CN111563336A - Deadlock-free scheduling method of flexible manufacturing system based on improved genetic algorithm - Google Patents
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Abstract
The invention belongs to the technical field of production scheduling of flexible manufacturing systems, and particularly relates to a deadlock-free scheduling method of a flexible manufacturing system based on an improved genetic algorithm, which comprises the following specific steps: establishing a flexible manufacturing system Petri net model, determining genetic parameters, encoding and decoding, generating an initialization population, detecting and repairing, calculating processing time and fitness, judging whether a termination rule is met or not, carrying out genetic operation and outputting an optimal individual, adjusting all chromosomes into control feasible chromosomes by a two-step forward-looking method, and decoding the control feasible chromosomes into a deadlock-free scheduling sequence; the genetic algorithm is optimized and improved in the design process of the scheduling strategy; meanwhile, in the mutation process, the chromosome gene is divided into a path gene part and a process gene part, and the mutation operation is carried out on the two parts at the same time, and the mutation rates are the same, so that the operation steps are simple, the production efficiency is greatly improved, and the application is environment-friendly.
Description
The technical field is as follows:
the invention belongs to the technical field of production scheduling of a Flexible Manufacturing System (Flexible Manufacturing System), and particularly relates to a deadlock-free scheduling method of the Flexible Manufacturing System based on an improved genetic algorithm.
Background art:
flexible manufacturing plays a significant role in the pursuit of multi-variety, small-lot production today. In order to survive and develop, more and more modern enterprises are using flexible manufacturing as an effective means to increase their competitiveness. The Flexible Manufacturing System consists of a unified information control System, a material storage and transportation System and a group of digital control processing equipment, and is an automatic Manufacturing System (Flexible Manufacturing System) which can adapt to the continuous change of processing objects, and the English abbreviation is FMS. The flexible manufacturing system includes a set of in-order machines connected and integrated via a computer system with the machines responsible for handling and transporting. Raw materials and substitute processing parts are loaded and unloaded on the transmission system, the parts are transmitted to the next machine after being processed on one machine, each machine receives an operation instruction, required tools are automatically loaded and unloaded, and manual participation is not needed. The flexible manufacturing system has higher equipment utilization rate and high operation flexibility, and can reduce equipment investment. Flexible manufacturing systems have found wide application in the parts processing industry and in areas related to processing and assembly. The scheduling problem for flexible manufacturing systems can be divided into two sub-problems: machine selection problems and process sequencing problems. The two problems are complicated and complex, and the scheduling problem of the flexible manufacturing system is easy to cause the defects of high complexity, low reliability and the like. On the other hand, in flexible manufacturing systems where resources are highly shared, when various different types of workpieces enter the system and compete for limited resources, if there is a lack of an efficient scheduling and control method, deadlock can occur. Once a deadlock occurs, tasks in the system are blocked forever and cannot be continued. System deadlock is divided into local deadlock and global deadlock. If the local deadlock in the system cannot be processed in time, the local deadlock can be diffused to the whole system, so that the whole system is in a paralyzed state (becomes a global deadlock), and the automatic production cannot be carried out, thereby bringing irreparable loss to the system. In summary, deadlock-free scheduling requires comprehensive consideration of two problems, namely deadlock control and optimal scheduling, which are complex combinatorial optimization problems, namely, processing of a deadlock problem in a system and optimization of a system performance index.
Genetic Algorithm (Genetic Algorithm) follows the principle of survival, excellence and decline of the fittest, and is a kind of randomized search Algorithm which uses natural selection and natural Genetic mechanism in the biology world for reference. The genetic algorithm is a classic intelligent algorithm and is widely applied to the workshop scheduling problem. The Petri net is a graphical mathematical modeling tool for describing the state change of the system, and the structural and behavior characteristics of the described system can be revealed by analyzing a Petri net model. Based on Petri nets and genetic algorithms, many methods have been studied to solve the problem of deadlock free scheduling in manufacturing systems. For example, a deadlock free scheduling algorithm based on a Petri net and a genetic algorithm is proposed in a doctor's academic paper "deadlock free scheduling and control in an automatic manufacturing system" (Huang Zhong Hua, Shanghai university of transportation, 2007), and is applied to a buffer free single resource allocation system (i.e., a buffer free Jobshop system) and a multi-resource allocation system. The algorithm encodes a transition sequence in the Petri network, and introduces a repairing process of an infeasible solution in a chromosome decoding process: the initiation sequence of the transition in the chromosome is adjusted by utilizing an efficient deadlock detection algorithm, so that more transitions can be smoothly initiated, the quality of the chromosome in the population is improved, and the search efficiency is improved; for the solution which is still infeasible after the gene sequence is adjusted, the fitness of the solution is reduced by adding a penalty term so as to avoid the convergence of a scheduling algorithm on the infeasible solution. By using the method, a deadlock-free processing sequence can be obtained, and the system can be ensured to obtain the optimal or suboptimal performance index. In a thesis of a flexible manufacturing system deadlock-free genetic scheduling algorithm based on a Petri network (No. 1 in volume 27 of 1 control theory and application in 1 month 2010), a Petri network is utilized to carry out logic modeling on workpiece procedure constraint and resource allocation constraint of a flexible manufacturing system by taking the minimized maximum completion time as an optimization target, and an optimal Petri network activity controller is established to avoid deadlock of the system; then subjecting to living by genetic algorithmAnd the control system carries out scheduling, detects and repairs chromosomes to enable the chromosomes to meet the resource constraint and the control constraint of the controlled model, so that the chromosomes