CN103309316A - Scheduling method of multi-stage variation hybrid flow shop with batch processor - Google Patents

Abstract

The invention relates to a scheduling method of a multi-stage variation hybrid flow shop with a batch processor and belongs to the field of an advanced manufacturing controlling and scheduling technology. A decision making problem of a combined dispatching rule is solved through a genetic algorithm based on a dispatching rule code; firstly, a problem model described by three sections of encoding is established according to different scheduling targets; a total sum of minimized maximum finishing time and minimized weighted delaying time is respectively used as a target according to a strategy searching genetic algorithm disclosed by the invention to search the suitable dispatching rule for each machine; and finally, the obtained combined dispatching rule is applied to solving a scheduling solution. According to the method disclosed by the invention, a multi-stage HFS (Hybrid Flow Shop) scheduling problem of two different equipment types including the batch processor and a signal processor can be solved at the same time; with the adoption of an encoding scheme facing the machines, actual environment information can be reflected, and the limitation of encoding according to phases is avoided to a certain extent; the encoding does not need to use a repairing mechanism; and the scheduling efficiency is guaranteed.

Description

The multistage variation hybrid flow workshop dispatching method that has batch processor

Technical field

The present invention relates to a kind of multistage variation hybrid flow workshop dispatching method that has batch processor, belong to advanced production control and dispatching technique field.

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 great challenge to manufacturing enterprise: manufacturing enterprise relates to machining operation and heat treatment step in process.How under this complex environment, to carry out production scheduling, guarantee the delivery date of different parts, reduce inventory cost simultaneously, keep the productive temp balance, improve the utilization factor of heat-treatment furnace etc., will become a challenging problem.

The hybrid flow workshop (Hybrid Flow Shop, HFS) be a kind of based on given objective function by the multistage Workshop Production scheduling problem 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 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.Above-mentioned assumed condition and actual production environment have big gap, therefore researched and proposed the HFS of various variations in a large number, common variation condition comprise allow part dynamically to arrive, consider to produce setup time (setup time), consider limited buffer zone (limited capacity of buffer), permission stage jump (stage skipping) etc., the HFS that has batch processor also is wherein a kind of.

Typical batch processor has (burn-in operation) equipment etc. of firing of the reacting furnace of chemical industry, manufacturing heat-treatment furnace and semi-conductor industry.In general, batch processor becomes the bottleneck of whole process of production easily, and reason is: (1) batch processor is relatively more expensive, and it is higher to start operating cost, so limited amount; (2) the batch processing time longer usually, and be disabled in when operation to other part; (3) some batch operation is last procedure of part, directly influences delivery date (for example pre-burning operation of semi-conductor chip etc.).Because the diversity of aspects such as production technology, device connection, intermediate storage strategy and resource restriction in the batch process, the production scheduling problems of batch processing is very complicated, in engineering is used, also mainly be fixed against dispatcher's experience, can't satisfy the requirement of system optimization.Yet, to compare with the variation HFS of other types, the HFS scheduling problem correlative study that has batch processor is also rare.Whether diversification can be divided into two classes according to device type in present research.

One class is the HFS that only contains batch processor.(Travel Sales Problem TSP) has designed a kind of heuritic approach and has found the solution two stages batch processing scheduling problem the traveling salesman problem of people such as Caricato by a kind of variation.Liu and Karimi are respectively under limited spatial cache and zero-waiting (Zero-Wait) condition, set up a plurality of mixed-integer programming models at equal parallel machine (identical parallel machine) and non-equal parallel machine environment, proposed integrated and find the solution this scheduling problem based on the method for order with based on the mixed method of the method for groove.Displacement Flow Shop (permutation flowshop) scheduling problem that people such as Damodaran are contained batch processor at each stage is used particle cluster algorithm, and (Particle Swarm Optimization PSO) finds the solution.

Yet in actual production environment, the diversification often of the equipment among the HFS, so some scholar's research contain the HFS of discrete machine and batch processor simultaneously.Feng has considered that the machine capacity is not 1 entirely, and namely the situation that machine is batch processor is regulation goal to minimize maximum completion date, adopts genetic algorithm to arrange the part processing order.Su and Chen adopt heuritic approach and branch and bound method solved elder generation through a discrete machine again through the two-stage Flow Shop scheduling problem of a batch processor, this problem model can be expressed as the single-batch model.People such as Yao and Frank S. have considered that part dynamically arrives, the method that adopts a plurality of heuritic approaches to combine solved elder generation through a batch processor again through the Flow Shop scheduling problem of a discrete machine, i.e. batch-single model.People such as J.Behnamian have considered the transfer time of part at machinery compartment, adopt mixed integer programming respectively above-mentioned single-batch and batch-single problem to be set up model, and respectively with the heuritic approaches solution of three steps.People such as Hao and Luo has considered two stage HFS, and there are 3 identical batch processors the phase one, and subordinate phase only has a discrete machine, has set up a mixed-integer programming model, and adopts genetic algorithm that this model is found the solution.

Though these comprehensive studies have been considered discrete machine and batch processor, problem model only limits to two stage Flow Shops, and per stage is in the majority with the unit model.Yet in actual production, particularly in the production run of complex parts, multistage situation is more general, and parallel machine and flexible path extensively exist, and therefore above-mentioned research is difficult to be applied to the actual schedule problem.Even Gupta has proved a stage and has only contained a machine that another stage is contained two stage HFS problems of two machines, all is np hard problem.The problem model that the present invention considers is owing to the intervention of factors such as multistage, polynary device type and flexible path has higher complicacy.

