CN105929690A - Flexible workshop robustness scheduling method based on decomposition multi-target evolution algorithm - Google Patents

Abstract

The invention discloses a flexible workshop robustness scheduling method based on a decomposition multi-target evolution algorithm. The method comprises the following steps: 1, reading such input information as operation, machine attributes and the like of a flexible operation workshop, defining an optimization object, and setting constraint conditions; 2, initializing parameters of the algorithm; 3, determining an adjacent domain of each subproblem, generating an initial parent group, and determining all Pereto non-dominant solutions from the initial group so as to form an external memory; 4, generating a child group, carrying out mating selection, breeding child individuals by use of an adaptive variation operator and a restoration-based intersection operator, and updating the external memory; 5, by use of the generated child group, updating a current optimal individual of each subproblem, and forming a new parent group; and 6, when it is determined that the individual object evaluation frequency reaches the maximum, outputting the external memory, i.e., a group of Pareto non-dominant flexible operation workshop scheduling solutions, and if the frequency does not reach the maximum, skipping to the fourth step. According to the invention, scheduling tasks in a flexible operation workshop can be rapidly and efficiency realized.

Description

A kind of based on the Flexible Workshop Robust Scheduling method decomposing multi-objective Evolutionary Algorithm

Technical field

The present invention relates to flexible job shop scheduling and control technical field, particularly a kind of based on decomposing multi-target evolution calculation The Flexible Workshop Robust Scheduling method of method.

Background technology

Flexible Job-shop Scheduling Problems is the vague generalization to classical Job-Shop problem, and it is a class np hard problem.? In Flexible Job-shop Scheduling Problems, it is allowed to a procedure is by multiple stage machining, therefore, every procedure of each operation it is required to be Distribute suitable machine, and determine the processing sequence of operation on each machine, with on the premise of meeting various constraints, it is achieved The optimization aim such as the completion date of operation is the shortest, the load balancing of each machine.

The production environment of compliance job shop also exists a lot of uncertain factor, as due to operation specification requirement Change cause process portion to change process time；Due to the transport delay of subcontractor, the release time of operation is caused to push away Late etc..When facing these disturbances, may be substantially reduced, the most urgently according to the performance of the optimal scheduling scheme of primary data generation A kind of novel flexible job shop Robust Scheduling method that can process uncertain factor need to be studied, to ensure completion date relatively While the performances such as the load more equilibrium of machine short, each, strengthen Job-Shop scheme to probabilistic antijamming capability, fall The low scheduling performance sensitivity to disturbance.The successful implementation to actual production system of the Robust Scheduling technology of flexible job shop Significant.

The class adaptive global optimization that evolution algorithm is the biological evolutionary process in natural environment of simulation and is formed is general Rate searching algorithm.Evolution algorithm can process the insoluble complicated optimum problem of traditional optimization, the most discontinuous, multimode The problems such as state, whole colony is implemented to select, intersect by it, variation etc. operates, can in the once operation of algorithm parallel search To multiple solutions, it has stronger environment self-adaption ability in addition, and therefore, evolution algorithm is particularly well-suited to solve flexible job car Between dispatch this kind of Multi-objective Robust optimization problem that simultaneously there is multiple Pareto non-domination solution.Based on the multi-target evolution decomposed Algorithm (MOEA/D) is proposed in 2007 first by Zhang Qingfu professor and doctor Li Hui.This algorithm give a kind of novel and General multi-objective framework.Multi-objective optimization question is decomposed into one group of single goal subproblem by it, and uses based on colony These subproblems of evolution algorithm Cooperative Solving.Due to its high efficiency, in recent years, MOEA/D has become as international academic community One of study hotspot, and MOEA/D is successfully applied in the solving of actual optimization problem by existing scholar.

Current existing flexible job shop scheduling method has the disadvantage that

(1) production environment of static state is mostly only accounted for.They assume that all information in flexible job shop are all pre- First understand and determine constant, it is clear that when actual production environment exists uncertain factor, the scheduling produced according to static method Scheme is the most applicable.

(2) more single to the processing mode of multiple optimization aim.The method that mostly has uses weighted sum method by multiple Target is converted to a target, and this method will introduce more parameter, and needs in advance each target to be carried out normalizing Change processes.Due to the most conflicting between multiple targets of Flexible Job-shop Scheduling Problems, therefore better way It is to use multi-objective Evolutionary Algorithm that multiple target parallel are processed, thus provides different between one group of reflection target for production manager The scheduling scheme of compromise degree, makes final decision-making for it and provides reference.

(3) local search ability is more weak, it is easy to be absorbed in local optimum, and dispatching efficiency is low.

Summary of the invention

The technical problem to be solved is to overcome the deficiencies in the prior art to provide a kind of based on decomposing multiple target The Flexible Workshop Robust Scheduling method of evolution algorithm, with in actual Workshop Production environment, optimize operation completion date, While promoting each machine loading equilibrium, reduce the uncertain negative effect to scheduling scheme performance as much as possible, and improve The local search ability of dispatching method, it is to avoid be absorbed in local optimum, it is achieved Job-Shop rapidly and efficiently.

The present invention solves above-mentioned technical problem by the following technical solutions:

A kind of based on decomposition multi-objective Evolutionary Algorithm the Flexible Workshop Robust Scheduling method proposed according to the present invention, including Following steps:

Step (1), the input information of reading flexible job shop, define optimization aim, setting constraints:

The input information in workshop includes every procedure assignable machine collection in the process number of each operation, each operation Close, each operation process time on corresponding machine, the machine number of normal work；Optimization aim include operation completion date, The maximum load of machine, the robustness of scheduling performance；Constraints includes operation priority restrictions and forbids the pact occupied of trying to be the first Bundle；

Step (2), initialization parameter based on the multi-objective Evolutionary Algorithm decomposed:

Arrange iterations NmbEvl, population size N is the number of subproblem, produce N number of equally distributed target power Vector λ¹,…,λ^N, neighborhood scale T of subproblem, probability δ that the parent individuality in breeding operator is chosen from neighborhood, neighborhood Body allows the maximum number n replaced by each offspring individual_r, uncertain scene number Q of sampling, Yi Jijiao when evaluating robustness Fork probability CR；

Step (3), determine the neighborhood of each subproblem, produce initial parent colony:

(3.1), to i-th subproblem, i=1 ..., N, determine neighborhood B (i)={ i₁,…,i_T}；Calculate i-th respectively Weight vector λ of problemⁱAnd the Euler's distance between other (N-1) individual subproblem weight vector, by T distance lambdaⁱNearest weight vectorCorresponding sub-group sequence number { i₁,…,i_TConstitute B (i)；

(3.2), initial parent colony { x is randomly generated¹,…,x^N, wherein, individual xⁱCurrent solution for i-th sub-group； Each individuality in colony includes operation sequence vector and machine assignment vector；One group of uncertainty scene θ of stochastical sampling_q, q= 1,2,...,Q；Calculate desired value f of each individuality in initial parent colony₁=makespan_I、f₂=workload_IAnd f₃= robustness；makespan_IAnd workload_IRepresent the operation completion date under initial scene and machine maximum load respectively, Robustness represents the robustness of scheduling performance；From initial parent colony, determine that all of Pareto non-domination solution is constituted External memory storage Arc；Objective appraisal counting how many times variable ct=N is set；Normalize each desired value, by each individual xⁱJth Individual desired value f_j(xⁱ) be mapped between interval [0,1], produce xⁱNormalized value fno in jth target_j(xⁱ), it may be assumed that