in the algorithm are guaranteed to correspond to the feasible scheduling of the system. The simulation result shows the feasibility and the effectiveness of the algorithm. Chinese patent 201610649102.5 discloses a flexible job shop scheduling system based on Petri net and improved genetic algorithm. The patent mainly examines the problem of minimizing the relationship between completion time and electricity cost of peak-to-valley electricity prices and indirect energy consumption. The system comprises an operation time selection module and a machine task allocation module, wherein the operation time selection module obtains a transition initiation time sequence F by establishing an energy time Petri network model and a time selection simulation algorithm TSSAsAnd transition processing sequence Ts(ii) a The machine task allocation module is used for simulating by improving a method of combining a genetic algorithm and a Petri network to find out the optimal transition processing sequence TsThe optimal or suboptimal solution of the flexible job shop scheduling TI-FJSP is obtained, the production plan is effectively optimized, the production mode with the lowest cost under the peak-valley electricity price is provided for enterprises, the production cost of the enterprises is reduced, the energy utilization rate is improved, and the maximization of the economic benefit of the enterprises is realized. However, in the prior art, a deadlock detection method with low efficiency is mostly adopted when deadlock is processed, so that deadlock of a repaired sequence can not be avoided in the operation process, and even if the repaired coding sequence is feasible, the repair method has certain limitation and is only specific to a specific system, such as a manufacturing system without central resources; for a flexible manufacturing system containing a central resource, the existing deadlock control algorithm cannot repair all infeasible coding sequences, so that the algorithm execution efficiency is reduced, even a local optimal value cannot be skipped, and the like, so that when the deadlock-free scheduling is performed on the flexible manufacturing system containing the central resource, a method capable of quickly finding a deadlock-free scheduling sequence which meets the production requirement and does not fall into the local optimal value is needed.
The invention content is as follows:
the invention aims to overcome the defects of the prior art, provides an optimized scheduling method capable of effectively avoiding deadlock in the production process aiming at a flexible manufacturing system containing a central resource, and can quickly find out a scheduling sequence meeting requirements, improve the scheduling speed and increase the production quantity.
In order to achieve the above object, the present invention relates to a deadlock free scheduling method for a flexible manufacturing system based on an improved genetic algorithm, which minimizes the completion time by considering deadlock free scheduling, and comprises the following specific steps:
the method comprises the following steps: establishing a Petri net model (N, M) of a flexible manufacturing system0) And its associated matrix a, and defines the elements as follows:
N＝(Psf∪P∪PRt, F) represents the structure of the model and is closely related to the system structure;
Psf＝{pis,pifis set of idle banks, where pisRepresenting an upload buffer, p, for storing type i workpiece blanksifI is more than or equal to 1 and less than or equal to m, and m represents the total type number of the workpieces;
P＝{pijis the library of operations, where pijRepresenting the jth operation process of the ith workpiece;
T＝{tijis a transition set, where tijIndicates the beginning of the jth operation, t, on the ith type of workpieceij+1Indicating the end of the jth operation of the ith workpiece; j is more than or equal to 1 and less than or equal to mi，miRepresenting the total operation number of the ith type of workpieces;
PR＝{rkis the set of resource pool, where rkRepresenting the kth machine, wherein k is more than or equal to 1 and less than or equal to n, and n represents the total number of machines;
M0：P∪PR"→ Z" is an initial flag indicating the number of workpieces or resources contained in each operation library or resource library of the system in the initial state, in other words, indicating the total number of workpieces to be processed and the maximum capacity of each machine, wherein Z is an integer set;
the incidence matrix A represents the complete logic relation of the Petri net, and A is a | T | × | P corresponding to the transition set and the library setsf∪P∪PRAn | order matrix, wherein | | | represents the number of elements contained in the set;
step two: determining genetic parameters including population size Unitnum, maximum iteration number Maxgen, cross factor Cross factor, variation factor mutationFactor and selection factor SelectFactor;
(1) population scale: i.e. the number of chromosomes in each generation of population; the population size will affect the final result of genetic optimization and the execution efficiency of the genetic algorithm; when population size is too small, genetic optimization is generally not too good; the probability that the genetic algorithm falls into the local optimal solution can be reduced by adopting a larger population scale, and the larger population scale means higher calculation complexity;
(2) maximum number of iterations: the method comprises the following steps that (1) in the whole scheduling process, a total population algebra generated through natural selection, intersection and variation represents that a genetic algorithm stops running after running to a specified evolution algebra, and the best individual in the current population is used as the optimal solution of the problem;
(3) cross-over factor: the cross factor controls the frequency of cross operation, larger cross factors can enhance the capability of genetic algorithm to open up a new search area, but the possibility that a high-performance mode is damaged is increased; on the contrary, if the cross factor is too low, the genetic algorithm search may be trapped in a dull state;
(4) variation factors: the mutation belongs to auxiliary search operation in a genetic algorithm, and the main purpose is to keep the diversity of the population; generally, the loss of important genes in a population can be prevented by low-frequency variation, and the genetic algorithm tends to be purely randomly searched by the high-frequency variation;
(5) selecting a factor: the selection factor determines how many excellent individuals are selected from the father generation and directly copied to the next generation group; the selection operation is also used to determine recombination or crossover individuals;
