CN110570134A - Scheduling method for solving transportation time of flexible workshop belt through improved cultural genetic algorithm - Google Patents
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Abstract
the invention relates to a scheduling method for solving the problem of flexible workshop belt transportation time by using an improved cultural genetic algorithm, which can effectively solve a flexible job workshop scheduling scheme with transportation time; the technical scheme for solving the problem is that the method comprises the following steps: the method comprises the following steps: setting parameters; step two: generating an initial population by three initialization methods; step three: calculating an optimal solution; step four: a crossover operator; step five: forming a new population; step six: calculating the maximum completion time of the population individuals; step seven: judging whether the algorithm is terminated; the coding mode of the invention is simple and easy to realize, the algorithm operation efficiency is improved, and the search efficiency is improved.
Description
Technical Field
The invention relates to the technical field of flexible job shop scheduling, in particular to a scheduling method for solving the problem of transportation time of a flexible job shop by using an improved cultural genetic algorithm.
Background
In recent years, more and more efficient intelligent automatic production modes are receiving wide attention of society. The product is developed towards more individuation and customization, and the production organization mode of the assembly line is more flexible, so that the scheduling problem becomes more complex. The Flexible Job Shop Scheduling Problem (FJSP) belongs to the NP-hard combination optimization Problem and is an important expansion of the Job Shop Scheduling Problem (JSP). In the JSP problem, the working procedures of the workpiece correspond to the machines one to one, which does not conform to the actual production status, while in the FJSP problem, the processing machine of each working procedure is not unique, and the processing time varies with the machine. On the basis, the FJSP problem with the transport time can take the transport situation of the workpieces among different processing machines into consideration, so that the solution space of the problem is larger, the constraint is more, and the problem is more difficult to solve, but if the objective conditions are ignored, the processing plan is easy to be violated with the actual production. Therefore, the scheduling result obtained by solving the FJSP problem with the transportation time is closer to the actual situation, and the requirement of actual production is met, so that the actual production is guided more scientifically.
the existing method for solving the FJSP problem comprises a group search algorithm and a local search algorithm based on meta-heuristic, but the algorithms have defects and shortcomings to a certain extent, the group search algorithm is low in search precision and low in convergence speed; the local search algorithm has a small search range and is easy to fall into a local optimal solution.
Therefore, the invention provides an improved cultural genetic algorithm for solving the scheduling method of the transportation time of the flexible workshop belt to solve the problem.
Disclosure of Invention
In view of the above situation, and in order to overcome the defects of the prior art, the invention aims to provide an improved cultural genetic algorithm which can effectively solve the scheduling scheme of the flexible job shop with transportation time.
The invention comprises the following steps:
The method comprises the following steps: setting parameters, including: population size NpopFull random initialization probability PApriority minimum machining time initialization probability PBPriority maximum remaining machining time initialization probability PCNumber of iterations NiterOptimal solution retention algebra Nrecross probability PxovrProbability of mutation PmutrInitial temperature T0End temperature TfNumber of disturbances LkTemperature attenuation coefficient alpha, adjustment coefficient t, elite library size NE；
Wherein, PA+PB+PC＝1，0<PA<1，0<PB<1，0<PC<1，0<Pxovr<1，0<Pmutr<1，0<α<1；
The termination conditions of the culture genetic algorithm are as follows: if the iteration number N is not reached yetiterthen, the current optimal solution remains NreThe generation does not change, and the algorithm is terminated; otherwise, running until the iteration times;
Step two: a two-section real number coding mode is adopted by combining the scheduling problem characteristic of the flexible job shop; generating an initial population by three initialization methods, wherein each individual in the population represents a group of flexible job shop scheduling schemes with transportation time;
step three: calculating the maximum completion time of all individuals through a target function, and recording the individual with the minimum maximum completion time as the current optimal solution;
Step four: picking N according to tournament selection method based on individual maximum completion timepopThe individuals are used as parents and the cross probability P is usedxovrPerforming a global crossover operator to generate NpopA plurality of children;
Step five: performing local search operation on the filial generation in sequenceAnd obtaining NpopMixing the obtained non-inferior individuals with parent individuals, and selecting N according to championship selection methodpopindividuals form next generation populations, a local search method is designed based on a simulated annealing algorithm, and the situation that a local optimal solution is trapped during searching can be effectively avoided; adding mutation operators to increase the diversity of the population and expand the search range;
step six: calculating the maximum completion time of the population individuals;
Step seven: judging whether the algorithm is terminated, and if the algorithm is terminated, outputting the current optimal solution; otherwise, if the algorithm is not terminated, the algorithm returns to the step four to continue to execute.
