CN105785963A - Steelmaking and continuous casting scheduling method based on artificial bee colony (ABC) - Google Patents

Abstract

The invention discloses a steelmaking and continuous casting scheduling method based on an artificial bee colony (ABC). The method remains a framework of the ABC (comprising an employed bee phase, an observation bee phase and a scouter bee phase), and is improved by combining a JADE algorithm. At the employed bee phase, a search strategy of the JADE is used for updating individuals in one population, and the diversity of the population can be increased by adopting an external archiving mechanism of the JADE; at the observation bee phase, updating operation of differential solution, and archiving composed of the current population is increased on the basis of a previous search strategy of the ABC; and at the scouter bee phase, the previous search strategy of the ABC at the phase is adopted. With the adoption of the method, the convergence of the population is accelerated under the condition of guaranteeing the diversity of the population, and an ideal scheduling result can be generated in relatively short time, so that the aims that the waiting time of workpieces in a steelmaking and continuous casting process and the machining cost is reduced are realized.

Description

A kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm

Technical field

The invention belongs to the job scheduling field in steel-making continuous casting process, particularly to a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm.

Background technology

Steel and iron industry be many other such as build, the basic industry of the industry such as automatization, World Economics is occupied critical role.Steelmaking process (SteelmakingProcess) refers to that the ferrum containing fixed mixing ratio chemical composition is smelt steel resolidification in high temperature environments becomes the process of steel plate, and it can help steel plant to carry out Plate Production effectively.Steelmaking process is roughly divided into ironmaking, steel-making continuous casting, hot rolling three phases, and wherein, the steel-making continuous casting stage plays a part to form a connecting link in whole steel manufacture process, is the key link in steelmaking process.Its concrete steps include: first, the raw material iron block of steel-making is added in smelting furnace, preliminary purification under refining and high temperature obtains the ferrum of molten condition, then putting it into purification furnace and add certain chemical drugs and carry out further purifying smelting the steel obtaining melting state, the steel of thawing is cooled down the steel plate manufacturing solid-state by the last continuous casting stage.

Steel-making continuous casting scheduling problem can regard the hybrid flow shop scheduling problem that a final stage workpiece packet produces as, specifically, refer to that workpiece casts continuously according to the priority orders set in advance in the form of packets at the last stage that steel-making continuous casting produces.It has the following characteristics that

(1) all different workpieces will sequentially pass through same process stage, i.e. steel-making, refine, three process segments of continuous casting, and processing machine corresponding to each stage respectively changes stove, purification furnace and conticaster；

(2) there is multiple parallel processing machine in each production and processing stage, the parallel machine in each stage is identical, and be workpiece at the ultimate unit of the first two stage process of processing, each workpiece can be processed on any one the machine in this stage；

(3) three phases processed is processed in units of foundry goods, and wherein each foundry goods comprises which workpiece and each foundry goods are processed setting in advance on which conticaster；

(4) workpiece being processed in refine and continuous casting stage, have to wait until available machines used when not having available machines used, and this can cause that the workpiece temperature waited declines, and can produce the cost that workpiece is heated again；

In (5) the 3rd process segments, dividing the workpiece at same group will be cast continuously on same conticaster by sequence number, these workpiece do not allow to be interrupted or occur the situation that conticaster is idle in the process of implementation.If desired, the workpiece in foundry goods to delay beginning to ensure that the workpiece on same foundry goods is continuously processed, in other words, it is ensured that in same foundry goods, the deadline of a upper workpiece is the time started of next workpiece；

(6) workpiece steel-making and refining stage to set up the time comparatively short, it is negligible, being absent from the time of setting up on conticaster before the different workpieces of same foundry goods, but the time of setting up of a new foundry goods is relatively long, this time to separate from the execution time of workpiece；

(7) workpiece there is also a delivery time between two process segments, but owing to capacity is huge, the configuration of intermediate transportation crane is left in the basket and disregards；

(8) delivery time between process time and the crane of all workpiece be non-negative, known, determine；

(9) at a time a workpiece can only perform on a machine, and a machine also can only process a workpiece；

(10) foundry goods should be performed in the predefined time started, shifts to an earlier date or execution of delaying can bring inventory cost problem respectively and incur loss through delay steel rolling problem.

Fig. 1 gives the process chart of steel-making continuous casting process.

Finally, workpiece is assigned in machinery equipment by the purpose of steel-making continuous casting scheduling exactly, and the workpiece on steel-making stage and each machine of refining stage is ranked up, determine that each workpiece is in time started in all stages and deadline, thus realizing the optimization to optimization aim simultaneously.

Owing to a series of process segments of smelting iron and steel are all complete in high temperature environments, time-lag between any link all can cause and stores in workpiece waiting process and maintain the cost needed for high temperature, therefore the research of steel-making continuous casting scheduling problem is particularly important.But, the existing method for steel-making continuous casting scheduling can not obtain desirable dispatching effect in the short period of time.

