CN109709916A - A kind of dispatching method based on Gibbs sampling method - Google Patents
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Abstract
The invention proposes a kind of dispatching methods based on Gibbs sampling method, the present invention not only allows for the architectural characteristic of task and the working ability of equipment, the transport relationship for also contemplating equipment room is scheduled judgement selection to each optional equipment using Gibbs Sampling Strategy.The present invention is using the load condition of each equipment as the foundation of scheduling decision, under the premise of considering that key equipment load minimizes, solves the production scheduling problems with fixed I/O constraint.
Description
Technical field
The invention belongs to the optimizing scheduling technical fields of more scheduling decision unit Coordination Decisions, and being mainly used in equipment has
The Distributed Manufacturing System of Flexible Manufacture ability, more particularly to a kind of dispatching method based on Gibbs sampling method.
Background technique
Production scheduling problems are a kind of scheduling problem with multiple constraint, special schedule constraints in the actual production process
It include: zero-waiting constraint, multitask dynamic dispatching constraint, equally loaded constraint, processing cost constraint, delivery date constraint etc..Cause
This needs to be correspondingly improved general dispatching algorithm in solving practical problems.The production model of modernization, is exchanged
Degree task proposes new " decentralization " constraint, i.e., the geography of logistics and distributed process equipment is considered in scheduling process
Influence of the position to whole industry.Since current production scheduling problems belong to flexible scheduling problem more, which is a kind of NP
Problem, without optimal solution in linear session.Therefore, in recent years to the research of production scheduling algorithm to reduce complexity as mesh
Mark, such method are mostly constrained using logistics, industrial chain, relation between supply and demand constraint as basic.It is highlighted on the basis of traditional mode of production
The effect of logistics transportation.
Research object of the invention is that the fixation input and output constraint of product is considered in the production model of " decentralization ".
Its schedule constraints under the conditions of fixed product input node and output node, from " flexible apparatus " of intermediate link, is looked for
The Route Scheduling relatively optimal to one makes whole production execute the time minimum.At present to the production scheduling of fixed I/O constraint
Research contents is less.The existing distributive knowledge network dispatching method towards fixed point output, is calculated including the scheduling based on dynamic rank
Method, backward are divided and ruled derivation algorithm, heuritic approach and dynamic backoff algorithm etc..The essence of these methods is with task path
Length and the height for transporting cost not by Flexible Equipment working ability and consider that the transport of equipment carries out as scheduling decision
Comprehensively consider.Innovation of the invention is that the transportation characterization of distributed apparatus is utilized, in consideration Flexible Equipment processing energy
While power, the transport relationship of equipment is considered.In this regard, the present invention not only needs to consider the architectural characteristic of task and adding for equipment
Work ability, it is also necessary to consider the transport relationship of equipment room, therefore, the method for the invention has preferable practicability.
Summary of the invention
The invention aims to solve existing technical problem, a kind of dispatching party based on Gibbs sampling method is provided
Method.The present invention not only allows for the architectural characteristic of task and the working ability of equipment, it is also contemplated that the transport relationship of equipment room,
Judgement selection is scheduled to each optional equipment using Gibbs Sampling Strategy.The present invention is using the load condition of each equipment as tune
The foundation for spending decision solves that there is the production scheduling of fixed I/O constraint to ask under the premise of considering that key equipment load minimizes
Topic.
The present invention is achieved by the following technical solutions, and the present invention proposes a kind of dispatching party based on Gibbs sampling method
Method,
Step 1: initial procedure being assigned on its designated equipment and is processed；
Step 2: when there is process completion of processing, judging whether to generate schedulable process B, i.e. front and continued process is machined complete
Complete process；Schedulable process B if it exists carries out each schedulable process by schedulable process number of plies l descending sequence
Scheduling；When being scheduled to a certain schedulable process, integrate-cost O of the schedulable process in each equipment is calculated；It is comprehensive
The calculation method for closing cost O is as follows:
O=VAM (1)
Wherein V is process processing cost matrix, and A is processing matrix, and M is equipment conveying cost matrix, member in integrate-cost O
Plain Oi,jIndicate a certain schedulable process vi∈ B is in equipment mjOn integrate-cost, Oi: and indicate schedulable process viIt is set all
Standby upper integrate-cost, integrate-cost Oi,jIt is smaller then by schedulable process viIt is assigned to mjThe reasonability of upper processing is higher；
Step 3: being schedulable process v using Gibbs sampling methodiProcess equipment is distributed,It is raw in section
At random number o,And press Oi,jValue is arranged, if o falls in Oi,jValue interval in, then
Select mjAs viProcess equipment；| m | it is the quantity of equipment, i and j are positive integer；
Step 4: repeating step 2- step 3 and each process is allocated, will finally terminate process E and be assigned to it and specified set
It is standby upper.
