CN106610658A - Neural network based algorithm for solving workshop scheduling problem - Google Patents
Neural network based algorithm for solving workshop scheduling problem Download PDFInfo
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- CN106610658A CN106610658A CN201610364170.7A CN201610364170A CN106610658A CN 106610658 A CN106610658 A CN 106610658A CN 201610364170 A CN201610364170 A CN 201610364170A CN 106610658 A CN106610658 A CN 106610658A
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- 238000013528 artificial neural network Methods 0.000 title abstract description 5
- 239000011159 matrix material Substances 0.000 claims abstract description 23
- 238000004364 calculation method Methods 0.000 claims abstract description 4
- 230000001537 neural effect Effects 0.000 claims abstract 2
- 230000006870 function Effects 0.000 claims description 42
- 210000002569 neuron Anatomy 0.000 claims description 24
- 238000010276 construction Methods 0.000 claims description 6
- 230000007935 neutral effect Effects 0.000 claims description 6
- 230000033228 biological regulation Effects 0.000 claims description 3
- 238000005516 engineering process Methods 0.000 claims description 3
- 230000005764 inhibitory process Effects 0.000 claims description 2
- 230000004044 response Effects 0.000 claims description 2
- 230000001960 triggered effect Effects 0.000 claims description 2
- 230000005284 excitation Effects 0.000 abstract 1
- 238000004519 manufacturing process Methods 0.000 description 7
- 210000005036 nerve Anatomy 0.000 description 3
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM]
- G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/32—Operator till task planning
- G05B2219/32252—Scheduling production, machining, job shop
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
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Abstract
The invention provides a neural network based algorithm for solving a workshop scheduling problem, and relates to the technical field of workshop scheduling. The algorithm mainly comprises the following steps that 1) time t and initial values of constants A, B and C are set, and A, B and C are constants greater than 0; 2) a coefficient matrix W is initialized; 3) a threshold vector is constructed; 4) a state function is constructed; 5) a relation function is calculated; 6) an energy function is constructed; 7) a neural input bias current (applied excitation) is calculated; 8) a coefficient matrix is adjusted; 9) an operation equation is determined; 10) calculation is carried out according to a runge-kutta formula; and 11) and whether a balance condition is reached is determined.
Description
Art
The present invention relates to solving job shop scheduling problem technical field.
Background technology
Job-shop scheduling problem (Job-Shop Scheduling Problem, JSP) is manufacturing execution system research
One of core and emphasis, its research is not only of great immediate significance, and with far-reaching theory significance.JSP is exactly
According to product manufacturing demand reasonable distribution resource, so reach rationally using product manufacturing resource, improve Business Economic Benefit
Purpose.JSP is the problem coexisted in product manufacturing industry, and it is with computer integrated manufacturing system (Computer Integrated
Manufacturing Systems, CIMS) factory management, product manufacturing level be closely related, be in CIMS fields study
Important topic.JSP is a typical NP-hard problem, and its research will necessarily play significant to the research of np problem
Affect.
Artificial neural network is a kind of information processing system of mimic biology brain 26S Proteasome Structure and Function, and it is a kind of large-scale
Parallel organization, the distributed storage of information and parallel processing, with good self adaptation, self-organizing and fault-tolerance, with stronger
Study, memory, association and identification function etc..Its main thought is to be connected with each other one computer of composition with artificial neuron
Network, parallel efficiently Solve problems.Neutral net solves the problems, such as that the main thought of Job-Shop is：By a Lyaplmov
The extreme value of energy function tectonic network, when network iteration convergence, energy function reaches minimum, makes mesh corresponding with energy function
Scalar functions are optimized.
But the efficiency of neutral net is affected very big by training, and when problem scale is larger, exist calculating speed slowly with
Structural parameters are difficult to the weakness for determining.
The content of the invention
For existing technology above shortcomings, the technical problem to be solved in the present invention is to provide a kind of new based on nerve
Network algorithm solves job-shop scheduling problem.
The purpose of the present invention is overcome present in prior art：When problem scale is larger, there is calculating speed weak slowly
Point.
The technical scheme that adopted for achieving the above object of the present invention is：A kind of algorithm based on neutral net solves operation
Job-Shop problem, the key step of the algorithm is as follows：
Step 1：Setting time t, constant A, the initial value of B, C, A, B, C>0, it is constant；
Step 2：Initialization coefficient matrix W
Step 3：Construction threshold vector
Step 4：Structural regime function
Step 5：Calculated relationship function
Step 6：Construction energy function
Step 7:Calculate nerve input bias current (extrinsic motivated) Ixi
Step 8：Regulation coefficient matrix
Step 9：It is determined that operation equation
Step 10：V is calculated according to quadravalence dragon lattice-storehouse tower (runge_kutta) formulaxi(t+1)
Step 11：Judge whether to reach equilibrium condition
The invention has the beneficial effects as follows：
1st, threshold vector is constructed by average threshold, the amount of calculation of algorithm is reduced to a certain extent.
