A scheduling optimization method based on the combination of tabu search algorithm and genetic algorithm

Abstract

A scheduling optimization method based on the combination of a taboo search algorithm and a genetic algorithm belongs to the technical field of flexible manufacturing production scheduling. The state space explosion problem encountered in the bottleneck detection process in the prior art is solved. The present invention is applicable to the Petri net model of a flexible manufacturing system, which adopts random scheduling and optimizes the Petri net model data using a genetic algorithm and a taboo search algorithm. The taboo search is: selecting the offspring generated by the genetic algorithm as a feasible solution X; in each iteration: generating multiple feasible solutions through the neighborhood of solution X to obtain candidate solutions, judging whether all candidate solutions meet the taboo breaking rule, if so, replacing X with a solution Y that meets the taboo breaking rule, and putting the taboo object corresponding to Y into a taboo table, if not, selecting the best solution corresponding to the non-taboo object in the candidate solution, putting the corresponding taboo object into the taboo table, and removing the taboo object that enters the taboo table earliest. The present invention is applicable to the scheduling of a flexible manufacturing system.

Description

Technical Field

[0001] The invention belongs to the technical field of flexible manufacturing production scheduling, and in particular relates to a scheduling optimization method based on the combination of a taboo search algorithm and a genetic algorithm. Background Art

[0002] In recent years, with the rapid development of computer technology and the increasing demand for industry, the requirements for production models have gradually diversified. In modern industrial production, data analysis and processing have become increasingly critical. In this context, more mathematics and computer theories are applied to industrial production, and stochastic Petri nets are one of them. It has good mathematical properties and good simulation effects on multi-variable and multi-dimensional production models in industrial production. Therefore, it has unique advantages in dealing with bottleneck detection and process optimization problems in industrial production.

[0003] At present, random Petri nets have been widely used in a variety of industrial production models and have developed many theories. The scheduling optimization problem of manufacturing systems is generally a non-deterministic problem with polynomial complexity. It is usually quite complex and difficult and there is no universal solution. It is necessary to select methods according to actual production requirements. Common methods include linear programming, goal programming, engineering software simulation, intelligent search algorithms, heuristic search methods, etc. However, the most primitive algorithm will produce state space explosion problems during analysis and bottleneck detection. Summary of the invention

[0004] The purpose of the present invention is to solve the state space explosion problem encountered in the process of bottleneck detection using a random Petri network model, and to provide an optimization method for the original scheduling method for this problem.

[0005] The present invention provides a scheduling optimization method based on the combination of a taboo search algorithm and a genetic algorithm. The scheduling optimization method is applicable to a Petri net model of a flexible manufacturing system. The Petri net model is randomly scheduled, and then the genetic algorithm and the taboo search algorithm are used to optimize the Petri net model data.

[0006] It is further defined that the composition of the Petri net model is:

[0007] Places P1, P2, ..., P n is the initial state of n kinds of workpieces, the initial state is the unprocessed state, the library P i The number of marks (i=1, 2, ..., n) represents the production quantity of workpiece i, which is the number of workpieces that need to be processed;

[0008] for Existence place sequence Said Indicates the state of the i-th workpiece in the m-th process;

[0009] Places M1, M2, …, M k It represents the right to use k types of machines, and the number of place marks under its initial identification and the upper limit of the number of place marks are both 1;

[0010] for There is a transition sequence represents the processing procedure of the i-th workpiece, is a random variable of time, Indicates change The average value of is the processing time of the i-th workpiece in the m-th process.

[0011] Further defined, the method for optimizing the Petri net model data is:

[0012] Construct an initial population of 100 individuals, set the number of iterations to k, and the initial value of k is 0;

[0013] Perform an iterative cycle and take the total processing time of each individual as the fitness;

[0014] Determine whether the termination condition is met. If so, select the optimal solution in the last generation of population as the final output result. If not, continue to iterate;

[0015] Perform selection, crossover and mutation operations on the population, and update the population to generate offspring populations;

[0016] When k>20, the taboo algorithm is used to optimize each individual;

[0017] When k>200, the loop ends and the optimal solution in the last generation of population is selected as the optimization result.