The problem model that the present invention considers derives from the actual production process of machine industry complex parts.Finding shows that in the actual production environment of enterprise, part begins not only to need to carry out turnning and milling from blank and digs machining operations such as abrasive drilling, also needs to anneal, heat treatment steps such as quenching, tempering, carburizing.According to statistics, in the actual production of complex partses such as vehicle transmission gear, the existing machine work order of about 35% part production run also has heat treatment step.From the result for retrieval of document, heat treated scheduling problem all is to study as a separate phases, and this mainly is because heat treatment time adds the time much larger than machine usually.Yet finding shows, in the production run of complex partses such as vehicle transmission gear, though the machine work order time is shorter, but quantity is more, the time that whole machine adds the stage accounts for about 39% of production overall process, and heat treatment stages then accounts for about 42%, and the two is about the same; On the other hand, reach thousands of minutes the process time of the existing complicated machine work order of part.These phenomenons machine that all makes adds stage and heat treatment stages in that most important optimization index---the time is mentioned in the same breath.Therefore, be necessary in the production scheduling process, to take all factors into consideration machine and add (discrete machine) and thermal treatment (batch processor), to obtain good scheduling result.

Unit's heuristic and various be to find the solution the common methods of HFS scheduling problem based on the method for assigning rule.Compare with assigning rule, first heuristic provides better solution performance to be based upon to expend on more search time of the basis, be difficult to accept finishing large-scale problem solving in the time.In actual production, the data scale of enterprise is very huge, assigns rule because having simply efficiently and dirigibility forms dispatching method into first-selection.The research about the HFS scheduling problem, assign rule and various rule-based heuristics and account for 50%, and first heuristics such as genetic algorithm, simulated annealing and tabu search algorithm only accounting for 19% from 1970 to 2009 in people such as Ruiz statistics.This shows, more favored based on the method for assigning rule for the HFS scheduling problem.Yet manufacturing system is complicated and changeable, can performance all be better than other rule under all environment and evaluation criterion without any a rule, that is to say, assigns rule dispatch environment and regulation goal are had strong dependence.Therefore, some have been researched and proposed combination and have assigned rule decision (Combinatorial Dispatching Rules Decision), and namely each stage uses different assignment rules to obtain more excellent scheduling solution performance.Barman and LaForge have analyzed combination first and have assigned rule to the effect of improving of workshop scheduling performance.Sarper and Henry adopt method of emulation that two stage Flow Shops have been studied six optional combinations of assigning rule.Barman has solved four optional three stage Flow Shop scheduling problems of assigning rule with full factor analysis method.The assignment rule index number coding that people such as Yang adopted each stage is assigned rule by the combination of genetic algorithm for solving optimum.

(Genetic Algorithm is a kind ofly to search for first heuritic approach of optimum solution by simulating Darwinian natural evolutionary process GA) to genetic algorithm, is taught in 1975 by the J.Holland of the U.S. at first to propose.Because it has preferably global optimizing ability, can adjust the direction of search adaptively, extensively be suitable 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 problem 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 problem 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, intersects and variation.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 the diversity of population by the method for genetic recombination, and forms such as real-valued reorganization and intersection are arranged; Mutation operation also makes algorithm have the ability of Local Search except enlarging the diversity of population, 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: earlier 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, circulation is carried out stopping when reaching maximum iteration time from calculating the ideal adaptation degree to the operation of variation.

Summary of the invention

The present invention is for solving the multistage HFS scheduling problem that contains discrete machine and two kinds of distinct device types of batch processor simultaneously, propose a kind of multistage variation hybrid flow workshop dispatching method that has batch processor, adopt decision search genetic algorithm (SSGA) to solve combination and assign the rule decision problem.

The present invention is by solving the decision problem that rule is assigned in combination based on the genetic algorithm of assigning rule encoding.In the problem model that the present invention sets up, even be in the machine in same stage, also may have different environmental informations, as machine capacity, process velocity, buffer pool size and buffer zone workpiece quantity etc.So decision search genetic algorithm (Strategy Search Genetic Algorithm of the present invention's proposition, SSGA) respectively to minimize maximum completion date (Cmax) and minimizing Weighted summation time delay (Total Weighted Tardiness, TWT) be target, be every suitable assignment rule of machine search.Use the combination assignment rule that obtains again and try to achieve the scheduling solution, the effectiveness of checking SSGA.

In general, scheduling problem mainly comprises two subproblems under the flexible path, namely assign (assignment) and ordering (sequencing), and the key issue of batch scheduling is how to organize to criticize.If the workpiece of organizing after criticizing is regarded as a logic workpiece, the processing object of so discrete machine and batch processor can be modeled as an entity.On this basis, SSGA solves ordering, assigns and group batch problem by an overall solution.

The present invention will have hybrid flow workshop (the Hybrid Flow Shop of batch processor, HFS) expand to the multistage, there is parallel machine in each stage, and one of them stage is made up of many identical (identical) batch processors, thereby will disperse machine and batch processor and the multistage HFS that deposits is integrated in the block mold.

The present invention adopts genetic algorithm that the scheduling solution is optimized.

The principal element that the present invention considers comprises: (1) has the multistage variation HFS of batch processor and discrete machine simultaneously; (2) flexible machining path; (3) produce setup time.

The present invention is applicable to the production and manufacturing environment that possesses following feature simultaneously:

(1) the workpiece collection contains N workpiece, need be by the HFS in M stage is arranged;

(2) workpiece has different time of arrival and delivery date;

(3) there are many aniso-parallel machines (non-identical parallel machine) in each stage, and wherein having and only have a stage is batch processor;

(4) each workpiece must pass through all stages in proper order;

(5) each workpiece is earlier through some discrete machines after the stage, and a plurality of workpiece will be formed and a collection ofly be processed simultaneously by batch processor, pass through the follow-up some discrete machine stage again, finish processing tasks;

(6) volume of all workpiece equates, batch size only relevant with contained workpiece quantity, and can not surpass both constant volumes of batch processor;

(7) before every machining arranged certain setup time (setup time), setup time is only relevant with workpiece, and irrelevant with the order of machine processing workpiece;

(8) processing time of each batch equals the required long process time of single workpiece in this batch, and all workpiece in same batch have identical start time and concluding time;

(9) machine is available always;

(10) workpiece is ignored in each stage inside and the transfer time between the stage;

(11) the workpiece synchronization can only be by a machining arbitrarily.