Summary of the invention

As mentioned above, existing steel-making continuous casting dispatching method can not obtain desirable dispatching effect within a short period of time, in order to overcome this technical problem, the present invention to save time, reduction cost as much as possible for starting point in steel-making continuous casting process, propose a kind of based on artificial bee colony algorithm (ArtificialBeeColonyAlgorithm, ABC) Memetic method (being called for short ABCMA), solves steel-making continuous casting scheduling problem.

In order to realize above-mentioned technical purpose, the technical scheme is that a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm comprises the following steps:

Step 1) relevant parameter in steel-making continuous casting scheduling process is set；

Step 2) actual steel-making continuous casting scheduling process is analyzed, it includes three process segments of steelmaking-refining-continuous casting.Consider the various boundary conditions impact on scheduling result, set up the object function needing to optimize in steel-making continuous casting scheduling process, according to object function and various constraints, set up the mathematical model of steel-making continuous casting scheduling；

Step 3) according to the mathematical model obtained, initialize ABCMA parameter, and initialize population；

Step 4) to adopt ABCMA be that individuality in population produces offspring individual, and adopt ranking value (ROV) that offspring individual carries out discretization to obtain comprising the sequence of all workpiece numbering；Determine the workpiece sequencing on every machine, in conjunction with the constraints in steel-making continuous casting scheduling process, it is determined that each workpiece is in the time started of different phase, deadline, and carrys out calculating target function value with this；According to target function value, adopt greedy system of selection that the individuality in population is updated；

Step 5) judge whether to meet stop condition, if meeting, terminate to run and record that there is the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise forward step 4 to)；

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 1) in, relevant parameter includes whole number pieces of needs processing, foundry goods number, the machine number in each stage；Number pieces, foundry goods that each foundry goods comprises sort in the conticaster numbering belonging to the 3rd process segment and the foundry goods on each conticaster；Workpiece the process time in each stage, workpiece the delivery time of different phase, foundry goods set up the time.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 2) in, described constraints includes: the constraint that all workpiece Continuous maching constraint on workpiece conversion time-constrain between different processing stages, the setup time constraint of the 3rd process segment foundry goods, the 3rd process segment each foundry goods, one machine of a certain moment can only process a workpiece and a workpiece can only be processed on a machine；Described steel-making continuous casting scheduling process need the object function optimized include: punishment workpiece residence time, the 3rd process segment foundry goods start punishment in advance, the 3rd process segment foundry goods is delayed and started punishment.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 4) in, described ABCMA comprises the following steps:

4.1) in decision space, randomly choose NP individualityConstitute initial population, individualRepresent a sequence comprising all workpiece, x_i,jIt isJth workpiece numbering, initialize population maximum iteration time maxcycle, parameter limit, JADE algorithm relevant parameter q, c, μ are given up in nectar source_F, μ_CR, and archive setCurrent algebraically cycle=0；Wherein,

F_iIt is individual in JADEZoom factor, CR_iIt is individual in JADECross-over control parameter, q for determine best in population before [q*NP] individuality, q ∈ (0,1], q*NP is carried out round by [q*NP], and c is used for controlling F_iAnd CR_iSelf adaptation degree, μ_FAnd μ_CRRespectively F_iAnd CR_iAuto-adaptive parameter；

4.2) calculate in population individualTarget function value

4.3) judging whether iterations reaches maxcycle, if reaching, stopping iteration, output has the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise turn 4.4)；

4.4) individuality is updated according to formula (1) (2)CR_iValue；

CR_i=randn_i(μ_CR,0.1)(1)

μ_CR=(1-c) * μ_CR+c*mean_A(S_CR)(2)

Wherein, randn_i(μ_CR, 0.1) represent with μ_CRFor average, be standard deviation with 0.1 normal distyribution function；S_CRIt is as all successful CR in former generation_iSet, mean_A() is arithmetic mean of instantaneous value；

4.5) individuality is updated according to formula (3) (4)F_iValue；

F_i=randc_i(μ_F,0.1)(3)

μ_F=(1-c) * μ_F+c*mean_L(S_F)(4)

Wherein, randc_i(μ_F, 0.1) represent with μ_FFor location parameter, with 0.1 be scale parameter Cauchy be distributed；S_FIt is as all successful F in former generation_iSet.mean_L() is the silent meansigma methods of Lay, is obtained by formula (5):

${\mathrm{mean}}_L\left(S_F\right)=\frac{{\Σ}_{F\∈S_F}{F}^2}{{\mathrm{\Σ}}_{F\∈S_F}F}---\left(5\right)$

4.6) utilize formula (6) to the individuality in populationCarry out mutation operation, obtain variation vector

${\stackrel{\→}{v}}_i={\stackrel{\→}{x}}_i+F_i*({\stackrel{\→}{x}}_{best}^q-{\stackrel{\→}{x}}_i)+F_i*({\stackrel{\→}{x}}_{r1}-{{\stackrel{\→}{x}}^{\′}}_{r2})---\left(6\right)$

Wherein,From the body one by one that current population randomly chooses [q*NP] individuality before best, q ∈ (0,1], q*NP is carried out round by [q*NP],It is being different from of selecting at random from current populationIndividuality,It is being different from of selecting at random from archive setWithIndividuality；