[0018] It is further defined that the steps of initializing the population are as follows:

[0019] For each workpiece, a process is randomly selected as the starting process;

[0020] If the process has been selected, reselect it; if it has not been selected, continue until the initialization process selection of all workpieces is completed.

[0021] It is further defined that the mutation operation on the population is performed with a probability of 0.05.

[0022] It is further defined that, in the crossover operation performed on the population, the mother for the crossover is selected randomly; the father is selected as the individual with the highest fitness among the parents.

[0023] Further defined, the process of the taboo search is as follows:

[0024] Initial solution generation: Select the offspring generated by the genetic algorithm as the feasible solution X and clear the taboo table;

[0025] Determine the termination condition. If the termination condition is met, the iteration ends; otherwise, continue.

[0026] In each iteration: multiple feasible solutions are generated through the neighborhood of solution X, and several candidate solutions are selected from them;

[0027] Analyze whether all candidate solutions satisfy the taboo-breaking rules. If so, select solution Y that satisfies the taboo-breaking rules to replace X and put the taboo object corresponding to Y into the taboo table, and remove the taboo object that entered the taboo table earliest. If not, select the best solution corresponding to the non-taboo object in the candidate solution as the new current solution, and put the corresponding taboo object into the taboo table, and remove the taboo object that entered the taboo table earliest.

[0028] It is further defined that the taboo table uses individual fitness as a taboo object, the length of the taboo table is fixed, and follows the first-in-first-out principle.

[0029] It is further defined that the structure of the neighborhood is to add disturbance to the process of the workpiece on the individual to generate the movement of the neighborhood, which is to exchange any two processes in a certain workpiece of the individual.

[0030] It is further defined that when an operation move can provide a better solution than the best solution so far, it can be used as a taboo object regardless of whether the operation move is in the taboo table. If all operation actions are in the taboo table and do not meet the taboo rule, a solution is randomly selected from the candidate solutions to proceed.

[0031] Beneficial effects: The present invention optimizes the existing scheduling method of flexible manufacturing system, thereby solving the state space explosion problem encountered in the bottleneck detection process in the prior art, shortening the processing time and improving the work efficiency.

[0032] The present invention is implemented based on an existing flexible manufacturing system. In practical applications, a random Petri net model of the flexible manufacturing system is established based on a physical model of the existing flexible manufacturing system. Based on the model, a fusion design is performed for the encoding, population generation, fitness function, selection operator, crossover operator and mutation operator of a genetic algorithm. A taboo search algorithm is used to improve the performance of the genetic algorithm. The genetic and taboo search algorithms are mixed and finally the mixed algorithm is applied to a specific model of the flexible manufacturing system to optimize the scheduling method.

[0033] The experimental results show that the hybrid algorithm of the present invention is superior to the standard genetic algorithm in terms of convergence speed and convergence results, which proves that the hybrid algorithm has better adaptability to flexible manufacturing systems. The present invention is suitable for scheduling flexible manufacturing production. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the physical model of the flexible manufacturing system;

[0035] Figure 2 It is a stochastic Petri net model for flexible manufacturing system;

[0036] Figure 3 Cross process for workpiece 1;

[0037] Figure 4 Search flowchart for taboo;

[0038] Figure 5 It is a hybrid algorithm strategy;

[0039] Figure 6 The flow chart of the hybrid algorithm of tabu search algorithm and genetic algorithm;

[0040] Figure 7 Partial model of stochastic Petri net for intelligent manufacturing system;

[0041] Figure 8 It is the relationship between the population size and convergence algebra of genetic algorithms;

[0042] Fig. 9 This is the relationship between the population size of the genetic algorithm and the time it takes to converge;

[0043] Fig.10 It is the optimal solution convergence curve of the standard genetic algorithm genetic and taboo search hybrid algorithm. Specific embodiments

[0044] The individual is the entire production sequence. A random Petri net solves the entire production sequence. In the network structure, it mainly corresponds to each artifact in the sequence. In genetic algorithms, because of the need for abstraction to generate multiple solutions, the concept of individuals appears. It corresponds to the entire production sequence, and the artifact in the individual is the sequence of a certain artifact in the entire production sequence.