preferably, in step two, an initial population is generated by three initialization methods, and each individual in the population represents a group of flexible job shop scheduling schemes with transportation time.
Preferably, a mutation operator is added in the step five to increase the diversity of the population and enlarge the search range; and (4) introducing an elite library strategy, and replacing the searched better solution into the elite library to avoid repeated searching.
Preferably, the optimal individual in the population is compared with the current optimal solution in the sixth step, and if the maximum completion time is smaller than the current optimal solution, the current optimal solution is replaced to be the optimal individual of the population, otherwise, the current optimal solution is unchanged.
The invention improves the traditional cultural genetic algorithm and expands the application field of the traditional cultural genetic algorithm to solve the problem of the scheduling scheme of the flexible job shop with transportation time. Each individual in the population adopts two-section integer coding to represent a feasible scheduling scheme, and the coding mode is simple and easy to realize; the method for generating the initial population by mixing the three initialization methods improves the quality of the overall initial solution of the population and improves the operation efficiency of the algorithm; the local search comprises a simulated annealing operator and a mutation operator, a new search mode is formed by combining the simulated annealing operator and the mutation operator by adopting a double-line parallel structure, an elite library concept is introduced, the neighborhood solution repeated search of excellent individuals is avoided through the elite library and the mutation probability, and the search efficiency is improved.
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FIG. 1 is a flow chart of the algorithm of the present invention.
FIG. 2 is a diagram illustrating an example of the problem of the present invention.
FIG. 3 is a diagram illustrating individual expressions of a population according to the present invention.
FIG. 4 is a schematic illustration of a tournament selection of the present invention.
FIG. 5 is a schematic diagram of the overall crossover operation of the present invention.
FIG. 6 is a schematic diagram of the perturbation operation of the present invention.
FIG. 7 is a schematic view of the Gantt chart of the present invention.
Detailed Description
The foregoing and other aspects, features and advantages of the invention will be apparent from the following more particular description of embodiments of the invention, as illustrated in the accompanying drawings in which reference is made to figures 1 to 7. The structural contents mentioned in the following embodiments are all referred to the attached drawings of the specification.
Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.
The method comprises the following steps: parameter setting
Setting culture genetic algorithm to solve the related parameters of FJSP with transportation time, including: population size NpopFull random initialization probability PAPriority minimum machining time initialization probability PBpriority maximum remaining machining time initialization probability PCNumber of iterations NiterOptimal solution retention algebra NreCross probability PxovrProbability of mutation PmutrInitial temperature T0End temperature TfNumber of disturbances LkTemperature attenuation coefficient alpha, adjustment coefficient t, elite library size NE。
The termination conditions of the culture genetic algorithm are as follows: if the iteration number N is not reached yetiterThen, the current optimal solution remains NreThe generation does not change, and the algorithm is terminated; otherwise, the operation is carried out until the iteration times.