Wherein,WithRepresent respectively current parent for the maximum in jth target of all individualities in colony and Minimum of a value, j=1,2,3；

(3.3), evolutionary generation t=0 is set；

Step (4), generation progeny population:

One group of uncertainty scene θ of stochastical sampling_q；Progeny population is setMake i=1；

(4.1), mating selects；

Produce equally distributed random number rand₁∈[0,1]；Renewal neighborhood P (i) of i-th subproblem is set:

3 different parents are produced individual based on following ruleWith

(4.2), breeding；

Use breeding operator based on differential evolution algorithm, byAnd xⁱGenerate offspring individual uⁱ；

(4.3), external memory storage is updated；

Evaluate uⁱDesired value, and normalize each desired value；Make ct=ct+1；By uⁱAdd external memory storage Arc；And delete Except in current Arc, all repetition solves and Pareto domination solution；If Chipop=Chipop is ∪ uⁱ；If i is ＜ N, then make i=i+1, Go to (4.1), otherwise perform step (5)；

Step (5), the renewal solved:

If population mixture Mixpop={x¹,…,x^N∪ Chipop, make i=1,

(5.1) counter c=0, is made；

(5.2), from renewal neighborhood P (i) of i-th subproblem, sequence number k of a sub-group, k ∈ P (i) are randomly selected；

(5.3), for kth subproblem, from Mixpop, optimum solution is determined；

If token variable mark=0；The weight vector of given kth subproblem For jth target Weights, And reference vector For the reference point of jth target, j= 1,2,3, employing Chebyshev method is tried to achieve any one individual x and at the synthesis object function of kth subproblem is:

$g^{te}\left(x\right|{\mathrm{\λ}}^k,z^{*})=\underset{1\≤j\≤3}{max}\left\{{\mathrm{\λ}}_j^k\right|{\mathrm{fno}}_j\left(x\right)-z_j^{*}\left|\right\}$

Owing to using normalization desired value, reference vector z is set^*=(0,0,0)；For each individual xy in Mixpop^l With kth subproblem currently solve x^kIf following 3 conditions having one meet: (i) g^te(xy^l|λ^k,z^*) ＜ g^te(x^k| λ^k,z^*)；(ii)g^te(xy^l|λ^k,z^*)=g^te(x^k|λ^k,z^*) and xy^lPareto arranges x^k；(iii)g^te(xy^l|λ^k,z^*)=g^te (x^k|λ^k,z^*) and xy^lAt robust performance f₃Desired value on=robustness is less than x^k, then x is made^k=xy^l, FV^k=F (xy^l), Fno^k=Fno (xy^l), and mark=1；Wherein, FV^kRepresent x^kObject vector, i.e. FV^k=F (x^k)=[f₁(x^k),f₂(x^k),f₃ (x^k)], F (xy^l) represent xy^lObject vector, i.e. F (xy^l)=[f₁(xy^l),f₂(xy^l),f₃(xy^l)], Fno^kRepresent x^kThrough returning Object vector after one change, i.e. Fno^k=[fno₁(x^k),fno₂(x^k),fno₃(x^k)], Fno (xy^l) represent xy^lAfter normalization Object vector, i.e. Fno (xy^l)=[fno₁(xy^l),fno₂(xy^l),fno₃(xy^l)]；

(5.4) if mark=1, then c=c+1 is made；

(5.5), from P (i), sequence number k is deleted；If c is ＜ n_rAnd P (i) nonvoid set, then go to (5.2)；Otherwise, if i ＜ N, then make i=i+1, goes to (5.1), otherwise goes to step (6)；

Step (6), stop criterion judge:

If ct is ＞ NmbEvl, then terminate iteration, export external memory storage Arc, the i.e. flexibility of one group of Pareto non-dominant Solving job shop scheduling problem solution；Otherwise, make t=t+1, go to step (4).

One is entered as a kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm of the present invention Step prioritization scheme, the operation completion date in optimization aim described in step (1) has represented owning in flexible job shop The time overhead that operation is spent, is defined as:

$f_1={\mathrm{makespan}}_I=\underset{v=1,2,...,n}{max}\left(C_v\right)-\underset{v=1,2,...,n}{min}\left(S_v\right)$

Wherein, C_vAnd S_vIt is illustrated respectively in v item operation, the time that machines of last procedure and first work The processing time started of sequence, v=1,2 ..., n, n are the sum of All Jobs in flexible job shop；I represents initial scene, i.e. For uncertainty attribute, if to be that a certain discreet value determines constant for its value, calculate operation completion date in the case；

Machine maximum load in step (1) described optimization aim represents the maximum of each machining time, definition For:

$f_2={\mathrm{workload}}_I=\underset{s=1,2,...,m}{max}\left(\underset{r=1}{\overset{w_s}{\Σ}}{\mathrm{pro}}^{O^{sr}}\right)$

Wherein, m is total number of units of flexible job shop inner machine；It is according to scheduling scheme, s platform machine is pressed Operation O that the r order is processed^srProcess time；w_sIt is assigned to the operation number on s platform machine；

In step (1) described optimization aim, the robustness of scheduling performance be weigh scheduling scheme operation completion date and The maximum load of the machine sensitivity to uncertain factor, is defined as:

$f_3=robustness=\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{makespan}}_q-{\mathrm{makespan}}_I}{{\mathrm{makespan}}_I},0\left)\right)}^2}+\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{workload}}_q-{\mathrm{workload}}_I}{{\mathrm{workload}}_I},0\left)\right)}^2};$

Robustness uses method based on scene definition, by a scheduling scheme in the multiple sampled value of uncertainty attribute {θ_q| q=1,2 ..., emulate under Q}, with the actual value of comparisons completion date and machine maximum load with initially estimate Difference between value；Wherein, makespan_qAnd workload_qIt is θ respectively_qThe most corresponding operation completion date and machine maximum are born Carry desired value；

Operation priority restrictions described in step (1) refers to that each procedure of each operation is to enter by pre-determined order Row processing；In flexible job shop problem, every procedure can add on arbitrary platform in the collection of machines that it allows Work；

The constraint occupied of trying to be the first of forbidding described in step (1) includes: the processing of (i) every procedure, can only be in same operation In come it before all process steps all complete after just can proceed by；(ii) if a procedure is allocated to certain machine Device, only before this machine completes after all process steps of scheduling, could start the processing of this procedure.

One is entered as a kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm of the present invention Step prioritization scheme, the initial population that randomly generates described in step (3.2) refers to, the operation sequence vector in each individuality by with All process steps in machine arrangement All Jobs generates；For machine assignment vector, per pass flow chart is assigned randomly to its machine It is processed on arbitrary platform in device set.

One is entered as a kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm of the present invention Step prioritization scheme, the Pareto domination described in step (4.3) and step (5.3) refers to: set x₁And x₂For multi-objective optimization question Two solutions, the target number of problem is m₁, it is assumed that all targets are both needed to minimize, and claim x₁Pareto arranges x₂And if only if

$\∀g\∈\{1,2,...,m_1\}:f_g\left(x_1\right)\≤f_g\left(x_2\right)$

And

Wherein, g and h represents some sequence number of target, f respectively_g(x₁) and f_g(x₂) represent x respectively₁And x₂At the g mesh Mark f_gOn desired value, f_h(x₁) and f_h(x₂) represent x respectively₁And x₂The h target f_hOn desired value.