step three: coding and decoding, firstly, respectively numbering all workpieces to be processed and processing paths (because the research object is a flexible manufacturing system, the processing path of each type of workpiece can be provided with a plurality of pieces), representing the processing sequence by the appearance sequence of the workpiece serial numbers, and coding the problem solution, namely, the combination sequence of the path numbers and the workpiece numbers, which is called as a gene sequence; the gene sequence is formed by combining a path gene and an operation gene, the path gene is connected with the operation gene in sequence from front to back, the path gene represents path selection, and the total length of the path gene is the total number of workpieces; the operation gene represents the processing sequence of the workpieces, and the total length of the operation gene is the total number of working procedures required by processing all the workpieces; by the coding scheme, the reverse decoding can be directly carried out, namely, the sequence is directly decoded into a scheduling sequence meeting the operation constraint, and for the same type of workpieces, if the processing paths are different, the transitions obtained in the decoding process are also different;
step four: generating an initialization population which consists of chromosomes with fixed scales, wherein the specific scales are the determined population scales in the step two; checking whether each randomly generated chromosome meets the coding requirement of the step three, and if not, correcting; wherein gen represents the iteration number of the population, and gen-0 represents the 0 th generation of population, namely the initialization population;
step five: detecting and repairing, combining incidence matrix A and initial mark M0Detecting the performance condition of the chromosome, and performing deadlock avoidance control on the system by using a two-step forward-looking method in an optimal deadlock control strategy to ensure that the repaired gene sequence can meet control constraints and resource constraints;
step six: calculating the processing time and the fitness, wherein the calculation method of the processing time comprises the following steps: comparing the time for finishing the current operation step of the chromosome with the time for finishing the last operation step of the workpiece, wherein the larger time is the processing time when the operation step is operated; when the last step is calculated, the processing time required by the completion of the current scheduling sequence is obtained; the direct functional relationship between the fitness Adapt and the processing Time is as follows: adapt ═ (Maxspan-Time + r)/(Maxspan-Minspan + r), where Maxspan represents the maximum processing Time for all chromosomes of the population, Minspan represents the minimum processing Time, Time represents the processing Time, and r is a constant value;
step seven: judging whether a termination rule is met, namely gen > Maxgen; if yes, entering the ninth step, and ending the program; if not, executing the step eight;
step eight: genetic operation, after the genetic operation is finished, the current population is updated to a next generation new population, namely gen +1, and the new population is returned to the fifth step to carry out feasibility detection and repair operation on each chromosome in the new population; the genetic manipulation comprises:
(1) selecting operation: according to the fitness of individuals, selecting a certain number of individuals from the previous generation population according to the fitness according to a certain rule or algorithm, wherein the specific number is the population scale Unitnum multiplied by a selection factor SelectFactor, and completely copying genes of chromosomes into the next generation population;
(2) and (3) cross operation: the method comprises the following specific steps: randomly selecting one chromosome from the chromosomes selected in the step (1), randomly determining the length of a gene segment, and randomly selecting an operation gene segment of which the chromosome meets the length; secondly, deleting the genes which are the same as the selected genes from the front to the back of the operation gene segment; thirdly, moving the selected gene segment to the forefront end of the operation gene segment; fourthly, another individual is randomly selected from the chromosomes of the population of the previous generation, and the second step and the third step are repeated; fifthly, repeating the first step to the fourth step until a complete new generation of population is generated;
(3) mutation operation: randomly selecting a chromosome from the newly generated chromosomes in the step (2), randomly selecting any gene in the chromosome, and changing all genes from the gene to the last path gene into another selectable path if the gene is in the path genes; if the gene is in the operation gene, exchanging the gene to the last gene from the middle position; total variation factor — population scale Unitnum × total gene length × variation factor mutationactor;
step nine: outputting the optimal individual, outputting the optimal or suboptimal scheduling sequence meeting the requirements after the termination rule of the step seven is met, and finishing the optimal scheduling of the flexible manufacturing system.
In the third step related by the invention, m workpieces are required to be processed, and the m workpieces are numbered as q (q is 1,2, …, m); assuming that the workpiece q has two processing paths, which are respectively marked as 1 and 2, the 2 appearing in the path gene means that the workpiece q selects the 2 nd path for processing. The first m genes of the gene sequence are path genes, and the path selection of each workpiece is determined; removing a path gene, wherein an operation gene represents the processing operation of all workpieces in the whole processing process, the frequency of occurrence of the same workpiece serial number represents that the workpiece is in the operation process of the next step at present, and if the workpiece q has O (q) operation processes, the k-th occurrence of the same number q in the operation gene (k is more than or equal to 0 and less than or equal to O (q)) represents that the workpiece q is subjected to the k-th process.
The concrete operation of the step five related by the invention is as follows:
(1) first transition t from operator gene1At the beginning, check t1At the current state M1Whether or not lower is enabled, and if not, slave ranks at t1One of the later enabled transitions is arbitrarily selected to be placed at t1A front face; if t is1At M1If the next step is enabled, the next step is carried out to judge whether the transition can be initiated;
(2) determining an Enable transition t1If the initiation is possible, a two-step forward looking method is adopted, and M is firstly allowed to be started1Initiation of t1I.e. M1[t1>M2To obtain a new mark M2Judgment of M2Whether it is a deadlock flag; if so, M is disabled1Initiated while slave ranks at t1One of the later enabled transitions is arbitrarily selected to be placed at t1A front face; otherwise, M is initiated2Any of the following enable transitions t2I.e. M2[t2>M3Get another new mark M3(ii) a If M is3If the deadlock identifier is detected, M is prohibited1Initiated while slave ranks at t1One of the later enabled transitions is arbitrarily selected to be placed at t1A front face; otherwise, t1At M1The following is enabled, can be initiated; any gene sequence can be repaired and then decoded into a viable scheduling sequence according to the methods described above.