4.7) rightWithThe crossover operator adopting JADE produces trial vectorCrossover operator used is that the binomial shown in formula (7) intersects；

$u_{i,j}=\left\{\begin{array}{cc}{v}_{i,j}& ifrand\left(0,1\right)\≤{\mathrm{CR}}_{i}orj=j_{rand}\\ x_{i,j}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j_randBeing the integer randomly choosed between [1, n], n is the total dimension of problem, and rand (0,1) is equally distributed random number between [0,1], due to j_randExistence ensure thatIt is different from

4.8) trial vector is calculatedCorresponding target function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.9) ifSubstituted forThen willStore to set A, by F_iAnd CR_iStore respectively to S_FAnd S_CR, and limit remains unchanged；Otherwise limit=limit+1；

4.10) if the number of individuals (being designated as | A |) in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.11) formula (8) is utilized to calculate each individual corresponding Probability p_i；

$p_i=\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}/{\mathrm{\Σ}}_{i=1}^{NP}\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}---\left(8\right)$

Wherein,It is individualTarget function value,Representing the nectar amount of i-th food source, NP is the number of food source, is also the individual amount in population；

4.12) according to Probability p_iSelecting individuality, utilizing formula (9) is the individuality selectedProduce offspring individual；

v_i,j=x_i,j+rand(-1,1)(x_i,j-x_k,j)(9)

Wherein, k represents that any one is different from the individual numbering of i, and j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, and rand (-1,1) represents equally distributed random number between [-1,1]；

4.13) calculateTarget function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.14) ifSubstituted forThen willStore to set A, and limit remains unchanged, otherwise limit=limit+1；

4.15) if the number of individuals (being designated as | A |) in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.16) if the limit value of certain individuality has reached the upper limit set, then this individuality is deleted (if the individuality reaching the upper limit has multiple, then random erasure one of them), and adopts formula (10) one new individuality of generation:

v_i,j=x_min,j+rand(0,1)(x_max,j-x_min,j)(10)

Wherein, j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, x_max,jAnd x_min,jBeing the bound of jth dimension respectively, rand (0,1) represents equally distributed random number between [0,1]；

4.17) record has the individuality of minimum target functional value and the target function value of correspondence, cycle=cycle+1, and goes to 4.3).

In above process, 4.4)-4.10) for employing the honeybee stage, 4.11)-4.15) for observing the honeybee stage, 4.16) for investigating the honeybee stage.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 4) in, determine the workpiece sequencing on every machine in accordance with the following methods: the workpiece that is ordered as according to comprising all workpiece numbering carries out machine choice, select the machine of current idle, when current idle machine is more than one, then arbitrarily specify one.Form in conjunction with the foundry goods on known conticaster and foundry goods distribution, finally give the workpiece sequencing being processed on every machine.

The method have technical effect that, utilize this method, it is possible under the premise ensureing population diversity, accelerate the convergence rate of population, thus reaching to shorten scheduling time, reduce the purpose of scheduling cost.The method that the present invention proposes is significantly better than that other common methods in convergence effect with convergence rate.

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

Accompanying drawing explanation

Fig. 1 is the process chart in steel-making continuous casting process；

Fig. 2 is the Job Scheduling schematic diagram of workpiece steel-making continuous casting process；

Fig. 3 is the scheduling Gantt chart example of 7 workpiece in steel-making continuous casting scheduling, wherein the number of machines of three phases respectively 3,2,2, it is assumed here that be π=[1,5,2,6,3,7,4] by the optimum workpiece sequencing obtained someway；

Fig. 4 is the flow chart of ABCMA；

The scheduling convergence curve figure of example 1 correspondence when Fig. 5 is NP=50, maxcycle=1000；

The scheduling convergence curve figure of example 2 correspondence when Fig. 6 is NP=50, maxcycle=2000；

The scheduling convergence curve figure of example 3 correspondence when Fig. 7 is NP=100, maxcycle=1000；

The scheduling convergence curve figure of example 4 correspondence when Fig. 8 is NP=100, maxcycle=2000；

Detailed description of the invention

Steel-making continuous casting process includes three process segments of steelmaking-refining-continuous casting, and its process chart is as shown in Figure 1.The problem solved in the present invention is the hybrid flow shop scheduling problem in steel-making continuous casting process, and the Job Scheduling schematic diagram of problems is as in figure 2 it is shown, it can regard the hybrid flow shop scheduling problem that a final stage workpiece packet produces as.In addition, solving the scheduling problem in actual production environment, it is necessary to consider a series of production constraints, 10 features of the steel-making scheduling problem provided in technical background, they are the constraints that this problem needs to consider simultaneously.

In providing the present invention before dispatching method more detailed description, first provide the model of steel-making continuous casting scheduling problem to be solved, as shown in table 1.

