A multi-objective discrete job-shop scheduling method based on knowledge mining and genetic algorithm

Abstract

The application discloses a multi-objective discrete workshop scheduling method combining knowledge mining and a genetic algorithm, first determines an optimization target, analyzes workpiece process information to be scheduled, attributes process attributes and divides process attribute values; then substitutes the workpiece process with attribute information into the multi-objective genetic algorithm, obtains non-dominated Pareto solutions through iterative evolution; then mines rule knowledge between process attributes and priorities in the non-dominated Pareto solutions; finally, formulates an initial population of the genetic algorithm under the knowledge mining, carries out multi-objective genetic evolution iteration on the obtained rule initial population, obtains an optimal scheduling solution, realizes more optimal scheduling results within an effective number of iterations, and compared with a conventional multi-objective genetic algorithm, can obtain non-dominated Pareto solutions with better quality within the same number of iterations or under a smaller initial population size, that is, can obtain more optimal scheduling results, thereby realizing efficient production of enterprises.

Description

Technical Field

[0001] This invention relates to the field of manufacturing workshop management technology, specifically a multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithms. Background Technology

[0002] The development of digitalization and artificial intelligence has facilitated the transformation and rapid development of the manufacturing industry, while also bringing both opportunities and challenges to many small and medium-sized manufacturing enterprises. The workshop, as the core unit of production and processing in manufacturing enterprises, is the convergence center for parts production, assembly, and data transmission, encompassing parts information, processing data, logistics management, production scheduling, and resource information. Workshop production scheduling, as the rule-based requirement for the sequential processing of parts throughout the entire production flow, systematically plans the use of workshop resources and equipment, playing a significant role in improving enterprise production efficiency and reducing production delays. Especially for discrete manufacturing workshops with diverse equipment and complex process routes, how to select appropriate equipment and determine the sequential processing order of workpieces are currently challenging problems to solve.

[0003] Currently, the solution to the multi-objective scheduling problem of discrete workshops mainly focuses on scheduling rules and artificial intelligence. The scheduling rule method has the advantages of speed and simplicity in solving practical scheduling problems, but the quality of the optimal solution still has a lot of room for improvement compared with artificial intelligence algorithms. Among artificial intelligence algorithms, genetic algorithms have been widely used in multi-objective discrete workshop scheduling problems due to their advantages such as wide applicability, low learning cost, group search, heuristic randomization, and parallel computing.

[0004] Existing genetic algorithms mainly include encoding, decoding, population initialization, crossover, mutation, and selection operations. First, similar to the relationship between chromosomes and genes, the optimization problem is transformed into several individuals in a population containing combinations of optimization information through encoding. These individuals are like chromosomes, and the optimization information corresponds to genes. Second, similar to crossover and mutation of biological chromosomes, these individuals are crossbred with superior individuals and mutated independently to generate the next generation. The difference is that the crossover and mutation rules must meet the constraints of the problem being solved. Then, the process is iterated until the conditions terminate, similar to biological evolution and survival of the fittest—this is the solution process of the genetic algorithm. However, in complex multi-objective discrete workshop scheduling problems, a single genetic algorithm, due to the limitations of its own mathematical model, struggles to obtain an ideal scheduling scheme. Each iteration of the genetic algorithm combines with a local optimum, and each local optimization consumes a significant amount of computation time, thus drastically increasing computational costs and reducing operational efficiency. Therefore, a multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithms is urgently needed to solve these problems. Summary of the Invention

[0005] This invention provides a multi-objective discrete workshop scheduling method that combines knowledge mining with genetic algorithms, achieving better scheduling results within an effective number of iterations, thereby enabling efficient production for enterprises and solving the problems existing in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithms, comprising the following steps:

[0007] S1. Determine the optimization objective, analyze the process information of the workpiece to be scheduled, assign process attributes, and divide the process attribute values;

[0008] S2. Substitute the workpiece process with attribute information into the multi-objective genetic algorithm to generate an initial population pPop. Perform ordinary non-dominated sorting on population pPop to obtain population pot. Perform genetic evolution operation on population pot to obtain offspring population qPop. Merge population pPop and population qPop, perform fast non-dominated sorting, compare crowding, eliminate inferior solutions, and obtain non-dominated Pareto solutions.

