CN109669423A - The method that part processes optimal scheduling scheme is obtained based on multiple target grey wolf algorithm is improved - Google Patents
The method that part processes optimal scheduling scheme is obtained based on multiple target grey wolf algorithm is improved Download PDFInfo
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Abstract
The present invention relates to a kind of based on the method for improving multiple target grey wolf algorithm acquisition part processing optimal scheduling scheme, and first multi-objective Job Shop production scheduling problems are carried out with the formalized description of mathematic sign；Then set up the constraint condition to be met in optimization process；Then it determines the target to be optimized, establishes corresponding multi-goal optimizing function；Then the improved multiple target grey wolf algorithm combined based on average Frechet Distance conformability degree matching principle with Pareto dominance relation is designed；It is finally iterated operation, exports optimal case set.The present invention is able to solve existing simple low using solution efficiency of the grey wolf algorithm when solving multi-objective Job Shop Scheduling, the problem of search performance difference.
Description
Technical field
It is especially a kind of grey based on multiple target is improved the present invention relates to the production scheduling technical field of Discrete Manufacturing Systems
The method that wolf algorithm obtains part processing optimal scheduling scheme.
Background technique
Production scheduling is as a kind of complicated optimum problem, due to many complexity of its own, such as multiple target, it is uncertain,
On a large scale, strong constraint and NP difficulty etc., the research topic for making it be known as that there is higher challenge, especially job-shop scheduling problem
Due to the extensive concern closer to actual production application, by researcher.
Traditional job-shop scheduling problem is usually using the maximum machining the time in manufacturing as optimization aim, but in reality
Policymaker needs to consider the meaning of the comprehensive guidance an of scheme from many aspects toward contact in the process on border.In order to abundant
It is fitted actual production situation, generally from the performance indicator based on machining the time, the performance indicator based on delivery date, based on library
It is chosen in the performance indicator three classes deposited, existing method has by being the solution of single integration objective by multiple targeted transformations, but thus
Often the selection of weight is artificially subjective, and objectivity is poor, there are also scholar it is more using based on Pareto dominance relation into
Comparison and selection between row individual solution can make population gradually converge to the Pareto that one is not dominated by any other solution non-
Bad optimal solution set is used successfully in many industrial circles.
The method for solving of Optimized Operation based on Swarm Intelligence Algorithm is either solving the time, or in obtained knot
In terms of fruit quality, very big superiority is suffered from, is the hot spot of current domestic and foreign scholars' research, such as genetic algorithm, particle therefore
A variety of present optimization algorithms such as group's algorithm, ant group algorithm are applied in the scheduling problem of job shop, and multiple target grey wolf is calculated
Method is as a kind of novel Swarm Intelligent Algorithm proposed in recent years, the features such as realizing simple fast convergence rate due to it, existing
When having started gradually to be applied to optimizing scheduling field, but having solved scheduling problem using existing multiple target grey wolf algorithm, selecting
It is exactly individual more outstanding in wolf pack that used roulette Filtering system, which not can guarantee the head wolf of selection, when the individual of leader, from
And making the solution efficiency of algorithm low, search performance decline is unfavorable for the solution of multiple target.
Summary of the invention
In view of this, the purpose of the present invention is to propose to one kind based on improve multiple target grey wolf algorithm obtain part processing it is optimal
The method of scheduling scheme is able to solve the existing simple solution effect using grey wolf algorithm when solving multi-objective Job Shop Scheduling
Rate is low, the problem of search performance difference.
The present invention is realized using following scheme: one kind processing optimal scheduling based on multiple target grey wolf algorithm acquisition part is improved
The method of scheme, specifically includes the following steps:
Step S1: multi-objective Job Shop production scheduling problems are carried out with the formalized description of mathematic sign；
Step S2: the constraint condition to be met in optimization process is established；
Step S3: it determines the target to be optimized, establishes corresponding multi-goal optimizing function；
Step S4: what design was combined based on average Frechet Distance conformability degree matching principle with Pareto dominance relation
Improved multiple target grey wolf algorithm；
Step S5: being iterated operation, exports optimal case set.