[0045] The total processing time of an individual is the time consumed by each individual in the entire production series.

[0046] Example 1.

[0047] 1. Random Petri Net Model of Flexible Manufacturing System: Figure 1A physical model of a flexible manufacturing system is shown in the paper, in which a production plan includes the type and quantity of finished products to be produced and the planned production sequence. Different workpieces need to be processed on various machines in turn to obtain the corresponding finished products, and finally put into the warehouse, thus completing a production process. In order to establish a stochastic Petri net model of a flexible manufacturing system, it is necessary to link the physical model of the flexible manufacturing system with the stochastic Petri net model of the flexible manufacturing system and determine the corresponding rules.

[0048] 2. The workpieces in the physical model of the flexible manufacturing system correspond to the places in the stochastic Petri net model. The number of places marked represents the number of workpieces of this type that need to be processed. The process of machine processing corresponds to the transition in the stochastic Petri net model. The average time t for the i-th machine to process the j-th workpiece is ij Corresponding to the average delay of this transition in the random Petri, since the transportation time is very short compared to the processing time, it can be ignored, and the right to use the machine can be represented by a library with a unique tag. Through the above analysis, the random Petri net model corresponding to the physical model can be obtained, as shown in Figure 2 shown.

[0049] Figure 2 The stochastic Petri net model corresponding to a flexible manufacturing system with two types of workpieces and four production machines is described in Indicates the various states of the first workpiece during processing. Indicates the various states of the second workpiece during processing. represents the right to use the four production machines, and plays the role of a catalyst for change in the stochastic Petri net. Indicates the various processes of the first type of workpiece, Represents the various processes of the second workpiece. From this stochastic Petri net model, it can be concluded that the processing of the first workpiece requires the use of the first, third, and fourth types of processing machines, and the processing of the second workpiece requires the use of the first, second, and fourth types of processing machines, which also creates a scheduling optimization problem. For a more general case, the definition of the stochastic Petri net model of the flexible manufacturing system can be obtained. The composition of the stochastic Petri net of the flexible manufacturing system is as follows:

[0050] (1) Places P1, P2, …, P n is the initial state of n kinds of workpieces, the initial state is the unprocessed state, the library P i The number of marks (i=1, 2, ..., n) represents the production quantity of workpiece i, which is the number of workpieces that need to be processed;

[0051] (2) For Existence place sequence Said Indicates the state of the i-th workpiece in the m-th process;

[0052] (3) Places M1, M2, …, M k It represents the right to use k types of machines, and the number of place marks under its initial identification and the upper limit of the number of place marks are both 1;

[0053] (4) For There is a transition sequence represents the processing procedure of the i-th workpiece, is a random variable of time, Indicates change The average value of is the processing time of the i-th workpiece in the m-th process.

[0054] In order to relatively simplify the scheduling problem of flexible manufacturing systems, the following constraints are stipulated:

[0055] (1) Each machine processes only one workpiece at a time;

[0056] (2) A process for a workpiece can only begin after the previous process is completed;

[0057] (3) The machine preheating process is negligible;

[0058] (4) The machine will not stop running due to unexpected factors such as failure;

[0059] (5) There is a processing sequence between the processes of the workpieces and it will not affect the processes of other workpieces;

[0060] (6) All artifacts have the same priority.

[0061] 2. The core concept of Genetic Algorithm (GA) is to imitate the genetic selection and natural elimination that occur in the process of biological evolution. It is an evolutionary algorithm that explores the optimal solution based on simulating the natural evolution process.

