A scheduling method for unrelated parallel machines in rocket tank assembly processes considering variable resources

Abstract

The present invention discloses a method for scheduling unrelated parallel machines in a rocket tank assembly process taking into account variable resources. This method targets multi-variety and small-batch rocket tank assembly tasks, comprehensively considers the impact of workers' skill constraints, skill proficiency, and the collaborative efficiency of worker combinations on scheduling optimization, and constructs an unrelated parallel machine scheduling model with the goal of minimizing completion time. By solving the scheduling optimization model, the optimal scheduling scheme is obtained to ensure a reasonable match between tasks, work centers, and workers, improve the utilization rate of work centers and the collaborative efficiency of workers, and thus effectively shorten the completion time of assembly tasks. Under the premise of meeting various constraints, the optimal scheduling scheme is applied to the rocket tank assembly process to improve assembly efficiency.

Description

Technical Field

[0001] The invention belongs to the field of rocket tank assembly process scheduling, and in particular relates to a rocket tank assembly process unrelated parallel machine scheduling method considering variable resources. Background Art

[0002] The tank is one of the main components of the launch vehicle. It is used to store liquid propellants and bear most of the structural load. It accounts for 60% of the mass of the rocket body and is a core element that affects the performance of the launch vehicle. In the production process of rocket tanks, the tank assembly process is a complex and delicate process involving multiple tasks and collaboration between worker combinations. Traditional scheduling methods usually adopt a fixed resource allocation strategy, ignoring the matching of worker skills and tasks, the proficiency of skills, and the differences in the collaborative efficiency of worker combinations. This will lead to low resource utilization, insufficient coordination between workers, affecting the overall assembly efficiency, and thus causing construction delays. With the rapid development of rocket technology, the efficiency requirements of the tank assembly process are getting higher and higher. How to improve the assembly efficiency by optimizing scheduling while ensuring quality has become an important problem to be solved. Therefore, a scheduling method for unrelated parallel machines in the rocket tank assembly process considering variable resources is invented to flexibly deal with problems such as differences in worker skills, proficiency, and collaborative efficiency, which has important practical significance and broad application prospects for improving the overall assembly efficiency. Summary of the invention

[0003] In response to the problems existing in the above-mentioned prior art, the present invention proposes an unrelated parallel machine scheduling method for rocket tank assembly processes taking into account variable resources, so as to comprehensively consider the impact of workers' skill constraints, skill proficiency and the collaborative efficiency of worker combinations on scheduling optimization, and obtain the optimal scheduling plan.

[0004] In order to achieve the above technical objectives, the present invention provides the following technical solutions:

[0005] A method for scheduling unrelated parallel machines for rocket tank assembly processes considering variable resources specifically comprises the following steps:

[0006] S1. Conduct detailed task analysis for multi-variety, small-batch rocket tank assembly tasks to identify the processing time of each task and its specific requirements for worker combinations;

[0007] S2. Record the skill set and proficiency data of each worker; the skill set is the specific tasks that each worker can perform, and the proficiency data is the skill proficiency of each worker in completing these tasks;

[0008] S3. Comprehensively consider the impact of workers' skill constraints, skill proficiency and the collaborative efficiency of worker combinations on scheduling optimization, and construct an unrelated parallel machine scheduling model for rocket tank assembly processes that takes variable resources into account with the goal of minimizing completion time; the skill constraints are the specific tasks that workers can perform;

[0009] S4. Solve the scheduling model constructed in step S3 to obtain the optimal scheduling plan, and apply the scheduling plan to the rocket tank assembly process to improve assembly efficiency.

