CN102929263A - Hybrid flow shop scheduling method - Google Patents
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Abstract
The invention relates to a hybrid flow shop scheduling method, which comprises the following steps of: dividing parts into multiple part sets based on different part families of the required parts; establishing a new batch for each part and performing batching based on the volume of a thermal treating funnel; after the batching, making a serial number for each batch and a machine, and encoding at each stage, wherein each stage comprises two sections of chromosomes, the first section of chromosome is a batch number, and the second chromosome is a machine serial number corresponding to the batch number; generating chromosomes at random when a user meets the conditions restricted by the machines; selecting N chromosomes, carrying out a pairwise cross operation on N selected chromosomes, carrying out a mutation operation on each chromosome, and then repairing the chromosomes; and repeating the steps of selection, cross operation, mutation and repairing till the maximum number of iterations is reached. With the method, the problem of a hybrid flow shop where the assembling affects the batching in the parallel batch processing phase can be solved, and the algorithm operation efficiency can be ensured.
Description
Technical field
The present invention relates to a kind of dispatching method of manufacturing system, particularly a kind of hybrid flow shop scheduling method that comprises parallel batching, serial batch processing and assembling belongs to advanced production control and the optimizing scheduling field of making.
Background technology
Along with developing rapidly of science and technology, various products are also more and more advanced, become increasingly complex, and this has proposed huge challenge to manufacturing enterprise: manufacturing enterprise relates to machining operation, heat treatment step and assembly process in process.How to carry out production scheduling under this complex environment, guarantee the delivery date of different parts, the inventory reduction expense keeps the productive temp balance simultaneously, improves the utilization factor of heat-treatment furnace etc., will become a challenging problem.
Complete manufacturing system generally comprises thermal treatment, machine adds and assemble subsystem.The regulation goal of thermal treatment subsystem is the heat-treatment furnace utilization factor, and the regulation goal that machine adds subsystem is often relevant with completion date, and therefore the assembling subsystem needs to consider the problem of load balance owing to need the consumption machine to add the part that subsystem is exported.
The production run of part relates to the stages such as thermal treatment, machine add, assembling.In general, the scheduling that usually machine is added stage and heat treatment stages considers that separately reason is that the heat treatment time of parts adds the time much larger than machine usually.But we show in the finding of enterprise: see that on the whole though the machine work order time is shorter, but machine work ordinal number amount is more, therefore whole machine adds the time in stage and accounts for 39% of production overall process, and heat treatment stages then accounts for 42%, and the two is about the same; On the other hand, reached thousands of minutes when the process time of the complicated machine work order of front portion, these are all so that machine adds stage and heat treatment stages in that most important optimization index---the time is mentioned in the same breath.
Finding also shows, the part that need to heat-treat accounts for 34.9% of sum, and the opportunity and the number of times that wherein occur according to thermal treatment are divided, thermal treatment only once and headed by operation account for 39.7%; Thermal treatment only once and non-first operation account for 35.3%; Thermal treatment have repeatedly and headed by one of them operation account for 13.1%; Thermal treatment have repeatedly and be not first operation account for 11.9%.
Hybrid flow workshop (HybridFlow Shop, HFS) be a kind of based on given objective function by the multistage Shop-floor Scheduling of n operation m stage sequential operation.This production scheduling problems contains two stages at least, per stage has a machine at least and has at least a stage to have parallel machine, all workpiece all will be according to identical production line processing, and a workpiece is processed a stage at least, and other stage can be skipped arbitrarily.HFS problem under the canonical form, all workpiece and machine all can be used zero the time, determine for given stage machine, and any machine can only carry out a kind of operation and any workpiece can only be by a machining a time a time; Setup time can be ignored, and forbids seizing, and the buffer pool size between the stage is not limit and problem data is to determine in advance and known.The HFS scheduling problem is very common in the actual production manufacture process, relates to the manufacturing fields such as industry, weaving, electronics, papermaking, concrete, cartridge film.
The canonical form of HFS problem must satisfy some constraints, comprise that workpiece unified arrives, identical parallel machine, do not consider setup time, machine uniqueness, workpiece uniqueness, forbid seizing, buffer pool size is unlimited etc.Because practical problems is difficult to meet fully the constraint of standard HFS problem, most researchs focus on the HFS problem of variation, and as allowing job dynamic arrival, buffer zone is limited etc. between the stage.
The hybrid flow Job Shop problem in most of the cases is np hard problem.Such as, being limited in the hybrid flow workshop of two stages scheduling, containing the problem model that two machines and another stage contain a unit in stage all is the NP difficulty, this can draw from the result of study of Gupta.Same, the people's such as Hoogeveen result of study shows, even m=2 can stop process operation and the HFS problem that again begins in another time period is np hard problem equally to machine before completion.In addition, for the special circumstances of only having a machine in each stage, i.e. Flow Shop, and contain the parallel machine environment of many machines a stage, all be the NP difficulty.Yet, for the problem model that specific properties and priority relationship are arranged, may be that polynomial expression can be separated.
