Improved genetic algorithm for job shop scheduling with single task due time constraint

Abstract

The application discloses a workshop scheduling method for improving genetic algorithm to meet single task completion time constraints, which introduces a penalty factor for overtime tasks in the fitness calculation function to control the result through the improved genetic algorithm, effectively guides the algorithm to quickly converge to the scheduling scheme meeting the user-specified task duration constraint by imposing a higher penalty on the default solution, meets the single task longest completion time specification in the flexible workshop scheduling problem, and enhances the practicality in the actual scene. Meanwhile, a new crossover and mutation mechanism is designed, which ensures that each offspring generated will meet the user's time constraints while maintaining the strong search ability of the genetic algorithm. The application combines the global search ability of the traditional genetic algorithm with the local satisfaction requirement of the user constraints, and provides an intelligent scheduling optimization scheme which guarantees the scheduling quality and meets the specific production time requirement.

Description

Technical Field

[0001] This invention belongs to the field of flexible workshop scheduling technology in industrial engineering, specifically involving an improved genetic algorithm for workshop scheduling that satisfies single task completion time constraints. Background Technology

[0002] In the manufacturing and production sectors, the Flexible Job Shop (FJSP) problem is a complex and crucial task. It aims to rationally arrange the execution sequence of production tasks and the allocation of processing resources to minimize production time, costs, and delays. The FJSP problem is a typical NP-hard problem, and traditional solutions (such as linear programming and branch and bound methods) often struggle to find feasible solutions or optimal solutions within a reasonable timeframe for large-scale problems.

[0003] Genetic algorithms (GA), as efficient heuristic search algorithms, are widely used in solving the Flexible Jobs Processing (FJSP) problem. However, traditional GAs often fail to consider specific user constraints in flexible workshops, such as the completion time requirements of specific tasks. This means that while the algorithm can find optimal scheduling schemes, these schemes do not always meet the actual needs and constraints of production. Therefore, the fitness evaluation function of the current GA is improved by imposing a higher penalty on solutions that violate the rules, thus naturally leading the algorithm to select solutions that satisfy the user's time constraints. Simultaneously, new crossover and mutation mechanisms are designed. These mechanisms maintain the powerful search capabilities of the GA while ensuring that each offspring satisfies the user's time constraints. Summary of the Invention

[0004] The purpose of this invention is to provide an improved genetic algorithm for shop floor scheduling that satisfies the single task completion time constraint.

[0005] This invention introduces an intelligent genetic algorithm framework, which aims to allow users to specify the longest completion time constraint for each task. The algorithm controls the result to meet the user-specified single task duration constraint by introducing a penalty factor for timed-out tasks in the fitness calculation function, and ensures that the solution generated in each step does not violate the user constraint through time-series crossover and constraint-aware mutation operations, while maintaining the exploration and utilization capabilities of the genetic algorithm.

[0006] This invention provides an improved genetic algorithm for workshop scheduling that satisfies single-task completion time constraints, comprising the following steps:

[0007] Step 1: Randomly generate multiple initial scheduling schemes that satisfy process sequence constraints, machine allocation constraints, and workpiece completion time constraints; each scheduling scheme is treated as a chromosome individual, and the machine code and process code of the scheduling scheme are treated as genes; each chromosome individual forms the initial population.

[0008] Step 2: Calculate the fitness of chromosome individuals in the initial population using the fitness function that is constrained by task duration.

[0009] The fitness function f(x) is expressed as follows:

[0010]

[0011] Among them, Penalty x (i)=t(i)-t exp (i), is the penalty factor for the i-th task in the x-th scheduling scheme; t(i) is the actual completion time of the i-th task; t exp (i) Specify the completion time for the user of the i-th task; H x (i) is a Boolean function that takes the value 1 if the actual completion time of the i-th task in the x-th scheduling scheme is greater than the user-specified completion time, and takes the value 0 otherwise; i = 1, 2, 3... n; x = 1, 2, 3... N; n is the number of tasks in the scheduling scheme; N is the number of scheduling schemes.

[0012] Step 3: Use a tournament selection strategy to select a new population from the initial population.