[0010] Furthermore, the scheduling model is represented by a three-field representation, specifically:

[0011]

[0012] Among them, R m Indicates that the machine environment is an unrelated parallel machine environment; It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; is a constraint condition;

[0013] In the above constraints, i and j represent tasks and workers respectively; f ij represents the proficiency coefficient of worker j for task i, s ij is a parameter used to evaluate whether worker j is competent for task i; W is the set of workers, α ij is a decision variable used to evaluate whether task i is assigned to worker j; r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i;

[0014] More specifically, the optimization goal of the scheduling model is:

[0015]

[0016] in, is the objective function of the scheduling model, C i is the end processing time of task i, T is the task set, i is the index representing a single task; the optimization goal is to minimize the maximum end processing time of all tasks.

[0017] Furthermore, the constraints of the scheduling model specifically include:

[0018]

[0019]

[0020] In the above constraint formula, the task set T = {1,2,…,n t}, with index i or i' representing a single task, and the work center set M = {1,2,…,n m}, with index k representing a single work center, and the worker set W = {1,2,…,n w}, with index j representing a single worker; n t 、n m 、n w are the number of tasks, work centers, and workers, respectively;

[0021] Constraint (1) ensures that each operation is completed in only one work center, β ik is a 0-1 decision variable. If task i is completed at work center k, then β ik =1, otherwise 0;

[0022] Constraint (2) ensures that workers are assigned to tasks only if they are competent for the task, α ij is a 0-1 decision variable. If task i is assigned to worker j to complete, then α ij =1, otherwise 0; s ij is the parameter, s ij =1 means worker j is competent for task i, otherwise 0;

[0023] Constraints (3) and (4) ensure that the number of workers assigned to a task is within the corresponding interval, where r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i;

[0024] Constraint (5) ensures that each worker is assigned at least one task;

[0025] Constraints (6) to (8) ensure that each task has a reasonable completion time; where u i represents the inverse of the number of workers who have completed task i; f ij represents the proficiency coefficient of worker j for task i, and its value range is 0.5 to 1.5. A value of 1 means that the worker can complete the task according to the standard time. The higher the proficiency, the higher the proficiency coefficient f ij The lower the value; i represents the average proficiency coefficient of workers who complete task i; S i represents the start processing time of task i; p ik represents the standard processing time of task i in work center k; the actual collaborative processing time of task i The standard processing time p of the work center ik and the average skill coefficient v of the combination of workers who complete the task i Joint decision making;

[0026] Constraint (9) stipulates that the same work center cannot start the next task before completing the previous task, so as to ensure that the work center can only process one task at a time; i' represents the start processing time of task i'; N represents a sufficiently large positive number; x ii'k is a 0-1 decision variable; if task i and task i' are adjacent and completed on work center k, and task i precedes task i', then x ii'k =1, otherwise 0;

[0027] Constraint (10) stipulates that the same worker cannot start the next task before completing the previous task, so as to ensure that the worker can only perform one task at a time; ii'k is a 0-1 decision variable. If task i and task i' are completed by worker j one after another, and task i precedes task i', then y ii'k =1, otherwise 0;

[0028] Constraints (11) to (15) ensure that the decision variables are within the feasible range.

[0029] Furthermore, in step S4, the Gurobi solver is used to optimize and solve the small-scale scheduling, and the hybrid particle swarm optimization algorithm is used to optimize and solve the large-scale scheduling; the hybrid particle swarm optimization algorithm specifically includes the following steps:

[0030] P1, initialize parameters and use the three-dimensional coding scheme to initialize the population;

[0031] P2, calculate the fitness of particles in the population;

[0032] P3, update the individual historical optimal position and the global optimal position;

[0033] P4, execute genetic operators to update particle positions;

[0034] P5. Determine whether the iteration stop condition is met. If so, output the optimal scheduling plan, otherwise return to P2.

[0035] Furthermore, the initialization of the population using the three-dimensional coding scheme in step P1 specifically includes:

[0036] Each particle contains the task sequence, work center and worker allocation information; the length of each dimension is the total number of tasks; the first dimension encodes the task sequence, and the value is the task number; the second dimension encodes the work center, and the value is the work center number that completes the task; the third dimension encodes the worker allocation, and the value is the combination of workers that completes the task.