(12) buffer size between the stage is not limit, and does not seize, and can not reentry.

The included concrete steps of dispatching method of the present invention are as follows:

The 1st step: define symbol variable:

Table 1 symbolic variable

Described entity is represented workpiece or the workpiece set of upward processing of machine (comprising discrete machine and batch processor).For discrete machine, an entity is represented a workpiece; For batch processor, an entity is represented one batch.

The 2nd step: according to different regulation goals, adopt three sections coding descriptive model α | β | (wherein α represents machine environment to γ, β describes detailed characteristics and the constraint of workpiece, and γ is regulation goal), the multistage variation hybrid flow solve job shop scheduling problems model that will have batch processor is summarized as:

${\mathrm{HF}}_K,{\left({\mathrm{PM}}^{\left(k\right)}\right)}_{k=1}^K|r_{j,}{S}_{\mathrm{snd}},{\mathrm{batch}}^{\left(k^{\′}\right)}|C_{\max }---\left(1\right)$

${\mathrm{HF}}_K,{\left({\mathrm{PM}}^{\left(k\right)}\right)}_{k=1}^K|r_{j,}{S}_{\mathrm{snd}},{\mathrm{batch}}^{\left(k^{\′}\right)}|\mathrm{TWT}---\left(2\right)$

α part in formula (1) and the formula (2) is identical with beat portion, wherein HF _KThe expression contain K stage the hybrid flow workshop (Hybrid Flow, HF);

The parallel machine (Parallel Machine) of representing the 1st stage to the K stage; r _jThe time of arrival (Reach Time) of expression workpiece j; S _SndThe setup time (Setup Time) of expression and order irrelevant (Sequence independent); Batch ^{(k ')}A certain stage k ' in the expression 1 to K is batch processor (Batch Machine).Gamma portion in formula (1) and the formula (2) is inequality, the C in its Chinese style (1) _MaxExpression is target to minimize maximum completion date (Maximum Completion Time), and the TWT in the formula (2) represents that postponing summation (Total Weighted Tardiness) with minimizing Weighted is target.

The 3rd step: problem constraint (as table 2) and the optimization aim (as table 3) of determining the scheduling problem model that the 2nd step set up.

The constraint of table 2 problem

Constraint (3) expression workpiece j can only be arranged on the machine M at stage k;

Constraint (4) expression workpiece j can only belong to an entity b at stage k;

Constraint (5) expression workpiece j must be scheduled at stage k, and can only dispatch once;

Just can go into operation after constraint (6) the expression workpiece j arrival system, namely time of arrival r _jSmaller or equal to the current time

Constraint (7) the expression actual treatment T.T. of workpiece j on the machine m of stage k

Be no earlier than under it among entity b any one workpiece j at the processing T.T. of stage k tt _Jk

Constraint (8) expression is except the phase one, after workpiece j finishes processing of k previous stage

The latter half k+1 just can go into operation

The different workpieces j of the same entity b of constraint (9) expression and j ' are in the start time of stage k

Identical;

Constraint (10) expression workpiece j is at the completion date C of stage k _JkMore than or equal to time of arrival

Add total processing time tt _Jk

The same time t of constraint (11) expression machine can not process two different workpieces j and j ' simultaneously;

Constraint (12) represents that the entity number of each batch can not surpass the capacity C M of machine m _m

Determine that target of the present invention is for minimizing maximum completion date C _MaxOr minimizing Weighted postpones summation TWT, i.e. formula (13) and formula (14):

Table 3 optimization aim

The 4th step: based on the problem model in the 2nd step, under the constraint in the 3rd step, adopt genetic algorithm to reach optimization aim.At first, design chromosomal form:

Chromosome in the genetic algorithm is designed to workpiece section, machine section and group batch section, assigning method, sort method and group in the corresponding process criticized method respectively, and three kinds of coding rules are set respectively, the chromosomal gene position of each section represent its call number of corresponding coding rule.Corresponding each workpiece of workpiece section chromosome is assigned to the rule of following on the corresponding machine, the rule that corresponding each the machine choice buffer zone workpiece of machine section chromosome is followed, the group batch corresponding batch processor of section is organized batch rule of following to the workpiece that is positioned at this batch processor buffer zone.The specific coding rule of workpiece section, machine section and group batch section is as shown in table 4.

Table 4 coding rule

Owing to encoding scheme of the present invention is not directly separated towards scheduling, therefore in ordering, appointment and group batch method, adopt consistent encoding scheme.Workpiece section, machine section and the group batch corresponding code index sequential combination of section is in the same place, has constituted a chromosome of problem model integral body.

The 5th step: the user arranges population quantity, generates chromosome at random according to the 4th chromosome form that goes on foot.The chromosome quantity that generates is identical with population quantity, and population quantity size is the even number between the 5-50.