Problem model of the present invention relates to the problems such as serial batch processing, parallel batching and assembling, and these three kinds of situations all belong to the HFS problem of variation.Three classes variation more than existing research has been considered in the HFS problem at present, the present invention adopts the method for Vignier, namely adopts three sections coding for alpha | β | and γ describes the HFS problem of variation, and wherein α represents machine environment, β describes detailed characteristics and constraint, and γ is the problem target.
The reason that the serial batch processing causes the HFS problem to produce variation mainly is that needs are considered setup time.Kim etc. have considered FH2, ((PM
(k))
K=1 2) | batch, S
Sd| C
MaxProblem model, namely contained for two stages, each stage is parallel machine, contain batch processing and depend on setup time of sequence of events, to minimize maximum completion date as target, transmission between two stages like this is the HFS problem in batches, and has proposed to be similar to respectively the scheduling rule of Johnson's rule (Johnson ' s Rule) for the situation with independence and dependent setup time.Hua Xuan etc. has considered shape such as FHm, ((PM
(1), PM
(2))) | batch
(m)| the HFS problem of F, m stage namely arranged, the phase one is identical parallel machine with subordinate phase, and each stage is batch processing, and target is the problem that minimizes total flow time, and has solved this problem based on Lagrangian Relaxation.
The variation that is assembled into the HFS problem is to consider uncorrelated machine owing to will add the stage at machine.CHUNG-YEELEE etc. have considered assembly problem in the HFS problem, problem model is FH2, ((P1
(1), 1
(2))) | assembly
(2)| C
MaxWherein assembly process is positioned at subordinate phase, and identical parallel machine and uncorrelated machine have been considered respectively in the phase one, target is to minimize maximum completion date, adopt the heuristic of dynamic programming (Dynamic Programming, DP) to solve backward and these two problems of forward direction Flow Shop.Dayid He etc. has considered the similar problem model with CHUNG-YEE LEE, adopts two step heuristics to address this problem.C S Sung etc. has considered FH2, ((2
(1), P2
(2))) | assembly
(2)| the F problem, wherein first stage comprises two uncorrelated machines and processes respectively different workpiece, they are based on improved shortest path tree rule (Shortest Path Tree, SPT) a kind of heuristic of branch-and-bound has been proposed, this shortest path tree rule that is modified has been considered this factor of free time, has played the effect of optimizing lower limit.
Because parallel batching does not satisfy machine unique constraints (namely a machine synchronization can only be processed 1 workpiece), so become the HFS problem of variation.At present about with the research of the variation HFS problem of parallel batching also seldom.Bellanger and Oulamara are at a FH2, FH2, ((PM
(1), PM
(2))) | batch
(2)| C
MaxConsidered parallel batching in subordinate phase in the problem, and maximum processing time (LargestProcessingTime proposed, LPT), maximum batch processing time (Largest Batching Processing Time, LBPT) and based on three kinds of heuristics of Johnson rule (Johnson ' s Rule).Reza and Ali have considered FHm, ((RM
(k))
m K=1) | batch|C
Max, namely under a plurality of stages, contain the parallel batching problem of unified machine, to minimize maximum completion date as target.They have proposed based on Johnson rule (Johnson ' sRule), parallel machine scheduling strategy and bounding theory (Theory of Constrains, TOC) three kinds of heuritic approaches, and utilize three-dimensional genetic algorithm (Three dimensional Genetic Algorithm, 3DGA) that solution is improved.
Practical problems is often complicated than above-mentioned monotropic different situation, has had in recent years increasing research to consider more complicated multiple variation.Yu Liu etc. has considered shape such as FHm, ((RM
(k))
m K=1) | batch, no-wait, S
Sd| the problem of several, m stage namely arranged, per stage be incoherent machine, parallel in batches, no-buffer, consideration depend on setup time of sequence of events, contain multiobject problem, and propose a kind of method based on mathematical programming.A.Alfieri has considered shape such as FHm, ((RM
(k))
m K=1) | S
SdReentry, batch | the problem of several, m stage namely arranged, per stage is incoherent parallel machine, consider to depend on sequence of events setup time, can reentry, comprise the multiple goal flowshop scheduling of batch processing, the heuritic approach based on tabu search has been proposed, and with the event simulation processing time factor of separation.Shanling Li has considered shape such as FH2, (1
(1), PM
(2))) | batch, S
Sd, split|C
MaxProblem, two stages are namely arranged, first stage only has a machine, second stage is the batch processing of identical parallel machine, considers that setup time, the workpiece family depend on sequence of events allow in batches, target is to minimize maximum completion date.Used two kinds of application strategies in the literary composition, a kind of is that traditional forward direction is heuristic, and another kind is unconventional backward heuristic, and uses effective ordering rule to remove further to improve efficiency of algorithm.Quadt and Kuhn have considered shape such as FHm, ((RM
(k))
m K=1)| batch, skip |
Problem, m stage namely arranged, per stage is incoherent parallel machine, comprising batch processing, stage can skip, and take average flow time and cost as target, has used the method for holistic approach and decomposition analysis to solve this problem.