[0009] S3. Discover the rule-based knowledge between process attributes and priorities in non-dominated Pareto solutions;

[0010] S4. Formulate the initial population of the genetic algorithm under knowledge mining, and perform multi-objective genetic evolution iteration on the optimized rule-based initial population to obtain the optimal scheduling solution.

[0011] Preferably, in step S1, the process attributes are assigned including priority, process characteristics, processing time and remaining time, wherein priority refers to the position segment of the process code where each process is located.

[0012] Preferably, in step S2, the population pPop is generated by random sorting, and each generated solution corresponds to a scheduling scheme.

[0013] Preferably, in step S2, the ordinary non-dominated sorting is specifically performed as follows:

[0014] a. According to the optimization objective, traverse every individual in the population. If no other individual dominates the individual, mark the individual as a non-dominated individual. Continue until the end of the loop. The first batch of non-dominated individuals is the Pareto front solution set of the population, i.e. the first level of non-dominated layer.

[0015] b. Ignore the obtained non-dominated individuals, and repeat the above operation on the remaining individuals to obtain the remaining non-dominated layers in sequence.

[0016] Preferably, in step S2, the genetic evolution operation specifically includes:

[0017] a. A tournament selection method is used to randomly select a certain number of individuals from the parent generation;

[0018] b. Based on the individual's non-dominated level and crowding value, select the optimal individual as the object of crossover and mutation with the parent individual. The crossover of the process code adopts the CSEX method, the crossover of the machine code adopts the two-point crossover method, the mutation of the process code adopts the swapping of gene positions, and the mutation of the machine code randomly selects other genes from the corresponding set of available machine tools.

[0019] Preferably, in step S2, the fast non-dominated sorting specifically involves:

[0020] a. Traverse each individual in the population to obtain the number of individuals dominated by that individual and the set of individuals that dominate it;

[0021] b. Select individuals with zero dominated individuals and save them to the current set;

[0022] c. Iterate through each individual in the current set, decrement the number of individuals dominated by that individual by one, select the individual with zero dominated individuals as the new individual, and repeat the above operation until the population classification is completed.

[0023] Preferably, in step S3, the rule knowledge between process attributes and priorities refers to the mapping pattern between the attribute set {process characteristics, processing time, remaining time, additional process attributes} and the attribute {priority}. The mining of rule knowledge adopts the priority class weight method.

[0024] Preferably, in step S4, based on the proportion of different {priorities} belonging to different attribute sets {process characteristics, processing time, remaining time, process additional attributes} in step S3, the priority with the largest value is taken as the initial priority of the process attribute; and all processes are traversed in turn to determine the initial priority of all processes, and the initial population under the rule knowledge is obtained in the order of "the higher the priority, the earlier the process is processed".

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention substitutes the workpiece process with attribute information into a multi-objective genetic algorithm, obtains non-dominated Pareto solutions through iterative evolution, and mines the rule knowledge between process attributes and priorities in the non-dominated Pareto solutions. By using knowledge mining combined with the strategy of genetic algorithm, a better scheduling result can be obtained within an effective number of iterations. Compared with the traditional multi-objective genetic algorithm, it can obtain a higher quality of non-dominated Pareto solutions with the same number of iterations or a smaller initial population size, that is, it can obtain a better scheduling result, thereby achieving efficient production for enterprises. Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0027] In the attached diagram:

[0028] Figure 1 This is a flowchart of the multi-objective discrete workshop scheduling method of the present invention;

[0029] Figure 2 This is a schematic diagram of the process code intersection in this invention;

[0030] Figure 3 This is a schematic diagram of the machine code intersection of the present invention;

[0031] Figure 4 This is a schematic diagram of the process code variation of the present invention;

[0032] Figure 5 This is a schematic diagram of the machine code variation of the present invention;

[0033] Figure 6 This is a diagram showing the information data of some of the processes to be explored in this invention;

[0034] Figure 7 This is a diagram showing the results of the rule knowledge of this invention;

[0035] Figure 8 This is a schematic diagram illustrating the initial priority of the processes in this invention;

[0036] Figure 9 This is a schematic diagram showing the final priority results of each process in this invention;

[0037] Figure 10 This is a graph showing the results of F1, F2, and RE with an initial population size of 100 in this invention.

[0038] Figure 11 This is a graph showing the results of F1, F2, and RE with an initial population size of 50 in this invention.

[0039] Figure 12 This is a graph showing the results of F1, F2, and RE with an initial population size of 25 in this invention.