[0062] Genetic algorithm mainly consists of key parts such as encoding, initial population formation, decoding, fitness analysis, selection, crossover, mutation, etc. The process of genetic algorithm is as follows:

[0063] Genetic algorithm is an iterative algorithm that continuously performs hybridization, mutation and selection. Each genetic mechanism is only related to the current population state, but not to the previous population state, so the genetic algorithm meets the definition of Markov chain.

[0064] Due to the complex and flexible characteristics of flexible manufacturing systems, this algorithm, unlike most genetic algorithms, uses matrix encoding. The matrix row numbers represent the processing steps, the matrix column numbers represent the type of workpiece, and the element values ​​in the matrix represent the machine number for processing.

[0065]

[0066] where g ij Indicates that the i-th process of the j-th workpiece is on machine g ij Upper processing.

[0067] Step 1: Use the method of randomly generating the initial solution. The purpose of using this method is to improve the randomness of the solution to a certain extent. The process is as follows:

[0068] (1) Randomly select a process as the starting process for each workpiece;

[0069] (2) Randomly select a process for each workpiece. If the process has been selected, reselect it; if it has not been selected, continue.

[0070] (3) Until all process selections for all workpieces are completed.

[0071] Step 2: Fitness function

[0072] Fitness, as a parameter that describes the degree of adaptation of an individual to the environment, directly determines the convergence trend of the genetic algorithm. A reasonable fitness function is the core of the algorithm's ability to converge to the optimal solution.

[0073] Step 3: Selection, crossover, mutation

[0074] The genetic process includes selection, crossover and mutation. The genetic algorithm simulates the natural evolution process of the population through the genetic mechanism, continuously generates a new generation of population, and makes the new generation of population have better properties. The selection operator selects individuals with better fitness from the parent generation and makes these individuals with better fitness have a greater probability of being retained in the offspring. From the selection rules of the selection operator, it can be seen that individuals with high fitness are more likely to be selected, and individuals with low fitness are more likely to be eliminated. After continuous selection, individuals with high fitness appear repeatedly. However, the problem with the selection operator is that it can only be within a fixed range. The result of the selection is always within the population range. Better individuals outside the population cannot be selected. Therefore, the selection result depends entirely on the initial population. At this time, if you want to obtain results outside the population, you need crossover and mutation.

[0075] Crossover is a genetic operator that is used to change local information from one generation to the next. It produces excellent offspring. The selection method of crossover depends on the encoding method. The logic of the corresponding process and the correspondence of the machine must be checked during the crossover process. To ensure randomness, the mother selection method of crossover is random selection.

[0076] Take the workpiece 1 process as an example, let P1 and P2 represent the first column vector of the parent matrix, C1 and C2 represent the first column vector of the child matrix, randomly divide the workpiece 1 process into two sets K1 and K2, copy the genes of P1 contained in K1 to C1, copy the genes of P2 contained in K2 to C2, and keep their positions unchanged. Similarly, copy the genes of P2 contained in K2 to C1, copy the genes of P1 contained in K1 to C2, and keep their positions unchanged. Figure 3 As shown in the figure, two new individuals can be obtained by exchanging the process of 12342314 and 12341234. In order to ensure the randomness of the results and the retention of the individuals with the highest fitness, the individuals with the highest fitness in the parent generation are selected and retained during the crossover process. For the offspring generated by the crossover, the individuals with higher fitness are selected with an 80% probability, and the individuals with lower fitness are selected in other cases.

[0077] The mutation operation refers to replacing the value at a random position in an individual code with other reasonable values, and then increasing the randomness of the population after the selection operation. The purpose of the mutation operation is to improve the local search ability by improving randomness. In order to ensure the feasibility of the individual after mutation, this paper adopts the sequential mutation method, that is, arbitrarily exchanging the order of two processes in the process of random workpieces, taking p m =0.05.