Description of values of variables: population size NpopThe value can be 100-400, and the value is taken according to the processing capacity of a computer or the scale of a problem;
Three kinds of initialization probabilities PA、PB、PCUsed for controlling each method to generate the number of initial individuals, the probability values are all less than 1, and PA+PB+PCGeneral name of P1AMaximum;
Number of iterations NiterThe iteration times and the population scale are similar, generally about 100, for example, 100; optimal solution preserving algebra NreWhen the algorithm falls into a local optimal solution, the method is used for jumping out of a loop and terminating the operation of the algorithm, so that the operation efficiency is improved;
Cross probability Pxovr，0<Pxovr<1, randomly taking a value, generally about 0.7, for example, 0.7;
probability of variation Pmutr，0<Pmutr<1, randomly taking a value, generally about 0.2, for example, 0.2;
Initial temperature T090-100, the value is randomly selected, generally about 100, for example, 100 can be selected;
Termination temperature Tf20-50, randomly taking a value, and stopping the simulated annealing operator condition, wherein the value is generally about 20, and for example, the value can be 20;
number of disturbances Lk5-20, the value is randomly selected, generally about 10, for example, 10 can be selected;
The temperature attenuation coefficient alpha, 0< alpha <1, is randomly selected, is generally about 0.7, and can be selected to be 0.7 for example;
Adjusting the coefficient t-1 < t <0, randomly taking a value, wherein the closer the value is to-1, the greater the capability of the simulated annealing operator for receiving the inferior solution is, generally about-0.05, and for example, the value can be-0.05;
Elite library size NE10-50, the storage size of the elite library, when the storage space reaches the upper limit, the worst individual in the library will be replaced, generally about 40, and for example, the value can be 40.
An example is given in fig. 2, which includes 8 workpieces, 5 machines, a partially flexible job shop scheduling problem with transit time. The variables in this example take the values: population size Npopat 200, the probability P is initialized completely randomlyAIs 0.8, the priority minimum processing time initialization probability PBIs 0.1, the maximum remaining machining time initialization probability P is prioritizedC0.1, number of iterations Niterfor 200, the optimal solution retains the algebraic number NreIs 30, cross probability PxovrIs 0.7, the mutation probability Pmutr0.2, initial temperature T0100, end temperature Tf20, number of perturbations Lk10, temperature attenuation coefficient alpha of 0.7, adjustment coefficient t of-0.05, elite library size NEis 40.
Step two: generation of initial populations by three initialization methods
There is a need to translate flexible job shop scheduling schemes with transport time into independent individual representations. Since the flexible job shop scheduling problem is discrete, there are two sub-problems of machine selection and process sequencing. In order to reduce the calculation complexity and ensure that all individuals in the operation process are feasible, therefore, a two-section integer coding mode is adopted to carry out individual coding. As shown in FIG. 3, each of the units is a string of integers, the total length is 2L, L is the number of all the steps, OiThe number of steps of the workpiece i is shown. The left side is a machine selection part, each integer represents the arrangement serial number of the selectable processing machines corresponding to the working procedure, for example, the number 3 of the position No. 1 represents the actual processing machine 4; the right side is a procedure sorting part, each integer represents a workpiece number, and the sorting sequence is the actual workpiece processing sequence, namely [ O ]2,1,O1,1,O1,2,O2,2,O2,3]In which O isj,hThe h-th step of the workpiece j is shown.
During initialization, three initialization methods are proposed, and N is generated in a mixed mannerpopAnd (4) individuals.
1) completely random: an individual machine selection part, wherein the integer of each position is the machine serial number randomly selected in the selectable processing machine set of the corresponding working procedure; the process sequencing part is that all the process sequences are randomly arranged.
2) preferential minimum processing time: an individual machine selection part, wherein the integer of each position is the machine serial number of the minimum processing time of the corresponding working procedure in the selectable processing machine; the process sequencing part is that all the process sequences are randomly arranged.
3) Preferential maximum remaining processing time: an individual machine selection part, wherein the integer of each position is the machine serial number randomly selected in the selectable processing machine set of the corresponding working procedure; the process sequencing part is used for preferentially sequencing the workpieces with the largest residual processing time.
Step three: computing an optimal solution
And calculating the maximum completion time of all individuals through an objective function, and recording the individual with the minimum maximum completion time as the current optimal solution.
By means of the objective function, the maximum completion time of all individuals is calculated, and the individuals are actually decoded. Since the individual includes two parts, namely, a machine selection part and a process sequencing part, the two parts need to be sequentially performed.
The machine selection is first decoded, the machine part chromosomes are read sequentially from left to right and converted to the machine matrix JmProcessing time matrix T1And a transportation time matrix T2。Jm(j, h) the machine number of the h step of the j workpiece; t is1(j, h) represents the h-th process machining time of the j-th workpiece; t is2(j, h, i) represents a transport time taken for the h-th process of the j-th workpiece to be transported to the machine i; j. the design is a squarem(j,h)、T1(j,h)、T2(j, h, i) correspond to each other.