Compared with the prior art, the invention has the following beneficial effects: the method is characterized in that a dead lock control strategy is embedded into a scheduling strategy based on a Petri network model of a flexible manufacturing system, and a new non-dead lock scheduling strategy is provided; all chromosomes are adjusted into feasible control chromosomes and decoded into deadlock-free scheduling sequences by a two-step forward-looking method, so that the flexible manufacturing system is guaranteed to perform optimized scheduling on the production process on the premise of deadlock avoidance, and the scheduling sequences meeting requirements are quickly found out; the invention optimizes and improves the genetic algorithm in the design process of the scheduling strategy, and because the coding scheme of the problem is related to path selection, in the coding process of the chromosome, the invention not only has the coding for the path selection of the workpiece, but also has the coding for the processing steps of the workpiece according to the determined path, so that even the same workpiece can cause different processing steps due to the selection of different processing paths in the coding process of the chromosome, and further the coding length of the chromosome is different; however, the number of processing steps of each workpiece is determined, and the number of times of occurrence of each workpiece number is determined corresponding to the chromosome code, so that in the crossing process of genetic operation, two parents are not selected to carry out crossing of the chromosome code, but one parent solution is randomly selected, and random crossing operation is carried out in the code.
The advantages of the operation of the invention are: because the chromosomes are crossed, the process constraint of the newly generated chromosomes is always satisfied; meanwhile, in the variation process, as the chromosome gene is divided into a path gene part and a process gene part, the variation operation is simultaneously carried out on the two parts, and the variation rates are the same, so that the operation steps are simple, the production efficiency is greatly improved, and the application is environment-friendly.
Description of the drawings:
FIG. 1 is a schematic diagram of a deadlock-free scheduling process of a flexible manufacturing system based on a genetic algorithm according to the present invention.
Fig. 2 is a Petri net model of a cutter cutting production unit in example 1 to which the present invention relates.
FIG. 3 is a chromosome coding diagram of the genetic algorithm in example 1 according to the present invention.
Fig. 4 is an interface diagram of an optimal scheduling result obtained by scheduling simulation of the cutter cutting production unit according to embodiment 1 of the present invention.
The specific implementation mode is as follows:
the invention is described in detail below with reference to specific embodiments and with reference to the accompanying drawings.
Example 1:
the embodiment is an application of a deadlock-free scheduling method of a flexible manufacturing system based on an improved genetic algorithm in a cutter cutting production unit. The cutter cutting production unit is used for producing two types of cutters by utilizing a cutting machine tool, a carrying robot and a grinding machine tool; different cutter processing sequencing codes correspond to different maximum completion times, the optimization goal of the scheduling strategy is to realize the rapid optimization of the maximum completion time based on an improved genetic algorithm, and the specific steps are as follows:
the method comprises the following steps: establishing a Petri net model of the cutter cutting production unit: the cutter cutting production unit manufacturing system consists of 3 machines, namely a cutting machine tool, a carrying robot and a grinding machine tool (r is used respectively1、r2、r3Expressed) composition; the system can process two types of cutters, wherein the operation sequence of the first type of cutter is cutting, carrying and polishing; the second type of cutter has the operation sequence of grinding, carrying and cutting; 3 kinds of machines r1，r2，r3The processing capacities of the two types of the cutting tools are respectively 2,1 and 2, and the number of the two types of the cutting tools required to be processed is 2; and each type of cutter blank product enters the production line through the uploading buffer area, is cut and polished, and leaves through the unloading buffer area after the processing is finished. The corresponding Petri net model of the system is shown in figure 2,
Psf＝{pis,pifi 1,2 is set of idle banks, where pisShowing an upload buffer, p, for storing tool blanks of type iifIndicating a relief buffer for storing the i-th tool product, pisThe number of the medium black points represents the number of blank products to be processed of the workpiece (when the number is larger, the black points are replaced by numbers);
P＝{piji is 1, 2; j ═ 1,2,3} is set of operation libraries, where pijIndicating type i toolJ (th) operation of pijThe outer number indicates the time required for this operation for the same type of tool;
T＝{tiji is 1, 2; j ═ 1,2,3} is a transition set, where tijIndicates the start of the jth operation of the ith tool, tij+1Indicating the end of the jth operation of the ith workpiece; j is more than or equal to 1 and less than or equal to 3;
PR＝{rkk is 1,2,3, where r is the set of resource poolkDenotes the k-th machine, rkThe number of medium black dots represents the maximum capacity of this type of machine (when the capacity is large, the black dots are replaced by numbers);
in particular, t11Indicating that the first type of blank product enters the cutting machine from the uploading buffer zone to be cut, t12Indicating that the cutting operation of the blank product is finished and then the blank product is carried by a robot; p is a radical of11Showing a first operating process of a first type of tool, cutting, by a cutting machine r1Is completed (by the slave r1To t11、t11To p11Two arc representations of); the operation releasing machine r after cutting1(from p)11To t12、t12To r1Two arcs of (a), p11The number 40 marked next indicates that the time required for this operation is 40 time units; p in FIG. 21s，p2sThe two black dots represent 2 blanks respectively1，r2，r3Black dots in (1) represent r1，r2，r3The processing capacity of (a) is 2,1, 2; the other operation libraries have no black points, which indicate that other operations are not started in the initial state, and the number of the black points forms the initial identifier M0＝(p1s,p11,p12,p13,p1f,p2s,p21,p22,p23,p2f,r1,r2,r3) (2,0,0,0,0,2, 1, 2). The specific meaning of each symbol in fig. 2 is shown in table 1, wherein the number shown next to each library (shown by a circle) is the operation time required for the corresponding operation.