[0037] The order in which tasks are processed by the work center and the order in which workers perform tasks are determined by the corresponding task number sequence in the first dimension.

[0038] Furthermore, step P4 is specifically as follows:

[0039] P41, take each particle in the population as the current particle and execute the mutation operator first;

[0040] P42. Generate a random number r between 0 and 1. If r<0.5, select the best position gbest among all particles and perform the crossover operator with the current particle. Otherwise, select the historical best position pbest obtained by the current particle and perform the crossover operator with the current particle.

[0041] More specifically, the execution of the variation calculation in step P41 specifically includes:

[0042] P411, randomly select two different columns of the current particle A;

[0043] P412, exchange the elements of the two selected columns;

[0044] P413. Recombine the exchanged third-dimensional worker allocation information to form a new worker combination.

[0045] More specifically, the execution of the crossover operator in step P42 specifically includes:

[0046] P421, particle A is the basic particle, and particle B is the inserted particle;

[0047] P422, randomly generate a 0-1 vector with the same length as the particle;

[0048] P423. According to the 0-1 vector, the columns corresponding to 1 in the basic particle are retained in the new particle in the original position order;

[0049] P424, insert the columns of the remaining tasks in the inserted particle into the new particle in order;

[0050] P425. Exchange the roles of particle A and particle B, repeat steps P423 and P424, and generate another new particle.

[0051] Based on the above technical solution, the present invention proposes a method for scheduling unrelated parallel machines for rocket tank assembly processes taking into account variable resources, which has the following beneficial effects:

[0052] For the multi-variety, small-batch rocket tank assembly task, the method proposed in this invention comprehensively considers the impact of workers' skill constraints, skill proficiency, and the collaborative efficiency of worker combinations on scheduling optimization, and constructs an unrelated parallel machine scheduling model with the goal of minimizing completion time. By solving the scheduling optimization model, the optimal scheduling plan is obtained to ensure a reasonable match between tasks, work centers, and workers, improve the utilization rate of work centers and the collaborative efficiency of workers, and effectively shorten the completion time of assembly tasks.

[0053] The method proposed in the present invention also adopts a hybrid particle swarm optimization algorithm and a three-dimensional coding scheme, which can effectively handle the complex relationship between tasks, work centers and worker allocations, and improve the adaptability of the algorithm to multi-dimensional problems; combined with the mutation and crossover operators of the genetic algorithm, it can better explore the solution space and avoid falling into the local optimum. Through the optimization solution of the algorithm, not only can a better solution be obtained in a shorter time, but the algorithm has high stability and effectively improves the scheduling efficiency. Under the premise of meeting various constraints, the optimal scheduling scheme is applied to the rocket tank assembly process to improve the assembly efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flowchart of a method for scheduling unrelated parallel machines for rocket tank assembly processes taking into account variable resources proposed by the present invention;

[0055] Figure 2 A flow chart of the hybrid particle swarm optimization algorithm implemented in the present invention;

[0056] Figure 3 This is an example diagram of a three-dimensional coding scheme in the present invention;

[0057] Figure 4 An example diagram of executing a mutation operator in the present invention;

[0058] Figure 5 This is an example diagram of executing the crossover operator in the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0061] In order to overcome the limitations of the prior art rocket tank assembly process scheduling scheme, in this embodiment, Figure 1 As shown, the present invention proposes a method for scheduling unrelated parallel machines for rocket tank assembly processes taking into account variable resources, which specifically includes the following steps:

[0062] S1. Conduct detailed task analysis for multi-variety, small-batch rocket tank assembly tasks to identify the processing time of each task and its specific requirements for worker combinations;

[0063] S2. Record the skill set and proficiency data of each worker; the skill set is the specific tasks that each worker can perform, and the proficiency data is the skill proficiency of each worker in completing these tasks;