The 6th step: the reduction scheduling is separated, because can not directly obtain scheduling by chromosome separates, so needing decoding scheme that the chromosome that generates is reduced into scheduling separates, SSGA method of the present invention adopts the discrete events simulation method, each bar chromosome that the 5th step generated is decoded respectively, be reduced into actual scheduling solution to obtain target function value.Adopt the discrete events simulation method to the detailed process of a wherein chromosome decoding to be:

6.1 initial time t=0;

6.2 whether check that all workpiece all have been scheduled and all machines free time all, if then change 6.15, otherwise carry out 6.3;

6.3 whether check has the workpiece that is not scheduled to arrive first stage in the hybrid flow workshop of containing K stage, if then change 6.4, otherwise to change 6.6;

6.4 the workpiece that arrives is joined the buffer zone of assigning machine according to the contained appointment rule of this workpiece chromosome, changes 6.5;

6.5 deletion has arrived workpiece in the workpiece that never the is scheduled tabulation, changes 6.6;

6.6 scan all processing machines by platform, check whether be idle condition, in case scan idle machine then change 6.7, otherwise change 6.13;

6.7 whether what check 6.4 described appointment machines currently has a workpiece that machines, if have, workpiece is assigned the machine unloading from this, be added to by the chromosomal buffer zone of assigning determined next the scheduling machine of rule of this workpiece, obtain the completion date of this workpiece on this appointment machine simultaneously, change 6.8;

6.8 check the buffer zone of all machines, if all be empty, change 6.13, otherwise change 6.9;

6.9 check that all buffer zones not for whether empty machine is batch processor, if then change 6.10, otherwise change 6.11;

Criticize rule and the workpiece group of buffer zone criticized be entity 6.10 criticize the contained group of chromosome according to the group of machine, change 6.12;

6.11 each workpiece of buffer zone is formed an entity, changes 6.12;

6.12 dispatch all entities in this machine buffer zone according to the contained ordering rule of machine dyeing body, obtain each entity and on this machine, beginning processing constantly, change 6.13;

6.13 check whether all machines are finished a scanning, if then change 6.14, continue scanning otherwise change 6.6;

6.14 time stepping: current total activation time t=t+1, change 6.2;

6.15 finishing scheduling.

Adopt the method for step 6.1-6.15 to reduce each bar chromosome, obtain the scheduling solution of each chromosome reality in this generation chromosome, i.e. each procedure processing of workpiece begin to process constantly and its machine of scheduling.

The 7th step: the chromosome after the reduction of the 6th step is selected operation.Traversal each chromosome in the population, for chromosome i (i=1,2 ..., size), when objective function obj (i) is C _MaxThe time, obtain corresponding completion date, as objective function obj (i) when being TWT, obtain weighting and postpone summation;

Then according to fitness function calculate chromosomal just when:

$\mathrm{fit}\left(i\right)=\frac{1}{(\mathrm{obj}\left(i\right)+1)}---\left(15\right)$

Output just when the highest chromosome as the optimum solution in this chromosome in generation.

Roulette (roulette wheel) method is adopted in chromosomal selection, and per generation is selected X chromosome (X is even number), and the selecteed probability of chromosome is:

$\mathrm{prob}\left(i\right)=\frac{\mathrm{fit}\left(i\right)}{\underset{i=1}{\overset{\mathrm{size}}{\mathrm{\Σ}}}\mathrm{fit}\left(i\right)}---\left(16\right)$

The 8th step: X the chromosome of selecting is carried out interlace operation in twos, and each bar chromosome only participates in an interlace operation, obtains X/2 to the filial generation after intersecting.Because chromosome adopts segment encoding, when two chiasmas, need the chromosome of each section be intersected respectively.For every chromosome, the step of an interlace operation is as follows:

8.1: carry out interlace operation under the situation of certain crossover probability satisfying: the user arranges crossover probability, and crossover probability is between 0.05-0.9.Between 0-1, produce a random number, if random number then changes 8.2 less than crossover probability, otherwise do not carry out interlace operation;

8.2: the workpiece in a chromosome, machine, the group section of criticizing are selected two different positions respectively at random, obtain three gene blocks (being made of the gene position between two positions);

8.3: in workpiece, machine, the group section of criticizing, the gene block of choosing in two parent chromosomes of corresponding exchange respectively produces the filial generation after two intersections.

The 9th step: the user arranges the variation probability, the variation probability is between 0.01-0.18, each chromosome that the 7th step was selected is carried out mutation operation, concrete grammar is: produce a random number, when the random number that produces is carried out the single-point variation to the chromosomal every section chromosome of parent during less than the variation probability, namely specify a position at random and replace this locational gene at random, make new chromosome meet the coding rule of table 4;

The 10th step: judge whether to surpass maximum iteration time (maximum iteration time is arranged by the user, between 25 to 100), if do not surpass, repeated for the 5th step to the 9th step, number of iterations of every repetition adds 1; If surpass maximum iteration time, finishing iteration then obtains the optimum solution in each generation, postpone summation according to each scheduling time or weighting for the optimum solution correspondence, and coding rule, determine corresponding scheduling strategy, thereby realize having the multistage variation hybrid flow workshop scheduling of batch processor.

Beneficial effect

The present invention is directed under the flexible path, machine adds the solution that replaces the problem proposition of mixed scheduling with batch processing, has solved the optimizing scheduling problem of workpiece, has compared to the prior art major advantage:

(1) can solve the multistage HFS scheduling problem that contains batch processor and two kinds of distinct device types of uniprocessor simultaneously;

(2) take all factors into consideration ordering, appointment and group and criticized problem;

(3) employing more can reflect actual environmental information towards the encoding scheme of machine, has avoided to a certain extent by the stage Limitation of Coding; Coding need not to adopt repair mechanism;

(4) dispatching efficiency is guaranteed.