Further, step S1 specifically: be defined as follows variable symbol:
M is processing machine quantity；N is the quantity of workpiece to be processed；viFor the operation quantity of workpiece to be processed i；For certainly
Plan variable；Si,j,KFor beginning process time of the process j on lathe K of workpiece i；ti,j,KFor workpiece i process j on lathe K
Process time；Ci,j,KIndicate completion date of the process j of workpiece i on lathe K；gzFor machine z manufacturing procedure quantity,
In, z ∈ { 1,2 ..., m }；FiFor workpiece jiCompletion date；DlFor workpiece jlDelivery date, wherein l ∈ { 1,2 ..., nl}；
SxFor the beginning process time of machine x, wherein x ∈ { 1,2 ..., m }；Tx,yProcessing for the y procedure on machine x starts
Time；Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxFor maximum machining the time；Ex,zFor machine x
The deadline of last upper procedure；
Wherein,
Further, the constraint condition in step S2 includes:
Process starting time constraint: Si,j,K≥Ci,j-1,K；
Completion date constraint: Ci,j,K=Si,j,K+ti,j,K；
Machine tooling constraint:
Work pieces process constraint:
In formula, Si,j,KFor beginning process time of the process j on lathe K of workpiece i；ti,j,KExist for the process j of workpiece i
Process time on lathe K；Ci,j,KIndicate completion date of the process j of workpiece i on lathe K；M is processing machine quantity；N is
The quantity of workpiece to be processed；viFor the operation quantity of workpiece to be processed i.
Further, step S3 specifically: determine that the target to be optimized is maximum completion process time f1, machine idle
Time f2And tardiness time f3, corresponding majorized function are as follows:
f1=max { Fl| i=1,2 ..., n }；
In formula, FiFor workpiece jiCompletion date；SxFor the beginning process time of machine x；Tx,yFor the road y on machine x
The process starting time of process；Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxWhen being completed the process for maximum
Between；Ex,zFor the deadline of last procedure on machine x；DlFor workpiece jlDelivery date, ClFor the completion date of workpiece i.
Further, step S4 specifically includes the following steps:
Step S41: defined variable；
Step S42: grey wolf individual UVR exposure and decoding process are determined；
Step S43: design based on the Frechet Distance conformability degree matching principle that is averaged combine with Pareto dominance relation come
Select the criterion of grey wolf individual；
Step S44: the criterion based on step S43 carries out the algorithm of multiple target grey wolf algorithm.
Further, step S41 specifically: definition npop is grey wolf population size；T is the current number of iterations of algorithm；
Maxgen is maximum number of iterations；The position vector of wolf pack when for the number of iterations being t；It is coefficient vector；Two random numbers of U [0,1] are obeyed for two；μqFor the mean value of q-th of target function value in the t times iteration group；σqFor
The standard deviation of q-th of target function value, maxf in the t times iteration groupqFor q-th of target function value in the t times iteration group
In maximum value；Wherein,
Grey wolf algorithm general frame is divided into two parts, mass society grade and hunting behavior pattern, the society etc. of group
Grade has 4 kinds, and in the algorithm according to the corresponding distribution of the size of fitness function, best individual is referred to as α wolf, and second is β wolf,
Third is δ wolf, it is remaining individual all be ω wolf, the optimization process of entire algorithm be all guided by α, β and δ, and ω wolf with
The corresponding position operation for updating wolf pack individual is carried out with the wolf of preceding 3 grades, it is as follows to update position calculation formula:
In formula,Respectively indicate the position of α wolf, the position of β wolf, δ wolf position.
Further, in step S42, coding mode uses the coding based on operation, i.e., the coding of each individual is by complete
One arrangement of the process composition of portion's workpiece, each workpiece frequency of occurrence are the quantity of its process；Decoded process is first will
Grey wolf body position is converted into an orderly operation table, and it is earliest with it to each operation to be then based on operation table and process constraint
Allow process time to be processed one by one, and then generates scheduling scheme.