[0078] 3. Tabu Search (TS) is a sub-heuristic random search algorithm. Starting from the initial feasible solution, it selects a series of feature search directions as tests to implement a search algorithm that allows the maximum change in the value of a specific objective function. In order to avoid falling into the local optimal solution, a flexible memory method is used in the search to record and select the optimization process to guide the next search direction. On this basis, the taboo standard is used to avoid cyclic search, and some good states are released through the taboo breaking standard, thereby ensuring a diverse and effective search. The taboo search flow chart is as follows: Figure 4 shown.

[0079] The general process for tabu search is as follows:

[0080] (1) Generation of initial solution: The initial solution is selected as the offspring generated by each genetic algorithm, the detailed parameters of the algorithm are set, the feasible solution X is taken, and the taboo table is cleared; the individual fitness is used as the taboo object, the length of the taboo table is fixed, and the first-in-first-out principle is followed.

[0081] (2) Determine the termination condition. If the termination condition is met, the iteration ends; otherwise, continue.

[0082] (3) Generate multiple feasible solutions through the neighborhood of solution X, and select several candidate solutions from them; add disturbances to the process of the workpiece on the individual to generate the movement of the neighborhood, that is, exchange any two processes in a certain workpiece of the individual;

[0083] (4) Analyze whether all candidate solutions satisfy the taboo-breaking rule. If so, select solution Y that satisfies the taboo-breaking rule to replace X and put the taboo object corresponding to Y into the taboo table, and remove the taboo object that entered the taboo table earliest. If not, select the best solution corresponding to the non-taboo object in the candidate solution as the new current solution, and put the corresponding taboo object into the taboo table, and remove the taboo object that entered the taboo table earliest. The taboo-breaking rule is that when an operation move can provide a better solution than the best solution so far, it is acceptable regardless of whether the operation move is in the taboo table. If all operation actions are in the taboo table and do not meet the taboo-breaking rule, select one randomly from the candidate solutions.

[0084] (5) Go to step (2).

[0085] In the implementation process of the taboo search algorithm, the local search capability is better than that of the genetic algorithm, but the characteristics of the taboo search algorithm determine that the algorithm has high requirements for the feasible solution initially set. If the initial solution is near the optimal solution, the efficiency of the algorithm iteration process will be very high, and a better solution can be searched in the solution space without a large number of iterations. If the initial solution is far away from the optimal solution or is near the local optimal solution, it will easily fall into the local optimal solution or the iteration efficiency will be very low, which will seriously affect its convergence speed.

[0086] Compared with genetic algorithms, taboo search has another disadvantage, that is, only one initial solution can be used in each iteration, that is, point-to-point operation. Its serial iterative search process is different from the parallel search of genetic algorithms. It operates multiple solutions simultaneously in each generation, that is, group-to-group operation. Therefore, the taboo search algorithm is not suitable for solving large-scale problems.

[0087] 4. Hybrid algorithm: First, iterate through the designed genetic algorithm, so that the individuals in the population can cover the solution space as much as possible during the iteration process. In this way, it is ensured that it will not converge to the local optimal solution too early. Then, a local search algorithm is used for each individual in the group to quickly improve the fitness of the individual solution. At the same time, in order to reduce the amount of calculation and improve efficiency, after the genetic algorithm has iterated a certain number of times, the position of individuals with high fitness is relatively fixed, and then taboo search is used for local search. The specific implementation strategy is as follows: Figure 5 shown.

[0088] The above strategy can be used to obtain the specific process of the genetic and taboo search hybrid algorithm:

[0089] (1) Initialize the algorithm parameters, randomly generate the initial population, and set the number of iterations k = 0;

[0090] (2) Calculate the fitness of each individual in the population;

[0091] (3) Determine whether the termination condition is met. If so, select the optimal solution in the last generation of population. If not, continue to iterate.

[0092] (4) Execute the selection, crossover, and mutation operators designed in the genetic algorithm to generate the offspring population;

[0093] (5) If the number of iterations k is greater than the set value, a taboo search is performed on each individual in the current population to obtain the optimized population;

[0094] (6) Go to step (2).