Description of drawings

Fig. 1 is multistage variation hybrid flow of the present invention workshop dispatching method process flow diagram;

Fig. 2 is chromosome decoding process figure in the dispatching method of multistage variation hybrid flow of the present invention workshop;

Fig. 3 is hybrid flow workshop synoptic diagram in the embodiment;

Fig. 4 is chromosome coding exemplary plot in the embodiment;

Fig. 5 is for minimizing the single-factor main effect figure under the Cmax target in the embodiment, wherein, (a) being population size factor ps main effect figure, (b) is crossover probability factor pc main effect figure, (c) for variation probability factor pm main effect figure, (d) be evolutionary generation factor gm main effect figure;

Fig. 6 is for minimizing the factor reciprocation figure under the Cmax in the embodiment;

Fig. 7 is for minimizing the single-factor main effect figure under the TWT target in the embodiment, wherein, (a) being population size factor ps main effect figure, (b) is crossover probability factor pc main effect figure, (c) for variation probability factor pm main effect figure, (d) be evolutionary generation factor gm main effect figure;

Fig. 8 is for minimizing the factor reciprocation figure under the TWT target in the embodiment;

Fig. 9 is for minimizing under the Cmax target batch processor in the embodiment to the SSGA Effect on Performance;

Figure 10 is for minimizing under the TWT target batch processor capacity in the embodiment to the SSGA Effect on Performance;

Figure 11 is for minimizing Cmax target following setup time in the embodiment to the SSGA Effect on Performance;

Figure 12 is for minimizing TWT target following setup time in the embodiment to the SSGA Effect on Performance;

Figure 13 is the rising tendency of the CPU time of SGA and GA_Yang in the embodiment, wherein, (a) for the SSGA algorithm in that to minimize Makespan(be Cmax) CPU time under the target, (b) be that the GA_Yang algorithm is in the CPU time that minimizes under the Makespan target, (c) for the SSGA algorithm in the CPU time that minimizes under the TWT target, (d) for the GA_Yang algorithm in the CPU time that minimizes under the TWT target.

Embodiment

Below in conjunction with accompanying drawing, specify preferred implementation of the present invention.

Hybrid flow workshop synoptic diagram as shown in Figure 3.The chromosome coding of this problem supposes that a HFS contains 6 machines as shown in Figure 4, and wherein the batch processing stage is contained 2 batch processors, needs 5 workpiece of scheduling.In workpiece section chromosome, the appointment rule of i the workpiece of numeric representation of gene position i.For example, the gene numerical value that this section chromosome is the 2nd is 3, then represents to adopt LU as assigning rule to the 2nd workpiece.Machine section chromosome and group batch section chromosome can in like manner be resolved.Need to prove that discrete machine is corresponding ordering rule only, be embodied in the relevant position of machine section; And batch processor not only has ordering rule to also have group batch rule, is embodied in the relevant position of machine section and group batch section respectively.

It is a multistage HFS scheduling problem that contains batch processor and two kinds of distinct device types of discrete machine simultaneously that the present invention considers, do not have suitable test case to use for reference at present, so the present invention has designed the validity that many groups test problem (test problem) comes verification algorithm.

Present embodiment is carried out following test simulation:

Emulation experiment adopts Java language to be programmed in Pentium4 3GHz, realizes on the PC of 1G internal memory.

The present invention has designed 18 groups of test problems altogether according to different machine setting and workpiece setting.The workpiece number is 10 to 95 not wait, and number of machines is 8 to 21 not wait, and number of stages is 3 to 7 not wait.Machine under the different scales distributes as shown in table 5, and platform number and the kind of data representation machine in the form represent to have a M1 machine as 1 M1.B represents the batch processing stage.The number of machines in per stage is obeyed the even distribution of [2,4], namely～U[2,4], the capacity～U[2 of batch processor, 5] even distribution.Workpiece setting is given birth to 2 groups according to the parameter generating common property shown in the table 6, then has 18 groups of test cases.Each test case adopts the notation of jN1mN2sN3, and for example J3M4S5 represents that this test case is the problem that contains 3 workpiece of 4 machinery requirement scheduling 5 stages.

The machine distribution table of table 5 test problem

Table 6 workpiece produces parameter list

Wherein, df is the factor at delivery date, characterizes the tightness at delivery date.MSET _kThe set of the contained machine of expression stage k.

The performance of genetic algorithms performance depends on the setting of algorithm parameter to a great extent, therefore need carry out performance evaluation to different parameter combinations, to determine the optimal algorithm parameter combinations.The SSGA parameter that the present invention considers has four, is respectively population size, crossover probability, variation probability and evolutionary generation.These four SSGA parameters are carried out full factorial design (full factor design) experiment, and each parameter is as a factor (factor), and (treatment) is as shown in table 7 for the level of each factor:

Table 7SSGA parameter factors and level

All parameter common properties have been given birth to 192 kinds of different arranging and have been adopted method of analysis of variance (ANalysis Of VAriance, ANOVA) the performance performance of the SSGA of analysis different parameters combination, thereby determine the optimal algorithm parameter combinations, all experiments are all carried out for 95% time in level of confidence.Different SSGA parameters as independent variable, target function value variable in response.Each SSGA is respectively moved 5 times under 18 test problems respectively.

Definition response variable (responsible variable, RV) be the target function value of SSGA with respect to the average behavior of reference value lifting number percent, computing formula is as follows:

$\mathrm{RV}=(\underset{i=1}{\overset{18}{\mathrm{\Σ}}}\frac{{\mathrm{SSGA}}_{\mathrm{ni}}-{\mathrm{Best}}_i}{{\mathrm{Best}}_i}\×100)/18---\left(18\right)$

SSGA wherein _NiIt is the target function value of finding the solution i test problem under the n group algorithm parameter; Best _iIt is the reference value of finding the solution the target function value of i test problem.The definition datum value is standard SSGA(ps=50, pc=0.8, pm=0.1, gm=500) target function value.As seen from formula (18), response variable is more little, and it is more excellent that SSGA separates performance.