Under job shop (job shop) environment, also can find the research about the multistage scheduling problem in addition.He etc. study the mixed scheduling of many machining equipments and a rigging equipment to minimize maximum completion date as target, propose two kinds of heuritic approaches, and optimum solution or suboptimal solution are provided under simple and complicated product structure respectively.The people such as Ham are studied for the multistage job shop problem that contains general-purpose machinery, set up first bigit plan model (Binary Integer Programming, BIP), on the basis of this model, they have proposed a kind of heuritic approach of Real-Time Scheduling, have solved the target that minimizes maximum completion date.The human ant colony optimization algorithms such as Chang have solved the multistage job shop Parallel Scheduling problem that contains parallel machine, a plurality of regulation goals have been considered, also with reference to market standard, they contrast ant colony optimization algorithm and genetic algorithm, find that ant group algorithm has more excellent performance.
No matter be that the problem model of above-mentioned research is all relatively simple under the HFS environment or under the job shop environment, consider simultaneously the research of parallel batching, setup time and assembling also seldom.And in actual production, for example in the production of vehicle transmission gear, the part that relates to simultaneously these three kinds of situations accounts for sum and reaches more than 1/3rd, and also do not consider simultaneously parallel batching in the prior art, the HFS problem effective workaround of setup time and assembling three classes variation.
Summary of the invention
The objective of the invention is for the deficiencies in the prior art, find efficient feasible dispatching method in the hybrid flow workshop that comprises parallel batching, serial batch processing and assembling, minimize maximum completion date as target take what guarantee the heat-treatment furnace utilization factor, by giving each workpiece in batches and using genetic algorithm, find the optimum solution of hybrid flow shop scheduling.
The present invention adopts genetic algorithm that the scheduling solution is optimized, genetic algorithm (Genetic Algorithm, GA) be a kind of meta-heuristic algorithm of searching for optimum solution by simulating Darwinian natural evolution process, the J.Hol land by the U.S. teaches in proposition in 1975 at first.Because it has preferably global optimizing ability, can adjust adaptively the direction of search, extensively applicable in the Combinatorial Optimization field.
The ultimate constituent of genetic algorithm comprises chromosomal coding method, fitness function and genetic manipulation.
Chromosomal coding method is the key problem of genetic algorithm, and it is expressed as chromosome corresponding to the solution with problem.Coding is the chromosome that the original expression mode of solution is converted to the bit string form, chromosomal each be a gene, represent the selection of a characteristic.
Fitness function is to describe the adaptive function of bion.Different according to solution and actual degree of closeness are determined chromosomal quality with the form of numerical value, and this function is common relevant with objective function.
Genetic manipulation comprises selection, crossover and mutation.Selection is the process of a survival of the fittest, and its purpose is to entail the next generation the individual directly heredity of optimizing or as parent.Rank, roulette and three kinds of systems of selection of championship are generally arranged; Intersection enlarges population diversity by the method for genetic recombination, and the forms such as real-valued restructuring and intersection are arranged; Mutation operation also makes algorithm have the ability of Local Search except enlarging population diversity, thus the degree of convergence of acceleration problem.Mutation operation also has real-valued variation and intersects two kinds of variation methods.
The order of genetic algorithm is: first problem is encoded, after producing initial population, select parent chromosome according to fitness function, the parent chromosome of selecting is carried out interlace operation obtain child chromosome, child chromosome is finished iteration one time by mutation operation, loop from calculating the ideal adaptation degree to the operation of variation, when reaching maximum iteration time, stop.Shown in Fig. 8 genetic algorithm part.The present invention is applicable to following production and manufacturing environment:
(1) production environment is multistage hybrid flow workshop, and first stage is the parallel batching stage, is comprised of many identical parallel machines, comprises heat treatment step one; Middle some stages are that machine adds the stage, are comprised of incoherent machine, have the characteristics of job shop; The last stage is assembling stage, is comprised of many identical parallel machines, comprises assembly process one;
(2) workpiece is by a plurality of workpiece group compositions, and there is various workpieces in each workpiece family, only has identical workpiece family to organize together and criticizes; But every kind of workpiece has different processing machines in each stage that machine adds, any one stage that adds for machine, but workpiece can only select one to process in the scope of processing machine; The workpiece that assembles both can also can be from different workpiece families from identical workpiece family;
(3) all workpiece can be used zero the time, before thermal treatment workpiece are carried out static state in batches, heat-treat after minute good batch, machine adds, assembly manipulation again, and scheduling is realization in dynamically;
(4) workpiece was ignored in the transfer time of stage or machinery compartment; Because the difference of workpiece family, add with assembling stage at machine and will consider that all serial is in batches with the expense of preparation time reduction; Family does not then cause switching if adjacent two batches of workpiece of same machine do not belong to same workpiece; Each stage has all independently that setup time is switching time, with workpiece family sequence independence;
(5) buffer size between the stage is not limit, and does not seize, and can not reentry;
Problem of the present invention can be summarized as:
FHm，(PM
(1)，(RM
(k))
m-1 k＝2)，PM
(m))|batch，assembly，M
j|C
max
Namely contain m stage, phase one and m stage are many parallel machines, and the second to m-1 stage was uncorrelated machine, and first stage is batch processing, and second to m-1 stage is that machine adds, and m stage is assembling, to minimize maximum completion date as target.Form turns to as shown in Figure 1.