[0064] S3. Comprehensively consider the impact of workers' skill constraints (i.e., the specific tasks that workers can perform), skill proficiency, and the collaborative efficiency of worker combinations on scheduling optimization, and construct an unrelated parallel machine scheduling model for rocket tank assembly processes that takes variable resources into account with the goal of minimizing completion time;

[0065] The establishment of the model needs to be based on the following assumptions: all tasks, work centers and workers are available at the beginning of scheduling; there is no priority between tasks; emergencies such as machine failures and task insertions are ignored; and the preparation time and adjustment time of work centers and workers are ignored. Therefore, in this embodiment, as a preferred method, the scheduling model constructed in step S3 is specifically:

[0066] Expressed using three-field notation (machine environment | constraints | optimization goal):

[0067]

[0068] Among them, R m Indicates that the machine environment is an unrelated parallel machine environment; It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; is a constraint condition;

[0069] In the above constraints, i and j represent tasks and workers respectively; f ij represents the proficiency coefficient of worker j for task i, s ij is a parameter used to evaluate whether worker j is competent for task i; W is the set of workers, α ijis a decision variable used to evaluate whether task i is assigned to worker j; r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i;

[0070] More specifically, the optimization goal of the scheduling model is:

[0071]

[0072] in, is the objective function of the scheduling model, C i is the end processing time of task i, T is the task set, i is the index representing a single task; the optimization goal is to minimize the maximum end processing time of all tasks.

[0073] More specifically, the constraints of the scheduling model include:

[0074]

[0075] In the above constraint formula, the task set T = {1,2,…,n t}, with index i or i' representing a single task, and the work center set M = {1,2,…,n m}, with index k representing a single work center, and the worker set W = {1,2,…,n w}, with index j representing a single worker; n t 、n m 、n w are the number of tasks, work centers, and workers, respectively.

[0076] Constraint (1) ensures that each operation is completed in only one work center, β ik is a 0-1 decision variable. If task i is completed at work center k, then β ik =1, otherwise 0;

[0077] Constraint (2) ensures that workers are assigned to tasks only if they are competent for the task, α ij is a 0-1 decision variable. If task i is assigned to worker j to complete, then α ij =1, otherwise 0; s ij is the parameter, s ij =1 means worker j is competent for task i, otherwise 0;

[0078] Constraints (3) and (4) ensure that the number of workers assigned to a task is within the corresponding interval, where r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i;

[0079] Constraint (5) ensures that each worker is assigned at least one task;

[0080] Constraints (6) to (8) ensure that each task has a reasonable completion time; where u i represents the inverse of the number of workers who have completed task i; f ij represents the proficiency coefficient of worker j for task i, and its value range is 0.5 to 1.5. A value of 1 means that the worker can complete the task according to the standard time. The higher the proficiency, the higher the proficiency coefficient f ij The lower the value; i represents the average proficiency coefficient of workers who complete task i; S i represents the start processing time of task i; p ik represents the standard processing time of task i in work center k; the actual collaborative processing time of task i The standard processing time p of the work center ik and the average skill coefficient v of the combination of workers who complete the task i Joint decision making;

[0081] Constraint (9) stipulates that the same work center cannot start the next task before completing the previous task, so as to ensure that the work center can only process one task at a time; i' represents the start processing time of task i'; N represents a sufficiently large positive number; x ii'k is a 0-1 decision variable; if task i and task i' are adjacent and completed on work center k, and task i precedes task i', then x ii'k =1, otherwise 0;

[0082] Constraint (10) stipulates that the same worker cannot start the next task before completing the previous task, so as to ensure that the worker can only perform one task at a time; ii'k is a 0-1 decision variable. If task i and task i' are completed by worker j one after another, and task i precedes task i', then y ii'k =1, otherwise 0;

[0083] Constraints (11) to (15) ensure that the decision variables are within the feasible range.