[0095] Result analysis: Convergence to local optimal solution: There are two reasons why the genetic algorithm converges to the local optimal solution: the first is that during the population iteration process, a small number of individuals will have a fitness that greatly exceeds that of other individuals. Without a large number of iterations, these individuals with high fitness will quickly cover the entire population during the iteration process, leading to convergence to the local optimal solution; the second is that during the genetic algorithm optimization process, competition between individuals only exists in the offspring, and there is no competition between the offspring and the parent, which will lead to the loss of individuals with high fitness in the parent generation.

[0096] Efficiency decreases after a certain number of iterations: When the genetic algorithm iterates to the vicinity of the optimal solution or the number of iterations reaches a certain number, the problem of not being able to accurately locate the optimal solution may occur due to the increase in randomness in the iteration process, resulting in a decrease in search efficiency after a certain number of iterations. In addition, crossover and mutation will also lead to a problem, that is, it will jump out of the optimal solution that has been searched, reducing efficiency.

[0097] In order to solve the problems that genetic algorithms do not make sufficient use of the system's feedback information, have relatively poor local search capabilities, and are prone to premature convergence, this project uses the taboo search in the local search algorithm to improve it, retaining the genetic algorithm's potential parallel optimization and global search capabilities, while combining the local search capabilities of the taboo search to more effectively solve the global optimal solution.

[0098] Figure 6 Flowchart of the hybrid algorithm of genetic algorithm and taboo search algorithm for optimizing the peri network model of flexible manufacturing:

[0099] Construct an initial population of 100 individuals, set the number of iterations to k, and the initial value of k is 0;

[0100] Perform an iterative cycle and take the total processing time of each individual as the fitness;

[0101] Determine whether the termination condition is met. If so, select the optimal solution in the last generation of population as the final output result. If not, continue to iterate;

[0102] Perform selection, crossover and mutation operations on the population, and update the population to generate offspring populations;

[0103] When k>20, the taboo algorithm is used to optimize each individual;

[0104] When k>200, the loop ends and the optimal solution in the last generation of population is selected as the optimization result.

[0105] Example 2.

[0106] The genetic and taboo search hybrid algorithm is experimentally simulated, and the algorithm parameters are set through examples. The experimental configuration is: Intel Core i7 9750H, 2.6GHz, 16GB memory, MacOS operating system, and the algorithm is based on Java programming.

[0107] 1. Random Petri Net Model and Algorithm Parameters

[0108] Taking a laboratory intelligent manufacturing system as a prototype, the production line automation unit of this manufacturing system is mainly composed of 5 intelligent processing machines, numbered 1, 2, 3, 4, and 5. Different workpieces need to be processed on different machines, and different processes of different workpieces have different processing times on these machines. Since the processing machines are relatively concentrated, conflicts will occur in the production of the machines.

[0109] The production plan should be arranged reasonably to minimize the overall processing time and maximize the production benefits. After abstraction, the following example is obtained. Taking 16 workpieces as an example, each workpiece requires 4 processing steps. The processing requirements and processing time are shown in Table 1 and Table 2.

[0110] Table 1 Machine numbers required for workpiece processing

[0111]

[0112] Table 2 Processing time of different steps for each workpiece

[0113]

[0114]

[0115] Based on the above information, the stochastic Petri net model of the intelligent manufacturing system can be obtained. Figure 7 Part of the model of the random Petri net is shown in , and the path optimization of the above random Petri net is performed using a hybrid algorithm of genetic and taboo search. Since the parameters of the algorithm in the hybrid algorithm of genetic and taboo search have a very large impact on the performance of the algorithm, it is very important to choose these parameters reasonably.

[0116] For the taboo search algorithm, since this algorithm is optimized based on the genetic algorithm, it is different from the point-to-point optimization of the original taboo search algorithm. It optimizes the population obtained by the genetic algorithm. Therefore, there is no need for large-scale search. Only a small-range search is required for each individual in the population obtained by the genetic algorithm. Therefore, the length of the taboo table is set to 10, the maximum number of iterations is 20, and the number of search neighborhoods for each individual is 50. Since the quality of the solution obtained in the early search of the genetic algorithm is low, the taboo search is performed after the number of iterations of the genetic algorithm is 20.