Target of the present invention is for minimizing maximum completion date under the prerequisite that guarantees the heat-treatment furnace utilization factor.For the manufacturing link that meets above characteristics.For production scheduling process of the present invention better is described, define the constraint of symbolic variable as shown in table 1 and the problem shown in the table 2:
：
Table 1 symbolic variable
Determine problem constraint as shown in the table:
The constraint of table 2 problem
Constraint (1) refers to that every batch workpiece quantity is every kind of workpiece quantity sum wherein;
Constraint (2) refers to for any workpiece, contained total number this workpiece and that be this workpiece in every batch;
Constraint (3) guarantees that every batch workpiece quantity is less than the heat-treatment furnace capacity;
Constraint (4) is the formula of heat-treatment furnace utilization factor;
Every batch heat treatment time of constraint (5) expression is the heat treatment time of the longest workpiece of heat treatment time wherein;
Constraint (6) adds the computing formula of every batch of process time of stage for machine;
Constraint (7) is that the computing formula of process time is criticized in each assembling of assembling stage;
Constraint (8) guarantees a collection of can only a processing at a machine of stage;
Workpiece during constraint (9) guarantees every batch is all from identical workpiece family;
Constraint (10) guarantees that the start time of every a collection of n+1 procedure is more than or equal to the concluding time of n procedure;
Constraint (11) but guarantee that every a collection of actual on-stream time in certain stage is more than or equal to the earliest on-stream time of the processing machine in this stage;
Constraint (12) expression workpiece the actual on-stream time of next stage equal on last stage actual on-stream time and upper stage process time and;
Constraint (13) guarantees at assembling stage, must wait for just can beginning to assemble after whole batches of assembly relation arrival is arranged;
Constraint (14) expression n criticizes in the actual on-stream time of stage i and criticizes in the setup time of stage i sum more than or equal to completion date and the n that n criticizes at stage i-1;
After the problem identificatioin constraint, determine target of the present invention under the prerequisite that guarantees the heat-treatment furnace utilization factor, minimizing maximum completion date, i.e. following formula (15):
Table 3 problem target
The present invention is achieved through the following technical solutions:
The invention provides a kind of hybrid flow shop scheduling method, may further comprise the steps:
The 1st step: parts are classified according to the difference of required workpiece place workpiece family, form a plurality of parts collection; For example all parts that only are assembled into by workpiece in workpiece family 1 and 2 are classified as a class;
The 2nd step: select a not parts collection of scanning; If all parts collection scan, then finish in batches, turned for the 6th step and begin coding;
The 3rd step: for this parts collection creates new batch, batch number is the workpiece family number that comprises; Batch capacity be the capacity of heat-treatment furnace; The parts that same parts are concentrated are divided into a plurality of groups, each group comprises the workpiece of the minimum number that satisfies certain assembly relation, for example organize 1 to the group 5 in every group comprise 1 of workpiece family 1 workpiece, workpiece is 2 in the workpiece family 2, satisfy assembling than being 1: 2, group 6 to the group 10 every group comprise 2 of workpiece family 1 workpiece, workpiece is 3 in the workpiece family 2, satisfies assembling than being 2: 3;
The 4th step: if concentrate to also have workpiece not in batches at these parts, then select to put into one group of workpiece of residual capacity mean difference minimum behind each batch, should organize workpiece and put into corresponding batch, and concentrate from parts and to delete this and organize workpiece; This step is carried out in circulation, until remaining any workpiece group all can't satisfy the capacity limit of each batch simultaneously; If all parts all in batches, this parts collection of mark turned for the 2nd step for scanning;
The 5th step: if also have workpiece not in batches and do not have the workpiece group can satisfy simultaneously the capacity limit of each batch, then lock these batches, turned for the 3rd step.
The 6th step: after in batches, be each batch and all identification numbers, and be each stage coding that each stage all comprises two sections chromosomes, first paragraph chromosome is batch number, and second segment chromosome is the identification number of batch correspondence; For assembling stage, be considered as a batch of collection with assembling some batches, and use separator separating adjacent batch collection, when carrying out subsequent operation, a batch collection is looked as a whole consideration; The coding in all stages has just consisted of whole chromosome coding group according to the stage sequential combination together.
Problem model of the present invention comprises a plurality of stages, and each stage all comprises two sections chromosomes, and the order of first paragraph chromosome for criticizing, subordinate phase are corresponding machine order.Because the present invention considered batch processing, thus the first paragraph coding corresponding be not single workpiece, but one batch, this batch may comprise a kind of even various workpieces.After in batches, be each Mission Number, the numeral on the chromosome namely represents corresponding batch number.The machine in per stage is also numbered, and uses equally numeral.
The chromosome coding in each stage separates with a room between Job Scheduling order and two sections codings of corresponding machine order as shown in Figure 2.
For heat treatment stages, suppose to have two identical parallel machines, there are four batches of workpiece to heat-treat, as shown in Figure 2, then the scheduling Gantt chart of its correspondence as shown in Figure 3, batch 4 and 1 thermal treatment on heat-treatment furnace 1, batch 3 and 2 thermal treatments on heat-treatment furnace 2.If adjacent batch belongs to different workpiece families, then need between to add switching time.