TABLE 1 meaning of the library and transition in the Petri Net model of the tool cutting production Unit
The Petri net shown in FIG. 2 can also be represented by the following correlation matrix A:
the detection and repair process of the chromosome in the later step is based on the matrix A;
step two: determining genetic parameters including population size Unitnum, maximum iteration number Maxgen, cross factor Cross factor, variation factor mutationFactor and selection factor SelectFactor;
population scale: i.e. the number of chromosomes in each generation of population; the population size will affect the final result of genetic optimization and the execution efficiency of the genetic algorithm; when population size is too small, genetic optimization is generally not too good; the probability that the genetic algorithm falls into the local optimal solution can be reduced by adopting a larger population scale, and the larger population scale means higher calculation complexity;
maximum number of iterations: the method comprises the following steps that (1) in the whole scheduling process, a total population algebra generated through natural selection, intersection and variation represents that a genetic algorithm stops running after running to a specified evolution algebra, and the best individual in the current population is used as the optimal solution of the problem;
cross-over factor: the cross factor controls the frequency of cross operation, larger cross factors can enhance the capability of genetic algorithm to open up a new search area, but the possibility that a high-performance mode is damaged is increased; on the contrary, if the cross factor is too low, the genetic algorithm search may be trapped in a dull state;
variation factors: the mutation belongs to auxiliary search operation in a genetic algorithm, and the main purpose is to keep the diversity of the population; generally, the loss of important genes in a population can be prevented by low-frequency variation, and the genetic algorithm tends to be purely randomly searched by the high-frequency variation;
selecting a factor: the selection factor determines how many excellent individuals are selected from the father generation and directly copied to the next generation group; the selection operation is also used to determine recombination or crossover individuals;
this example determines the genetic parameters as follows: the population size unitenum is 100, the maximum iteration number Maxgen is 2000, the cross factor crossfactor is 0.95, the variation factor mutatiofector is 0.05, and the selection factor SelectFactor is 0.95;
step three: coding and decoding, wherein the coding of the problem solution is a combined sequence of a path number and a workpiece number, all processing paths and tools to be processed are numbered, and the processing path of each type of tool in the system of the embodiment is only one, so that only 1 is used for representing path selection in the path coding; the system has two types of cutters to be machined, each type of cutter has 2 blank products to be machined, so 1 and 2 are used for representing 2 blank products of a first type of cutter, and 3 and 4 are used for representing 2 blank products of a second type of cutter; because the sequence of the workpiece numbers represents the processing operation sequence, and each cutter has 4 operation processes (including unloading finished products in the unloading area), each number in the operation gene sequence needs to appear 4 times, which indicates that all workpieces are processed by respective processing steps; according to the system shown in fig. 2, one possible code is pi ═ (1,1,1,1,1,2,3,4,1,3,1,2,1,4,3,2,4,3,4, 2); the code interpretation is shown in FIG. 3, where the first four 1 s are pathway genes, indicating that all four workpieces selected the first pathway, where J1Denotes tools of the first kind, J2Denotes a second type of tool, q1And q is2Respectively represents J1Two blanks (numbered 1 and 2) of a cutter-like tool, q3And q is4Respectively represents J2Two blanks (numbered 3 and 4) of the cutter-like tool; the last 12 digits constitute the operator gene, the first 1 occurring in the operator gene representing q1The first 2 denotes q2The first operation of (1), the second 1 represents q1The first 3 denotes q3The first operation is repeated in this way to obtain a gene sequence pi;
the decoding process is as follows: firstly, the serial number workpiece is searchedThe path gene of (2) determines which processing path in the Petri net is selected by the workpiece, and then further determines that the workpiece is processed in the next step according to the number of times of occurrence of the number. According to the Petri network model shown in FIG. 2, a one-to-one relationship exists between each operation and the corresponding pre-transition of the operation (such as p)11The corresponding pre-transition is t11) Therefore, according to the rule, the coding sequence can be finally converted into a transition sequence. For example, in the above pi, the first four 1 are pathway genes, and the rest are operator genes; four 1 s in the path gene means that four blanks each select the corresponding path No. 1 (the only path in this embodiment). The following operator genes were decoded as follows: the first occurrence of 1 means q1The first operation of (1), i.e. t11Initiating; 2 immediately following means q2The first operation of (1), i.e. t11Initiation, the first 3 means q3The first operation of (1), i.e. t21Initiation, the last 1 represents q1The fourth step of operation, i.e. t14Triggering, and so on, decoding the operation sequence in pi into a transition sequence of α -t11t11t21t21t12t22t13t1 2t14t22t23t13t23t24t24t14. The coding sequence is a scheduling sequence satisfying operation constraint and resource constraint;
step four: generating an initialization population, randomly generating 100 chromosomes with the length of 20 by using C # software, and checking whether each randomly generated chromosome meets the coding requirement of the step three or not, and if not, correcting;