Further, step S43 specifically includes the following steps:
Step S431: it selects the ideal solution of every generation: being located at the every generation group selected by dominance relation
Pareto solution is concentrated, and the objective function optimized is (f1,f2,...,fk), then t is individual for i-th of grey wolf of group in iteration
It is by its scheduling scheme target value obtainedThe optimal value of each target, structure are selected from group respectively
Build the ideal solution in the t times iteration
Step S432: building curve: data are pre-processed with structure using z-score standardization and the normalization of MAX value
Build ideal solution functional value curve and the front end Pareto curve；For there are three the solutions of target function valueBuilding
Method is as follows:
(1) z-score is standardized:
(2) MAX value normalizes:
(3) curve is constructed: via above two step by each solution FtIn include target function valueAll corresponding place
Manage into valueIt can be constituted with the two valuesCoordinate points in x-y planeIt is sequentially connected just by q point
It is solution FtCorresponding curve.
Step S433: it calculates average Frechet distance: being obtained by above step every in ideal function value curve and group
Thus the target function value curve of individual calculates being averaged for each individual goal functional value curve and ideal function value curve
Criterion of the Frechet apart from alternatively grey wolf individual calculates the average Fr é of all individuals and ideal value curve in group
After chet distance, it is ranked up from small to large, the smallest value, that is, curve similarity is highest to be selected as a wolf α wolf, and according to this
Select β and δ wolf.
Further, step S44 specifically includes the following steps:
Step S441: it is random to generate the initial population that scale is npop, and grey wolf individual initial position and speed are generated at random
Degree；Enable t=1；
Step S442: its target function value is calculated to the group in t generation；
Step S443: t is selected for the external archive in group using Pareto dominance relation；
Step S444: each ash is calculated using based on average Frechet Distance conformability degree matching principle in external archive
Fitness value corresponding to wolf individual, and select best individual by the size of fitness pair and be referred to as α wolf, second is β
Wolf, third are δ wolf；
Step S445: the position of individual i each in the new mechanism group of grey wolf algorithm is utilizedAnd it calculates every
The objective function of individual, if generated new individual goal functional value dominates the objective function of corresponding previous generation individual
Value, then by the position of newly generated individualSubstitute previous generation individualPosition, with 1/2 if not dominating
Whether probability selection substitutes；
Step S446: if t < maxgen, return step S443, otherwise algorithm stops.
Further, in step S433, average Frechet distance is calculated specifically:
Step S4331: the Euclidean distance matrix MD between two curve points is calculated(i,j)=dE(L(1,i),L(2,j))；Wherein
L(1,i)With L(2,j)Represent i point, the j point on curve L1, L2, dEIndicate the Euclidean distance between two o'clock；
Step S4332: discrete Fr é chet matrix F M is calculated, in which:
FM(i,j)=max (dE(L(1,i),L(2,j)),min(FM(i-1,j),FM(i,j-1),FM(i-1,j-1)))；
Step S4333: MD and FM are overlapped and generate a two-dimensional matrix C(i,j)；Wherein:
C(i,j)=(FM(i,j),MD(i,j))；
Step S4334: above-mentioned C is utilized(i,j)With the curve point pair for selecting the condition of satisfaction less than or equal to operation, i.e. shortest path
Diameter；
Wherein, described to be less than or equal to operation are as follows: to set x1,y1,x2,y2It is real number, constitutes point to (x1,y1), (x2,y2)；Such as
Fruit meets one of following conditions:
One, x1< x2；
Two, x1=x2, and y1≤y2；
Then have: (x1,y1)≤(x2,y2), (x at this time1,y1) be the condition that meets point pair；To C(i,j)Matrix, which uses, to be less than
It is from distal point C equal to operation(n,m)Start to find forward until first point C(1,1), find out all points pair for meeting above-mentioned condition；It is right
In C(n,m)Its previous point for meeting condition of point is in C(n-1,m)、C(n,m-1)、C(n-1,m-1)Three centerings generate, and so recycle
Iteration is until point C forward(1,1)；
Step S4335: if all points for meeting condition are to C(i,j)There is N number of, then average Fr é chet distance
Compared with prior art, the invention has the following beneficial effects:
1, the present invention is under the conditions ofs meeting the manufacturing and process constraint etc., when always idle with maximum process time, machine
Between, total tardiness time be optimization aim, the improved multiple target grey wolf algorithm of use can effectively obtain part processing most
Excellent scheduling scheme collection.