Add the stage for machine, its coded system is identical with heat treatment stages, just require batch can only process at some machine, therefore in the selection of machine code must with batch in the type of workpiece be consistent.
For assembling stage, the coding of machine order is with top similar, but owing to will operate simultaneously a plurality of batches during assembling, and therefore batch dispatching sequence's coding has and differs from coded system before.Here adopt coding form as shown in Figure 4, be considered as a batch of collection with assembling some batches, and between adjacent batch of collection, cut apart with 0, when carrying out subsequent operation, a batch collection is looked as a whole consideration, Fig. 4 represents batches 4 and 3 in machine 1 assembling, and batches 1 and 2 in machine 2 assemblings.
With the coding in above all stages according to the stage sequential combination together, add newline behind the coding in each stage and separate, just consisted of the two-dimentional chromosome coding group of problem integral body, each stage corresponding delegation chromosome.
The 7th step: the user arranges population quantity, then generates at random chromosome under the condition of machine-limited satisfying, and the quantity of generation is identical with population quantity, and population quantity is the integer between the 20-100;
The 8th step: select: select to operate each chromosome that will travel through in the population, for chromosome r
k(k=1,2 ..., size; Size is maximum population scale), at first to calculate corresponding completion date, i.e. the target function value that scheduling is separated
Then according to fitness function calculate chromosomal just when:
E (r
k)=J
Max-J (r
k), J
MaxBe all chromosomal J (r
k) maximal value;
The probability selection method is adopted in chromosomal selection, determine individual selected probability with the method for linear ordering, after calculating each individual fitness value, according to fitness value the individuality in the colony is sorted by from big to small order, then obtain selected probability according to ordering, i individual selected probability and its are just when being directly proportional, and the selecteed probability of chromosome is:
I=1 wherein, 2 ..., N, N are the size of population, i is that chromosome is in the sequence number in ordering;
In per generation, selected N chromosome, at first selects two chromosomes that come first and second according to the order that sorts before and directly remain into the next generation as high-quality chromosome, then remaining chromosome selected all the other N-2 chromosome according to the method for roulette;
When selecting to operate, fitness function only comprises maximum completion date, does not comprise the utilization factor of heat-treatment furnace, and this is because for problem model of the present invention, and average heat-treatment furnace utilization factor is only with the result is relevant in batches, and is irrelevant with the dispatching sequence.
The 9th step: intersect: N the chromosome of selecting is carried out interlace operation in twos, if 100 chromosomes are arranged, then to carry out 50 interlace operations to 50 pairs of chromosomes, chromosome adopts segment encoding, need to every section chromosome in each stage be intersected respectively, wherein batch dispatching sequence also need simply revise after intersecting, and removes to repeat batch.For every chromosome, the step of an interlace operation is as follows:
Step 1: the user arranges crossover probability, and crossover probability produces a random number between 0.4-0.8, if then turn Step2 less than crossover probability, otherwise do not carry out interlace operation;
Step 2: select at random respectively two different points in batch dispatching sequence's chromosome in each stage, can only select terminal and decollator at assembling stage;
Step 3: exchange the gene block of choosing in two parent chromosomes, produce two filial generations;
Step 4: find out the genic value that lacks and repeat;
Step 5: according to two filial generation chromosomes of mapping relations correction, change the genic value that repeats into lack genic value;
Step 6: select at random respectively two different points in the machine order chromosome in two each stages of filial generation chromosome that step5 produces, the gene block that exchange is chosen produces two new filial generations.
Fig. 5 has represented the process of chiasmas of three stage problems.In the intersection process, machine adds order part and the gene that repeats occurred, and will choose the duplicate factor outside the gene to delete, and adds unduplicated genic value with from left to right order again from parent.
The 10th step: the user arranges the variation probability, the variation probability is between 0.01-0.2, each chromosome that the 9th step produced is carried out mutation operation: produce a random number, every section batch of dispatching sequence's chromosome of a parent chromosome is carried out 2 variations when the random number that produces during less than the variation probability, namely specify at random two positions and exchange correspondence position chromosome; Every section machine order chromosome is carried out the single-point variation, by specifying at random a position and this value being changed to random number satisfying machine and add under the condition of stage machine constraint;
Fig. 6 has represented the process of variations of three stage chromosomes.Parent chromosome has formed a filial generation chromosome after through variation, and arrow represents the position that makes a variation.
The 11st step: repair: have the machine constraint because machine adds the stage, workpiece can only be processed by some machine within the stage, be not that all machines all can be processed, therefore when carrying out the crossover and mutation operation, can produce machine and the chromosome that workpiece does not conform to, be necessary this chromosome is repaired.
The reparation strategy that adopts is to find the chromosome that does not meet machine-limited, and finds out concrete position, selects arbitrarily afterwards a machine number that meets machine-limited, and replaces original numeral with this numeral of choosing.
Superincumbent machine adds in the case, supposes that after cross and variation chromosomal first position of phase one machine order is 3, because batches 4 can not be in machine 3 processing, so will repair operation to this chromosome, repair process as shown in Figure 7.