[0040] Figure 13 This is a schematic diagram of the Cov and Spacing values ​​of the present invention after 100 iterations.

[0041] Figure 14 This is a schematic diagram of the Cov and Spacing values ​​of the present invention after 300 iterations. Detailed Implementation

[0042] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0043] Example: Figure 1 As shown, a multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithms includes the following steps:

[0044] S1. Determine the optimization objective, analyze the process information of the workpiece to be scheduled, assign process attributes, and divide the process attribute values;

[0045] The process attributes include priority, process characteristics, processing time and remaining time, and delivery date;

[0046] Among them, the attributes are defined as follows: Priority - the position of each process in the process code (the processing order of processes in the genetic algorithm). The closer the process is to the beginning of the process code, the higher the priority; Process characteristics refer to the processing position of the process on the workpiece; Processing time is the processing time required for each process on the specified machine tool; Remaining time refers to the total processing time required for the remaining processes on the workpiece after completing this process, which is used to indicate the processing progress of the workpiece; Workpiece additional attributes refer to physical quantities that are directly related to the optimization objective semantics or indirectly related to the optimization objective.

[0047] Classifying process attribute values: The larger the scale of discrete workshop scheduling or the more complex the product process, the larger the total number of processes, and the higher the corresponding priority number. Here, the square root of the total number of processes is used as the priority number for classification. The classification of process characteristics, processing time, remaining time and additional process attribute values ​​can be evenly divided into 2-3 categories according to the numerical distribution.

[0048] In one specific embodiment, taking completion time and total production delay as examples, the objective function for optimization is:

[0049]

[0050] Where F1 and F2 are the required completion time and total production delay, respectively, i is the workpiece index, Ci is the completion time of workpiece i, n is the number of workpieces, and Di is the delivery deadline of workpiece i.

[0051] Process attribute values ​​are divided as follows: Taking LA18 (10*10, 10 workpieces, 10 processes, totaling 100 processes) as an example, the process code is divided into ten equal parts without interruption, and represented by integers from priority 0 to 9. The smaller the value, the higher the priority level; that is, a value of 0 means the highest priority level, and a value of 9 means the lowest priority level. Workpiece characteristics are represented by five categories: "first, secondary, middle, ... "Later" and "Last" correspond to the first, second to third, fourth to sixth, seventh to ninth, and tenth processes, respectively. Processing time is evenly distributed into three categories: "short," "middle," and "long," representing processing times of less than 37 units, 37 to 66 units, and more than 66 units, respectively. Remaining time is also evenly distributed into three categories: "short," "middle," and "long," representing remaining processing time of less than 202 units, 202 to 402 units, and more than 402 units, respectively. Delivery time is evenly divided into two categories: "tight" and "slack," representing delivery times of less than 1200 units and greater than or equal to 1200 units, respectively.

[0052] S2. Substitute the workpiece process with attribute information into the multi-objective genetic algorithm;

[0053] Generate the initial population pPop: The population pPop is generated using a random sorting method. Each generated solution corresponds to a scheduling scheme. Random sorting means that the processing order of the processes is arbitrarily random under the constraints of the encoding rules, and the equipment selected for each process is also arbitrarily random. In a specific embodiment, the process code is: 094782315693210…, where different values ​​represent different workpiece numbers, and the j-th occurrence of the same value means the j-th process of that workpiece; the machine code is: 00000000…, where each value represents the machine number selected for different processes, i.e., the default machine tool 0; the process code and machine code form a population individual, and finally, this series of individuals forms the population for the initial iteration of the genetic algorithm.

[0054] The population pPop is sorted using a normal non-dominated sort to obtain the population pot. The normal non-dominated sort iterates through each individual in the population according to the objective function. If no other individual dominates an individual, that individual is marked as non-dominated, and this process continues until the end of the loop. Domination here refers to: if x1 and x2 are two feasible solutions, when... There is f i (x1)≤f i(x2), x1 dominates x2 or x1 is equivalent to x2, denoted as x1≤x2; the set of the first batch of non-dominated individuals is the Pareto front solution set of the population, i.e. the first level of non-dominated layer; ignoring the obtained non-dominated individuals, the above operation is repeated for the remaining individuals to obtain the remaining non-dominated layers in turn.