[0117] The above taboo search parameters are used to simulate the genetic algorithm. The test is performed when the number of individuals in the population is 100, 200, 300, 400, and 500. The test results are as follows: Figure 8 As shown. It can be seen that as the population size increases, the number of individual solutions increases, the coverage of the solution space by the entire population increases, and the possibility of obtaining a solution with high fitness also increases. Therefore, the degree of exploration of the solution space becomes higher, and the number of iterations required for convergence also decreases. However, the increase in population size will directly lead to an increase in the amount of calculation and time consumption in each iteration process, such as Fig. 9 As shown, considering the time cost comprehensively, this paper chooses to use a population size parameter of 100. Since the number of iterations to convergence under the condition of a population size of 100 during the test period did not exceed 200, the termination condition of the genetic algorithm is set to terminate the iteration when the number of iterations reaches 200.

[0118] Comparative Example 1.

[0119] Compare the performance of the hybrid genetic and taboo search algorithm and the standard genetic algorithm in solving the flexible manufacturing system model scheduling problem. In order to reduce the randomness of the experiment, the same feasible solution is used as the initial solution, and the optimization results of the hybrid genetic and taboo search algorithm and the standard genetic algorithm are compared under the condition that the remaining experimental parameters are the same. After 10 experimental tests, the results are shown in Table 3.

[0120] Table 3 Experimental results of genetic and tabu search hybrid algorithm and standard genetic algorithm

[0121]

[0122]

[0123] The experimental results show that under the model conditions, the optimal values ​​obtained by the genetic and taboo search hybrid algorithm and the standard genetic algorithm are 503 and 525 respectively. In terms of the average value, the genetic and taboo search hybrid algorithm is also better, with an average processing time of only 518.1, which is 27.4 units less than the standard genetic algorithm. Therefore, from the experimental data of the random Petri net, the genetic and taboo search hybrid algorithm has improved the problem that the standard genetic algorithm is more likely to converge to the local optimal solution, thus proving the feasibility of the genetic and taboo search hybrid algorithm.

[0124] Fig.10 Comparing the convergence of the optimal solution of the standard genetic algorithm (GA) and the genetic and taboo search hybrid algorithm (GA&TS), Fig.10 It can be seen from the middle curve that the performance of the standard genetic algorithm in the initial stage of convergence is not much different from that of the genetic and taboo search hybrid algorithm. As the number of iterations increases, the convergence speed of the standard genetic algorithm gradually slows down and gradually lags behind the genetic and taboo search hybrid algorithm. The fitness of the final converged solution is also lower than that of the hybrid algorithm. From a theoretical analysis, the optimal solution obtained by the standard genetic algorithm is not satisfactory compared with the genetic and taboo search hybrid algorithm. This is mainly because the general genetic algorithm falls into the "premature phenomenon", which causes the genetic algorithm to converge to a local optimal solution instead of a better solution. Since the hybrid algorithm uses taboo search to enhance the local search ability of the algorithm, there is a higher probability that it is not limited to the local optimal solution in the iteration of the genetic algorithm. Therefore, the experimental results of the genetic and taboo search hybrid algorithm are better than those of the general genetic algorithm in terms of both optimal results and average results. The optimal solution obtained by the genetic and taboo search hybrid algorithm is

[0125]

[0126] It meets the processing logic requirements of each workpiece, which further proves that the optimal solution obtained by the hybrid algorithm of genetic and taboo search is practical.

[0127] In view of the defects of genetic algorithm, the taboo search algorithm is used to improve the performance of genetic algorithm, and a genetic and taboo search hybrid algorithm is proposed. Finally, the hybrid algorithm is applied to the specific model of flexible manufacturing system. The experimental results show that the hybrid algorithm is superior to the standard genetic algorithm in terms of convergence speed and convergence result. This proves that the hybrid algorithm has better adaptability to flexible and changeable flexible manufacturing systems.