One is entered as a kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm of the present invention Step prioritization scheme, the Pareto non-domination solution described in step (3) and step (6) refers to, appoints if do not existed in a certain set What it solves x'Pareto domination and solves x, then the Pareto non-domination solution during x is called this set.

One is entered as a kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm of the present invention Step prioritization scheme, the breeding operator described in step (4.2) refers to, based on the mutation operator in differential evolution algorithm and the calculation that intersects Son, designs the adaptive mutation rate of a kind of improvement and based on the crossover operator repaired, individual by parentWith The current individual x of i-th subproblemⁱ, generate offspring individual uⁱ；Wherein, the implementation of the adaptive mutation rate of improvement is such as Under:

β=e^-0.015t,

$y^i=\mathrm{\β}\[x_p^1+F_1(x_p^2-x_p^3)\]+(1-\mathrm{\β})\[x^i+F_2(x_p^2-x_p^3)+F_3(x_{best}^i-x^i)\].$

Wherein, F₁, F₂And F₃It is mutagenic factor, the uniformly random generation from [0.5,1] respectively of their value；It is current In external memory storage Arc, distance xⁱNearest solution,The value of parameter beta changes along with the value of evolutionary generation t；yⁱIt is The individuality generated by the adaptive mutation rate improved；

For individual operation sequence vector and machine assignment vector, implement the TSP question of improvement described above respectively Operator；For the y generatedⁱIn operation sequence vector ysⁱ, its each element is arranged by order from small to large, To ysⁱOrdering vector tysⁱ, and by each element after sequence at former vector ysⁱIn location index record at index vector IⁱIn；By xⁱOperation sequence vector xsⁱIn each element arrange by order from small to large, obtain xsⁱOrdering vector txsⁱ, and make ysⁱ(Iⁱ)=txsⁱ, ysⁱ(Iⁱ) represent ysⁱIn all at IⁱElement on the position of record；For the y generatedⁱIn Machine assignment vector ymⁱ, for each element, search for the collection of machines of its corresponding operation, therefrom determine and this element value Immediate machine, and this machine is substituted this element；If there are more than two machines to meet this condition simultaneously, the most random A machine is selected to replace corresponding element；Operation sequence vector ys after renewalⁱWith machine assignment vector ymⁱConstitute new individual yⁱ；

Described implementation based on the crossover operator repaired is as follows:

(a), the individual y that will be generated by the adaptive mutation rate improvedⁱWith xⁱCombination, constitutes offspring individual uⁱ:

Wherein,It is u respectivelyⁱ,yⁱ,xⁱThe ll element, L is individual xⁱLength, CR ∈ [0,1] be hand over Fork probability,It is a number of uniformly random generation from [0,1], IrandⁱBe from set 1,2 ..., L} randomly chooses An integer；

In the method for expressing of machine assignment vector, yⁱMachine assignment vector ymⁱWith xⁱMachine assignment vector x mⁱ? Machine in same position corresponds to same procedure；Above-mentioned crossover operator directly acts on ymⁱAnd xmⁱ, intersect the result that obtains It is offspring individual uⁱMachine assignment vector umⁱ；

For yⁱOperation sequence vector ysⁱWith xⁱOperation sequence vector xsⁱ, implement the steps of further:

(b), the u that step (a) is tried to achieveⁱOperation sequence vector usⁱIn, xs will be come fromⁱElement position index record At No. 1 index vector index₁In, ys will be come fromⁱElement position index record at No. 2 index vector index₂In；Make usⁱ =xsⁱ, interim index vector tempindex₂=index₂, test vector test=usⁱ(index₁), usⁱ(index₁) represent usⁱIn all at index₁Element on the position of record, vector donor_delete=[], [] expression null set deleted in index；

(c), to each element ue in test, determine at ysⁱ(index₁Whether there is some elements equal to ue in)；As Fruit exists, and selects an element the most uniformly randomly, by the element chosen at ysⁱIn location index add donor_ Delete, and by this index from index₁Middle deletion；Otherwise, find out at ysⁱ(index₂The element of ue it is equal to, the most uniformly in) Choose one randomly, by it at ysⁱIn location index add donor_delete, and by this index from index₂Middle deletion； Wherein, ysⁱ(index₁) represent ysⁱIn all at index₁Element on the position of record, ysⁱ(index₂) represent ysⁱMiddle institute Have at index₂Element on the position of record；

(d), by the element in donor_delete from set 1,2 ..., L} removes, even index retain vector Donar_reserve={1,2 ..., L} donar_delete, and usⁱ(tempindex₂)=ysⁱ(donar_reserve)； Wherein, represent removal, usⁱ(tempindex₂) represent usⁱIn all at tempindex₂Element on the position of record, ysⁱ (donar_reserve) ys is representedⁱIn all donar_reserve record position on elements.

The present invention uses above technical scheme compared with prior art, has following technical effect that

1) present invention can process uncertain factor present in flexible job shop production environment, is ensureing completion date While the performances such as shorter, machine loading more equilibrium, strengthen Job-Shop scheme to probabilistic antijamming capability, reduction The scheduling performance sensitivity to disturbance；It can treatment process sort and machine assignment both scheduling strategies simultaneously, therefore, Compared with prior art, there is the flexible job shop scheduling of uncertain factor and ask in the present invention in being more suitable for the Coping with Reality world Topic.The Robust Scheduling technology that the present invention proposes is significant to the successful implementation of actual production system；

2) present invention optimizes efficiency index (completion date, machine maximum load) and the robust of flexible job shop simultaneously Property, and use the multi-objective Evolutionary Algorithm based on decomposing that multiple target parallel are processed such that it is able to provide for production manager Between one group of reflection target, the scheduling scheme of different compromise degree, makes, for it, the reference that final decision-making provides strong；

3) present invention devises a kind of novel, it is possible to effectively utilize the subproblem more New Policy of global information；Outside arranging It is individual that portion's memory preserves Pareto non-dominant, and these elite individual organic can be participated in the generation of offspring individual；Adopt With the adaptive mutation rate of a kind of improvement and carry out breeding operation, to help preferably safeguarding calculation based on the crossover operator repaired Method balance between " exploration " and " utilization "；These mechanism can be effectively improved the local search ability of the present invention, it is to avoid It is absorbed in local optimum, realizes the scheduler task in flexible job shop quickly and efficiently.

Accompanying drawing explanation

Fig. 1 is the main process figure of the present invention.

Fig. 2 is individual method for expressing exemplary plot.

Fig. 3 is scheduling scheme solution Solution_aGantt chart under initial scene.

Fig. 4 is scheduling scheme solution Solution_aGantt chart in disturbance cases.

Fig. 5 is scheduling scheme solution Solution_bGantt chart under initial scene.

Fig. 6 is scheduling scheme solution Solution_bGantt chart in disturbance cases.

Detailed description of the invention

Below in conjunction with the accompanying drawings technical scheme is described in further detail:

In one flexible job shop, there are 5 machines, 4 operations to be processed.Every procedure of each operation is the most permissible 5 machines are processed respectively.In these operations, the process time with the presence of process portion is uncertain.4 operations comprise Operation number, every procedure each allow on processing machine initially to estimate process time as shown in table 1.