Decoding the procedure sequence, reading the individual procedure sequence parts from left to right in sequence, and sequencing by combining the transportation time of the workpieces; if the process O is carried outj,hIs the first process of the workpiece j and the first process of the machine i, and the workpiece is directly processed from the time after the machine adjustment is finished, if the workpiece O is processedj,hThe first step of the machine i, not the first step of the workpiece j, is the step Oj,(h-1)The sum of the time required for transporting the workpiece to the machine i is compared with the time required for completing the preceding process on the machine i, the larger of which is taken as the process Oj,hstarting the processing time; when the process O is carried outj,hIf the workpiece is not the first pass of the workpiece and the machine i has already machined the workpiece, then the process O needs to be consideredj,hThe machining is performed as early as possible without disturbing the machining of other processes on the machine i, i.e. the idle sections on the machine i are found out and an insertion is attempted. Assume that the idle interval start time is TSi,kEnd time of TEi,k. When k processes are completed on the machine i, at most k-1 idle sections may be generated. When the process O is carried outj,hTaking the starting time TS of the gap when machining on machine ii,kAnd process Oj,hLast process Oj,(h-1)End time plus transit time T2(j, h, i) is larger, and a step O is addedj,hMachining time T of1(j, h) if the ending time is less than the time TE of the gapi,kThe insertion is satisfied, if not, the next idle interval is judged, if not, the procedure O is executedj,hArranged in sequence backwards.
Step four: crossover operator
picking N according to tournament selection method based on individual maximum completion timepopthe individuals are used as parents and the cross probability P is usedxovrperforming a global crossover operator to generate NpopAnd (4) a child. Tournament selection is shown in fig. 4 and crossover operations are shown in fig. 5.
Step five: forming a new population
The filial generations are sequentially subjected to local search operation to obtain NpopMixing the obtained non-inferior individuals with parent individuals, and selecting N according to championship selection methodpopIndividuals form next generation populations, a local search method is designed based on a simulated annealing algorithm, and the situation that a local optimal solution is trapped during searching can be effectively avoided; adding mutation operators to increase the diversity of the population and expand the search range; and (4) introducing an elite library strategy, and replacing the searched better solution into the elite library to avoid repeated searching. The specific flow is shown in figure 1.
Wherein the elite library is a limited repository, and the initial elite library is an empty set. And (4) regarding the individuals output by the simulated annealing operator as better individuals, storing the better individuals into the elite library, and replacing the worst individuals if the elite library is filled. And screening the individuals to be subjected to local search later, and when the individuals are found to exist in the elite library, not executing the simulated annealing operator, but executing the mutation operator.
The main purposes of mutation are to increase population diversity, expand search range, and perform simply and efficiently, which are not applicable. The algorithm combines the characteristics of FJSP and designs a method for only partially mutating a chromosome machine:
1) Selecting a plurality of positions for the individual machine selection section;
2) And sequentially selecting a replaceable original machine from the selectable machine set of the working procedure corresponding to the selected position at random to finish the variation.
Perturbation is actually a search of the neighborhood solution of the current individual, as shown in FIG. 6. Because the disturbance frequency is set to be LkFinally, the L of the current individual can be obtainedkAnd selecting the optimal individual in the neighborhood solution to be compared with the current individual by the individual neighborhood solution, and judging whether the receiving condition is met. The acceptance condition is that if the new individual is better than the current individual, the current individual is replaced, otherwise, the probability is usedAnd receiving and replacing the current individual, wherein f (X') is the target value of the new individual, f (X) is the target value of the current individual, T is the current temperature, and T is the adjusting coefficient.
Step six: calculating the maximum completion time of the population individuals
And comparing the optimal individuals in the population with the current optimal solution, and replacing the current optimal solution into population optimal individuals if the maximum completion time is less than that of the current optimal solution, otherwise, keeping the current optimal solution unchanged.