Table 8 minimizes C _MaxANOVA table under the target

S=0.442242 R-Sq=95.70% R-Sq(adjusts)=93.92%

As can be seen from Table 6, all single-factors all are significant (P value≤0.05).As shown in Figure 5, along with the increase of ps, pm, gm, SSGA obtains optimal value in pc=0.6.Combinations of factors ps*pc as known from Table 6, ps*pm, ps*gm, there is conspicuousness in the reciprocation between pm*gm, therefore also needs between analysis factor reciprocation to the influence of response variable.As can be seen from Figure 6, the variation tendency of response variable is consistent with single-factor as the time spent under the double factor effect.Be example with ps*gm, when pm=0.18, ps=48, SSGA obtains optimal value.The analysis of other combinations of factors in like manner.

Comprehensive above the analysis minimizing C _MaxTarget under, the present invention is decided to be the parameter value of SSGA: population size ps=48, crossover probability pc=0.6, variation Probability p m=0.18, evolutionary generation gm=100.

In like manner, to minimize TWT when being target, his-and-hers watches 9, Fig. 7 and Fig. 8 can do similar analysis, and the value that draws parameter at last is population size ps=48, crossover probability pc=0.9, variation Probability p m=0.18, evolutionary generation gm=100.

Table 9 minimizes the ANOVA table under the TWT

S=0.739551 R-Sq=99.40% R-Sq(adjusts)=99.14%

After determining the SSGA algorithm parameter, need the validity of verification algorithm and analyze its efficient.The present invention will be from the validity of following two aspect verification algorithms: (1) carries out performance relatively with a plurality of rules of combination; (2) performance between the different coding mode relatively.

(1) with the comparison of rule of combination

In all rules of combination, 5 rules of combination that the present invention chooses the average behavior optimum as with the comparison other of SSGA.That chooses is regular as shown in table 10.Experimental result is shown in table 11 and table 12, and SSGA all has more excellent solution performance than other common combinations rules under two targets.Minimizing under the Cmax target, SSGA has on average promoted 19.5% than rule of combination; Minimizing under the TWT target, SSGA has on average promoted 64.0% than rule of combination.This shows, utilizes the validity of the mechanism of the different orderings of SSGA search, appointment and group batch principle combinations.

5 of control experiment rules under table 10 different target

Table 11 minimizes C _MaxThe performance of following SSGA and 5 more excellent rules of combination relatively

The performance that table 12 minimizes SSGA and 5 more excellent rules of combination under the TWT target relatively

(2) comparison of different coding mode

The solution performance of SSGA and Yang etc. are compared by the GA search groups method normally of stage coding, remember that its algorithm is GA_Yang.For not losing fairness, the group of GA_Yang is criticized the scheme that problem and Assignment Problems all adopt the present invention to propose.

GA_Yang makes T _iRepresent the extension of the chromosomal scheduling solution of i bar, F _iThe expression fitness function, computing formula is: F _i=max{T _i}-T _iThe actual emulation result shows, adopts the fitness function performance performance of GA_Yang definition unsatisfactory, therefore according to fitness function of the present invention GA_Yang is improved, and experimental result is shown in table 13 and table 14.Compare with the fitness function of GA_Yang, fitness function of the present invention makes the performance of finding the solution of SSGA on average promote 34.4% minimizing under the Cmax target, and on average promoted 78.4% under the TWT target minimizing, show that fitness function of the present invention is more suitable for solving this type of problem.Under Cmax and two targets of TWT, SSGA almost all is better than GA_Yang, is especially minimizing under the TWT target, and optimization rate is up to 48.0%; And minimizing under the Cmax target, optimization rate from 0.4% to 10.4% does not wait.

Table 13 minimizes C _MaxThe comparison of SSGA and GA_Yang under the target

Table 14 minimizes the comparison of SSGA and GA_Yang under the TWT target

For the influence test to SSGA of setup time and batch processor capacity, the present invention arranges batch processor capacity b and is respectively 2,3,4 and 5, setup time per is respectively and handles 25%, 50%, 75% and 125% of man-hour, analyzes the solution performance impact to SSGA under 18 groups of test problems.Be benchmark with b_size=2 and per=25%, Fig. 9～Figure 12 has drawn the ratio of algorithm performance under each parameter.From Fig. 9 and Figure 10 as can be known, by improving the capacity of batch processor, with respect to 11 times of the highest liftings of reference value, and the highlyest under the Cmax target only promote 1 times in the solution that minimizes SSGA under the TWT target.Therefore minimizing under the TWT target, can make the more excellent solution of the easier acquisition of SSGA by the capacity that improves batch processor.It can also be seen that from Figure 10 minimizing under the TWT target, along with the increase of problem scale, the capacity that improves batch processor can make the lifting ratio of algorithm performance descend; Under the Cmax target, separate performance boost and then show a kind of curve more stably.For different setup times, the solution performance change of SSGA also presents similar trend.Under the TWT target, the test problem scale is more big, and the mis-behave that the increase of setup time brings is more little; And under the Cmax target, no matter the scale of test problem, the solution performance performance of SSGA can't worsen rapidly because of the increase of setup time.

For the counting yield of algorithm, the present invention adopts 18 groups of identical test cases on different data scales the algorithm of SSGA and GA_Yang to be compared, and is minimizing the CPU time of having tested two kinds of algorithms under two targets of Cmax and TWT.