Further, elements A in the processing matrix Ai,jIndicate process viIn equipment mjTime required for upper processing, square
The i-th row of battle array A indicates process viThe vector that process time on all devices is constituted.
Further, the process processing cost matrix V is by the process dominance relation of process processing cost model foundation
Matrix, target are that subsequent handling is established with the angle of task structure to the influence power of schedulable process；The model is with a certain work
Sequence vjTo another process viInfluence power depend on the two before distance be principle, using function shown in formula (2) as vjWith
viDistance metric:
Wherein succ (vi) indicate process viSubsequent handling set, α be distance controlling parameter, value interval be 0 < α < 3,
liIndicate process viThe number of plies in task, ljIndicate process vjThe number of plies in task.
Further, element M in the equipment conveying cost matrix Mi,jIt is equipment miTo equipment mjRelative Link Importance, build
The transition probability matrix H of vertical equipment room, expression formula are as follows:
Wherein, adj (mi) indicate and miThe equipment of direct neighbor；RjIf indicating a certain schedulable process vkIt is assigned to equipment mj
And mjIt is in machining state, then RsTo need the time waited；mbFor process vkPrecedence activities process equipment；meFor fixation
Output equipment；U (i, j) indicates equipment miWith equipment mjBetween haulage time；U (b, j) indicates schedulable process vkPrecedence activities
Process equipment mbWith equipment mjBetween haulage time；U (j, e) indicates equipment mjWith fixed output equipment meBetween haulage time；u
(b, s) indicates equipment mbWith equipment msBetween haulage time；U (s, e) indicates equipment msWith fixed output equipment meBetween transport when
Between；U (i, s) indicates equipment miWith equipment msBetween haulage time；
With the l of equipment roomiWalk transfer matrixJudge equipment relative to schedulable process viDispatching priority, i.e. equipment
Transport cost matrix
The invention has the advantages that:
1. greatly possibly guaranteeing the high process of the priority equipment high in priority using Gibbs Sampling strategy
Upper processing, and make each optional equipment and have the possibility selected, to reduce the load of key equipment.Meanwhile the strategy
Also guarantee that all devices have dispatcher meeting, so as to avoid the fairness of task schedule.
It 2. establish processing cost model, is input with task structure, quantitative expression subsequent handling is to alternative procedure
Influence.Therefore, processing cost model is the index of process different degree, embodies the dispatching priority of process.Processing cost mould
Type expresses influence of position of the process in task to its dispatching priority from processing tasks structural point.
It 3. establish transport Cost Model, is input with the processing environment of equipment, quantitative expression device location is to standby
The influence of optional equipment.Therefore, transport Cost Model is the index of Chemical Apparatus Importance Classification, embodies the dispatching priority of equipment.Transport
Cost Model expresses influence of position of the equipment in processing network to its dispatching priority from processing environment angle.
Detailed description of the invention
Fig. 1 is task DAG structure chart of the invention；
Fig. 2 is the device distribution state diagram of task shown in Fig. 1；
Fig. 3 is execution time of the manufacturing procedure shown in Fig. 1 on each process equipment, i.e. processing matrix schematic diagram；
Fig. 4 is the haulage time schematic diagram of each equipment room shown in Fig. 2；
Fig. 5 is the processing cost matrix schematic diagram between process；
Fig. 6 is the transition probability matrix schematic diagram of equipment room；
Fig. 7 is the transport cost matrix schematic diagram of the equipment room as α=0.5；
Fig. 8 is each process v3-v9Scheduling process figure；
Fig. 9 is the value analysis chart of each parameter alpha.
Specific embodiment
Technical solution in the embodiment of the present invention that following will be combined with the drawings in the embodiments of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts
Example is applied, shall fall within the protection scope of the present invention.