Object function (1) is that the summation after penalty coefficient is multiplied by the punishment performing to cause of shift to an earlier date/delaying of workpiece residence time, foundry goods；Constraints (2) represents that each workpiece must sequentially pass through three process segments, and a workpiece can only be processed on a certain the machine in a certain stage sometime；Constraints (3) is technological constraint, represent that same workpiece is in the course of processing of three successive stages, later process operation have to wait for previous process operation be finished and workpiece be transferred to later process operation needed for machine after just start perform；Constraints (4) indicates the Starting Executing Time constraint of first foundry goods in the upper processing of the 3rd process segment machine (conticaster)；Constraints (5) specifies the seriality requirement of the workpiece being processed on same foundry goods；Constraints (6) represents the setup time constraint between two continuous castings being processed on same conticaster.

Table 1 problem model

Wherein,

Φ₁Represent workpiece penalty term residence time；

Φ₂Represent that foundry goods shifts to an earlier date time started penalty term；

Φ₃Represent that foundry goods is delayed time started penalty term；

N represents the total number of workpiece；

CP₁Represent workpiece penalty coefficient residence time；

CP₂Represent that foundry goods shifts to an earlier date time started penalty coefficient；

CP₃Represent that foundry goods is delayed time started penalty coefficient；

J represents any one workpiece, and J is the set of all workpiece；

S represents the process segment, s ∈ 1,2,3}, 3 stages respectively make steel, refine, continuous casting；

M_sRepresent the collection of machines in s stage；

f_s,j,kCharacterizing jth workpiece whether the s stage is assigned on kth machine, it is yes that value takes 1, and it is no that value takes 0；

S_s,jRepresent the jth workpiece time started in the s stage；

P_s,jRepresent the jth workpiece execution time in the s stage；

T_s,s+1Represent the delivery time between two stages, s ∈ { 1,2}；

R_3,mRepresent the release time of the 3rd process segment machine m；

On expression m-th conticaster, first foundry goods sets up the time；

Represent the unit one on first foundry goods on m-th conticaster；

CN represents conticaster set；

Represent the foundry goods numbering on m-th conticaster；

It is the scheduling Gantt chart example of 7 workpiece shown in accompanying drawing 3, figure gives relevant workpiece residence time, workpiece conversion time and foundry goods and sets up the noun lexical or textual analysis such as time.Assume that by obtaining workpiece sequencing someway be π=[1,5,2,6,3,7,4], then this Gantt chart means that according to the Job Scheduling effect that this workpiece sequencing obtains.

The present invention is exactly under the premise considering relevant constraint restriction, workpiece residence time described in his-and-hers watches 1, foundry goods shifts to an earlier date the time started, the object functions such as time started delayed by foundry goods, adopt a kind of Memetic method based on artificial bee colony algorithm, namely ABCMA is optimized, described in comprising the following steps that:

Step 1) relevant parameter in steel-making continuous casting scheduling process is set；

Step 2) actual steel-making continuous casting scheduling process is analyzed, it includes three process segments of steelmaking-refining-continuous casting.Consider the various boundary conditions impact on scheduling result, set up the object function needing to optimize in steel-making continuous casting scheduling process, according to object function and various constraints, set up the mathematical model of steel-making continuous casting scheduling；

Step 3) according to the mathematical model obtained, initialize ABCMA parameter, and initialize population；

Step 4) to adopt ABCMA be that individuality in population produces offspring individual, and adopt ranking value (ROV) that offspring individual carries out discretization to obtain comprising the sequence of all workpiece numbering；Determine the workpiece sequencing on every machine, in conjunction with the constraints in steel-making continuous casting scheduling process, it is determined that each workpiece is in the time started of different phase, deadline, and carrys out calculating target function value with this；According to target function value, adopt greedy system of selection that the individuality in population is updated；

Step 5) judge whether to meet stop condition, if meeting, terminate to run and record that there is the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise forward step 4 to)；

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 1) in, relevant parameter includes whole number pieces of needs processing, foundry goods number, the machine number in each stage；Number pieces, foundry goods that each foundry goods comprises sort in the conticaster numbering belonging to the 3rd process segment and the foundry goods on each conticaster；Workpiece the process time in each stage, workpiece the delivery time of different phase, foundry goods set up the time.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 2) in, described constraints includes: the constraint that all workpiece Continuous maching constraint on workpiece conversion time-constrain between different processing stages, the setup time constraint of the 3rd process segment foundry goods, the 3rd process segment each foundry goods, one machine of a certain moment can only process a workpiece and a workpiece can only be processed on a machine；Described steel-making continuous casting scheduling process need the object function optimized include: punishment workpiece residence time, the 3rd process segment foundry goods start punishment in advance and the 3rd process segment foundry goods is delayed and started punishment.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 4) in, described ABCMA comprises the following steps:

4.1) in decision space, randomly choose NP individualityConstitute initial population, individualRepresent a sequence comprising all workpiece, x_i,jIt isJth workpiece numbering, initialize population maximum iteration time maxcycle, parameter limit, JADE algorithm relevant parameter q, c, μ are given up in nectar source_F, μ_CR, and archive setCurrent algebraically cycle=0；Wherein,

F_iIt is individual in JADEZoom factor, CR_iIt is individual in JADECross-over control parameter, q for determine best in population before [q*NP] individuality, q ∈ (0,1], q*NP is carried out round by [q*NP], and c is used for controlling F_iAnd CR_iSelf adaptation degree, μ_FAnd μ_CRRespectively F_iAnd CR_iAuto-adaptive parameter；