Table 1

	O11	O12	O13	O21
					Estimate process time	2,5,4,1,2	5,4,5,7,5	4,5,5,4,5	2,5,4,7,8
	O22	O23	O31	O32
					Estimate process time	5,6,9,8,5	4,5,4,54,5	9,8,6,7,9	6,1,2,5,4
	O33	O34	O41	O42
					Estimate process time	2,5,4,2,4	4,5,2,1,5	1,5,2,4,12	5,1,2,1,2

The flexible job shop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm using the present invention to propose solves The scheduling scheme of this flexible job shop embodiment, main process figure is as it is shown in figure 1, specifically comprise the following steps that

(1) initialize.Read the input information of flexible job shop, including in the process number of each operation, each operation The every assignable collection of machines of procedure, each operation initially estimate process time (being shown in Table 1) on corresponding machine；Definition optimizes Target, setting constraints:

" operation completion date " in optimization aim has represented the time that the All Jobs in flexible job shop spent Between expense, it is defined as:

$f_1={\mathrm{makespan}}_I=\underset{v=1,2,...,n}{max}\left(C_v\right)-\underset{v=1,2,...,n}{min}\left(S_v\right)$

Wherein, C_vAnd S_vRepresent v item operation J respectively_vIn, the time that machines of last procedure and first work The processing time started of sequence, v=1,2 ..., n；N is the sum of All Jobs in flexible job shop, in this example, n=4；I Represent initial scene, in this example, for this uncertainty attribute process time, it is assumed that its value is that initial discreet value determines not Become, calculate the operation completion date under initial scene in the case；

" machine maximum load " in optimization aim represents the maximum of each machine total process time, and it is defined as:

$f_2={\mathrm{workload}}_I=\underset{s=1,2,...,m}{max}\left(\underset{r=1}{\overset{w_s}{\Σ}}{\mathrm{pro}}^{O^{sr}}\right)$

Wherein, m is total number of units of flexible job shop inner machine, in this example, m=5；It is according to current scheduling Scheme, operation O being processed by the r order on s platform machine^srProcess time；w_sIt is assigned on s platform machine Operation number；I represents initial scene；

In optimization aim, the maximum of operation completion date and machine that " robustness of scheduling performance " weighs scheduling scheme is born Carrying the sensitivity to uncertain factor, it is defined as:

$f_3=robustness=\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{makespan}}_q-{\mathrm{makespan}}_I}{{\mathrm{makespan}}_I},0\left)\right)}^2}+\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{workload}}_q-{\mathrm{workload}}_I}{{\mathrm{workload}}_I},0\left)\right)}^2}$

Robustness uses method based on scene definition, by multiple in uncertain operation process time of a scheduling scheme Sampled value { θ_q| q=1,2 ..., emulate under Q}, with the actual value of comparisons completion date and machine maximum load with just Difference between beginning discreet value；Wherein, θ_qBeing the q-th sampled value of uncertain operation process time, Q is number of samples； makespan_qAnd workload_qIt is sampled value θ respectively_qThe most corresponding operation completion date and machine maximum load desired value；

Operation priority restrictions refers to that each procedure of each operation is processed by pre-determined order；Soft Property job shop problem in, every procedure can be processed on arbitrary platform in the collection of machines that it allows；

The constraint that forbidding tries to be the first occupies includes: the processing of (i) every procedure, before can only coming it in same operation All process steps just can proceed by after all completing；(ii) if a procedure being allocated to certain machine, only at this After machine completes all process steps dispatched before, the processing of this procedure could be started；

(2) parameter based on the multi-objective Evolutionary Algorithm decomposed is initialized:

Arrange objective appraisal times N mbEvl be 15000, population size (i.e. the number of subproblem) N be 500, produce N number of Equally distributed target weight vector λ¹,…,λ^N, neighborhood scale T of subproblem be 50, the parent in breeding operator is individual from neighborhood In the probability δ that chooses be 0.7, neighborhood individuality allow the maximum number n that replaced by each offspring individual_rIt is 5, when evaluating robustness Uncertain scene number Q of sampling is 30, and crossover probability CR is 0.3；

(3) determine the neighborhood of each subproblem, produce initial parent colony:

(3.1) to i-th subproblem, i=1 ..., N, determine neighborhood B (i)={ i₁,…,i_T}.Calculate i-th respectively Weight vector λ of problemⁱAnd the Euler's distance between other (N-1) individual subproblem weight vector, by T distance lambdaⁱNearest weight vectorCorresponding sub-group sequence number { i₁,…,i_TConstitute B (i)；

(3.2) initial parent colony { x is randomly generated¹,…,x^N, wherein individual xⁱCurrent solution for i-th sub-group；Group Each individuality in body includes operation sequence vector and machine assignment vector；One group of uncertainty scene θ of stochastical sampling_q, q=1, 2,...,Q；Calculate desired value f of each individuality in initial parent colony₁=makespan_I、f₂=workload_IAnd f₃= robustness；From initial parent colony, determine that all of Pareto non-domination solution constitutes external memory storage Arc；Mesh is set Mark evaluates counting how many times variable ct=N；Normalize each desired value, by each individual xⁱJth desired value f_j(xⁱ) it is mapped to district Between between [0,1], produce xⁱNormalized value fno in jth target_j(xⁱ), it may be assumed that

Wherein,WithRepresent respectively current parent for the maximum in jth target of all individualities in colony and Minimum of a value, j=1,2,3.

(3.3) evolutionary generation t=0 is set；

Initial parent colony is made up of the individuality of N number of stochastic generation.In the present invention, body includes two vectors one by one: (i) Operation sequence vector；(ii) machine assignment vector.Fig. 2 gives the example of individual method for expressing.For operation sequence vector, adopt With method for expressing based on operation, the operation of same operation all represents with this job number.Such as, in Fig. 2, operation O₁₁、O₁₂、O₁₃ Both function as industry number 1 to represent.The order that every procedure occurs in operation sequence vector according to it is changed.Such as, operation sequence In column vector, first numeral 3 occurred represents operation O₃₁, second 3 occurred represents O₃₂, the rest may be inferred.Therefore, can will scheme Operation sequence vector in 2 is construed to:

Wherein,Represent the waiting list that operation a is firstly added its institute's dispensation machines, dispatch operation b the most again.

The machine of every procedure distribution is given in machine assignment vector representation.Its allocation order is: make from current sequence number minimum The first operation of industry is to last procedure of sequence number maximum operation.Such as, in the machine assignment vector of Fig. 2, first Element 2 represents first operation O of operation 1₁₁Distributing to machine 2, second element 3 represents the second operation work of operation 1 O₁₂Distributing to machine 3, the rest may be inferred, and machine assignment vector may be interpreted as:

O₁₁→ machine 2, O₁₂→ machine 3, O₁₃→ machine 5, O₂₁→ machine 4,

O₃₁→ machine 5, O₃₂→ machine 3, O₄₁→ machine 1, O₄₂→ machine 2

Wherein, → represent and operation is distributed to corresponding machine.