When process is completed to process, consider whether its subsequent handling can start to process, if its subsequent handling becomes adjustable
Process is spent, then utilizes Gibbs Sampling Strategy, selects a process-equipment to as scheduling result.A certain process is selected to process
It is scheduled when complete, because only that subsequent handling is likely to become schedulable process when process completion of processing.
The present invention proposes a kind of dispatching method based on Gibbs sampling method, comprising the following steps:
Step 1: initial procedure being assigned on its designated equipment and is processed；
Step 2: when there is process completion of processing, judging whether to generate schedulable process B, i.e. front and continued process is machined complete
Complete process；Schedulable process B if it exists carries out each schedulable process by schedulable process number of plies l descending sequence
Scheduling；When being scheduled to a certain schedulable process, integrate-cost O of the schedulable process in each equipment is calculated；It is comprehensive
The calculation method for closing cost O is as follows:
O=VAM (1)
Wherein V is process processing cost matrix, and A is processing matrix, and M is equipment conveying cost matrix, member in integrate-cost O
Plain Oi,jIndicate a certain schedulable process vi∈ B is in equipment mjOn integrate-cost, Oi: and indicate schedulable process viIt is set all
Standby upper integrate-cost, integrate-cost Oi,jIt is smaller then by schedulable process viIt is assigned to mjThe reasonability of upper processing is higher；
Step 3: being schedulable process v using Gibbs sampling methodiProcess equipment is distributed,It is raw in section
At random number o,And press Oi,jValue is arranged, if o falls in Oi,jValue interval in, then
Select mjAs viProcess equipment；| m | it is the quantity of equipment, i and j are positive integer；
Step 4: repeating step 2- step 3 and each process is allocated, will finally terminate process E and be assigned to it and specified set
It is standby upper.
Elements A in the processing matrix Ai,jIndicate process viIn equipment mjTime required for upper processing, the i-th of matrix A
Row indicates process viThe vector that process time on all devices is constituted.
The process processing cost matrix V is by the process precedence relation matrix of process processing cost model foundation, mesh
Mark is that subsequent handling is established with the angle of task structure to the influence power of schedulable process；The model is with a certain process vjTo another
Process viInfluence power depend on the two before distance be principle, using function shown in formula (2) as vjWith viApart from degree
Amount:
Wherein succ (vi) indicate process viSubsequent handling set, α be distance controlling parameter, value interval be 0 < α < 3,
Optimal value interval is [1.3,2.4], liIndicate process viThe number of plies in task, ljIndicate process vjThe number of plies in task.
Element M in the equipment conveying cost matrix Mi,jIt is equipment miTo equipment mjRelative Link Importance, establish equipment room
Transition probability matrix H, expression formula is as follows:
Wherein, adj (mi) indicate and miThe equipment of direct neighbor；RjIf indicating a certain schedulable process vkIt is assigned to equipment mj
And mjIt is in machining state, then RsTo need the time waited；mbFor process vkPrecedence activities process equipment；meFor fixation
Output equipment；U (i, j) indicates equipment miWith equipment mjBetween haulage time；U (b, j) indicates schedulable process vkPrecedence activities
Process equipment mbWith equipment mjBetween haulage time；U (j, e) indicates equipment mjWith fixed output equipment meBetween haulage time；u
(b, s) indicates equipment mbWith equipment msBetween haulage time；U (s, e) indicates equipment msWith fixed output equipment meBetween transport when
Between；U (i, s) indicates equipment miWith equipment msBetween haulage time；
With the l of equipment roomiWalk transfer matrix(the l of HiPower) judge equipment relative to schedulable process viScheduling it is excellent
Elder generation's property, i.e. equipment conveying cost matrix
The purpose of the present invention is to minimize process time as target, examine on the basis of meeting fixed input and output constraint
The load for considering crucial process equipment, ensures the robustness of system of processing.In this regard, the present invention is devised based on Gibbs Sampling Strategy
Dispatching method.This method guarantees that the high process of priority is processed in the high equipment of priority with maximum probability, and makes each
Optional equipment has the possibility selected, to reduce the load of key equipment.In addition, the present invention devises processing cost mould
Type and transport Cost Model.Wherein processing cost model is input with task structure, and quantitative expression subsequent handling is to alternative work
The influence of sequence, processing cost model are the indexs of process different degree, embody the dispatching priority of process；Transport Cost Model with
The processing environment of equipment is input, quantitative expression influence of the device location to optional equipment.Therefore, processing cost model is work
The index of sequence different degree embodies the dispatching priority of process；Transport Cost Model is the index of Chemical Apparatus Importance Classification, embodies and sets
Standby dispatching priority.Processing cost model and transport Cost Model are suitable for DAG scheduling model, for process priority and can set
The quantization of standby priority provides reference.