[0013] Step 4: Perform a time-series crossover operation on the new population to obtain the offspring population.

[0014] Step 5: Perform mutation operations on the offspring population.

[0015] Step 6: Iterate through steps 2 to 5 until the set number of iterations is reached, and select the chromosome individual with the highest fitness from the last generation of new population as the final scheduling scheme.

[0016] Preferably, in step three, the tournament selection strategy is as follows: randomly select multiple chromosome individuals from the initial population, compare the fitness of the selected chromosome individuals, and select the individual with the highest fitness to join the new population; repeat this process until the number of individuals in the new population reaches the preset proportion of the number of individuals in the initial population.

[0017] Preferably, in step four, the temporal crossover operation is performed as follows: two chromosome individuals are selected from the new population as parent generation 1 and parent generation 2, and the process of performing the process code temporal selection crossover method or the machine code two-point crossover method with equal probability is executed to generate new offspring individuals. The offspring individuals are then added to the offspring population, and this process is repeated until the size of the offspring population reaches the preset value N or the number of iterations reaches the maximum number of cycles.

[0018] As a preferred embodiment, the process code timing selection crossover method is as follows:

[0019] (1) Randomly generate two values, take the smaller value as the starting point of this crossover, and the larger value as the ending point. The process code between the starting point and the ending point is the part that needs to be crossed; the part that needs to be crossed in the process code of parent generation 1 is A1, and the part that needs to be crossed in the process code of parent generation 2 is A2.

[0020] (2) Create child generation 1 and child generation 2; set the machine code of child generation 1 to be the same as the machine code of parent generation 1, and the machine code of child generation 2 to be the same as the machine code of parent generation 2; set the process code of both child generation 1 and child generation 2 to empty.

[0021] (3) Use loop traversal to traverse from the starting point to the ending point of the operation code, copy the part A1 that needs to be crossed in parent generation 1 to the corresponding position in child generation 2; copy the part A2 that needs to be crossed in parent generation 1 to the corresponding position in child generation 1.

[0022] (4) Iterate through each position in offspring individual 1. If the process code (gene) at the traversed position is empty, iterate through parent 1, select a gene that does not conflict with the empty gene of offspring 1, assign the gene to the empty gene of offspring 1, and repeat the process until there are no empty genes in offspring 1. Iterate through each position in offspring 2. If the gene at the traversed position is empty, iterate through parent 2, select a gene that does not conflict with the empty gene of offspring 2, assign the gene to the empty gene of offspring 2, and repeat the process until there are no empty genes in offspring 2.

[0023] (5) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

[0024] Preferably, the two-dot intersection method for the machine code is as follows:

[0025] (1) Copy parent generation 1 and parent generation 2 as child generation 1 and child generation 2 respectively.

[0026] (2) Two values ​​are randomly generated. The smaller value is used as the starting point of this crossover, and the larger value is used as the ending point. The machine code between the starting point and the ending point is the part that needs to be crossed. The part that needs to be crossed in the machine code of child 1 is A1, and the part that needs to be crossed in the machine code of child 2 is A2.

[0027] (3) Swap the A1 part in sub-sub1 and the A2 part in sub-sub2.

[0028] (4) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

[0029] Preferably, the constraint-aware mutation operation process is as follows: randomly exchange the genes at two positions of the chromosome individual process code, randomly select a certain position of the machine code, and replace the gene at that position with another available machine for the corresponding process.

[0030] The beneficial effects of this invention are:

[0031] 1. This invention improves the genetic algorithm by introducing a penalty factor for timed-out tasks into the fitness calculation function to control the results. This effectively guides the algorithm to converge quickly to a scheduling scheme that meets the user-specified task duration constraint, thus satisfying the maximum single-task completion time specification in the flexible workshop scheduling problem and enhancing its practicality in real-world scenarios.