The 12nd step: judge whether to surpass maximum iteration time, maximum iteration time determines that according to different problem scales the larger iterations of scale is larger by the user; If do not surpass, turned for the 8th step, if surpass, finish, export the optimum solution in last generation, determine to organize according to optimum solution and criticize and scheduling strategy.
Beneficial effect
The present invention is directed under the flexible path, machine adds and assembles the alternately solution of the problem proposition of mixed scheduling, has solved the Problems of Optimal Dispatch of workpiece, mainly contains following 3 beneficial effects:
(1) can solve the hybrid flow Job Shop problem that exists assembling that the parallel batching stage is affected in batches;
(2) can process with parallel batching, serial batch processing and the scheduling of assembling the product with complicated technology constraint of three classes variations;
(3) the algorithm operational efficiency is guaranteed.
Description of drawings
Fig. 1 is the complicated HFS problem model that comprises serial parallel batch processing and assembling;
Fig. 2 is that thermal treatment and machine add stage chromosome coding structure figure;
Fig. 3 is that Gantt chart is separated in the thermal treatment scheduling;
Fig. 4 is assembling stage chromosome coding structure figure;
Fig. 5 is that chromosome once intersects process;
Fig. 6 is mutation process of chromosome;
Fig. 7 is repair process of chromosome;
Fig. 8 is overall flow figure;
Fig. 9 is the variation of solution corresponding to different population size;
Figure 10 is the relation of the time of finding the solution and Population Size;
Figure 11 is that Population Size is 50 o'clock different aberration rates and solution corresponding to crossing-over rate;
Figure 12 is the iterations of different problems and the variation relation figure of solution;
Embodiment
Below in conjunction with accompanying drawing, specify preferred implementation of the present invention.
Present embodiment is according to the mixed scheduling algorithm of the parallel batching based on heat-treatment furnace surplus minimal difference method and genetic algorithm, serial batch processing and the assembling of the realization of the execution in step in summary of the invention the present invention proposition, as shown in Figure 8.
Solution of the present invention is divided into two stages: group is criticized and batch scheduling.Phase one group batch is very crucial step, because group batch not only directly affects the utilization factor of heat-treatment furnace, and result that more can the remote effect scheduling.If the effect of group batch is bad, there have so good again dispatching algorithm also may cause dispatching the effect of solution to be bad.Therefore, in order to verify the validity of the in batches heuristic that the present invention proposes, carried out a series of experiment here.
Present embodiment is carried out following test simulation:
Emulation experiment adopts Java language to be programmed in Intel (R) Core (TM) i3-2310CPU@2.10GHz, realizes on the PC of 4.0G internal memory.
The present invention is directed to different problem scales, designed 12 groups of experiments, 4 groups of its middling and small scale problems (workpiece number＜=10), 5 groups of middle scale problems (10＜workpiece number＜=20), 3 groups of extensive problems (workpiece number 〉=20).The information such as workpiece family, workpiece, machine, parts and stage that each use-case comprises are shown in following table 4-1.Other information are at random and generate, and wherein the heat treatment time scope of workpiece is [60,120], and machine adds time scope [5,50], installation time scope [10,30], the setup time scope [20,40] in each stage, the demand of parts [5,16].
Table 412 experiment arranges details
GA at first will determine 4 parameters before finding the solution, Population Size represents chromosomal quantity, and crossover probability is two probability that chromosome carries out interlace operation, and the variation probability is the probability that chromosome carries out mutation operation, and iterations is chromosomal algebraically.The difference of above parameter tends to cause separating the deviation of effect, and therefore, for the effect that guarantees to separate, the present invention at first tests the series of parameters of GA.
Population Size, aberration rate and crossing-over rate often have certain range constraint, and there is comparatively closely coupled relation three inside.Relatively above three class parameters, the scope of iterations is just larger, may differ tens times between minimum and the maximum, so the present invention lists the experiment of iterations separately, at first determine Population Size, aberration rate and these three parameters of crossing-over rate, carry out again afterwards the experiment of iterations.
In general, Population Size is between 20 to 100, and aberration rate is between 0.01 to 0.2, and crossing-over rate is between 0.4 to 0.8.The present invention chooses three different experiment values for each parameter, and Population Size is that { 20,50,100}, aberration rate are that { 0.05,0.1,0.2}, crossing-over rate are { 0.4,0.6,0.8}.Three values of three parameters make up respectively, consist of altogether 27 groups of experiments, carry out respectively 5 experiments for a fixing parameter in every group of experiment, 13 sampled points are set up in each experiment, be respectively { 0,100,500,1000,200 ..., 10000}, the minimum makespan of homologue in the population is got in each sampling, and the mean value that calculates 5 experiments is as experimental result.Here choose the use-case of a minor issue scale broad in the middle, namely Case7 is as test case.
Data are further analyzed and can be found, according to the also to some extent difference of effect of the difference solution of Population Size.As shown in Figure 9, the minimum makespan of population reduces along with increasing of population quantity, the better effects if of solution.Simultaneously, data also show time and the population quantity correlation of Solve problems.As shown in figure 10, along with the rising of population quantity, find the solution the time of scheduling problem of the present invention and also rise thereupon, and present positive correlation.