The method of the invention is illustrated with a specific example in conjunction with Fig. 1-Fig. 9:
Fig. 1 is the DAG structure chart of product of the present invention task, shows the relationship between each process, and Fig. 2 is appointed shown in Fig. 1
The device distribution state diagram of business, the relationship between each equipment is shown in figure, and Fig. 3 shows manufacturing procedure shown in Fig. 1 each
Execution time on process equipment, i.e. processing matrix, Fig. 4 show the haulage time of each equipment room shown in Fig. 2, and Fig. 5 shows work
Processing cost matrix between sequence, Fig. 6 show the transition probability matrix of equipment room, and Fig. 7 shows the equipment room as α=0.5
Transport cost matrix.
In conjunction with Fig. 8, as t=0, due to equipment m1,m2For initial task v1,v2Corresponding fixation process equipment, because
This, needs equipment m1,m2Distribute to task v1,v2；
As t=6, v1Completion of processing, at this time v3As schedulable process.Due to v1Process equipment be m1, therefore v3's
Precedence activities process equipment mbFor m1, v3In equipment m1-7On early start process time be respectively 6,7,10,10,12,12,
15}.The t=6 moment equipment occupied state shown in Fig. 8 (a) is it is found that equipment m2At the t=7 moment, the occupied and end time is
8, if therefore v3In m2Upper processing needs to start waiting at the t=7 moment, the waiting time 1, therefore, R2=1.It is set on other
It is standby unoccupied, therefore, R1=0, R3-7=0.V can be obtained at this time3Integrate-cost matrix O, the 3rd behavior O3:=
[17.37,17.58,17.20,16.84,21.32,14.43,17.73] indicates v3In each equipment m1-7On integrate-cost, then 1/
O3,1=0.0576,1/O3,2=0.0569,1/O3,3=0.0581,1/O3,4=0.0594,1/O3,5=0.0469,1/O3,6=
0.0693,1/O3,7=0.0564,The Gibbs sampling method according to shown in step 3, by cumsum () letter
Number is it is found that O3,1Sampling range be (0,0.0576], O3,2Sampling range be (0.0576,0.1145], O3,3Sampling range
For (0.1145,0.1726], O3,4Sampling range be (0.1726,0.2320], O3,5Sampling range be (0.2320,
0.2789], O3,6Sampling range be (0.2789,0.3482], O3,7Sampling range be (0.3482,0.4046].If (0,
0.4046) section takes random number o=0.3296, i.e. o to fall in O3,6Section (0.2789,0.3482] in, therefore, by v3Point
It is fitted on m6Upper processing, time started 12, process time A3,6=1；
As t=8, v2Completion of processing, at this time v4And v5As schedulable process, due to l4=l5, therefore v4And v5Tune
It is identical to spend order, presses elder generation v4V afterwards5Scheduling sequence be scheduled.Due to v1Process equipment be m1, v2Process equipment be m2,
Therefore v4And v5Precedence activities process equipment be respectively m1{ m1,m2}.For v4Equipment holding time is R1-7=0, for
v5Equipment holding time R3=6.Using Gibbs sampling method, at this time by v4It is assigned to m3Upper processing, by v5It is assigned to m5Upper processing,
Its time started is respectively 12 and 13, and process time is respectively 5 and 8, shown in scheduling process such as Fig. 8 (b)；
When t={ 13,17,21 }, v6,v7,v8Successively become schedulable process, using above-mentioned dispatching method, successively will
v6,v7,v8It is assigned to m6,m7,m5Upper processing, scheduling process is respectively as shown in Fig. 8 (c)-(e)；
As t=34, v7Completion of processing, at this time v9As schedulable process, due to v9It is the termination process of task, therefore
v9It needs in fixed output equipment m7Upper processing, shown in scheduling process such as Fig. 8 (f), the end time of task shown in Fig. 1 is 41.