[0032] 2. This invention ensures that the solutions generated at each step do not violate user constraints through temporal crossover and constraint-aware mutation operations, while maintaining the exploration and utilization capabilities of the genetic algorithm and guaranteeing the feasibility of the solutions. Furthermore, this method combines the global search capability of traditional genetic algorithms with the local satisfaction requirements of user constraints, providing an intelligent scheduling optimization scheme that guarantees scheduling quality while also meeting specific production time requirements. Attached Figure Description

[0033] Figure 1 The flowchart illustrates the improved genetic algorithm for workshop scheduling that satisfies the single-task completion time constraint of this invention.

[0034] Figure 2 This is a schematic diagram of chromosome individuals in the randomly generated initial population in Embodiment 1 of the present invention.

[0035] Figure 3 This is a schematic diagram of the process code and machine code of parent generation 1 and 2 in Embodiment 1 of the present invention. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] like Figure 1 As shown, the improved genetic algorithm-based workshop scheduling method that satisfies the single-task completion time constraint includes the following steps:

[0038] Step 1: Population initialization.

[0039] The random algorithm is iterated several times to randomly generate N initial scheduling schemes that satisfy the constraints of process sequence, machine allocation, and workpiece (task) completion time. Each scheduling scheme is treated as a chromosome individual, and the machine code and process code of the scheduling scheme are treated as genes. The chromosome individuals form the initial population.

[0040] Step 2: Calculate the fitness of individuals (scheduling scheme) in the initial population using the improved fitness function.

[0041] To better calculate the fitness of individuals in the initial population, the traditional fitness function is improved. The expression for the traditional fitness function f(x) is:

[0042] f9x)=α / Makespan(x)+β*LoadBalance(x)+γ*MachineUtil(x)

[0043] Where f(x) is the cost estimate for task scheduling using scheduling scheme x; Makespan(x) is the total time to complete all tasks according to scheduling scheme x; LoadBalance(x) is the workload balancing across different machines; MachineUtil(x) is the average utilization of all machines when scheduling according to scheduling scheme x; x = 1, 2, 3...N; α, β, γ are the weights of each metric in the fitness function; and N is the number of scheduling schemes.

[0044] The fitness function f(x) is a linear superposition of the three terms mentioned above: cost estimation, total time to complete all tasks, and load balancing. Traditional genetic algorithms often focus on minimizing the total time to complete all tasks, rather than allowing users to specify the maximum completion time for each task according to their actual needs. To address this, this invention proposes an improved genetic algorithm that introduces a penalty for timed-out tasks into the fitness evaluation function f(x), resulting in a new fitness function. In the improved fitness function, the total task completion time Makespan(x) and the timeout penalty are weighted by α and β respectively and placed in the denominator. This allows schemes with shorter total task completion times and those satisfying the maximum completion time constraints for each task to have higher fitness. The higher the individual fitness value, the better the scheduling scheme. This fitness function minimizes the overall completion time of all tasks while also satisfying the individual task completion time constraints as much as possible, increasing practicality. The expression for the improved task duration constraint-aware fitness function f(x) is:

[0045]

[0046] Among them, Penalty x (i)=t(i)-t exp (i) is the penalty factor for the i-th job in the x-th scheduling scheme, t(i) is the actual completion time of the i-th task, and t exp (i) Specify the completion time for the user of the i-th task, x = 1, 2, 3...N. H x (i) is a Boolean function, which takes the value 1 when the actual completion time of the i-th task in the x-th scheduling scheme is greater than the user-specified completion time, and 0 otherwise; i = 1, 2, 3...n. n is the number of tasks in the scheduling scheme; N is the number of scheduling schemes.

[0047] Step 3: Use the tournament selection strategy to generate a new population (parent population).

[0048] A tournament selection strategy is adopted, in which multiple chromosome individuals are selected from the initial population, the fitness of the selected chromosome individuals is compared, and the individual with the highest fitness is selected as the individual of the new population. This process is repeated until the number of individuals in the new population reaches a certain proportion of the number of individuals in the initial population.

[0049] Step 4: Perform time-series crossover operations on the new population.

[0050] Two chromosome individuals are randomly selected from the new population as parent 1 and parent 2. Crossover is performed according to the time selection of the operation code or the double-point crossover of the machine code with equal probability to generate new offspring individuals. The offspring individuals are then added to the offspring population. This process is repeated until the size of the offspring population reaches the preset value N or the newly generated offspring individuals do not meet the constraints, at which point the maximum number of loops MAX_C is reached.