2nd, by the way that energy function and standard energy function are compared, weight coefficient is corrected, makes the solution of algorithm more
Accurately, while accelerating convergence, unnecessary search time is reduced.
3rd, by adding imitative bipolar S type functions neuron state is carried out to approach renewal, algorithm is more accurate.
Description of the drawings
Fig. 1 represents the basic flow sheet of the present invention
Fig. 2 represents the layering exemplary plot of neural network algorithm
Specific embodiment
Below in conjunction with accompanying drawing, the present invention is described in detail.
Neural network algorithm, with reference to Fig. 2, it can be seen that it is divided into input layer, hidden layer, three layers of output layer, in job shop
In scheduling problem, using the state abstraction of workpiece as the input block in neutral net.
According to principles above, with reference to Fig. 1, the detailed implementation steps of this algorithm are as follows.
Step 1：Setting time t, constant A, the initial value of B, C, A, B, C>0, it is constant；
Step 2：Initialization coefficient matrix W：For the discrete hopfield networks being made up of n neuron, then have
N*n weight coefficient matrix W：
W={ wij, i, j=1,2 ..., n
Step 3：Construction threshold vector：There is n to tie up threshold vector θ：
θ=[f (θ1), f (θ2) ..., f (θn)]T
Wherein, c is an average threshold,
In general, W and θ can determine a unique discrete hopfield networks net=W × θ；
Step 4：Structural regime function：Use Yj(t)The state of j-th neuron, i.e. node j in moment t is represented, then node
The next moment (t+1) state can obtain it is as follows：
Step 5：Calculated relationship function：Calculate the relation function W between neuronXi, yi：
Wxiyj=-A δxy(1-δij)-B-Cδi1δj1
Wherein
Step 6：Construction energy function：E=E1+E2+E3
Row constraint condition：
Wherein, VxiRepresent state V=Y of i-th neuron；A>0, it is constant, E1For row constraint, and if only if each square
More than one " 1 " element, when remaining element is " 0 ", E are not contained in battle array boat1Ensure when every a line of matrix v is not more than one
When individual " 1 ", E1Reach minimum, now E1min=0；
In the same manner, column constraint condition is constituted
Wherein, B>0, it is constant, E2Ensure when every a line of matrix v is not more than one " 1 ", E2Reach minimum E2min=
0；
Global constraints：
Wherein, C>0, it is constant, E3Ensure as exactly mn 1 in matrix V, i.e., one total mn 1 in whole matrix,
E3Reach minimum E3min=0；
Step 7:Calculate nerve input bias current (extrinsic motivated) Ixi；
Step 8：Regulation coefficient matrix：
First, the energy difference between the energy function in step 4 and standard energy function is sought：
Standard energy function is：
Energy difference：
Δ E=E-Em
If | Δ E | is≤ε, return to step 4 otherwise goes to step 9, according to this energy difference to weight coefficient WxiyjAdjust
Whole, adjustment mode is as follows：
Wxiyj=-A δxy(1-ΔE)-B-Cδi1δj1
Step 9：It is determined that operation equation：Calculate VxiT (), between each neuron output and input Sigmoid functions are met
Characteristic, arranges u0Initial value：
Wherein,
Sigmoid functions make g (vxi) value between 0 to 1, in order to avoid workpiece calling (partly using money by part
Source), start to v0One larger value, so as to a relatively low gain come iterative network, through the iteration of certain number of times
Afterwards, v0Value be substantially reduced, gain is brought up to into a larger value, for larger gain, Sigmoid functions and hard-limiting
Functional similarity, the output valve of neuron can so avoid interference the problem of partial scheduling close to 1, while can also avoid
The unstable networks caused using clip functions；
τ=R in formulaxi=CxiFor time constant, for simplicity, if τ=Rxi=Cxi=1；
For meet the constraint condition, high inhibition can be carried out to some neurons so that these neurons are not triggered,
Do not allowed from relying on, so the neuron of (i, i+1) (i=0,1 ..., mn) position should be in matrix according to each operation of JSP
Electric current；For there is order of priority relation and not in the startup of 0 moment operation, 0 is arranged in the response position of its matrix electric
Stream, it is 0 to make these neurons when stable state is exported, and calculates energy type for minimum；
Step 10：V is calculated according to quadravalence dragon lattice-storehouse tower (runge_kutta) formulaxi(t+1)：
K1=f (xi, vxi(t))
K4=f (xi+ h, vxi(t)+hK3`)
Wherein, f (xi, vxi(t)) it is to imitate bipolar S type functions：
Step 12：Judge whether to reach equilibrium condition：It is then to terminate this program；It is no, then return to step 4；
(1) state balance condition：Using neuron dynamic calculation equation, Δ v is calculatedxi(t),
If from after a certain moment, state no longer changes network, then claim network to be in steady statue, now meet
Δvxi(t) ∈ (0, c)
V (t+ Δ t)=v (t), Δ t ＞ 0