step five: chromosome detection and repair, wherein the detection and repair are performed on the transition sequence obtained after the gene sequence is decoded, and whether each transition in the transition sequence can be triggered in the current state needs to be checked. If each transition can be triggered, the gene sequence is a scheduling sequence without deadlock, and a scheduling optimization result is obtained after decoding. The specific detection and repair process of this embodiment is as follows: selectingA chromosome, e.g., (1,1,1,1,2, 3,4,1,3,1,2,1,4,3,2,4,3, 4) with a corresponding transition sequence of α ═ t (t), and a corresponding cell, e.g., a chromosome, with a corresponding transition sequence of pi11t11t21t21t12t22t13t12t14t22t23t13t23t24t24t14Is a transition sequence (N, M) satisfying both operational and resource constraints in the system shown in FIG. 20) Is M0＝(p1s,p11,p12,p13,p1f,p2s,p21,p22,p23,p2f,r1,r2,r3) (2,0,0,0,0,2, 1,2) by adding to M0Lower initiating transition sequence t11t11t21Obtaining μm0[t11t11t21>Μ1Wherein M is1(0,2,0,0,0,1,1,0,0,0,0,1, 1); at M1Lower, t21Can be initiated. Suppose M1[t21>Μ2Wherein M is2(0,2,0,0,0,0,2,0,0,0,0,1, 0); at M2Lower, t12Is triggerable, but if t is triggered12A deadlock identification M is obtained3That is (0,1,1,0,0,0,2,0,0,0,1,0,0), we know t using the two-step look-ahead detection algorithm21In the mark M1The following cannot be initiated. At M1Lower, t12And t22Can be initiated, and t12Is arranged at t22So will t12Move to t21The repaired transition sequence is α' ═ t11t11t2 1t12t21t22t13t12t14t22t23t13t23t24t24t14. Memory M1[t12>M4，M4(0,1,1,0,0,1,1,0,0,0,1,0, 1). At M4Next continued initiation of t21If so, a deadlock flag is raised, so t will be13Move to t21The above results in a new transition sequence α ″＝t11t1 1t21t12t13t21t22t12t14t22t23t13t23t24t24t14. Continuing the analysis, finally obtaining feasible chromosome pi' ═ (1,1,1,1,1,2,3,1,1, 4,3,3,2,2,4,4,3,4, 2);
step six: calculating the processing time and fitness, in this embodiment, the processing time is calculated by demonstrating chromosome pi ″ (1,1,1,1, 3,4,3,3,1,3,2,1,2,1,2,4,2,4,4), and the scheduling sequence corresponding to pi ″ is t ″11t21t21t22t23t12t24t1 1t13t12t14t13t22t14t23t24The processing time calculation process is as follows: t is t11First initiation, representing q1Starting to carry out the first step operation; t is t21Initiation, denotes q3Starting the first operation, since the first operation of the two types of blanks uses unused machines, the two operations are carried out in parallel, both starting from zero time; 2 nd t21Initiation, denotes q4The first operation is started because of the machine r to which it applies3Has a margin, so the 2 nd t21The processing is started from zero time; t is t22The moment of initiation is obviously at the first t21After the completion, the operation is started because the first operation of the second type workpiece requires 35 (time unit) and the machine r required for the step is used2At idle time, so first t22Has an initiation time of 35; next t23The same discussion applies to the initiation of22After the corresponding operation is finished, 35+21 is 56; immediately after, t12Must be initiated at t11After that and with the need for machine r2Is idle, so t12Max {40, 56} ═ 56; t is t24Is initiated at t23After that and without the need for machinery, so t24Is 56+33 ═ 89; second t11Is indicative of q2Start the first operationBecause it requires the use of a machine r1There is a margin, so this t11The start time of (2) is 0 time; t is t13Is required to be initiated at the front t12After completion, and machine r is required3With idle (since this step operates using a machine r3) Therefore t is13Max {56+55, 35} ═ 111; second t12Is also required at the second t11Initiation and first t13After the initiation, the initiation time is max {40, 111} ═ 111; for the same reason t14Is 111+50 ═ 161; second t13Should be at the second t12Thereafter and machine r used therewith3The trigger time is max {111+55,111+50} -, 166, since there is a free time; next, a second t22Should be at the second t21Then and the machine r2When there is a vacancy, the triggering time is max {35,166} -, 166; second t14Is max {166+50,161} ═ 216; second t23So that the second t is 187+ 166+2124Since the triggering time of (1) is 187+33 ═ 220, the processing time after the completion of the scheduling sequence corresponding to the chromosome is max {216, 220} -, 220;
the fitness function is calculated as follows: taking chromosome (1,1,1,1,2,1,4, 4,3,2,4,1,2,3,3,3,2) with corresponding scheduling sequence t as 0.2, wherein r is equal to11t11t21t12t13t22t23t21t12t24t14t13t22t23t24t14The processing completion Time is 225 (Time: 225). In this generation population, Maxspan 277 and Minspan 220, so the fitness value of the chromosome is Adapt ═ (Maxspan-Time + r)/(Maxspan-Minspan + r) ═ 0.912 (277-;
step seven: judging whether a termination rule is satisfied, wherein the termination rule of the embodiment is whether to iterate to the 2000 th step; if yes, entering the ninth step, and ending the program; if not, executing the step eight; in the sixth step, the chromosome pi' is the result of the iteration to 2000 th output;
step eight: genetic operation, wherein the biological genetic algorithm is to transmit the information of the current parent population to the next generation (filial generation) mainly through three processes of selection, crossing and mutation, and correspondingly, the genetic algorithm is to update chromosomes by utilizing the selection operation, the crossing operation and the mutation operation; the algorithm selects any one of high-quality individuals, crossed parent chromosomes and random variation individuals in the population according to the fitness function values of the chromosomes. The specific genetic manipulations of this example are as follows:
(1) selecting operation: each time, selecting 100 × 0.95 ═ 95 individuals from the previous generation to copy directly into the next generation population;