[0051] (a) The timing selection and crossover method for operation codes is as follows:

[0052] (1) Generate two random numbers, take the smaller value as the starting point of this crossover, and the larger value as the ending point. The process code between the starting point and the ending point is the part that needs to be crossed. The part that needs to be crossed in the process code of parent generation 1 is A1, and the part that needs to be crossed in the process code of parent generation 2 is A2.

[0053] (2) Create child generation 1 and child generation 2, and set their machine codes to be the same as those of parent generation 1 and parent generation 2, respectively, and set their operation codes to empty.

[0054] (3) Use a loop to traverse from the starting point to the ending point, and copy the parts A1 and A2 that need to be crossed in the parent generation to the corresponding positions in the child generation 2 and child generation 1 respectively;

[0055] (4) Iterate through each position in offspring individual 1. If the gene at the traversed position is empty, iterate through parent 1, select a gene in parent 1 that does not conflict with the empty gene in offspring 1, assign the gene to the empty gene in offspring 1, and repeat the process until there are no empty genes in offspring 1. Iterate through each position in offspring individual 2. If the gene at the traversed position is empty, iterate through parent 2, select a gene in parent 2 that does not conflict with the empty gene in offspring 2, assign the gene to the empty gene in offspring 2, and repeat the process until there are no empty genes in offspring 2.

[0056] (5) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

[0057] (b) The double-dot interleaving method for machine code is as follows:

[0058] (1) Copy parent generation 1 and parent generation 2 to child generation 1 and child generation 2 respectively.

[0059] (2) Generate two random numbers as the starting and ending points of this crossover. The part of the machine code of the offspring 1 that needs to be crossed is A1, and the part of the machine code of the offspring 2 that needs to be crossed is A2.

[0060] (3) Swap the A1 part in sub-sub1 and the A2 part in sub-sub2.

[0061] (4) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

[0062] Step 5: Perform constrained sensing mutation operations on the offspring population.

[0063] Mutation operations are performed on individual chromosomes in the offspring population with a certain probability. The mutation operation involves randomly exchanging the genes at two positions of the process code of the individual chromosome, randomly selecting a position of the machine code, and replacing the gene at that position with another available machine for the corresponding process.

[0064] Step six: Iterate through steps two through five until the set number of iterations is reached, and select the individual with the highest fitness from the last generation of the new population as the final scheduling scheme.

[0065] Example 1

[0066] In this embodiment, the workshop scheduling timetable of the improved genetic algorithm-based workshop scheduling method that satisfies the single task completion time constraint is shown in Table 1.

[0067]

[0068] Table 1 Workshop Scheduling and Processing Schedule

[0069] Step 1, as follows Figure 2 As shown, the initial population P = {1,2,3,4} contains 4 initial individuals (i.e., chromosome individuals) that can be decoded into a valid scheduling scheme. Figure 2 In the OS layer, the first "1" represents the first operation of workpiece 1, the first "2" represents the first operation of workpiece 2, the second "1" represents the second operation of workpiece 1, and so on. The MS layer uses sequential coding, starting from the first operation of workpiece 1 and proceeding sequentially to the third operation of workpiece 3. The OS layer and MS layer are of equal length.

[0070] Step 2: The expression for the improved fitness function f(x) of this invention is as follows:

[0071]

[0072] Among them, Penalty x (i)=t(i)-t exp (i) is the penalty factor for the i-th job in the x-th scheduling scheme, t(i) is the actual completion time of the i-th task, and t exp (i) Specify the completion time for the user of the i-th task; H x (i) is a Boolean function. It takes the value 1 when the actual completion time of the i-th job in the x-th scheduling scheme is greater than the user-specified completion time (i.e., the longest completion time constraint), and 0 otherwise. i = 1, 2, 3; x = 1, 2, 3, 4; weights α and β are assigned the values ​​0.5 and 0.5 respectively.