[0055] Genetic evolutionary operations are performed on the population `popot` to obtain the offspring population `qPop`. These genetic evolutionary operations involve selection, crossover, and mutation to generate new offspring. Tournament selection is used to obtain crossover and mutated individuals, selecting the optimal individuals based on their non-dominant level and crowding value as the crossover and mutation targets with their parents. The crossover of operation codes is performed using the CSEX method, such as... Figure 2 As shown, the cross-sampling of machine code uses a two-point cross-sampling method, such as... Figure 3 As shown, the process code mutation involves swapping gene positions, such as... Figure 4 As shown, the machine code is randomly selected from the corresponding set of available machine tools, such as other genes. Figure 5 As shown, in a specific embodiment, the parameter settings are as follows: population size (25, 50, 100), mutation rate (0.002), crossover rate (0.9), tournament size (10), and number of iterations (100, 300);

[0056] Merge population pPop and population qPop, and perform fast non-dominated sorting: Fast non-dominated sorting works by traversing each individual in the population to obtain the number of dominated individuals and the set of dominant individuals for that individual; select individuals with zero dominated individuals and save them to the current set; traverse each individual in the current set, decrement the number of dominated individuals for that individual by one, select individuals with zero dominated individuals as the new individual, and repeat the above operations until the population classification is completed.

[0057] Crowding comparisons are performed to eliminate inferior solutions and obtain non-dominated Pareto solutions. Crowding comparison is primarily used to compare the quality of individuals within the same solution set, as dominant individuals are considered superior to dominated individuals. The crowding degree is calculated using the maximum rectangle side length method, setting the crowding degree of all individuals in the population to zero. For each optimization objective function, individuals are sorted by function value, with the first and last individuals having infinite crowding degrees. For the remaining individuals, the function difference between the individual and the individuals before and after them is calculated. The sum of these differences across all objective functions gives the individual's crowding degree. A higher crowding degree indicates a greater distance between the individual and the individuals before and after it, and a wider distribution within the solution set. Crowding degree calculation plays a crucial role in ensuring population diversity in multi-objective genetic algorithms.

[0058] S3. Mining the rule knowledge between process attributes and priorities in non-dominated Pareto solutions; where the rule knowledge between process attributes and priorities is the mapping pattern between process characteristics, processing time, remaining time, additional process attributes and priorities; the mining of rule knowledge adopts the priority class weight method, that is, calculating the proportion of process characteristics, processing time, remaining time and additional process attributes to different priorities; the higher the proportion, the greater the probability that the process belongs to that priority under the rule knowledge mined;

[0059] In one specific embodiment, after running step S2 independently 30 times, duplicate solutions were removed, resulting in 6645 sets of non-dominated solutions, totaling 493 sets of Pareto front solutions. Then, 66 sets were evenly selected from these 493 sets. Since each set contains 100 steps, a total of 6600 pieces of information were obtained. Some of the process information data to be mined is listed below. Figure 6 As shown;

[0060] Statistical calculations are performed on the proportions of process characteristics, processing time, remaining time, and additional process attributes at different priorities. The rule-based results are as follows: Figure 7 As shown;

[0061] There are 37 sets of rule knowledge. For example, rule knowledge 0 means that when a certain process meets the following conditions, its priority is {priority: 0, weight: 0.67; priority: 1, weight: 0.15; priority: 2, weight: 0.14; priority: 3, weight: 0.05}. That is, the probability of this process having a priority of 0 is the highest, and it is located in the earliest processing position segment.

[0062] S4. Develop an initial population for the genetic algorithm under knowledge mining. Perform multi-objective genetic evolutionary iterations on the optimized initial population to obtain the optimal scheduling solution.

[0063] In step S3, based on the proportion of different {priorities} belonging to different attribute sets {process characteristics, processing time, remaining time, additional process attributes}, the priority with the highest value is taken as the initial priority of that process attribute. Then, all processes are traversed sequentially to determine the initial priority of all processes. The initial population under the rule knowledge is obtained according to the order of "higher priority, earlier processing". Figure 8 As shown, the marked sections indicate the initial priority of each process.

[0064] Based on the constraints, the final initial population is obtained: the constraints include the priority number constraint from step S1 and the process route constraint, that is, each priority can only contain its own number of operations, and the operations of each workpiece must satisfy the processing sequence of the process route. The final priority results of each operation after constraints are as follows: Figure 9The marked part represents the final priority of each process, and the initial population under the final rule knowledge mining is formulated based on the priority results.