(2) and (3) cross operation: and (3) performing intersection operation on the chromosome pi ═ in the step five (1,1,1,1,1,2,3,4,1,3,1,2,1,4,3,2,4,3,4,2), wherein the first four 1 represent the selection of paths, so that the selection intersection point starts from the fifth 1. First, the first 3 is selected as a cross point, the cross length is 4, and three numbers are counted from the 3 to the right, so that a number segment 3413 with the length of 4 is obtained; then advancing the number to 1 of 5 th to obtain new chromosome pi1＝(1,1,1,1,3,4,1,3,1,2,1,2,1,4,3,2,4,3,4,2)；
(3) Mutation operation in this example, each time 100 × 16 × 0.05.05-80 chromosomes are selected for mutation, there is no selection path in this example, so the mutation operation is performed only in the operation gene2＝(1,1,1,1,1,2,4,3,1,3,1,2,1,4,3,2,4,3,4,2)；
Through the five-step inspection, pi1And pi2All do not satisfy control constraints;
step nine: and outputting the optimal individuals when the step 2000 is iterated, and outputting the optimal individuals (1,1,1,1,1,3,4,3,3,1,3,2,1,2,1,2,4,2,4,4) when the step 2000 is iterated, wherein the optimal time is 220.
The manufacturing system shown in fig. 4 performs a scheduling result simulation. The simulation platform was based on the 1.90GHz InterCorei 3 PC, Visual Studio 2013. The simulation parameters of the embodiment are set as follows: terminate and enterThe number of generations is 2000, the number of individuals included in the population is 100, and the shortest processing time, which is the optimal scheduling result obtained in this embodiment, is 220. The optimal scheduling sequence obtained by other algorithms (K.Y.Xing, L.B.Han, M.C.Zhou, F.Wang, Deadlock-free genetic scheduling algorithm for automatic manufacturing systems based on delay control policy, IEEETrans.Syst., Man, Cybern, B.Cybern,42(3): 603) 615, 2012;) is t21t1 1t21t22t23t12t11t13t22t14t24t23t12t13t24t14The optimum time is 237.
Claims (3)
1. A deadlock-free scheduling method of a flexible manufacturing system based on an improved genetic algorithm is characterized by comprising the following specific steps:
the method comprises the following steps: establishing a Petri net model (N, M) of a flexible manufacturing system0) And its associated matrix a, and defines the elements as follows:
N＝(Psf∪P∪PRt, F) represents the structure of the model and is closely related to the system structure;
Psf＝{pis,pifis set of idle banks, where pisRepresenting an upload buffer, p, for storing type i workpiece blanksifI is more than or equal to 1 and less than or equal to m, and m represents the total type number of the workpieces;
P＝{pijis the library of operations, where pijRepresenting the jth operation process of the ith workpiece;
T＝{tijis a transition set, where tijIndicates the beginning of the jth operation, t, on the ith type of workpieceij+1Indicating the end of the jth operation of the ith workpiece; j is more than or equal to 1 and less than or equal to mi，miRepresenting the total operation number of the ith type of workpieces;
PR＝{rkis the set of resource pool, where rkRepresenting the kth machine, wherein k is more than or equal to 1 and less than or equal to n, and n represents the total number of machines;
M0：P∪PR"→ Z" is an initial flag indicating the number of workpieces or resources contained in each operation library or resource library of the system in the initial state, in other words, indicating the total number of workpieces to be processed and the maximum capacity of each machine, wherein Z is an integer set;
the incidence matrix A represents the complete logic relation of the Petri net, and A is a | T | × | P corresponding to the transition set and the library setsf∪P∪PRAn | order matrix, wherein | | | represents the number of elements contained in the set;
step two: determining genetic parameters including population scale, maximum iteration times, cross factors, variation factors and selection factors;
step three: coding and decoding, firstly, respectively numbering all workpieces to be processed and processing paths, representing the processing sequence by the appearance sequence of the workpiece serial numbers, and coding the problem solution, namely a combined sequence of the path numbers and the workpiece numbers, which is called a gene sequence; the gene sequence is formed by combining a path gene and an operation gene, the path gene is connected with the operation gene in sequence from front to back, the path gene represents path selection, and the total length of the path gene is the total number of workpieces; the operation gene represents the processing sequence of the workpieces, and the total length of the operation gene is the total number of working procedures required by processing all the workpieces; by the coding scheme, the reverse decoding can be directly carried out, namely, the sequence is directly decoded into a scheduling sequence meeting the operation constraint, and for the same type of workpieces, if the processing paths are different, the transitions obtained in the decoding process are also different;
step four: generating an initialization population which consists of chromosomes with fixed scales, wherein the specific scales are the determined population scales in the step two; checking whether each randomly generated chromosome meets the coding requirement of the step three, and if not, correcting; wherein gen represents the iteration number of the population, and gen-0 represents the 0 th generation of population, namely the initialization population;
step five: detection and repair, binding AssociationMatrix A and initial identity M0Detecting the performance condition of the chromosome, and performing deadlock avoidance control on the system by using a two-step forward-looking method in an optimal deadlock control strategy to ensure that the repaired gene sequence can meet control constraints and resource constraints;