2, the present invention use based on average Frechet Distance conformability degree matching principle in conjunction with Pareto dominance relation
Filtering system not only guaranteed that the increase of search capability improved the search efficiency of algorithm, but also can obtain Pareto optimal solution set, for
Manager chooses the scheduling scheme for being best suitable for factory's practical application from different processing schemes.
Detailed description of the invention
Fig. 1 is the algorithm flow schematic diagram of the embodiment of the present invention.
Fig. 2 to Fig. 6 is that the solution scale of the embodiment of the present invention is the scheduling result figure of 6 × 6 problems.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
As shown in Figure 1, present embodiments providing a kind of based on the optimal tune of improvement multiple target grey wolf algorithm acquisition part processing
The method of degree scheme, specifically includes the following steps:
Step S1: multi-objective Job Shop production scheduling problems are carried out with the formalized description of mathematic sign；
Step S2: the constraint condition to be met in optimization process is established；
Step S3: it determines the target to be optimized, establishes corresponding multi-goal optimizing function；
Step S4: what design was combined based on average Frechet Distance conformability degree matching principle with Pareto dominance relation
Improved multiple target grey wolf algorithm；
Step S5: being iterated operation, exports optimal Pareto set, as final scheduling scheme set, and generates
Corresponding Gantt chart.
In the present embodiment, step S1 specifically: be defined as follows variable symbol:
M is processing machine quantity；N is the quantity of workpiece to be processed；viFor the operation quantity of workpiece to be processed i；For certainly
Plan variable；Si,j,KFor beginning process time of the process j on lathe K of workpiece i；ti,j,KFor workpiece i process j on lathe K
Process time；Ci,j,KIndicate completion date of the process j of workpiece i on lathe K；gzFor machine z manufacturing procedure quantity,
In, z ∈ { 1,2 ..., m }；FiFor workpiece jiCompletion date；DlFor workpiece jlDelivery date, wherein l ∈ { 1,2 ..., nl}；
SxFor the beginning process time of machine x, wherein x ∈ { 1,2 ..., m }；Tx,yProcessing for the y procedure on machine x starts
Time；Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxFor maximum machining the time；Ex,zFor machine x
The deadline of last upper procedure；
Wherein,
In the present embodiment, the constraint condition in step S2 includes:
Process starting time constraint: Si,j,K≥Ci,j-1,K；
Completion date constraint: Ci,j,K=Si,j,K+ti,j,K；
Machine tooling constraint:
Work pieces process constraint:
In formula, Si,j,KFor beginning process time of the process j on lathe K of workpiece i；ti,j,KExist for the process j of workpiece i
Process time on lathe K；Ci,j,KIndicate completion date of the process j of workpiece i on lathe K；M is processing machine quantity；N is
The quantity of workpiece to be processed；viFor the operation quantity of workpiece to be processed i.
In the present embodiment, step S3 specifically: determine that the target to be optimized is maximum completion process time f1, machine
Free time f2And tardiness time f3, corresponding majorized function are as follows:
f1=max { Fl| i=1,2 ..., n }；
In formula, FiFor workpiece jiCompletion date；SxFor the beginning process time of machine x；Tx,yFor the road y on machine x
The process starting time of process；Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxWhen being completed the process for maximum
Between；Ex,zFor the deadline of last procedure on machine x；DlFor workpiece jlDelivery date, ClFor the completion date of workpiece i.
In the present embodiment, step S4 specifically includes the following steps:
Step S41: defined variable；
Step S42: grey wolf individual UVR exposure and decoding process are determined；
Step S43: design based on the Frechet Distance conformability degree matching principle that is averaged combine with Pareto dominance relation come
Select the criterion of grey wolf individual；
Step S44: the criterion based on step S43 carries out the algorithm of multiple target grey wolf algorithm.