Claims

1. A scheduling optimization method based on the combination of taboo search algorithm and genetic algorithm, the scheduling optimization method is applicable to the Petri net model of flexible manufacturing system, characterized in that: The Petri net model is randomly scheduled, and then the Petri net model data is optimized using a genetic algorithm and a taboo search algorithm; The composition of the Petri net model: Places P1, P2, ..., P n is the initial state of n kinds of workpieces, the initial state is the unprocessed state, the library P i The number of marks represents the production quantity of workpiece i, where the production quantity is the number of workpieces that need to be processed, i=1, 2, ..., n; for Existence place sequence Said Indicates the state of the i-th workpiece in the m-th process; Places M1, M2, …, M k It represents the right to use k types of machines, and the number of place marks under its initial identification and the upper limit of the number of place marks are both 1; for There is a transition sequence represents the processing procedure of the i-th workpiece, is a random variable of time, Indicates change The average value of is the processing time of the i-th workpiece in the m-th process; Methods for optimizing Petri net model data: Construct an initial population of 100 individuals, set the number of iterations to k, and the initial value of k is 0; Perform an iterative cycle and take the total processing time of each individual as the fitness; Determine whether the termination condition is met. If so, select the optimal solution in the last generation of population as the final output result. If not, continue to iterate; Perform selection, crossover and mutation operations on the population, and update the population to generate offspring populations; When k>20, the taboo algorithm is used to optimize each individual; When k>200, the loop ends and the optimal solution in the last generation of population is selected as the optimization result; The process of taboo search is as follows: Initial solution generation: Select the offspring generated by the genetic algorithm as the feasible solution X and clear the taboo table; Determine the termination condition. If the termination condition is met, the iteration ends; otherwise, continue. In each iteration: Generate multiple feasible solutions through the neighborhood of solution X, and select several candidate solutions from them; Analyze whether all candidate solutions satisfy the taboo-breaking rule. If so, select solution Y that satisfies the taboo-breaking rule to replace X and put the taboo object corresponding to Y into the taboo table, and remove the taboo object that entered the taboo table earliest. If not, select the best solution corresponding to the non-taboo object in the candidate solution as the new current solution, and put the corresponding taboo object into the taboo table, and remove the taboo object that entered the taboo table earliest. The genetic algorithm uses the following matrix encoding: The row number of the matrix represents the processing step, the column number of the matrix represents the type of workpiece, and the element value in the matrix represents the machine number of the processing; ef The e-th process of the f-th workpiece on machine g ef Upper processing; In the crossover operation on the population, the mother of the crossover is selected randomly; the father is selected as the individual with the highest fitness among the parents.

2. The scheduling optimization method according to claim 1, characterized in that: The steps of initializing the population are as follows: For each workpiece, a process is randomly selected as the starting process; If the process has been selected, reselect it; if it has not been selected, continue until the initialization process selection of all workpieces is completed.

3. The scheduling optimization method according to claim 1, characterized in that: The mutation operation on the population is performed with a probability of 0.

05.

4. The scheduling optimization method according to claim 1, characterized in that: The taboo table takes individual fitness as the taboo object, and the length of the taboo table is fixed and follows the first-in-first-out principle.

5. The scheduling optimization method according to claim 1, characterized in that: The structure of the neighborhood is to add disturbance to the process of the workpiece on the individual to generate the movement of the neighborhood, which is to exchange any two processes in a certain workpiece of the individual.

6. The scheduling optimization method according to claim 1, characterized in that: The taboo-breaking rule is that when an operation move can provide a better solution than the best solution so far, the operation move is regarded as a taboo object. If all operation actions are in the taboo table and do not meet the taboo-breaking rule, a solution is randomly selected from the candidate solutions to proceed.

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