According to Fig. 9, population scale is that the effect of 100 o'clock homographic solutions is best, secondly is that population scale is 50 solution, and both are more or less the same, and what effect was the poorest is that population scale is 20 solution.But from the time of finding the solution, population scale is that time of finding the solution of 100 almost is that population scale is 50 twice, and population scale is that time of finding the solution of 20 solution is minimum.Based on above discussion, consider and find the solution effect and finding the solution the time, the selected population size is 50 as final experiment parameter here.
Be 50 solution for all Population Sizes, the effect of its solution as shown in figure 11.As we know from the figure, best one group of the effect of solution is a group of pink colour, and namely aberration rate is that 0.2 crossing-over rate is a group of 0.6 correspondence.Therefore, in follow-up experiment, all will use Population Size 50, crossing-over rate 0.6, aberration rate 0.2 this group parameter.
In GA, the iterations of different experiment correspondences often has larger gap, and therefore the present invention is directed to all 12 groups of problems carries out respectively the experiment of iterations.Other three parameter values are decided according to top experimental result, experiment method is to top similar, each Case represents one group of experiment, every group of experiment comprises 5 experiments, 13 iterations sampled points (with top identical) are set up in each experiment, the minimum makespan of homologue in the population is got in each sampling, and the mean value that calculates 5 experiments is as experimental result, and the result who obtains as shown in figure 12.
Along with the change of problem scale is large, the speed of convergence of optimum solution slows down, and the iterations that needs increases.Black dotted lines represents the change trend curve of the steady point of becoming of different problems among the figure, becoming surely, point is the very little point of amplitude of variation of optimum solution, here be defined as with the difference of sampled point solution last time less than 1% point, be current generation chromosome optimum solution and previous generation chromosome optimum solution difference less than 1% point, the completion date difference of the completion date of current generation minimum and previous generation minimum is less than 1%, and the solution of this point is not equal to initial solution.Along with the increase of problem scale, after the steady point that becomes also more and more leaned on, therefore for different problems, needed iterations was not identical.In experiment from now on, the steady point that just will become is defined as the terminal point of iteration, determines iterations according to the scope of following table.Take case 1 as example, if problem model comprises 2 workpiece families, 4 kinds of workpiece, 4 machines, 2 kinds of parts and 3 stages, then iterations is 60 times.
Determining of table 5 iterations
As a kind of optimization, the minimum makespan in the chromosome of new generation and the minimum makespan in the parent are compared, if the difference of completion date less than 1%, finishing iteration then.
In order to verify the validity of the SDHM group batch heuristic that the present invention proposes, here SDHM is compared with group batch common a few class heuristics, respectively ALPT (Average Longest Processing Time, average the longest process time), ASPT (Average Shortest Processing Time, average the shortest process time), SAV (Smallest Average Volume, the minimum average B configuration volume) and BAV (Biggest AverageVolume, maximum average external volume).
It at first is that the central parts of each parts collection sort that these four kinds of methods need, and the standard of ordering is average processing time or the average external volume (being par in the present invention) of every group of workpiece (several workpiece with assembly relation are called one group of workpiece).ALPT be the longest workpiece group of average processing time preferentially in batches, ASPT be the shortest workpiece group of average processing time preferentially in batches, SAV be average radix minimum the workpiece group preferentially in batches, BAV be average radix maximum the workpiece group preferentially in batches.
Experimental technique is identical with experiment before, and the parameters of GA is respectively Population Size 20, crossing-over rate 0.6, aberration rate 0.2, and iterations is as the criterion with the iterations size of SDHM heuristic.Experiment contrasts in batches lot number, heat-treatment furnace average utilization and target of the present invention respectively.
Following table 4-2 has shown that the group of each heuristic criticizes the result.Can find out that in 12 groups of experiments, SDHM group lot number amount has 10 groups minimum (comprising side by side), accounted for 83.3%, and from the mean value of lot number, the lot number of SDHM method is minimum.The relative additive method of SDHM method has improved 1.62% to 4.22%.
Each group crowd heuristic lot number result in batches of table 6
Following table 4-3 has shown the average heat-treatment furnace utilization factor that each heuristic is corresponding.In all 12 groups experiments, the experiment of the heat-treatment furnace utilization factor of SDHM method maximum (comprising side by side) has 10 groups, and with regard to the mean value of the heat-treatment furnace utilization factor of all examples, the relative additive method of SDHM method has improved 5.44% to 8.92%.
The average heat-treatment furnace utilization factor of each group batch heuristic of table 7
Following table 4-4 has shown the minimax completion date (Cmax) that each heuristic is corresponding.In all 12 groups experiments, the experiment of the Cmax of SDHM method minimum (comprising side by side) has 7 groups, and in all the other 5 groups of experimental results, the Cmax of SDHM method has also come front three, with regard to the mean Cmax of all Case, the relative additive method of SDHM method has shortened 7.96% to 13.70%.