In the present embodiment, step S41 specifically: definition npop is grey wolf population size；T is the current iteration of algorithm
Number；Maxgen is maximum number of iterations；The position vector of wolf pack when for the number of iterations being t； Be coefficient to
Amount；Two random numbers of U [0,1] are obeyed for two；μqFor the mean value of q-th of target function value in the t times iteration group；
σqFor the standard deviation of q-th of target function value in the t times iteration group, maxfqFor q-th of objective function in the t times iteration group
Maximum value in value；Wherein,
Grey wolf algorithm general frame is divided into two parts, mass society grade and hunting behavior pattern, the society etc. of group
Grade has 4 kinds, and in the algorithm according to the corresponding distribution of the size of fitness function, best individual is referred to as α wolf, and second is β wolf,
Third is δ wolf, it is remaining individual all be ω wolf, the optimization process of entire algorithm be all guided by α, β and δ, and ω wolf with
The corresponding position operation for updating wolf pack individual is carried out with the wolf of preceding 3 grades, it is as follows to update position calculation formula:
In formula,Respectively indicate the position of α wolf, the position of β wolf, δ wolf position.
In the present embodiment, in step S42, coding mode uses the coding based on operation, i.e., the coding of each individual is
An arrangement being made of the process of whole workpiece, each workpiece frequency of occurrence are the quantity of its process；Decoded process is,
An orderly operation table first is converted by grey wolf body position, is then based on operation table and process constraint to each operation with it
Allow process time to be processed one by one earliest, and then generates scheduling scheme.
In the present embodiment, step S43 specifically includes the following steps:
Step S431: it selects the ideal solution of every generation: being located at the every generation group selected by dominance relation
Pareto solution is concentrated, and the objective function optimized is (f1,f2,...,fk), then t is individual for i-th of grey wolf of group in iteration
It is by its scheduling scheme target value obtainedThe optimal value of each target, structure are selected from group respectively
Build the ideal solution in the t times iteration
Step S432: building curve: data are pre-processed with structure using z-score standardization and the normalization of MAX value
Build ideal solution functional value curve and the front end Pareto curve；For there are three the solutions of target function valueBuilding
Method is as follows:
(1) z-score is standardized:
(2) MAX value normalizes:
(3) curve is constructed: via above two step by each solution FtIn include target function valueAll corresponding place
Manage into valueIt can be constituted with the two valuesCoordinate points in x-y planeIt is sequentially connected just by q point
It is solution FtCorresponding curve.
Step S433: it calculates average Frechet distance: being obtained by above step every in ideal function value curve and group
Thus the target function value curve of individual calculates being averaged for each individual goal functional value curve and ideal function value curve
Criterion of the Frechet apart from alternatively grey wolf individual calculates the average Fr é of all individuals and ideal value curve in group
After chet distance, it is ranked up from small to large, the smallest value, that is, curve similarity is highest to be selected as a wolf α wolf, and according to this
Select β and δ wolf.
In the present embodiment, step S44 specifically includes the following steps:
Step S441: it is random to generate the initial population that scale is npop, and grey wolf individual initial position and speed are generated at random
Degree；Enable t=1；
Step S442: its target function value is calculated to the group in t generation；
Step S443: t is selected for the external archive in group using Pareto dominance relation；
Step S444: each ash is calculated using based on average Frechet Distance conformability degree matching principle in external archive
Fitness value corresponding to wolf individual, and select best individual by the size of fitness pair and be referred to as α wolf, second is β
Wolf, third are δ wolf；
Step S445: the position of individual i each in the new mechanism group of grey wolf algorithm is utilizedAnd it calculates every
The objective function of individual, if generated new individual goal functional value dominates the objective function of corresponding previous generation individual
Value, then by the position of newly generated individualSubstitute previous generation individualPosition, with 1/2 if not dominating
Whether probability selection substitutes；
Step S446: if t < maxgen, return step S443, otherwise algorithm stops.