step six: calculating the processing time and the fitness, wherein the calculation method of the processing time comprises the following steps: comparing the time for finishing the current operation step of the chromosome with the time for finishing the last operation step of the workpiece, wherein the larger time is the processing time when the operation step is operated; when the last step is calculated, the processing time required by the completion of the current scheduling sequence is obtained; the direct functional relationship between the fitness Adapt and the processing Time is as follows: adapt ═ (Maxspan-Time + r)/(Maxspan-Minspan + r), where Maxspan represents the maximum processing Time for all chromosomes of the population, Minspan represents the minimum processing Time, Time represents the processing Time, and r is a constant value;
step seven: judging whether a termination rule is met, namely gen > Maxgen; if yes, entering the ninth step, and ending the program; if not, executing the step eight;
step eight: genetic operation, after the genetic operation is finished, the current population is updated to a next generation new population, namely gen +1, and the new population is returned to the fifth step to carry out feasibility detection and repair operation on each chromosome in the new population; the genetic manipulation comprises:
(1) selecting operation: according to the individual fitness, selecting a certain number of individuals from the previous generation population according to the fitness according to a certain rule or algorithm, wherein the specific number is the population size multiplied by a selection factor, and completely copying the genes of the chromosomes into the next generation population;
(2) and (3) cross operation: the method comprises the following specific steps: randomly selecting one chromosome from the chromosomes selected in the step (1), randomly determining the length of a gene segment, and randomly selecting an operation gene segment of which the chromosome meets the length; secondly, deleting the genes which are the same as the selected genes from the front to the back of the operation gene segment; thirdly, moving the selected gene segment to the forefront end of the operation gene segment; fourthly, another individual is randomly selected from the chromosomes of the population of the previous generation, and the second step and the third step are repeated; fifthly, repeating the first step to the fourth step until a complete new generation of population is generated;
(3) mutation operation: randomly selecting a chromosome from the newly generated chromosomes in the step (2), randomly selecting any gene in the chromosome, and changing all genes from the gene to the last path gene into another selectable path if the gene is in the path genes; if the gene is in the operation gene, exchanging the gene to the last gene from the middle position; total variation factor — population scale Unitnum × total gene length × variation factor mutationactor;
step nine: outputting the optimal individual, outputting the optimal or suboptimal scheduling sequence meeting the requirements after the termination rule of the step seven is met, and finishing the optimal scheduling of the flexible manufacturing system.
2. The deadlock free scheduling method for the flexible manufacturing system based on the improved genetic algorithm as claimed in claim 1, wherein in step three, m workpieces are set to be processed, and m workpieces are numbered as q (q is 1,2, …, m); assuming that the workpiece q has two processing paths, which are respectively marked as 1 and 2, the 2 appearing in the path gene means that the workpiece q selects the 2 nd path for processing. The first m genes of the gene sequence are path genes, and the path selection of each workpiece is determined; removing a path gene, wherein an operation gene represents the processing operation of all workpieces in the whole processing process, the frequency of occurrence of the same workpiece serial number represents that the workpiece is in the operation process of the next step at present, and if the workpiece q has O (q) operation processes, the k-th occurrence of the same number q in the operation gene (k is more than or equal to 0 and less than or equal to O (q)) represents that the workpiece q is subjected to the k-th process.
3. The deadlock free scheduling method of the flexible manufacturing system based on the improved genetic algorithm as claimed in claim 1, characterized in that the specific operation of the fifth step is as follows:
(1) first transition t from operator gene1At the beginning, check t1At the current state M1Whether or not lower is enabled, and if not, slave ranks at t1Rear, and enabledOne of the transitions is arbitrarily selected to be placed at t1A front face; if t is1At M1If the next step is enabled, the next step is carried out to judge whether the transition can be initiated;
(2) determining an Enable transition t1If the initiation is possible, a two-step forward looking method is adopted, and M is firstly allowed to be started1Initiation of t1I.e. M1[t1>M2To obtain a new mark M2Judgment of M2Whether it is a deadlock flag; if so, M is disabled1Initiated while slave ranks at t1One of the later enabled transitions is arbitrarily selected to be placed at t1A front face; otherwise, M is initiated2Any of the following enable transitions t2I.e. M2[t2>M3Get another new mark M3(ii) a If M is3If the deadlock identifier is detected, M is prohibited1Initiated while slave ranks at t1One of the later enabled transitions is arbitrarily selected to be placed at t1A front face; otherwise, t1At M1The following is enabled, can be initiated; any gene sequence can be repaired and then decoded into a viable scheduling sequence according to the methods described above.
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| CN117314078B (en) * | 2023-09-26 | 2024-05-14 | 南通大学 | Deadlock-free scheduling method of flexible manufacturing system based on Petri network and neural network |
| CN117852825A (en) * | 2024-01-10 | 2024-04-09 | 南通大学 | Deadlock-free scheduling method of flexible manufacturing system containing central resources based on deep learning |
| CN117852825B (en) * | 2024-01-10 | 2024-09-03 | 南通大学 | Deadlock-free scheduling method of flexible manufacturing system containing central resources based on deep learning |
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