The minimax completion date of each group batch heuristic of table 8
Above-described instantiation is further to explain to of the present invention, and the protection domain that is not intended to limit the present invention is all within principle of the present invention and spirit, the change of doing and to be equal to replacement all should be within protection scope of the present invention.
Claims (2)
1. hybrid flow shop scheduling method may further comprise the steps:
The 1st step: parts are classified according to the difference of required workpiece place workpiece family, form a plurality of parts collection;
The 2nd step: select a not parts collection of scanning; If all parts collection scan, then finish in batches, turned for the 6th step and begin coding;
The 3rd step: for this parts collection creates new batch, batch number is the workpiece family number that comprises; Batch capacity be the capacity of heat-treatment furnace; The parts that same parts are concentrated are divided into a plurality of groups, and each group comprises the workpiece of the minimum number that satisfies certain assembly relation;
The 4th step: if concentrate to also have workpiece not in batches at these parts, then select to put into one group of workpiece of residual capacity mean difference minimum behind each batch, should organize workpiece and put into corresponding batch, and concentrate from parts and to delete this and organize workpiece; This step is carried out in circulation, until remaining any workpiece group all can't satisfy the capacity limit of each batch simultaneously; If all parts all in batches, this parts collection of mark turned for the 2nd step for scanning;
The 5th step: if also have workpiece not in batches and do not have the workpiece group can satisfy simultaneously the capacity limit of each batch, then lock these batches, turned for the 3rd step.
The 6th step: after in batches, be each batch and all identification numbers, and be each stage coding that each stage all comprises two sections chromosomes, first paragraph chromosome is batch number, and second segment chromosome is the identification number of batch correspondence; For assembling stage, be considered as a batch of collection with assembling some batches, and use separator separating adjacent batch collection, when carrying out subsequent operation, a batch collection is looked as a whole consideration; The coding in all stages has just consisted of whole chromosome coding group according to the stage sequential combination together;
The 7th step: the user arranges population quantity, then generates at random chromosome under the condition of machine-limited satisfying, and the quantity of generation is identical with population quantity;
The 8th step: select: select to operate each chromosome that will travel through in the population, calculate each chromosome r
kCorresponding completion date J (r
k), then calculate chromosomal just when i.e. all chromosome J (r
k) maximal value deduct the (r as prochromosome J
k) difference that obtains; The probability selection method is adopted in chromosomal selection, determine individual selected probability with the method for linear ordering, after calculating each individual fitness value, according to fitness value the individuality in the colony is sorted by from big to small order, then obtain selected probability according to ordering, i individual selected probability and its are just when being directly proportional, and the selecteed probability of chromosome is:
I=1 wherein, 2 ..., N, N are the size of population, i is that chromosome is in the sequence number in ordering;
In per generation, selected N chromosome, at first selects two chromosomes that come first and second according to the order that sorts before and directly remain into the next generation as high-quality chromosome, then remaining chromosome selected all the other N-2 chromosome according to the method for roulette;
The 9th step: intersect: N the chromosome of selecting is carried out interlace operation in twos, and the step of an interlace operation is as follows:
Step 1: the user arranges crossover probability, produces a random number, if then turn Step2 less than crossover probability, otherwise does not carry out interlace operation;
Step 2: select at random respectively two different points in batch dispatching sequence's chromosome in each stage, can only select terminal and decollator at assembling stage;
Step 3: exchange the gene block of choosing in two parent chromosomes, produce two filial generations;
Step 4: find out the genic value that lacks and repeat;
Step 5: according to two filial generation chromosomes of mapping relations correction, change the genic value that repeats into lack genic value;
Step 6: select at random respectively two different points in the machine order chromosome in two each stages of filial generation chromosome that step5 produces, the gene block that exchange is chosen produces two new filial generations;
The 10th step: the user arranges the variation probability, each chromosome that the 9th step produced is carried out mutation operation: produce a random number, every section batch of dispatching sequence's chromosome of a parent chromosome is carried out 2 variations when the random number that produces during less than the variation probability, namely specify at random two positions and exchange correspondence position chromosome; Every section machine order chromosome is carried out the single-point variation, by specifying at random a position and this value being changed to random number satisfying machine and add under the condition of stage machine constraint;
The 11st step: have the machine constraint because machine adds the stage, workpiece can only be processed by some machine within the stage, be not that all machines all can be processed, therefore when carrying out the crossover and mutation operation, can produce the chromosome that machine and workpiece do not conform to, be necessary this chromosome is repaired, the reparation strategy that adopts is to find the chromosome that does not meet machine-limited, and find out concrete position, select arbitrarily afterwards a machine number that meets machine-limited, and replace original numeral with this numeral of choosing;
The 12nd step: judge whether to surpass maximum iteration time, the larger iterations of scale is larger; If do not surpass, turned for the 8th step, if surpass, finish, export the optimum solution in last generation, determine to organize according to optimum solution and criticize and scheduling strategy.
2. a kind of hybrid flow shop scheduling method according to claim 1, it is characterized in that, in the 12nd step, if do not surpass maximum iteration time, minimum makespan in the chromosome of new generation and the minimum makespan in the parent are compared, if the difference of completion date is less than 1%, finishing iteration then.
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