In the present embodiment, in step S433, average Frechet distance is calculated specifically:
Step S4331: the Euclidean distance matrix MD between two curve points is calculated(i,j)=dE(L(1,i),L(2,j))；Wherein
L(1,i)With L(2,j)Represent i point, the j point on curve L1, L2, dEIndicate the Euclidean distance between two o'clock；
Step S4332: discrete Fr é chet matrix F M is calculated, in which:
FM(i,j)=max (dE(L(1,i),L(2,j)),min(FM(i-1,j),FM(i,j-1),FM(i-1,j-1)))；
Step S4333: MD and FM are overlapped and generate a two-dimensional matrix C(i,j)；Wherein:
C(i,j)=(FM(i,j),MD(i,j))；
Step S4334: above-mentioned C is utilized(i,j)With the curve point pair for selecting the condition of satisfaction less than or equal to operation, i.e. shortest path
Diameter；
Wherein, described to be less than or equal to operation are as follows: to set x1,y1,x2,y2It is real number, constitutes point to (x1,y1), (x2,y2)；Such as
Fruit meets one of following conditions:
One, x1< x2；
Two, x1=x2, and y1≤y2；
Then have: (x1,y1)≤(x2,y2), (x at this time1,y1) be the condition that meets point pair；To C(i,j)Matrix, which uses, to be less than
It is from distal point C equal to operation(n,m)Start to find forward until first point C(1,1), find out all points pair for meeting above-mentioned condition；It is right
In C(n,m)Its previous point for meeting condition of point is in C(n-1,m)、C(n,m-1)、C(n-1,m-1)Three centerings generate, and so recycle
Iteration is until point C forward(1,1)；
Step S4335: if all points for meeting condition are to C(i,j)There is N number of, then average Fr é chet distance
Particularly, for the present embodiment by taking certain manufacturing shop as an example, which undertakes the processing tasks of 6 kinds of workpiece, workshop
Possess 6 lathes, lathe corresponding to every procedure of each workpiece and process time as shown in table 1 and table 2.
The process of each workpiece of table 1. processes table
2. each process process time of table and delivery date table
It initially sets up the initial population that scale is 100 to be encoded, the number that iteration is arranged is 100, is then completed according to this
Target value in algorithm calculates, and the operation such as location updating, the Pareto optimal solution set for finally exporting for 100 generations is as shown in table 3, and root
Drawing solution according to the result of the optimization concentrates processing Gantt chart corresponding to each solution as shown in Fig. 2-Fig. 6, can utilize these processing
Gantt chart stresses demand and carries out the arrangement of processing tasks in actual production application according to different.
Table 3.Pareto optimal solution set
The present embodiment can be used for the optimizing scheduling of the job shop of multi-work piece Alternative, can meet the manufacturing and work
Under the conditions of skill constraint etc., using maximum process time, machine total free time, total tardiness time as optimization aim, the improvement of use
Multiple target grey wolf algorithm can effectively obtain part processing optimal scheduling scheme collection.Simultaneously the present embodiment use based on
Average Filtering system of the Frechet Distance conformability degree matching principle in conjunction with Pareto dominance relation, both guarantees search capability
Increase the search efficiency for improving algorithm, and Pareto optimal solution can be obtained, so that manager selects from different processing schemes
Take the scheduling scheme for being best suitable for factory's practical application.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification, is all covered by the present invention.
Claims (10)
1. a kind of based on the method for improving multiple target grey wolf algorithm acquisition part processing optimal scheduling scheme, it is characterised in that: packet
Include following steps:
Step S1: multi-objective Job Shop production scheduling problems are carried out with the formalized description of mathematic sign；
Step S2: the constraint condition to be met in optimization process is established；
Step S3: it determines the target to be optimized, establishes corresponding multi-goal optimizing function；
Step S4: the improvement that design is combined based on average Frechet Distance conformability degree matching principle with Pareto dominance relation
Multiple target grey wolf algorithm；
Step S5: being iterated operation, exports optimal case set.