4.2) calculate in population individualTarget function value

4.3) judging whether iterations reaches maxcycle, if reaching, stopping iteration, output has the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise turn 4.4)；

4.4) individuality is updated according to formula (1) (2)CR_iValue；

CR_i=randn_i(μ_CR,0.1)(1)

μ_CR=(1-c) * μ_CR+c*mean_A(S_CR)(2)

Wherein, randn_i(μ_CR, 0.1) represent with μ_CRFor average, be standard deviation with 0.1 normal distyribution function；S_CRIt is as all successful CR in former generation_iSet, mean_A() is arithmetic mean of instantaneous value；

4.5) individuality is updated according to formula (3) (4)F_iValue；

F_i=randc_i(μ_F,0.1)(3)

μ_F=(1-c) * μ_F+c*mean_L(S_F)(4)

Wherein, randc_i(μ_F, 0.1) represent with μ_FFor location parameter, with 0.1 be scale parameter Cauchy be distributed；S_FIt is as all successful F in former generation_iSet.mean_L() is the silent meansigma methods of Lay, is obtained by formula (5):

${\mathrm{mean}}_L\left(S_F\right)=\frac{{\Σ}_{F\∈S_F}{F}^2}{{\mathrm{\Σ}}_{F\∈S_F}F}---\left(5\right)$

4.6) utilize formula (6) to the individuality in populationCarry out mutation operation, obtain variation vector

${\stackrel{\→}{v}}_i={\stackrel{\→}{x}}_i+F_i*({\stackrel{\→}{x}}_{best}^q-{\stackrel{\→}{x}}_i)+F_i*({\stackrel{\→}{x}}_{r1}-{{\stackrel{\→}{x}}^{\′}}_{r2})---\left(6\right)$

Wherein,From the body one by one that current population randomly chooses [q*NP] individuality before best, q ∈ (0,1], q*NP is carried out round by [q*NP],It is being different from of selecting at random from current populationIndividuality,It is being different from of selecting at random from archive setWithIndividuality；

4.7) rightWithThe crossover operator adopting JADE produces trial vectorCrossover operator used is that the binomial shown in formula (7) intersects；

$u_{i,j}=\left\{\begin{array}{cc}{v}_{i,j}& ifrand\left(0,1\right)\≤{\mathrm{CR}}_{i}orj=j_{rand}\\ x_{i,j}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j_randBeing the integer randomly choosed between [1, n], n is the total dimension of problem, and rand (0,1) is equally distributed random number between [0,1], due to j_randExistence ensure thatIt is different from

4.8) trial vector is calculatedCorresponding target function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.9) ifSubstituted forThen willStore to set A, by F_iAnd CR_iStore respectively to S_FAnd S_CR, and limit remains unchanged；Otherwise limit=limit+1；

4.10) if the number of individuals (being designated as | A |) in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.11) formula (8) is utilized to calculate each individual corresponding Probability p_i；

$p_i=\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}/{\mathrm{\Σ}}_{i=1}^{NP}\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}---\left(8\right)$

Wherein,It is individualTarget function value,Representing the nectar amount of i-th food source, NP is the number of food source, is also the individual amount in population；

4.12) according to Probability p_iSelecting individuality, utilizing formula (9) is the individuality selectedProduce offspring individual；

v_i,j=x_i,j+rand(-1,1)(x_i,j-x_k,j)(9)

Wherein, k represents that any one is different from the individual numbering of i, and j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, and rand (-1,1) represents equally distributed random number between [-1,1]；

4.13) calculateTarget function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.14) ifSubstituted forThen willStore to set A, and limit remains unchanged, otherwise limit=limit+1；

4.15) if the number of individuals (being designated as | A |) in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.16) if the limit value of certain individuality has reached the upper limit set, then this individuality is deleted (if the individuality reaching the upper limit has multiple, then random erasure one of them), and adopts formula (10) one new individuality of generation:

v_i,j=x_min,j+rand(0,1)(x_max,j-x_min,j)(10)

Wherein, j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, x_max,jAnd x_min,jBeing the bound of jth dimension respectively, rand (0,1) represents equally distributed random number between [0,1]；

4.17) record has the individuality of minimum target functional value and the target function value of correspondence, cycle=cycle+1, and goes to 4.3).

In above process, 4.4)-4.10) for employing the honeybee stage, 4.11)-4.15) for observing the honeybee stage, 4.16) for investigating the honeybee stage.

Described a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm, described step 4) in, determine the workpiece sequencing on every machine in accordance with the following methods: the workpiece that is ordered as according to comprising all workpiece numbering carries out machine choice, select the machine of current idle, when current idle machine is more than one, then arbitrarily specify one.Form in conjunction with the foundry goods on known conticaster and foundry goods distribution, finally give the workpiece sequencing being processed on every machine.