The comparison of the CPU time of table 15 SSGA and GA_Yang (unit millisecond)

As can be seen from Table 15, when solving identical test case, the SSGA algorithm is consuming time than GA_Yang, and this is because SSGA has bigger search volume than GA_Yang towards the coded system in stage towards the coded system of machine.Minimizing under Cmax and the TWT target, the solution performance of SSGA is compared GA_Yang and is had 5.2% and 16.5% lifting respectively.The test case j95m21s7 that SSGA finds the solution maximum-norm only needs 27s, can think that SSGA can try to achieve near-optimum solution in acceptable computation time.As can be seen from Figure 13, adopt the GA search groups method normally of SSGA or GA_Yang, CPU time presents the near-linear growth when the test case increase in size, the CPU time factor can not occur and increase and the situation of sharp increase according to scale, this shows that SSGA possesses the ability of handling fairly large scheduling problem.

Above-described instantiation is further to explain to of the present invention, and is not intended to limit the scope of the invention, and 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 (5)

1. have the multistage variation hybrid flow workshop dispatching method of batch processor, it is characterized in that: specifically comprise the steps:

The 1st step: define symbol variable:

Described entity is represented workpiece or the workpiece set of processing in discrete machine and the batch processor; For discrete machine, an entity is represented a workpiece; For batch processor, an entity is represented one batch;

The 2nd step: according to different regulation goals, adopt three sections coding descriptive model α | β | γ, wherein α represents machine environment, and β describes detailed characteristics and the constraint of workpiece, and γ is regulation goal; The multistage variation hybrid flow solve job shop scheduling problems model that will have batch processor is summarized as:

${\mathrm{HF}}_K,{\left({\mathrm{PM}}^{\left(k\right)}\right)}_{k=1}^K|r_{j,}{S}_{\mathrm{snd}},{\mathrm{batch}}^{\left(k^{\′}\right)}|C_{\max }---\left(1\right)$

${\mathrm{HF}}_K,{\left({\mathrm{PM}}^{\left(k\right)}\right)}_{k=1}^K|r_{j,}{S}_{\mathrm{snd}},{\mathrm{batch}}^{\left(k^{\′}\right)}|\mathrm{TWT}---\left(2\right)$

α part in formula (1) and the formula (2) is identical with beat portion, wherein HF _KExpression contains the hybrid flow workshop in K stage;

The parallel machine of representing the 1st stage to the K stage; r _jThe time of arrival of expression workpiece j; S _SndThe setup time that expression and order are irrelevant; Batch ^{(k ')}A certain stage k ' in the expression 1 to K is batch processor; Gamma portion in formula (1) and the formula (2) is inequality, the C in its Chinese style (1) _MaxExpression is target to minimize maximum completion date, and the TWT in the formula (2) represents that postponing summation with minimizing Weighted is target;

The 3rd step: problem constraint and the optimization aim of determining the scheduling problem model that the 2nd step set up;

The problem constraint

Constraint (3) expression workpiece j can only be arranged on the machine M at stage k;

Constraint (4) expression workpiece j can only belong to an entity b at stage k;

Constraint (5) expression workpiece j must be scheduled at stage k, and can only dispatch once;

Just can go into operation after constraint (6) the expression workpiece j arrival system, namely time of arrival r _jSmaller or equal to the current time

Constraint (7) the expression actual treatment T.T. of workpiece j on the machine m of stage k

Be no earlier than under it among entity b any one workpiece j at the processing T.T. of stage k tt _Jk

Constraint (8) expression is except the phase one, after workpiece j finishes processing of k previous stage

The latter half k+1 just can go into operation

The different workpieces j of the same entity b of constraint (9) expression and j ' are in the start time of stage k

Identical;

Constraint (10) expression workpiece j is at the completion date C of stage k _JkMore than or equal to time of arrival

Add total processing time tt _Jk

The same time t of constraint (11) expression machine can not process two different workpieces j and j ' simultaneously;

Constraint (12) represents that the entity number of each batch can not surpass the capacity C M of machine m _m

Determine that target of the present invention is for minimizing maximum completion date C _MaxOr minimizing Weighted postpones summation TWT:

Optimization aim

The 4th step: based on the problem model in the 2nd step, under the constraint in the 3rd step, adopt genetic algorithm to reach optimization aim;

At first, design chromosomal form: the chromosome in the genetic algorithm is designed to workpiece section, machine section and group batch section, assigning method, sort method and group in the corresponding process criticized method respectively, and three kinds of coding rules are set respectively, the chromosomal gene position of each section represent its call number of corresponding coding rule; Corresponding each workpiece of workpiece section chromosome is assigned to the rule of following on the corresponding machine, the rule that corresponding each the machine choice buffer zone workpiece of machine section chromosome is followed, the group batch corresponding batch processor of section is organized batch rule of following to the workpiece that is positioned at this batch processor buffer zone; In ordering, appointment and group batch method, adopt consistent encoding scheme; Workpiece section, machine section and the group batch corresponding code index sequential combination of section is in the same place, constitutes a chromosome of problem model;

Coding rule

The 5th step: the user arranges population quantity, generates chromosome at random according to the 4th chromosome form that goes on foot; The chromosome quantity that generates is identical with population quantity;

The 6th step: the reduction scheduling is separated, because can not directly obtain scheduling by chromosome separates, so needing decoding scheme that the chromosome that generates is reduced into scheduling separates, SSGA method of the present invention adopts the discrete events simulation method, each bar chromosome that the 5th step generated is decoded respectively, be reduced into actual scheduling solution to obtain target function value; Adopt the discrete events simulation method to the detailed process of a wherein chromosome decoding to be:

6.1 initial time t=0;

6.2 whether check that all workpiece all have been scheduled and all machines free time all, if then change 6.15, otherwise carry out 6.3;

6.3 whether check has the workpiece that is not scheduled to arrive first stage in the hybrid flow workshop of containing K stage, if then change 6.4, otherwise to change 6.6;

6.4 the workpiece that arrives is joined the buffer zone of assigning machine according to the contained appointment rule of this workpiece chromosome, changes 6.5;

6.5 deletion has arrived workpiece in the workpiece that never the is scheduled tabulation, changes 6.6;