2. according to claim 1 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S1 specifically: be defined as follows variable symbol:
M is processing machine quantity；N is the quantity of workpiece to be processed；viFor the operation quantity of workpiece to be processed i；For decision change
Amount；Si,j,KFor beginning process time of the j on lathe K of workpiece i process；ti,j,KFor process j the adding on lathe K of workpiece i
Between working hour；Ci,j,KIndicate completion date of the workpiece i process j on lathe K；gzFor machine z manufacturing procedure quantity, wherein z ∈
{1,2,...,m}；FiFor workpiece jiCompletion date；DlFor workpiece jlDelivery date, wherein l ∈ { 1,2 ..., nl}；SxFor machine
The beginning process time of device x, wherein x ∈ { 1,2 ..., m }；Tx,yFor the process starting time of the y procedure on machine x；
Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxFor maximum machining the time；Ex,zIt is last on machine x
The deadline of one procedure；
Wherein,
3. according to claim 1 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: the constraint condition in step S2 includes:
Process starting time constraint: Si,j,K≥Ci,j-1,K；
Completion date constraint: Ci,j,K=Si,j,K+ti,j,K；
Machine tooling constraint:
Work pieces process constraint:
In formula, Si,j,KFor beginning process time of the process j on lathe K of workpiece i；ti,j,KFor workpiece i process j in lathe K
On process time；Ci,j,KIndicate completion date of the process j of workpiece i on lathe K；M is processing machine quantity；N is to be added
The quantity of work workpiece；viFor the operation quantity of workpiece to be processed i.
4. according to claim 1 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S3 specifically: determine that the target to be optimized is maximum completion process time f1, machine idle
Time f2And tardiness time f3, corresponding majorized function are as follows:
f1=max { Fl| i=1,2 ..., n }；
In formula, FiFor workpiece jiCompletion date；SxFor the beginning process time of machine x；Tx,yFor the y procedure on machine x
Process starting time；Ex,(y-1)For the end time of machine x upper (y-1) procedure；TmaxFor maximum machining the time；
Ex,zFor the deadline of last procedure on machine x；DlFor workpiece jlDelivery date, ClFor the completion date of workpiece i.
5. according to claim 1 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S4 specifically includes the following steps:
Step S41: defined variable；
Step S42: grey wolf individual UVR exposure and decoding process are determined；
Step S43: design combines to select based on average Frechet Distance conformability degree matching principle with Pareto dominance relation
The criterion of grey wolf individual；
Step S44: the criterion based on step S43 carries out the algorithm of multiple target grey wolf algorithm.
6. according to claim 5 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S41 specifically: definition npop is grey wolf population size；T is the current number of iterations of algorithm；
Maxgen is maximum number of iterations；The position vector of wolf pack when for the number of iterations being t；Be coefficient to
Amount；Two random numbers of U [0,1] are obeyed for two；μqFor the mean value of q-th of target function value in the t times iteration group；
σqFor the standard deviation of q-th of target function value in the t times iteration group, maxfqFor q-th of objective function in the t times iteration group
Maximum value in value；Wherein,
Grey wolf algorithm general frame is divided into two parts, mass society grade and hunting behavior pattern, and the Social Grading of group has 4
Kind, in the algorithm according to the corresponding distribution of the size of fitness function, best individual is referred to as α wolf, and second is β wolf, third
It is δ wolf, remaining individual is all ω wolf, and the optimization process of entire algorithm is all to be guided by α, β and δ, and ω wolf follows preceding 3
The wolf of a grade carries out the corresponding position operation for updating wolf pack individual, and it is as follows to update position calculation formula:
In formula,Respectively indicate the position of α wolf, the position of β wolf, δ wolf position.
7. according to claim 5 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: in step S42, coding mode uses the coding based on operation, i.e., the coding of each individual is by whole
One arrangement of the process composition of workpiece, each workpiece frequency of occurrence are the quantity of its process；Decoded process is, first will be grey
Wolf body position is converted into an orderly operation table, is then based on operation table and process constraint and is permitted earliest with it each operation
Perhaps process time is processed one by one, and then generates scheduling scheme.