Randomly generating initial population to refer to, the operation sequence vector in each individuality is by random alignment All Jobs All process steps generates；For machine assignment vector, per pass flow chart is assigned randomly on the arbitrary platform in its collection of machines It is processed；

Pareto domination refers to: set x₁And x₂For two solutions of multi-objective optimization question, the target number of problem is m₁, false If all targets are both needed to minimize, claim x₁Pareto arranges x₂And if only if

Wherein, g and h represents some sequence number of target, f respectively_g(x₁) and f_g(x₂) represent x respectively₁And x₂At the g mesh Mark f_gOn desired value, f_h(x₁) and f_h(x₂) represent x respectively₁And x₂The h target f_hOn desired value.

Pareto non-domination solution refers to, if there is not any other in a certain set to solve x'Pareto domination x, then claims X is the Pareto non-domination solution (abbreviation non-domination solution) in this set.Improve Pareto non-domination solution in any one target Performance, all inevitably result in its performance at least one target remaining and reduce；

(4) progeny population is generated:

One group of uncertainty scene θ of stochastical sampling_q；Progeny population is setMake i=1；

(4.1) mating selects；

Produce equally distributed random number rand₁∈[0,1]；Renewal neighborhood P (i) of i-th subproblem is set:

3 different parents are produced individual based on following ruleWith

(4.2) breeding；

Use breeding operator based on differential evolution algorithm, byAnd xⁱGenerate offspring individual uⁱ；

(4.3) external memory storage is updated；

Evaluate uⁱDesired value, and normalize each desired value；Make ct=ct+1；By uⁱAdd external memory storage Arc；And delete Except in current Arc, all repetition solves and Pareto domination solution；If Chipop=Chipop is ∪ uⁱ；If i is ＜ N, then make i=i+1, Go to (4.1), otherwise perform step (5)；

Breeding operator described in step (4.2) refers to, based on the mutation operator in differential evolution algorithm and crossover operator, if Count the adaptive mutation rate of a kind of improvement and based on the crossover operator repaired, individual by parentWith i-th The current individual x of problemⁱ, generate offspring individual uⁱ；Wherein, the implementation of the adaptive mutation rate of improvement is as follows:

β=e^-0.015t,

$y^i=\mathrm{\β}\[x_p^1+F_1(x_p^2-x_p^3)\]+(1-\mathrm{\β})\[x^i+F_2(x_p^2-x_p^3)+F_3(x_{best}^i-x^i)\].$

Wherein, F₁, F₂And F₃It is mutagenic factor, the uniformly random generation from [0.5,1] respectively of their value；It is current In external memory storage Arc, distance xⁱNearest solution,The value of parameter beta changes along with the value of evolutionary generation t；yⁱIt is The individuality generated by the adaptive mutation rate improved；

For individual operation sequence vector and machine assignment vector, implement the TSP question of improvement described above respectively Operator；After having implemented, the Partial Elements generated in vector may be non-integer, the most infeasible value.In order to solve this problem, For the y generatedⁱIn operation sequence vector ysⁱ, its each element is arranged by order from small to large, obtains ysⁱ Ordering vector tysⁱ, and by each element after sequence at former vector ysⁱIn location index record at index vector IⁱIn； By xⁱOperation sequence vector xsⁱIn each element arrange by order from small to large, obtain xsⁱOrdering vector txsⁱ, And make ysⁱ(Iⁱ)=txsⁱ(ysⁱ(Iⁱ) represent ysⁱIn all at IⁱElement on the position of record)；For the y generatedⁱIn machine Device allocation vector ymⁱ, for each element, search for the collection of machines of its corresponding operation, therefrom determine and connect most with this element value Near machine, and this machine is substituted this element；If there are more than two machines to meet this condition simultaneously, the most therefrom randomly choose Corresponding element replaced by one machine；Operation sequence vector ys after renewalⁱWith machine assignment vector ymⁱConstitute individual yⁱ；

Described implementation based on the crossover operator repaired is as follows:

A individual y that () will be generated by the adaptive mutation rate improvedⁱWith xⁱCombination, constitutes offspring individual uⁱ:

Wherein,It is u respectivelyⁱ,yⁱ,xⁱThe ll element, L is individual xⁱLength, CR ∈ [0,1] be hand over Fork probability,It is a number of uniformly random generation from [0,1], IrandⁱBe from set 1,2 ..., L} randomly chooses An integer；

In the method for expressing of machine assignment of the present invention vector, yⁱMachine assignment vector ymⁱWith xⁱMachine assignment vector xmⁱMachine in same position corresponds to same procedure.Therefore, above-mentioned crossover operator can directly act on ymⁱAnd xmⁱ, The result obtained of intersecting is offspring individual uⁱMachine assignment vector umⁱ。

For operation sequence vector, the enforcement of above-mentioned crossover operator may produce infeasible result, work the most after the intersection In sequence sequence vector, the flow chart of redundancy occurs, and lost other operation.In order to solve this problem, pin of the present invention To yⁱOperation sequence vector ysⁱWith xⁱOperation sequence vector xsⁱ, need to implement the steps of further:

B u that step (a) is tried to achieve by ()ⁱOperation sequence vector usⁱIn, come from xsⁱElement position index record 1 Number index vector index₁In, ys will be come fromⁱElement position index record at No. 2 index vector index₂In；Make usⁱ= xsⁱ, interim index vector tempindex₂=index₂, test vector test=usⁱ(index₁)(usⁱ(index₁) represent usⁱ In all at index₁Element on the position of record), vector donor_delete=[] deleted in index, and [] represents null set；

C (), to each element ue in test, determines at ysⁱ(index₁)(ysⁱ(index₁) represent ysⁱIn all index₁Element on the position of record) in whether there is some elements equal to ue；If it is present select the most uniformly randomly Select an element, by the element chosen at ysⁱIn location index add donor_delete, and by this index from index₁In Delete；Otherwise, find out at ysⁱ(index₂)(ysⁱ(index₂) represent ysⁱIn all at index₂Element on the position of record) In equal to the element of ue, choose one, by it at ys the most uniformly randomlyⁱIn location index add donor_delete, And by this index from index₂Middle deletion；

(d) by the element in donor_delete from set 1,2 ..., L} removes, even index retain vector Donar_reserve={1,2 ..., L} donar_delete (represent removal), and usⁱ(tempindex₂)=ysⁱ (donar_reserve)(usⁱ(tempindex₂) represent usⁱIn all at tempindex₂Element on the position of record, ysⁱ (donar_reserve) ys is representedⁱIn all donar_reserve record position on elements).