(2) energy balance condition：Energy function is constantly reduced in the network operation, finally reaches stable Δ Ei≤0
。
Claims (1)
1. a kind of algorithm based on neutral net solves job-shop scheduling problem, and the algorithm is related to solving job shop scheduling problem technology neck
Domain, is characterized in that：This algorithm constructs threshold vector using average threshold, and energy function is compared with standard energy function, right
Weight coefficient makees amendment and imitates bipolar S type functions and carry out approaching renewal to neuron state by adding, and being embodied as of algorithm walks
It is rapid as follows：
Step 1：Setting time t, constant A, the initial value of B, C, A, B, C>0, it is constant；
Step 2：Initialization coefficient matrix W：For the discrete hopfield networks being made up of n neuron, then there is n*n to weigh
Coefficient matrix W：
Step 3：Construction threshold vector：There is n to tie up threshold vector：
Wherein, c is an average threshold,；
In general, W andCan determine a unique discrete hopfield networks；
Step 4：Structural regime function：WithThe state of j-th neuron, i.e. node j in moment t is represented, then under node
One moment（t+1）State can obtain it is as follows：
Step 5：Calculated relationship function：Calculate the relation function between neuron：
Wherein
；
Step 6：Construction energy function：
Row constraint condition：
Wherein,Represent state V=Y of i-th neuron；A>0, it is constant,For row constraint, and if only if each matrix
More than one " 1 " element is not contained in boat, when remaining element is " 0 ",Ensure when every a line of matrix v is not more than one
When " 1 ",Reach minimum, now；
In the same manner, column constraint condition is constituted
Wherein, B>0, it is constant,Ensure when every a line of matrix v is not more than one " 1 ",Reach minimum；
Global constraints：
Wherein, C>0, it is constant,Ensure as exactly mn 1 in matrix V, i.e., one total mn 1 in whole matrix,
Reach minimum
Step 7:Calculate neural input bias current（Extrinsic motivated）；
Step 8：Regulation coefficient matrix：
First, the energy difference between the energy function in step 4 and standard energy function is sought：
Standard energy function is：
Energy difference：
If, return to step 4 otherwise goes to step 9, according to this energy difference to weight coefficientAdjust,
Adjustment mode is as follows：
Step 9：It is determined that operation equation：Calculate, meet Sigmoid function characteristics between each neuron output and input,
ArrangeInitial value：
Wherein,
Sigmoid functions makeThe value between 0 to 1, in order to avoid workpiece calling by part（Part uses money
Source）, start toOne larger value, so as to a relatively low gain come iterative network, through certain number of times repeatedly
Dai Hou,Value be substantially reduced, gain is brought up to into a larger value, for larger gain, Sigmoid functions and hard
Clip functions are similar, and the output valve of neuron can so avoid interference the problem of partial scheduling, while can also close to 1
Avoid the unstable networks caused using clip functions；
In formulaFor time constant, for simplicity, if；
For meet the constraint condition, high inhibition can be carried out to some neurons so that these neurons are not triggered, according to
Each operation of JSP is not allowed from relying on, so in matrix（i,i+1）（i=0,1,…,mn）The neuron of position should be electric current；
For there is order of priority relation and not in the startup of 0 moment operation, 0 electric current is set in the response position of its matrix, makes
These neurons are 0 when stable state is exported, and calculate energy type for minimum；
Step 10：According to quadravalence dragon lattice-storehouse tower（runge_kutta）Formula is calculated：
Wherein,To imitate bipolar S type functions：
Step 12：Judge whether to reach equilibrium condition：It is then to terminate this program；It is no, then return to step 4；
（1）State balance condition：Using neuron dynamic calculation equation, calculate,
If from after a certain moment, state no longer changes network, then claim network to be in steady statue, now meet：
（2）Energy balance condition：Energy function is constantly reduced in the network operation, is finally reached stable
。
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110163409A (en) * | 2019-04-08 | 2019-08-23 | 华中科技大学 | A kind of convolutional neural networks dispatching method applied to displacement Flow Shop |
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| CN1947074A (en) * | 2004-04-27 | 2007-04-11 | Abb研究有限公司 | Scheduling of industrial production processess |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110163409A (en) * | 2019-04-08 | 2019-08-23 | 华中科技大学 | A kind of convolutional neural networks dispatching method applied to displacement Flow Shop |
| CN110163409B (en) * | 2019-04-08 | 2021-05-18 | 华中科技大学 | Convolutional neural network scheduling method applied to replacement flow shop |
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