In order to reflect present invention effect in steel-making continuous casting scheduling problem more truly, it is necessary to assure the input condition of experiment is close to actual production environment.Therefore, in conjunction with the narration to experimental situation of other related article, the present invention, with reference to the practical condition of Shanghai Baoshan steel plant, creates 20 production instances to simulate real steel-making continuous casting scheduling process.In all of 20 examples, each example contain need the number pieces of processing, foundry goods number, conticaster belonging to foundry goods, workpiece the process time in each stage, workpiece the delivery time of different phase, foundry goods set up the input information such as time.It addition, for the effect comparing distinct methods liberally, the relevant parameter that existing unified given distinct methods relates to: limit=100, q=0.05, c=0.01, NP=50 or 100.And, the experimental result of each example is the meansigma methods obtained after independent operating same number.All experiments all carry out under identical software and hardware environment.

Finding through Experimental comparison, the ABCMA proposed in the present invention is substantially better than other common methods in convergence effect with convergence rate.The effectiveness of comprehensive verification the method is carried out below from two aspects.

1) the hybrid flow shop scheduling problem in steel-making continuous casting process is solved with the ABCMA of discrete version

Owing to when solving actual steel-making continuous casting scheduling problem, the individuality of ABCMA adopts discrete codes, is therefore referred to as the ABCMA of discrete version.The ABCMA of checking discrete version scheduling performance in steel-making continuous casting process is the emphasis of the present invention, in order to verify the effectiveness of the method, have chosen multiple different stopping criterion and compares, 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 Memetic method (referred to as ABCMA) based on artificial bee colony algorithm proposed in the classical artificial bee colony algorithm (referred to as DABC) of discrete version, the artificial bee colony algorithm with heuristic (referred to as DABC_heu) of discrete version and the present invention.The all experimental results of this part are all the meansigma methodss obtained after running 5 times on 20 examples of hybrid flow shop scheduling problem in steel-making continuous casting process, and obtained target function value is more little, and the performance of method for expressing is more good.For each example, the best result in three kinds of methods is indicated with runic.Table 2 gives the experimental result that experiment (1) is corresponding.

The scheduling result of steel-making continuous casting problem during table 2 t=30s deadline

As shown in table 2, when adopting t=30s as when terminating criterion, on 20 examples, the result that ABCMA obtains all is substantially better than DABC and the DABC_heu result obtained.Specifically, compared with DABC, the whole result that ABCMA obtains improves 76.73% in performance；Compared with DABC_heu, the whole result that ABCMA obtains improves 42.06% in performance.As can be seen here, relative to other two kinds of methods existing, ABCMA is when deadline is identical, and dispatching effect is obviously improved, and this illustrates that ABCMA has convergence rate faster.

Experiment (2)～(5) are that the present invention casts aside the restrictive condition of t=30s in Practical Project, the research of method performance time respectively to maximum iteration time maxcycle=1000 and maxcycle=2000.Due to the poor-performing relative to DABC_heu and ABCMA, DABC, therefore in further experiment, only DABC_heu and ABCMA is carried out Performance comparision.

Table 3 gives when NP=50 and NP=100, maxcycle=1000, the experimental result of DABC_heu and ABCMA, and two kinds of methods best result in different instances represents with runic.As NP=50 and maxcycle=1000, from table 3 it is observed that the result that ABCMA obtains on all 20 examples is all substantially better than DABC_heu.And, the whole result that ABCMA obtains improves 67.73% than the DABC_heu whole result obtained in performance.When NP is changed to 100 from 50, the performance of DABC_heu is not obviously improved, and the overall performance of ABCMA improves 29.18%.This is because, ABCMA is the new Memetic method being made up of ABC and JADE, JADE adopts [q*NP] individual best individuality before in population that other individuality in population is guided, NP=100 can ensure that the selection space of defect individual in population is bigger, thus avoiding population to be absorbed in local optimum in convergence process.

Table 3 distinct methods scheduling result to steel-making continuous casting problem when maxcycle=1000

When NP=50, maxcycle=2000, as shown in table 4, the result that ABCMA obtains maintains essentially in about 10000.But, the result difference relatively big (between 20000-60000) that DABC_heu obtains in different instances, its whole result obtained on 20 examples is 4.01 times of ABCMA.When NP=100, when the result that DABC_heu obtains and NP=50, change is little, and the result that ABCMA obtains improves 20.83%.Generally speaking, compared with DABC_heu, along with further iteration, the result of ABCMA has been always maintained at downward trend.

The result of experiment (2)～(5) illustrates, under identical experiment condition, ABCMA has and better restrains effect.And, ABCMA result after 1000 iteration is even substantially better than DABC_heu result after 2000 iteration.

Table 4 distinct methods scheduling result to steel-making continuous casting problem when maxcycle=2000

In order to more intuitively compare two kinds of methods performance difference during evolution, the present invention sets forth population convergence curve in 1000 generations and 2000 generations during NP=50 and NP=100.As shown in Figure 5-Figure 8, no matter NP=50 or NP=100, ABCMA all illustrate better performance, but the result decrease speed of DABC_heu is slow.

Summary, when solving steel-making continuous casting scheduling problem, the ABCMA that the present invention proposes has better convergence rate and convergence effect than DABC and DABC_heu.