8. according to claim 5 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S43 specifically includes the following steps:
Step S431: it selects the ideal solution of every generation: being located at the Pareto solution for the every generation group selected by dominance relation
It concentrates, the objective function optimized is (f1,f2,...,fk), then t is dispatched for i-th of grey wolf individual of group by it in iteration
Scheme target value obtained isThe optimal value of each target is selected from group respectively, is constructed the t times
Ideal solution in iteration
Step S432: building curve: data are pre-processed using z-score standardization and the normalization of MAX value to construct reason
Want to solve functional value curve and the front end Pareto curve；
Step S433: it calculates average Frechet distance: being obtained in ideal function value curve and group by above step per each and every one
Thus the target function value curve of body calculates being averaged for each individual goal functional value curve and ideal function value curve
Criterion of the Frechet apart from alternatively grey wolf individual calculates the average Fr é of all individuals and ideal value curve in group
After chet distance, it is ranked up from small to large, the smallest value, that is, curve similarity is highest to be selected as a wolf α wolf, and according to this
Select β and δ wolf.
9. according to claim 5 a kind of part processing optimal scheduling scheme is obtained based on improving multiple target grey wolf algorithm
Method, it is characterised in that: step S44 specifically includes the following steps:
Step S441: it is random to generate the initial population that scale is npop, and grey wolf individual initial position and speed are generated at random；It enables
T=1；
Step S442: its target function value is calculated to the group in t generation；
Step S443: t is selected for the external archive in group using Pareto dominance relation；
Step S444: each grey wolf is calculated using based on average Frechet Distance conformability degree matching principle in external archive
Fitness value corresponding to body, and select best individual by the size of fitness pair and be referred to as α wolf, second is β wolf, the
Three be δ wolf；
Step S445: the position of individual i each in the new mechanism group of grey wolf algorithm is utilizedAnd calculate each individual
Objective function, if generated new individual goal functional value dominates the target function value of corresponding previous generation individual,
By the position of newly generated individualSubstitute previous generation individualPosition, with 1/2 probability if not dominating
It chooses whether to substitute；
Step S446: if t < maxgen, return step S443, otherwise algorithm stops.
10. according to claim 8 a kind of based on improvement multiple target grey wolf algorithm acquisition part processing optimal scheduling scheme
Method, it is characterised in that: in step S433, calculate average Frechet distance specifically:
Step S4331: the Euclidean distance matrix MD between two curve points is calculated(i,j)=dE(L(1,i),L(2,j))；Wherein L(1,i)With
L(2,j)Represent i point, the j point on curve L1, L2, dEIndicate the Euclidean distance between two o'clock；
Step S4332: discrete Fr é chet matrix F M is calculated, in which:
FM(i,j)=max (dE(L(1,i),L(2,j)),min(FM(i-1,j),FM(i,j-1),FM(i-1,j-1)))；
Step S4333: MD and FM are overlapped and generate a two-dimensional matrix C(i,j)；Wherein:
C(i,j)=(FM(i,j),MD(i,j))；
Step S4334: above-mentioned C is utilized(i,j)With the curve point pair for selecting the condition of satisfaction less than or equal to operation, i.e. shortest path；
Wherein, described to be less than or equal to operation are as follows: to set x1,y1,x2,y2It is real number, constitutes point to (x1,y1), (x2,y2)；If full
Foot states one of condition:
One, x1< x2；
Two, x1=x2, and y1≤y2；
Then have: (x1,y1)≤(x2,y2), (x at this time1,y1) be the condition that meets point pair；To C(i,j)Matrix, which uses, to be less than or equal to
Operation is from distal point C(n,m)Start to find forward until first point C(1,1), find out all points pair for meeting above-mentioned condition；For
C(n,m)Its previous point for meeting condition of point is in C(n-1,m)、C(n,m-1)、C(n-1,m-1)Three centerings generate, so recycle to
Preceding iteration is until point C(1,1)；
Step S4335: if all points for meeting condition are to C(i,j)There is N number of, then average Fr é chet distance
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