indicate j-th of dimension, and n is the total dimension of problem,
Rand (- 1,1) indicates the equally distributed random number between [- 1,1]；
4.13) calculateTarget function valueUsing greedy selection method to individualIt is updated：IfThenOtherwiseIt remains unchanged；
4.14) ifIt is substitutedThen willIt stores to set A, and limit is remained unchanged, otherwise limit=limit+
1；
4.15) if the number of individuals in set A is | A | it is more than NP, a individual of random erasure (| A |-NP)；
If 4.16) the limit values of some individual have reached the upper limit of setting, which is deleted, if reaching of the upper limit
Body have it is multiple, then random erasure one of them, and using formula (10) generate a new individual：
vi,j=xmin,j+rand(0,1)(xmax,j-xmin,j) (10)
Wherein, j ∈ [1, n] indicate j-th of dimension, and n is the total dimension of problem, xmax,jAnd xmin,jIt is the bound of jth dimension respectively,
Rand (0,1) indicates the equally distributed random number between [0,1]；
4.17) individual and its corresponding target function value of the record with minimum target functional value, cycle=cycle+1, and turn
To 4.3)；
In above process, it is 4.4) -4.10) to employ the bee stage, 4.11) -4.15) it is to observe the bee stage, 4.16) it is investigation bee
Stage；
Step 5) judges whether to meet stop condition, if satisfied, terminating to run and recording the individual with minimum target functional value
And its corresponding target function value；Otherwise step 4) is gone to.
2. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 1, which is characterized in that institute
In the step 4) stated, the workpiece sequencing on every machine is determined in accordance with the following methods：According to the sequence numbered comprising all workpiece
Machine choice is carried out for workpiece, selects the machine of current idle, when current idle machine is more than one, then arbitrarily specifies one
Platform；It is formed in conjunction with the casting on known conticaster and casting distributes, finally obtain the work being processed on every machine
Part sorts.
3. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 2, which is characterized in that stop
Only condition is to complete preset population maximum iteration maxcycle.
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