[0073] Based on this fitness function, the larger the fitness value of an individual, the better the scheduling scheme corresponding to that individual. The fitness of an individual is calculated using the improved fitness function f(x), as shown in Table 2.

[0074]

[0075]

[0076] Table 2. Individual chromosome fitness

[0077] Step 3: Using a tournament selection strategy, select chromosome individuals from the initial population, selecting chromosome 1 and chromosome 2. Based on the fitness function calculated above, chromosome 2 has a higher fitness than chromosome 1, so add chromosome 2 to the new population (parent population). Repeat this process until the number of individuals in the new population reaches 50% of the number of individuals in the initial population.

[0078] Step 4, as follows Figure 3 As shown, two chromosome individuals from the new population are selected as parents 1 and 2. The selected parent chromosome individuals are subjected to a time-sequence selection crossover operation to generate new offspring individuals. The offspring individuals are then added to the offspring population. This process is repeated until the size of the offspring population reaches the preset value N or the number of iterations reaches the set maximum number of loops MAX_C.

[0079] The process of timing selection and crossover of operation codes is as follows:

[0080] (1) Generate two random numbers 2 and 4 as the starting and ending points of this crossover. The segment A1 that needs to be crossed for the parent generation 1 process code is 1,2,1, and the segment A2 that needs to be crossed for the chromosome 2 process code is 1,1,3.

[0081] (2) Create child generation 1 and child generation 2. Set their machine codes directly to be the same as those of parent generation 1 and parent generation 2, respectively. Set their operation codes to empty. Empty values ​​are represented by -1. Then the operation codes of child generation 1 and child generation 2 are both -1, -1, -1, -1, -1, -1, -1.

[0082] (3) Use a loop to traverse from the starting point 2 to the ending point 4, and copy A2 to the corresponding position of child 1. Then child 1 becomes -1,1,1,3,-1,-1,-1,-1; then copy A1 to the corresponding position of child 2. Then child 2 becomes -1,1,2,1,-1,-1,-1,-1.

[0083] (4) Use a loop to traverse each position in offspring individual 1. If the gene at that position is empty (value -1), then traverse parent generation 1 until a gene that does not conflict with the gene in offspring 1 is found and the empty position is assigned that value. Therefore, the process code of offspring 1, i.e., -1,1,1,3,-1,-1,-1,-1, is filled in sequentially, becoming 2,1,1,3,3,3,1,2; the process code of offspring 2, i.e., -1,1,2,1,-1,-1,-1,-1, is filled in as 3,1,2,1,2,3,1,3.

[0084] (5) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

[0085] Step 5: Perform mutation operations on the offspring population individuals according to probability. Select the chromosome individual (process code 3,1,2,1,2,3,1,3, machine code 2,3,2,1,2,3,1,1) for mutation operation. Randomly swap the genes of process codes 1 and 4, and the chromosome individual's process code becomes 1,1,2,3,2,3,1,3. Then select the gene at machine code position 5, and replace the gene value 2 at this position with another available machine for the process with natural code 5. According to Table 1, the process with natural code 5 has machine 3 available in addition to machine 2. Therefore, replace the machine code at this position with 3. After the replacement, the machine code of chromosome 1 is 2,3,2,1,3,3,1,1.

[0086] Step 6: Iterate through steps 2 to 5 until the set number of iterations is reached (100). Then stop iterating and select the individual with the highest fitness from the last generation of the population as the final solution.