Step seven: determining whether the algorithm is terminated
Judging whether the algorithm is terminated or not according to the setting of the algorithm termination condition in the parameters, and if the algorithm is terminated, outputting the current optimal solution; otherwise, if the algorithm is not terminated, the algorithm returns to the step four to continue to execute.
According to the invention, the application field of the traditional cultural genetic algorithm is expanded to solve the problem of solving the scheduling scheme of the flexible job shop with transportation time by improving the traditional cultural genetic algorithm, each individual in the population adopts two-section integer coding to represent a feasible scheduling scheme, and the coding mode is simple and easy to realize; the method for generating the initial population by mixing the three initialization methods improves the quality of the overall initial solution of the population and improves the operation efficiency of the algorithm; the local search comprises a simulated annealing operator and a mutation operator, a new search mode is formed by combining the simulated annealing operator and the mutation operator by adopting a double-line parallel structure, an elite library concept is introduced, repeated search of a neighborhood solution of a good individual is avoided through the elite library and the mutation probability, and the search efficiency is improved.
Claims (4)
1. An improved cultural genetic algorithm scheduling method for solving the problem of transportation time of a flexible workshop belt is characterized by comprising the following steps:
The method comprises the following steps: setting parameters, including: population size NpopFull random initialization probability PAPriority minimum machining time initialization probability PBPriority maximum remaining machining time initialization probability PCNumber of iterations NiterOptimal solution retention algebra NreCross probability PxovrProbability of mutation PmutrInitial temperature T0End temperature TfNumber of disturbances LkTemperature attenuation coefficient alpha, adjustment coefficient t, elite library size NE；
Wherein, PA+PB+PC＝1，0<PA<1，0<PB<1，0<PC<1，0<Pxovr<1，0<Pmutr<1，0<α<1；
The termination conditions of the culture genetic algorithm are as follows: if the iteration number N is not reached yetiterthen, the current optimal solution remains NreThe generation does not change, and the algorithm is terminated; otherwise, running until the iteration times;
Step two: a two-section real number coding mode is adopted by combining the scheduling problem characteristic of the flexible job shop; generating an initial population by three initialization methods, wherein each individual in the population represents a group of flexible job shop scheduling schemes with transportation time;
step three: calculating the maximum completion time of all individuals through a target function, and recording the individual with the minimum maximum completion time as the current optimal solution;
Step four: picking N according to tournament selection method based on individual maximum completion timepopthe individuals are used as parents and the cross probability P is usedxovrPerforming a global crossover operator to generate NpopA plurality of children;
Step five: the filial generations are sequentially subjected to local search operation to obtain NpopMixing the obtained non-inferior individuals with parent individuals, and selecting N according to championship selection methodpopIndividuals form next generation populations, a local search method is designed based on a simulated annealing algorithm, and the situation that a local optimal solution is trapped during searching can be effectively avoided; adding mutation operators to increase the diversity of the population and expand the search range;
Step six: calculating the maximum completion time of the population individuals;
Step seven: judging whether the algorithm is terminated, and if the algorithm is terminated, outputting the current optimal solution; otherwise, if the algorithm is not terminated, the algorithm returns to the step four to continue to execute.
2. The improved cultural genetic algorithm for scheduling flexible workshop transportation time according to claim 1, wherein in the second step, an initial population is generated through three initialization methods, and each individual in the population represents a group of flexible workshop scheduling schemes with transportation time.
3. The improved cultural genetic algorithm scheduling method for solving the transportation time of the flexible workshop according to claim 1, wherein in the fifth step, mutation operators are added to increase the population diversity and enlarge the search range; and (4) introducing an elite library strategy, and replacing the searched better solution into the elite library to avoid repeated searching.
4. the improved cultural genetic algorithm scheduling method for solving the transportation time of the flexible workshop according to claim 1, wherein in the sixth step, the optimal individuals in the population are compared with the current optimal solution, and if the maximum completion time is smaller than the current optimal solution, the current optimal solution is replaced to be the population optimal individuals, otherwise, the current optimal solution is unchanged.
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| CN115730432B (en) * | 2022-11-09 | 2024-05-28 | 国网湖南省电力有限公司 | Scheduling method and system of data processing task of Internet of things, equipment and storage medium |
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