2) Numerical Optimization is solved with the ABCMA of continuous version

In the experiment of this part, the present invention have chosen 5 representative test functions (see table 5) from IEEE evolutionary computation conference in 2005, and these test functions include single mode (F₁-F₄) and multimode (F₅) feature, their optimal value is 0.Owing to when solving these Numerical Optimizations, the individuality of ABCMA adopts continuous real coding, is therefore referred to as the ABCMA of continuous version.The common methods such as ABCMA and ABC, JADE, CLPSO has carried out performance comparison.For the purpose of justice, when all of 5 test functions are tested, the Population Size of these methods is NP=100, individual dimension n=30.It is said that in general, the present invention adopts 300000 object function evaluations as end condition.For some test case, after 300000 object functions are evaluated can not the performance difference of differentiating method well, now adopt 150000 object function evaluations as end condition.

5 the test function situations used in table 5 Numerical Optimization

Experimental result provides in table 6, and each of which experimental result is all the meansigma methods obtained after independent operating 25 times, and adopts scientific notation to remain 2 significant digits.As shown in table 6, compared to other 3 kinds of methods, the overall performance of ABCMA has absolute advantages.Specifically, ABCMA is at 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 experimental result illustrates, the ABCMA successful fusion respective advantage of ABC and JADE, and shows better overall performance, and this also absolutely proves that the present invention is successful in conjunction with ABC and the JADE new Memetic method of design.

The experimental result contrast on different test functions of table 6 distinct methods

Experimental result when summary two broad aspect, various different contrast, can fully find out the effectiveness of the ABCMA proposed in the present invention, it has good performance when solving discrete steel-making continuous casting scheduling problem and continuous print Numerical Optimization, may apply to other practical problem and Numerical Optimization future.

Claims (6)

1. the steel-making continuous casting dispatching method based on artificial bee colony algorithm, referred to as ABCMA, it is characterized in that, the convergence rate of population is accelerated under the premise ensureing population diversity, it is achieved thereby that within a short period of time produces desirable workpiece sequencing, and then instruct the hybrid flow shop scheduling in steel-making continuous casting process, comprise the following steps:

Step 1) relevant parameter in steel-making continuous casting scheduling process is set；

Step 2) actual steel-making continuous casting scheduling process is analyzed, it includes three process segments of steelmaking-refining-continuous casting；Consider the various boundary conditions impact on scheduling result, set up the object function needing to optimize in steel-making continuous casting scheduling process, according to object function and various constraints, set up the mathematical model of steel-making continuous casting scheduling；

Step 3) according to the mathematical model obtained, initialize ABCMA parameter, and initialize population；

Step 4) to adopt ABCMA be that individuality in population produces offspring individual, and adopt ranking value that offspring individual carries out discretization to obtain comprising the sequence of all workpiece numbering；Determine the workpiece sequencing on every machine, in conjunction with the constraints in steel-making continuous casting scheduling process, it is determined that each workpiece is in the time started of different phase, deadline, and carrys out calculating target function value with this；According to target function value, adopt greedy system of selection that the individuality in population is updated；

Step 5) judge whether to meet stop condition, if meeting, terminate to run and record that there is the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise forward step 4 to).

2. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 1, it is characterised in that described step 1) in, relevant parameter includes whole number pieces of needs processing, foundry goods number, the machine number in each stage；Number pieces, foundry goods that each foundry goods comprises sort in the conticaster numbering belonging to the 3rd process segment and the foundry goods on each conticaster；Workpiece the process time in each stage, workpiece the delivery time of different phase, foundry goods set up the time.

3. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 1, it is characterized in that, described step 2) in, described constraints includes: the constraint that the Continuous maching constraint of all workpiece on workpiece conversion time-constrain between different processing stages, the setup time constraint of the 3rd process segment foundry goods, the 3rd process segment each foundry goods, one machine of a certain moment can only process a workpiece and a workpiece can only be processed on a machine；Described steel-making continuous casting scheduling problem needs the object function optimized to include: workpiece punishment residence time, the 3rd process segment foundry goods start punishment in advance, the 3rd process segment foundry goods is delayed and started punishment.

4. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 1, it is characterised in that described step 4) in, described ABCMA comprises the following steps:

4.1) in decision space, randomly choose NP individualityConstitute initial population, individualRepresent a sequence comprising all workpiece, x_i,jIt isJth workpiece numbering, initialize population maximum iteration time maxcycle, parameter limit, JADE algorithm relevant parameter q, c, μ are given up in nectar source_F, μ_CR, and archive setCurrent algebraically cycle=0；Wherein,

F_iIt is individual in JADEZoom factor, CR_iIt is individual in JADECross-over control parameter, q for determine best in population before [q*NP] individuality, q ∈ (0,1], q*NP is carried out round by [q*NP], and c is used for controlling F_iAnd CR_iSelf adaptation degree, μ_FAnd μ_CRRespectively F_iAnd CR_iAuto-adaptive parameter；

4.2) calculate in population individualTarget function value

4.3) judging whether iterations reaches maxcycle, if reaching, stopping iteration, output has the individuality of minimum target functional value and the target function value of correspondence thereof；Otherwise turn 4.4)；