6.6 scan all processing machines by platform, check whether be idle condition, in case scan idle machine then change 6.7, otherwise change 6.13;

6.7 whether what check 6.4 described appointment machines currently has a workpiece that machines, if have, workpiece is assigned the machine unloading from this, be added to by the chromosomal buffer zone of assigning determined next the scheduling machine of rule of this workpiece, obtain the completion date of this workpiece on this appointment machine simultaneously, change 6.8;

6.8 check the buffer zone of all machines, if all be empty, change 6.13, otherwise change 6.9;

6.9 check that all buffer zones not for whether empty machine is batch processor, if then change 6.10, otherwise change 6.11;

Criticize rule and the workpiece group of buffer zone criticized be entity 6.10 criticize the contained group of chromosome according to the group of machine, change 6.12;

6.11 each workpiece of buffer zone is formed an entity, changes 6.12;

6.12 dispatch all entities in this machine buffer zone according to the contained ordering rule of machine dyeing body, obtain each entity and on this machine, beginning processing constantly, change 6.13;

6.13 check whether all machines are finished a scanning, if then change 6.14, continue scanning otherwise change 6.6;

6.14 time stepping: current total activation time t=t+1, change 6.2;

6.15 finishing scheduling;

Adopt the method for step 6.1-6.15 to reduce each bar chromosome, obtain the scheduling solution of each chromosome reality in this chromosome in generation;

The 7th step: the chromosome after the reduction of the 6th step is selected operation: each chromosome in the traversal population, for chromosome i, i=1,2 ..., size is when objective function obj (i) is C _MaxThe time, obtain corresponding completion date, as objective function obj (i) when being TWT, obtain weighting and postpone summation;

According to fitness function calculate chromosomal just when:

$\mathrm{fit}\left(i\right)=\frac{1}{(\mathrm{obj}\left(i\right)+1)}---\left(15\right)$

Output just when the highest chromosome as the optimum solution in this chromosome in generation;

The roulette method is adopted in chromosomal selection, and per generation is selected X chromosome, and X is even number, and the selecteed probability of chromosome is:

$\mathrm{prob}\left(i\right)=\frac{\mathrm{fit}\left(i\right)}{\underset{i=1}{\overset{\mathrm{size}}{\mathrm{\Σ}}}\mathrm{fit}\left(i\right)}---\left(16\right)$

The 8th step: X the chromosome of selecting is carried out interlace operation in twos, and each bar chromosome only participates in an interlace operation, obtains X/2 to the filial generation after intersecting; When two chiasmas, need the chromosome of each section be intersected respectively; For every chromosome, the step of an interlace operation is as follows:

8.1: carry out interlace operation under the situation of certain crossover probability satisfying: the user arranges crossover probability, and crossover probability is between 0.05-0.9; Between 0-1, produce a random number, if random number then changes 8.2 less than crossover probability, otherwise do not carry out interlace operation;

8.2: the workpiece in a chromosome, machine, the group section of criticizing are selected two different positions respectively at random, obtain three gene blocks;

8.3: in workpiece, machine, the group section of criticizing, the gene block of choosing in two parent chromosomes of corresponding exchange respectively produces the filial generation after two intersections;

The 9th step: the user arranges the variation probability, the variation probability is between 0.01-0.18, each chromosome that the 7th step was selected is carried out mutation operation, concrete grammar is: produce a random number, when the random number that produces is carried out the single-point variation to the chromosomal every section chromosome of parent during less than the variation probability, specify a position and replace this locational gene at random, make new chromosome meet the coding rule of table 4;

The 10th step: judge whether to surpass maximum iteration time, if do not surpass, repeated for the 5th step to the 9th step, number of iterations of every repetition adds 1; If surpass maximum iteration time, finishing iteration then obtains the optimum solution in each generation, postpone summation according to each scheduling time or weighting for the optimum solution correspondence, and coding rule, determine corresponding scheduling strategy, realize having the multistage variation hybrid flow workshop scheduling of batch processor.

2. the multistage variation hybrid flow workshop dispatching method that has a batch processor according to claim 1 is characterized in that: be applicable to the production and manufacturing environment that possesses following feature simultaneously:

(1) the workpiece collection contains N workpiece, needs by the HFS in M stage is arranged;

(2) workpiece has different time of arrival and delivery date;

(3) there are many aniso-parallel machines in each stage, and wherein having and only have a stage is batch processor;

(4) each workpiece must pass through all stages in proper order;

(5) each workpiece is earlier through some discrete machine stages, and a plurality of workpiece compositions are a collection of to be processed simultaneously by batch processor, passes through the follow-up some discrete machine stage again, finishes processing tasks;

(6) volume of all workpiece equates, batch size only relevant with contained workpiece quantity, and be no more than both constant volumes of batch processor;

(7) before every machining arranged setup time, setup time is only relevant with workpiece;

(8) processing time of each batch equals the required long process time of single workpiece in this batch, and all workpiece in same batch have identical start time and concluding time;

(9) machine is available always;

(10) workpiece is disregarded in each stage inside and the transfer time between the stage;

(11) any workpiece synchronization is only by a machining;

(12) buffer size between the stage is not limit, and does not seize, and can not reentry.

3. the multistage variation hybrid flow workshop dispatching method that has a batch processor according to claim 1, it is characterized in that: maximum iteration time is arranged by the user, between 25 to 100.

4. the multistage variation hybrid flow workshop dispatching method that has a batch processor according to claim 1, it is characterized in that: population quantity size is the even number between the 5-50.

5. the multistage variation hybrid flow workshop dispatching method that has a batch processor according to claim 1 is characterized in that: described scheduling solution be each procedure processing of workpiece begin to process constantly and its machine of scheduling.

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