(5) renewal solved:

If population mixture Mixpop={x¹,…,x^N∪ Chipop, make i=1,

(5.1) counter c=0 is made；

(5.2) from renewal neighborhood P (i) of i-th subproblem, randomly select sequence number k of a sub-group, k ∈ P (i)；

(5.3) for kth subproblem, from Mixpop, optimum solution is determined；

If token variable mark=0；The weight vector of given kth subproblem(For jth mesh Target weights,) and reference vector Reference for jth target Point, uses Chebyshev method to try to achieve any one individual x at the synthesis object function of kth subproblem to be:

$g^{te}\left(x\right|{\mathrm{\λ}}^k,z^{*})=\underset{1\≤j\≤3}{max}\left\{{\mathrm{\λ}}_j^k\right|{\mathrm{fno}}_j\left(x\right)-z_j^{*}\left|\right\}$

Owing to using normalization desired value, reference vector z is set^*=(0,0,0)；For each individual xy in Mixpop^l With kth subproblem currently solve x^kIf following 3 conditions having one meet: (i) g^te(xy^l|λ^k,z^*) ＜ g^te(x^k| λ^k,z^*)；(ii)g^te(xy^l|λ^k,z^*)=g^te(x^k|λ^k,z^*) and xy^lPareto arranges x^k；(iii)g^te(xy^l|λ^k,z^*)=g^te (x^k|λ^k,z^*) and xy^lAt robust performance f₃Desired value on=robustness is less than x^k, then x is made^k=xy^l, FV^k=F (xy^l), Fno^k=Fno (xy^l), and mark=1；Wherein, FV^kRepresent x^kObject vector, i.e. FV^k=F (x^k)=[f₁(x^k),f₂(x^k),f₃ (x^k)], F (xy^l) represent xy^lObject vector, i.e. F (xy^l)=[f₁(xy^l),f₂(xy^l),f₃(xy^l)], Fno^kRepresent x^kThrough returning Object vector after one change, i.e. Fno^k=[fno₁(x^k),fno₂(x^k),fno₃(x^k)], Fno (xy^l) represent xy^lAfter normalization Object vector, i.e. Fno (xy^l)=[fno₁(xy^l),fno₂(xy^l),fno₃(xy^l)]；

(5.4) if mark=1, then c=c+1 is made；

(5.5) from P (i), sequence number k is deleted；If c is ＜ n_rAnd P (i) nonvoid set, then go to (5.2)；Otherwise, if i is ＜ N, then make i=i+1, goes to (5.1), otherwise goes to step (6)；

Step (6) stop criterion judges:

If ct is ＞ NmbEvl, then terminate iteration, export external memory storage Arc, the i.e. flexibility of one group of Pareto non-dominant These solutions are supplied to production manager and carry out reference by solving job shop scheduling problem solution, and are selected one by him and meet production The satisfactory solution required is as scheduling scheme；Otherwise, make t=t+1, go to step (4).

The effect of the present invention can be further illustrated by following emulation experiment:

1. experiment condition:

CPU be Intel core Duo 2.2GHz, internal memory 4GB, WINDOWS 7 use in system Matlab 2010 to enter Row emulation.

2. experiment content:

The present invention is directed to above-mentioned have 5 machines, the flexible job shop embodiment of 4 operations solves production scheduling side Case.In the present embodiment, every procedure of each operation all can be processed on 5 machines respectively.In these operations, there is part work There is uncertainty in the process time of sequence.The operation number that 4 operations comprise, every procedure allow on processing machine at each Initially estimate process time and as shown in table 1 by the actual process time after disturbance.

3. experimental result

The present invention runs once, can be in the hope of the flexible job shop scheduling solution of one group of Pareto non-dominant.Solve from this group In select 2 scheduling scheme solutions Solution_aAnd Solution_b, when facing identical uncertainty process time, provide it Comparison in efficiency performance (operation completion date, machine maximum load) and robust performance.Every procedure is each permission Process time and as shown in table 2 by the actual process time after disturbance is initially estimated on processing machine.Two solutions are initially Estimate the operation completion date makespan under scene_I, machine maximum load workload_I, disturbed dynamic in the case of operation completion Time makespan_q, machine maximum load workload_q, and their robust desired value is as shown in table 3.Can from table 3 Go out, in order to obtain more preferable robustness, Solution_bInitial job completion date makespan_IWith machine maximum load workload_IIt is inferior to Solution_a.But, when facing identical disturbance process time, Solution_aOperation completion date makespan_qWith machine maximum load workload_qThe most not only it is inferior to Solution_bAnalog value in disturbance cases, also inferior to Solution_bMakespan in initial scene_IAnd workload_I.Thus illustrate, Solution_bThe excellent robust being had Property, compensate for its efficiency performance (makespan in initial scene_IAnd workload_I) weak tendency so that it has higher anti- Interference performance, reduces its efficiency performance sensitivity to disturbance.Fig. 3 is scheduling scheme solution Solution_aAt initial scape Gantt chart in as, Fig. 4 is scheduling scheme solution Solution_aGantt chart in disturbance cases, Fig. 5 is scheduling scheme solution Solution_bGantt chart in initial scene, Fig. 6 is scheduling scheme solution Solution_bGantt chart in disturbance cases.From Gantt chart can be retrieved as the processing machine of every procedure distribution, the beginning process time of every procedure and end time, every The priority processing sequence of each operation on the beginning process time of operation and end time, and every machine.

Table 2

Every 5 values of row respectively each operation estimating or disturbance process time on each machine in each cell

Table 3

Use the inventive method, and two existing classical multi-objective Evolutionary Algorithm MOEA/D-DE and NSGA-II respectively Solve the present embodiment, the Pareto non-dominant disaggregation tried to achieve is compared on constringency performance and distribution performance.Convergence is surveyed Degree uses hypervolume ratio (hypervolume ratio is called for short HVR) tolerance.The value of HVR is the biggest, illustrates what algorithm was tried to achieve Pareto non-dominant disaggregation convergence on object space is the best, is distributed the widest.Distribution performance is measured with estimating Spread, Spread is the least, illustrates that the distribution of the Pareto non-dominant disaggregation that algorithm tries to achieve is the broadest and the most uniform.By the inventive method and Other two kinds existing algorithms run 30 times the most in the present embodiment, the Wilcoxon sum of ranks inspection using significance to be 0.5 Method of testing carries out statistical test to 3 kinds of algorithms 30 operating performances, and result is as shown in table 4.In table 4, p value is Wilcoxon The return value of rank test method, it is assumed that the distribution of two groups of samples has identical intermediate value, then p value represents that sample data supports this vacation If evidence, p value is the biggest, and evidence is the strongest.Symbol ' +/-/=' represent respectively, in algorithm A vs. algorithm B, according to being used The Wilcoxon rank test method that significance is 0.5, algorithm A is significantly better than B, or algorithm A is significantly inferior to B, or algorithm A And between B, there is no marked difference.From table 4, in the present embodiment, HVR and distribution performance are estimated with estimating for convergence Spread, the present invention is all significantly better than MOEA/D-DE and NSGA-II, illustrates that the present invention can compared with two kinds of existing methods There is provided a component cloth broader for production manager, and convergence more preferable Pareto non-domination solution.

Table 4

To sum up, the flexible job shop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm that the present invention proposes, by In have employed novel subproblem more New Policy, utilizing the elite individuality in external memory storage to participate in offspring individual and generating, and Use the adaptive mutation rate improved and breed based on the crossover operator repaired, such that it is able to better profit from overall situation letter Breath, and the balance that maintenance algorithm is between " exploration " and " utilization ", improve convergence of algorithm characteristic and distribution performance.These machines System is effectively improved the search capability of the present invention, overcomes that traditional production scheduling method local search ability is more weak, is prone to It is absorbed in the shortcoming that local optimum, dispatching efficiency are low, it is possible to realize the scheduler task in flexible job shop quickly and efficiently.This Outward, by introducing robust performance index, the present invention can process uncertain factor present in flexible job shop production environment, While ensureing the performances such as shorter, the machine loading more equilibrium of completion date, strengthen Job-Shop scheme to probabilistic Antijamming capability.

Above example is only the technological thought that the present invention is described, it is impossible to limit protection scope of the present invention with this, every The technological thought proposed according to the present invention, any change done on the basis of technical scheme, each fall within scope Within.