Fig. 9 is the value analysis chart of parameter alpha, wherein x=li-ljIndicate that the distance of two-step, value are integer, therefore
Exp (- α (x)) is discrete value.The discrete value comparison that Fig. 9 is exp (- α (x)) under the different value of α.It can from the comparison of Fig. 9
Know, when the value of α is larger, the value of remote x is smaller, i.e. the more big remote process of the value of α is to schedulable shadow
Sound is smaller, and as α > 3, influence power is bordering on 0.Effective value interval to this α is 0 < α < 3.
It above to a kind of dispatching method based on Gibbs sampling method provided by the present invention, is described in detail, herein
In apply that a specific example illustrates the principle and implementation of the invention, the explanation of above example is only intended to sides
Assistant solves method and its core concept of the invention；At the same time, for those skilled in the art, think of according to the present invention
Think, there will be changes in the specific implementation manner and application range, in conclusion the content of the present specification should not be construed as pair
Limitation of the invention.
Claims (4)
1. a kind of dispatching method based on Gibbs sampling method, which is characterized in that
Step 1: initial procedure being assigned on its designated equipment and is processed；
Step 2: when there is process completion of processing, judging whether to generate schedulable process B, i.e., front and continued process is machined finishes
Process；Schedulable process B if it exists is scheduled each schedulable process by the descending sequence of schedulable process number of plies l；
When being scheduled to a certain schedulable process, integrate-cost O of the schedulable process in each equipment is calculated；Integrate-cost
The calculation method of O is as follows:
O=VAM (1)
Wherein V is process processing cost matrix, and A is processing matrix, and M is equipment conveying cost matrix, element in integrate-cost O
Oi,jIndicate a certain schedulable process vi∈ B is in equipment mjOn integrate-cost, Oi: and indicate schedulable process viIn all devices
On integrate-cost, integrate-cost Oi,jIt is smaller then by schedulable process viIt is assigned to mjThe reasonability of upper processing is higher；
Step 3: being schedulable process v using Gibbs sampling methodiProcess equipment is distributed,In section generate with
Machine numberAnd press Oi,jValue is arranged, if o falls in Oi,jValue interval in, then select
mjAs viProcess equipment；| m | it is the quantity of equipment, i and j are positive integer；
Step 4: repeating step 2- step 3 and each process is allocated, will finally terminate process E and be assigned to its designated equipment
On.
2. the method according to claim 1, wherein elements A in the processing matrix Ai,jIndicate process viIt is setting
Standby mjThe i-th row of time required for upper processing, matrix A indicate process viThe vector that process time on all devices is constituted.
3. according to the method described in claim 2, it is characterized in that, the process processing cost matrix V is to process generation by process
The process precedence relation matrix of valence model foundation, target are that subsequent handling is established with the angle of task structure to schedulable process
Influence power；The model is with a certain process vjTo another process viInfluence power depend on the two before distance be principle, utilize
Function shown in formula (2) is as vjWith viDistance metric:
Wherein succ (vi) indicate process viSubsequent handling set, α be distance controlling parameter, value interval be 0 < α < 3, liTable
Show process viThe number of plies in task, ljIndicate process vjThe number of plies in task.
4. according to the method described in claim 3, it is characterized in that, element M in the equipment conveying cost matrix Mi,jIt is equipment
miTo equipment mjRelative Link Importance, establish the transition probability matrix H of equipment room, expression formula is as follows:
Wherein, adj (mi) indicate and miThe equipment of direct neighbor；RjIf indicating a certain schedulable process vkIt is assigned to equipment mjAnd mj
It is in machining state, then RsTo need the time waited；mbFor process vkPrecedence activities process equipment；meIt is defeated for fixation
Equipment out；U (i, j) indicates equipment miWith equipment mjBetween haulage time；U (b, j) indicates schedulable process vkPrecedence activities add
Construction equipment mbWith equipment mjBetween haulage time；U (j, e) indicates equipment mjWith fixed output equipment meBetween haulage time；u(b,
S) equipment m is indicatedbWith equipment msBetween haulage time；U (s, e) indicates equipment msWith fixed output equipment meBetween haulage time；
U (i, s) indicates equipment miWith equipment msBetween haulage time；
With the l of equipment roomiWalk transfer matrixJudge equipment relative to schedulable process viDispatching priority, i.e. equipment conveying
Cost matrix
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