4.4) individuality is updated according to formula (1) (2)CR_iValue；

CR_i=randn_i(μ_CR,0.1)(1)

μ_CR=(1-c) * μ_CR+c*mean_A(S_CR)(2)

Wherein, randn_i(μ_CR, 0.1) represent with μ_CRFor average, be standard deviation with 0.1 normal distyribution function；S_CRIt is as all successful CR in former generation_iSet, mean_A() is arithmetic mean of instantaneous value；

4.5) individuality is updated according to formula (3) (4)F_iValue；

F_i=randc_i(μ_F,0.1)(3)

μ_F=(1-c) * μ_F+c*mean_L(S_F)(4)

Wherein, randc_i(μ_F, 0.1) represent with μ_FFor location parameter, with 0.1 be scale parameter Cauchy be distributed；S_FIt is as all successful F in former generation_iSet；mean_L() is the silent meansigma methods of Lay, is obtained by formula (5):

${\mathrm{mean}}_L\left(S_F\right)=\frac{{\mathrm{\Σ}}_{F\∈S_F}{F}^2}{{\mathrm{\Σ}}_{F\∈S_F}F}---\left(5\right)$

4.6) utilize formula (6) to the individuality in populationCarry out mutation operation, obtain variation vector

${\stackrel{\→}{v}}_i={\stackrel{\→}{x}}_i+F_i*({\stackrel{\→}{x}}_{best}^q-{\stackrel{\→}{x}}_i)+F_i*({\stackrel{\→}{x}}_{r1}-{\stackrel{\→}{x}}_{r2}^{\′})---\left(6\right)$

Wherein,From the body one by one that current population randomly chooses [q*NP] individuality before best, q ∈ (0,1], q*NP is carried out round by [q*NP],It is being different from of selecting at random from current populationIndividuality,It is being different from of selecting at random from archive setWithIndividuality；

4.7) rightWithThe crossover operator adopting JADE produces trial vectorCrossover operator used is that the binomial shown in formula (7) intersects；

$u_{i,j}=\left\{\begin{array}{cc}{v}_{i,j}& \begin{array}{cc}if& rand(0,1)\≤{\mathrm{CR}}_{i}orj=j_{rand}\end{array}\\ x_{i,j}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j_randBeing the integer randomly choosed between [1, n], n is the total dimension of problem, and rand (0,1) is equally distributed random number between [0,1], due to j_randExistence ensure thatIt is different from

4.8) trial vector is calculatedCorresponding target function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.9) ifSubstituted forThen willStore to set A, by F_iAnd CR_iStore respectively to S_FAnd S_CR, and limit remains unchanged；Otherwise limit=limit+1；

4.10) if the number of individuals (being designated as | A |) in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.11) formula (8) is utilized to calculate each individual corresponding Probability p_i；

$p_i=\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}/{\mathrm{\Σ}}_{i=1}^{NP}\frac{1}{f\left({\stackrel{\→}{x}}_i\right)+1}---\left(8\right)$

Wherein,It is individualTarget function value,Representing the nectar amount of i-th food source, NP is the number of food source, is also the individual amount in population；

4.12) according to Probability p_iSelecting individuality, utilizing formula (9) is the individuality selectedProduce offspring individual；

v_i,j=x_i,j+rand(-1,1)(x_i,j-x_k,j)(9)

Wherein, k represents that any one is different from the individual numbering of i, and j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, and rand (-1,1) represents equally distributed random number between [-1,1]；

4.13) calculateTarget function valueAdopt greedy system of selection to individualityIt is updated: ifThenOtherwiseRemain unchanged；

4.14) ifSubstituted forThen willStore to set A, and limit remains unchanged, otherwise limit=limit+1；

4.15) if number of individuals i.e. | the A | in set A is more than NP, then random erasure (| A |-NP) individual individuality；

4.16) if the limit value of certain individuality reached set the upper limit, then by this individuality delete, if the individuality reaching the upper limit has multiple, then random erasure one of them, and adopt formula (10) generation one new individuality:

v_i,j=x_min,j+rand(0,1)(x_max,j-x_min,j)(10)

Wherein, j ∈ [1, n] represents jth dimension, and n is the total dimension of problem, x_max,jAnd x_min,jBeing the bound of jth dimension respectively, rand (0,1) represents equally distributed random number between [0,1]；

4.17) record has the individuality of minimum target functional value and the target function value of correspondence, cycle=cycle+1, and goes to 4.3)；

In above process, 4.4)-4.10) for employing the honeybee stage, 4.11)-4.15) for observing the honeybee stage, 4.16) for investigating the honeybee stage.

5. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 1, it is characterized in that, described step 4) in, determine the workpiece sequencing on every machine in accordance with the following methods: the workpiece that is ordered as according to comprising all workpiece numbering carries out machine choice, select the machine of current idle, when current idle machine is more than one, then arbitrarily specify one；Form in conjunction with the foundry goods on known conticaster and foundry goods distribution, finally give the workpiece sequencing being processed on every machine.

6. a kind of steel-making continuous casting dispatching method based on artificial bee colony algorithm according to claim 4, it is characterised in that stop condition has been the population maximum iteration time maxcycle preset.