[0084] S4. Solve the scheduling model constructed in step S3 to obtain the optimal scheduling plan, and apply the scheduling plan to the rocket tank assembly process to improve assembly efficiency.

[0085] The unrelated parallel machine scheduling model for rocket tank assembly process considering variable resources proposed in the present invention is a typical NP-hard problem. Therefore, as a preferred implementation of step S4, in a small-scale scheduling example, the Gurobi solver is used to optimize and solve the example; and in a large-scale scheduling example, the hybrid particle swarm optimization algorithm is used to solve the NP-hard problem.

[0086] like Figure 2 As shown in the figure, in a large-scale scheduling example, the scheduling solution is solved by a hybrid particle swarm optimization algorithm, which includes the following steps:

[0087] P1, initialize parameters and use the three-dimensional coding scheme to initialize the population;

[0088] The coding scheme is a bridge between the model and the algorithm. Considering the characteristics of the rocket tank assembly process unrelated parallel machine scheduling model considering variable resources of the present invention, this embodiment proposes an effective three-dimensional coding scheme. Figure 3 As shown in (a), each particle contains task sequence, work center and worker allocation information, and the length of each dimension is the total number of tasks. The first dimension encodes the task sequence, and the value is the task number; the second dimension encodes the work center, and the value is the work center number that completes the task; the third dimension encodes the worker allocation, and the value is the combination of workers that complete the task.

[0089] For example, in Figure 3 In (a), the first column indicates that task 5 is completed by workers 2, 3, 4, and 6 in work center 2. The order of task processing in the work center is determined by the order of the corresponding task numbers in the first dimension. For example, for work center 2, the corresponding task number order is task 5, task 4, task 7, and task 2. Then the processing order of work center 2 is also task 5, task 4, task 7, and task 2. Similarly, the order of processing tasks in other work centers can be obtained, as shown in the figure. Figure 3 (b) The order in which workers execute tasks is determined by the order of the corresponding task numbers in the first dimension. For example, for worker 2, the corresponding task number sequence is task 5 and task 7, so the execution order of worker 2 is also task 5 and task 7, and the task execution order of other workers can be deduced in the same way, as shown in the figure below. Figure 3 (c) as shown.

[0090] P2, calculate the fitness of particles in the population;

[0091] P3, update individual historical optimal position and global optimal position;

[0092] P4, execute genetic operators to update particle positions;

[0093] As a preferred implementation of step P4, it specifically includes:

[0094] P41, take each particle in the population as the current particle and execute the mutation operator first;

[0095] More specifically, the process of executing the mutation operator is:

[0096] P411, randomly select two different columns of the current particle A;

[0097] P412, exchange the elements of the two selected columns;

[0098] P413. Recombine the exchanged third-dimensional worker allocation information to form a new worker combination.

[0099] This embodiment provides a mutation operator diagram, such as Figure 4 As shown in the figure, the information of the first dimension before mutation is {1,6,7,8,3,5,4,2,9,10}, the information of the second dimension is {3,1,2,2,1,2,1,1,3,1}, and the information of the third dimension is {(2,4,6),(1),(2),(1,4),(1,3,4),(3,6),(1,3,6),(2,3,4),(2),(2,5)}. If two different columns are randomly selected as the 3rd column and the 8th column, the 3rd column {7,2,(2)} and the 8th column {2,1,(2,3,4)} are swapped, and the worker allocation information of the third dimension after the swap is recombined, the third dimension of the 3rd column after the swap is mutated to (2,4), and the third dimension of the 8th column after the swap is mutated to (1,3). Therefore, the information of the new particle three-dimensional encoding schemes after mutation are {1,6,2,8,3,5,4,7,9,10}, {3,1,1,2,1,2,1,2,3,1}, {(2,4,6),(1),(2,4),(1,4),(1,3,4),(3,6),(1,3,6),(1,3),(2),(2,5)}.