Claims

1. An improved genetic algorithm-based workshop scheduling method that satisfies single-task completion time constraints, characterized by: Includes the following steps: Step 1: Randomly generate multiple initial scheduling schemes that satisfy process sequence constraints, machine allocation constraints, and workpiece completion time constraints; Each scheduling scheme is treated as a chromosome individual, and the machine code and process code of the scheduling scheme are treated as genes; each chromosome individual constitutes the initial population. Step 2: Calculate the fitness of chromosome individuals in the initial population using the fitness function that is constrained by task duration. The fitness function f(x) is expressed as follows: in, , where is the penalty factor for the i-th task in the x-th scheduling scheme; t(i) is the actual completion time of the i-th task; t exp (i) Specify the completion time for the user of the i-th task; H x (i) is a Boolean function that takes the value 1 if the actual completion time of the i-th task in the x-th scheduling scheme is greater than the user-specified completion time, and takes the value 0 otherwise; i=1,2,3...n; x=1,2,3...N; n is the number of tasks in the scheduling scheme; N is the number of scheduling schemes; Step 3: Use a tournament selection strategy to select a new population from the initial population; Step 4: Perform a time-series crossover operation on the new population to obtain the offspring population; The process of temporal crossover is as follows: Select two chromosome individuals from the new population as parent generation 1 and parent generation 2, execute the sequential selection crossover method of the operation code or the double-point crossover method of the machine code with equal probability to generate new offspring individuals, and add the offspring individuals to the offspring population. Repeat this process until the size of the offspring population reaches the preset value N or the number of iterations reaches the maximum number of cycles. The operation code timing selection crossover method is as follows: (1) Two values ​​are randomly generated. The smaller value is taken as the starting point of this crossover, and the larger value is taken as the ending point. The process code between the starting point and the ending point is the part that needs to be crossed. The part that needs to be crossed in the process code of parent 1 is A1, and the part that needs to be crossed in the process code of parent 2 is A2. (2) Create child generation 1 and child generation 2; set the machine code of child generation 1 to be the same as the machine code of parent generation 1, and the machine code of child generation 2 to be the same as the machine code of parent generation 2; set the process code of both child generation 1 and child generation 2 to empty. (3) Use loop traversal to traverse from the starting point to the ending point, copy the part A1 that needs to be crossed in parent generation 1 to the corresponding position in child generation 2; copy the part A2 that needs to be crossed in parent generation 1 to the corresponding position in child generation 1. (4) Iterate through each position in offspring individual 1. If the process code (gene) at the traversed position is empty, iterate through parent 1, select a gene that does not conflict with the empty gene of offspring 1, assign the gene to the empty gene of offspring 1, and repeat the process until there are no empty genes in offspring 1. Iterate through each position in offspring 2. If the gene at the traversed position is empty, iterate through parent 2, select a gene that does not conflict with the empty gene of offspring 2, assign the gene to the empty gene of offspring 2, and repeat the process until there are no empty genes in offspring 2. (5) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded. Step 5: Perform mutation operations on the offspring population; Step 6: Iterate through steps 2 to 5 until the set number of iterations is reached, and select the chromosome individual with the highest fitness from the last generation of new population as the final scheduling scheme.

2. The improved genetic algorithm-based workshop scheduling method according to claim 1, which satisfies the single-task completion time constraint, is characterized in that: In step three, the tournament selection strategy is as follows: multiple chromosome individuals are randomly selected from the initial population, the fitness of the selected chromosome individuals is compared, and the individual with the highest fitness is selected to join the new population; this process is repeated until the number of individuals in the new population reaches the preset proportion of the number of individuals in the initial population.

3. The improved genetic algorithm-based workshop scheduling method according to claim 1, which satisfies the single-task completion time constraint, is characterized in that: The two-dot crossover method for the machine code is as follows: (1) Copy parent generation 1 and parent generation 2 as child generation 1 and child generation 2 respectively; (2) Two values ​​are randomly generated. The smaller value is used as the starting point of this crossover, and the larger value is used as the ending point. The machine code between the starting point and the ending point is the part that needs to be crossed. The part that needs to be crossed in the machine code of child 1 is A1, and the part that needs to be crossed in the machine code of child 2 is A2. (3) Swap the A1 part in child 1 and the A2 part in child 2; (4) If the offspring after crossover meet the time constraints of a single task, the offspring obtained will be added to the offspring population; otherwise, they will be discarded.

4. The improved genetic algorithm-based workshop scheduling method according to claim 1, which satisfies the single-task completion time constraint, is characterized in that: In step five, the mutation operation is performed as follows: randomly swap the genes at two positions of the chromosome individual process code; randomly select a position of the machine code and replace the gene at that position with another available machine for the corresponding process.

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