Claims (6)

1. a Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm, it is characterised in that include following step Rapid:

Step (1), the input information of reading flexible job shop, define optimization aim, setting constraints:

The input information in workshop includes every assignable collection of machines of procedure in the process number of each operation, each operation, each Operation process time on corresponding machine, the machine number of normal work；Optimization aim includes operation completion date, machine Maximum load, the robustness of scheduling performance；Constraints includes operation priority restrictions and forbids the constraint occupied of trying to be the first；

Step (2), initialization parameter based on the multi-objective Evolutionary Algorithm decomposed:

Arrange iterations NmbEvl, population size N is the number of subproblem, produce N number of equally distributed target weight vector λ¹,…,λ^N, neighborhood scale T of subproblem, breeding operator in parent individuality choose from neighborhood probability δ, neighborhood individuality permit Permitted the maximum number n replaced by each offspring individual_r, uncertain scene number Q of sampling when evaluating robustness, and intersect general Rate CR；

Step (3), determine the neighborhood of each subproblem, produce initial parent colony:

(3.1), to i-th subproblem, i=1 ..., N, determine neighborhood B (i)={ i₁,…,i_T}；Calculate i-th subproblem respectively Weight vector λⁱAnd the Euler's distance between other (N-1) individual subproblem weight vector, by T distance lambdaⁱNearest weight vectorCorresponding sub-group sequence number { i₁,…,i_TConstitute B (i)；

(3.2), initial parent colony { x is randomly generated¹,…,x^N, wherein, individual xⁱCurrent solution for i-th sub-group；Colony In each individuality include operation sequence vector and machine assignment vector；One group of uncertainty scene θ of stochastical sampling_q, q=1, 2,...,Q；Calculate desired value f of each individuality in initial parent colony₁=makespan_I、f₂=workload_IAnd f₃= robustness；makespan_IAnd workload_IRepresent the operation completion date under initial scene and machine maximum load respectively, Robustness represents the robustness of scheduling performance；From initial parent colony, determine that all of Pareto non-domination solution is constituted External memory storage Arc；Objective appraisal counting how many times variable ct=N is set；Normalize each desired value, by each individual xⁱJth Individual desired value f_j(xⁱ) be mapped between interval [0,1], produce xⁱNormalized value fno in jth target_j(xⁱ), it may be assumed that

Wherein,WithRepresent that current parent is for the maximum in jth target of all individualities in colony and minimum respectively Value, j=1,2,3；

(3.3), evolutionary generation t=0 is set；

Step (4), generation progeny population:

One group of uncertainty scene θ of stochastical sampling_q；Progeny population is setMake i=1；

(4.1), mating selects；

Produce equally distributed random number rand₁∈[0,1]；Renewal neighborhood P (i) of i-th subproblem is set:

3 different parents are produced individual based on following ruleWith

(4.2), breeding；

Use breeding operator based on differential evolution algorithm, byAnd xⁱGenerate offspring individual uⁱ；

(4.3), external memory storage is updated；

Evaluate uⁱDesired value, and normalize each desired value；Make ct=ct+1；By uⁱAdd external memory storage Arc；And delete work as In front Arc, all repetition solves and Pareto domination solution；If Chipop=Chipop is ∪ uⁱ；If i is ＜ N, then makes i=i+1, go to (4.1) step (5), is otherwise performed；

Step (5), the renewal solved:

If population mixture Mixpop={x¹,…,x^N∪ Chipop, make i=1,

(5.1) counter c=0, is made；

(5.2), from renewal neighborhood P (i) of i-th subproblem, sequence number k of a sub-group, k ∈ P (i) are randomly selected；

(5.3), for kth subproblem, from Mixpop, optimum solution is determined；

If token variable mark=0；The weight vector of given kth subproblem Power for jth target Value,And reference vector For the reference point of jth target, j=1,2, 3, employing Chebyshev method is tried to achieve any one individual x and at the synthesis object function of kth subproblem is:

$g^{te}\left(x\right|{\mathrm{\λ}}^k,z^{*})=\underset{1\≤j\≤3}{max}\left\{{\mathrm{\λ}}_j^k\right|{\mathrm{fno}}_j\left(x\right)-z_j^{*}\left|\right\}$

Owing to using normalization desired value, reference vector z is set^*=(0,0,0)；For each individual xy in Mixpop^lWith K subproblem currently solve x^kIf following 3 conditions having one meet: (i) g^te(xy^l|λ^k,z^*) ＜ g^te(x^k|λ^k,z^*)； (ii)g^te(xy^l|λ^k,z^*)=g^te(x^k|λ^k,z^*) and xy^lPareto arranges x^k；(iii)g^te(xy^l|λ^k,z^*)=g^te(x^k|λ^k, z^*) and xy^lAt robust performance f₃Desired value on=robustness is less than x^k, then x is made^k=xy^l, FV^k=F (xy^l), Fno^k= Fno(xy^l), and mark=1；Wherein, FV^kRepresent x^kObject vector, i.e. FV^k=F (x^k)=[f₁(x^k),f₂(x^k),f₃(x^k)], F(xy^l) represent xy^lObject vector, i.e. F (xy^l)=[f₁(xy^l),f₂(xy^l),f₃(xy^l)], Fno^kRepresent x^kAfter normalization Object vector, i.e. Fno^k=[fno₁(x^k),fno₂(x^k),fno₃(x^k)], Fno (xy^l) represent xy^lTarget after normalization Vector, i.e. Fno (xy^l)=[fno₁(xy^l),fno₂(xy^l),fno₃(xy^l)]；

(5.4) if mark=1, then c=c+1 is made；

(5.5), from P (i), sequence number k is deleted；If c is ＜ n_rAnd P (i) nonvoid set, then go to (5.2)；Otherwise, if i is ＜ N, then Make i=i+1, go to (5.1), otherwise go to step (6)；

Step (6), stop criterion judge:

If ct is ＞ NmbEvl, then terminate iteration, export external memory storage Arc, the i.e. flexible job of one group of Pareto non-dominant Job-Shop solution；Otherwise, make t=t+1, go to step (4).

A kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm the most according to claim 1, its Being characterised by, described in step (1), the operation completion date in optimization aim has represented all works in flexible job shop The time overhead that industry is spent, is defined as:

$f={\mathrm{makespan}}_I=\underset{v=1,2,...,n}{max}\left(C_v\right)-\underset{v=1,2,...,n}{min}\left(S_v\right)$

Wherein, C_vAnd S_vIt is illustrated respectively in v item operation, time that machines of last procedure and first operation The processing time started, v=1,2 ..., n, n are the sum of All Jobs in flexible job shop；I represents initial scene, i.e. for Uncertainty attribute, if to be that a certain discreet value determines constant for its value, calculates operation completion date in the case；

Machine maximum load in step (1) described optimization aim represents the maximum of each machining time, is defined as:

$f_2={\mathrm{workload}}_I=\underset{s=1,2,...,m}{max}\left(\underset{r=1}{\overset{w}{\Σ}}{\mathrm{pro}}^{O^{sr}}\right)$

Wherein, m is total number of units of flexible job shop inner machine；It is according to scheduling scheme, by r on s platform machine Operation O that individual order is processed^srProcess time；w_sIt is assigned to the operation number on s platform machine；

In step (1) described optimization aim, the robustness of scheduling performance is to weigh operation completion date and the machine of scheduling scheme The maximum load sensitivity to uncertain factor, be defined as:

$f_3=robustness=\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{makespan}}_q-{\mathrm{makespan}}_I}{{\mathrm{makespan}}_I},0\left)\right)}^2}+\sqrt{\frac{1}{Q}\underset{q=1}{\overset{Q}{\Σ}}max{\left(\right(\frac{{\mathrm{workload}}_q-{\mathrm{workload}}_I}{{\mathrm{workload}}_I},0\left)\right)}^2};$

Robustness uses method based on scene definition, by a scheduling scheme at the multiple sampled value { θ of uncertainty attribute_q| q= 1,2 ..., emulate under Q}, with between comparisons completion date and the actual value of machine maximum load and initial discreet value Difference；Wherein, makespan_qAnd workload_qIt is θ respectively_qThe most corresponding operation completion date and machine maximum load target Value；

Operation priority restrictions described in step (1) refers to that each procedure of each operation is to add by pre-determined order Work；In flexible job shop problem, every procedure can be processed on arbitrary platform in the collection of machines that it allows；

The constraint occupied of trying to be the first of forbidding described in step (1) includes: the processing of (i) every procedure, can only arrange in same operation All process steps before it just can proceed by after all completing；(ii) if a procedure is allocated to certain machine, Only before this machine completes after all process steps of scheduling, the processing of this procedure could be started.

A kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm the most according to claim 1, its Being characterised by, the initial population that randomly generates described in step (3.2) refers to, the operation sequence vector in each individuality is by random All process steps in arrangement All Jobs generates；For machine assignment vector, per pass flow chart is assigned randomly to its machine It is processed on arbitrary platform in set.

A kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm the most according to claim 1, its Being characterised by, the Pareto domination described in step (4.3) and step (5.3) refers to: set x₁And x₂For multi-objective optimization question two Individual solution, the target number of problem is m₁, it is assumed that all targets are both needed to minimize, and claim x₁Pareto arranges x₂And if only if

$\∀g\∈\{1,2,...,m_1\}:f_g\left(x_1\right)\≤f_g\left(x_2\right)$

And $\&Exists;h\&Element;\{1,2,...,m_1\}:f_h\left(x_1\right)<f_h\left(x_2\right)$

Wherein, g and h represents some sequence number of target, f respectively_g(x₁) and f_g(x₂) represent x respectively₁And x₂The g target f_g On desired value, f_h(x₁) and f_h(x₂) represent x respectively₁And x₂The h target f_hOn desired value.

A kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm the most according to claim 1, its Being characterised by, the Pareto non-domination solution described in step (3) and step (6) refers to, if not existing any in a certain set Other solves x'Pareto domination and solves x, then the Pareto non-domination solution during x is called this set.

A kind of Flexible Workshop Robust Scheduling method based on decomposition multi-objective Evolutionary Algorithm the most according to claim 1, its Being characterised by, the breeding operator described in step (4.2) refers to, based on the mutation operator in differential evolution algorithm and crossover operator, Design the adaptive mutation rate of a kind of improvement and based on the crossover operator repaired, individual by parentWith i-th The current individual x of individual subproblemⁱ, generate offspring individual uⁱ；Wherein, the implementation of the adaptive mutation rate of improvement is as follows:

β=e^-0.015t,

$y^i=\mathrm{\&beta;}\&lsqb;x_p^1+F(x_p^2-x_p^3)\&rsqb;+(1-\mathrm{\&beta;})\&lsqb;x^i+F_2(x_p^2-x_p^3)+F_3(x_{best}^i-x^i)\&rsqb;.$

Wherein, F₁, F₂And F₃It is mutagenic factor, the uniformly random generation from [0.5,1] respectively of their value；It it is current external In memory Arc, distance xⁱNearest solution,The value of parameter beta changes along with the value of evolutionary generation t；yⁱIt is by changing The individuality that the adaptive mutation rate entered generates；

For individual operation sequence vector and machine assignment vector, the TSP question implementing improvement described above respectively is calculated Son；For the y generatedⁱIn operation sequence vector ysⁱ, its each element is arranged by order from small to large, obtains ysⁱOrdering vector tysⁱ, and by each element after sequence at former vector ysⁱIn location index record at index vector Iⁱ In；By xⁱOperation sequence vector xsⁱIn each element arrange by order from small to large, obtain xsⁱOrdering vector txsⁱ, and make ysⁱ(Iⁱ)=txsⁱ, ysⁱ(Iⁱ) represent ysⁱIn all at IⁱElement on the position of record；For the y generatedⁱIn Machine assignment vector ymⁱ, for each element, search for the collection of machines of its corresponding operation, therefrom determine and this element value Immediate machine, and this machine is substituted this element；If there are more than two machines to meet this condition simultaneously, the most random A machine is selected to replace corresponding element；Operation sequence vector ys after renewalⁱWith machine assignment vector ymⁱConstitute new individual yⁱ；

Described implementation based on the crossover operator repaired is as follows:

(a), the individual y that will be generated by the adaptive mutation rate improvedⁱWith xⁱCombination, constitutes offspring individual uⁱ:

Wherein,It is u respectivelyⁱ,yⁱ,xⁱThe ll element, L is individual xⁱLength, CR ∈ [0,1] be intersect general Rate,It is a number of uniformly random generation from [0,1], IrandⁱBe from set 1,2 ..., randomly choosed in L} Individual integer；

In the method for expressing of machine assignment vector, yⁱMachine assignment vector ymⁱWith xⁱMachine assignment vector x mⁱIn identical bits The machine put corresponds to same procedure；Above-mentioned crossover operator directly acts on ymⁱAnd xmⁱ, the result obtained of intersecting is son Generation individual uⁱMachine assignment vector umⁱ；

For yⁱOperation sequence vector ysⁱWith xⁱOperation sequence vector xsⁱ, implement the steps of further:

(b), the u that step (a) is tried to achieveⁱOperation sequence vector usⁱIn, xs will be come fromⁱElement position index record 1 Number index vector index₁In, ys will be come fromⁱElement position index record at No. 2 index vector index₂In；Make usⁱ= xsⁱ, interim index vector tempindex₂=index₂, test vector test=usⁱ(index₁), usⁱ(index₁) represent usⁱ In all at index₁Element on the position of record, vector donor_delete=[], [] expression null set deleted in index；

(c), to each element ue in test, determine at ysⁱ(index₁Whether there is some elements equal to ue in)；If deposited , select an element, by the element chosen at ys the most uniformly randomlyⁱIn location index add donor_ Delete, and by this index from index₁Middle deletion；Otherwise, find out at ysⁱ(index₂The element of ue it is equal to, the most uniformly in) Choose one randomly, by it at ysⁱIn location index add donor_delete, and by this index from index₂Middle deletion； Wherein, ysⁱ(index₁) represent ysⁱIn all at index₁Element on the position of record, ysⁱ(index₂) represent ysⁱMiddle institute Have at index₂Element on the position of record；

(d), by the element in donor_delete from set 1,2 ..., L} removes, even index retain vector donar_ Reserve={1,2 ..., L} donar_delete, and usⁱ(tempindex₂)=ysⁱ(donar_reserve)；Wherein, Represent and remove, usⁱ(tempindex₂) represent usⁱIn all at tempindex₂Element on the position of record, ysⁱ(donar_ Reserve) ys is representedⁱIn all donar_reserve record position on elements.