[0065] In one specific embodiment, the F1, F2, and RE results were obtained with an initial population size of 100 under different iteration numbers and different population sizes, as follows: Figure 10 The F1, F2, and RE results for an initial population size of 50 are as follows: Figure 11 The F1, F2, and RE results for an initial population size of 25 are as follows: Figure 12 The Cov and Spacing values ​​at 100 iterations are as follows: Figure 13 Figure 14 shows the Cov and Spacing values ​​after 300 iterations.

[0066] The results show that, under different initial populations and different iteration numbers, the new rule-based knowledge method outperforms the traditional random method in most performance metrics (F1, F2, RE, Cov, Spacing). In other words, the scheduling results obtained by this method are superior to those obtained by the traditional multi-objective genetic algorithm.

[0067]

[0068] in, It is the average of F1 or F2, F best It is the optimal value of F1 or F2;

[0069]

[0070] Where A and B are the solution sets for calculating the dominance performance, and a and b are subsets of A and B, respectively;

[0071]

[0072] Where the number of Pareto front solution sets is n, d i It is the minimum distance between the i-th solution set and its nearest neighboring solution sets. It is to traverse all d i The average result obtained.

[0073] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithms, characterized in that, Includes the following steps: S1. Determine the optimization objective, analyze the process information of the workpiece to be scheduled, assign process attributes, and divide the process attribute values; S2. Substitute the workpiece process with attribute information into the multi-objective genetic algorithm to generate an initial population pPop. Perform ordinary non-dominated sorting on population pPop to obtain population pot. Perform genetic evolution operation on population pot to obtain offspring population qPop. Merge population pPop and population qPop, perform fast non-dominated sorting, compare crowding, eliminate inferior solutions, and obtain non-dominated Pareto solutions. S3. Discover the rule-based knowledge between process attributes and priorities in non-dominated Pareto solutions; S4. Formulate the initial population of the genetic algorithm under knowledge mining, and perform multi-objective genetic evolution iteration on the optimized rule-based initial population to obtain the optimal scheduling solution.

2. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S1, the process attributes are assigned, including priority, process characteristics, processing time and remaining time. The priority refers to the position segment of the process code where each process is located.

3. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S2, the population pPop is generated by random sorting, and each generated solution corresponds to a scheduling scheme.

4. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S2, the ordinary non-dominated sort is performed as follows: a. According to the optimization objective, traverse every individual in the population. If no other individual dominates the individual, mark the individual as a non-dominated individual. Continue until the end of the loop. The first batch of non-dominated individuals is the Pareto front solution set of the population, i.e. the first level of non-dominated layer. b. Ignore the obtained non-dominated individuals, and repeat the above operation on the remaining individuals to obtain the remaining non-dominated layers in sequence.

5. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S2, the genetic evolution operation specifically involves: a. A tournament selection method is used to randomly select a certain number of individuals from the parent generation; b. Based on the individual's non-dominated level and crowding value, select the optimal individual as the object of crossover and mutation with the parent individual. The crossover of the process code adopts the CSEX method, the crossover of the machine code adopts the two-point crossover method, the mutation of the process code adopts the swapping of gene positions, and the mutation of the machine code randomly selects other genes from the corresponding set of available machine tools.

6. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S2, the fast non-dominated sorting is specifically as follows: a. Traverse each individual in the population to obtain the number of individuals dominated by that individual and the set of individuals that dominate it; b. Select individuals with zero dominated individuals and save them to the current set; c. Iterate through each individual in the current set, decrement the number of individuals dominated by that individual by one, select the individual with zero dominated individuals as the new individual, and repeat the above operation until the population classification is completed.

7. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S3, the rule knowledge between process attributes and priorities refers to the mapping pattern between the attribute set {process characteristics, processing time, remaining time, additional process attributes} and the attribute {priority}. The mining of rule knowledge adopts the priority class weight method.

8. The multi-objective discrete workshop scheduling method combining knowledge mining and genetic algorithm according to claim 1, characterized in that: In step S4, based on the proportion of different {priorities} belonging to different attribute sets {process characteristics, processing time, remaining time, additional process attributes} in step S3, the priority with the largest value is taken as the initial priority of the process attribute; and all processes are traversed in turn to determine the initial priority of all processes, and the initial population under the rule knowledge is obtained in the order of "the higher the priority, the earlier the process is processed".

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