[0100] P42. Generate a random number r between 0 and 1. If r<0.5, select the best position gbest among all particles and perform the crossover operator with the current particle. Otherwise, select the historical best position pbest obtained by the current particle and perform the crossover operator with the current particle.

[0101] More specifically, the process of executing the crossover operator is:

[0102] P421, particle A is the basic particle, and particle B is the inserted particle;

[0103] P422, randomly generate a 0-1 vector with the same length as the particle;

[0104] P423. According to the 0-1 vector, the columns corresponding to 1 in the basic particle are retained in the new particle in the original position order;

[0105] P424, insert the columns of the remaining tasks in the inserted particle into the new particle in order;

[0106] P425. Exchange the roles of particle A and particle B, repeat steps P423 and P424, and generate another new particle.

[0107] This embodiment provides a schematic diagram of a crossover operator, such as Figure 5 As shown, with particle A as the base particle and particle B as the inserted particle, the information of the three-dimensional coding scheme of particle A before crossing is {1,6,7,8,3,5,4,2,9,10}, {3,1,2,2,1,2,1,1,3,1}, {(2,4,6),(1),(2),(1,4),(1,3,4),(3,6),(1,3,6),(2,3,4),(2),(2,5)}, and the information of the three-dimensional coding scheme of particle B before crossing is {5,7,4,8,2,1,6,3,9,10}, {2,1,3,2,2,3,3,3,1,2}, {(2,3,6),(1,3,6),(4,5),(1,3,4,5),(3),(1,4,6),(1,6),(1,3,6),(2,3,4),(3,5)}. If the information of the randomly generated 0-1 vector is {1,0,0,1,1,1,0,0,0,1}, the 1st, 4th, 5th, 6th, and 10th columns corresponding to 1 in particle A are retained in the new particle in the original order, and the columns of the remaining tasks in particle B are inserted into the new particle in sequence. The information of the three-dimensional encoding scheme of the new particles obtained after crossover is {1,7,4,8,3,5,2,6,9,10}, {3,1,3,2,1,2,2,3,1,1}, {(2,4,6),(1,3,6),(4,5),(1,4),(1,3,4),(3,6),(3),(1,6),(2,3,4),(2,5)}.

[0108] P5. Determine whether the iteration stop condition is met. If so, output the optimal scheduling plan, otherwise return to P2.

[0109] In addition, this embodiment further illustrates the effectiveness and feasibility of the unrelated parallel machine scheduling method for rocket tank assembly processes taking into account variable resources proposed by the present invention through the following experiments.

[0110] First, in the small-scale scheduling example, the Gurobi solver is used for optimization. Second, in the large-scale scheduling example, the hybrid particle swarm optimization algorithm is used for optimization. All experiments are implemented in Python and conducted on a computer running Microsoft Windows 11 operating system, equipped with an Intel(R) Ultra 3800MHz processor and equipped with 1TB of memory. The Gurobi solver version is 11.0.3.

[0111] (1) Experimental design

[0112] In order to simulate the real rocket tank assembly environment, the specific values ​​of this experiment are as follows: the lower bound of the worker number interval l i The value ranges from 1 to 3, with an upper bound of r i The value ranges from 2 to 6, and the upper bound of the interval of the number of workers for the same task i is greater than the lower bound; the standard processing time p ik The value ranges from 2 to 10; the proficiency coefficient f ij The value ranges from 0.5 to 1.5.

[0113] The scheduling instance naming rule is {scheduling instance scale}'{number}-{number of tasks}-{number of work centers}-{number of workers}. The scheduling instance scale is divided into two types: s and l, which represent small-scale and large-scale instances respectively. For example, instance s'01-10-3-6 means: the scheduling instance belongs to a small-scale instance, numbered 01, and contains 10 tasks, 3 work centers, and 6 workers.

[0114] (2) Optimization solution

[0115] For small-scale scheduling instances, the present invention uses the Gurobi solver for solving, and the experimental results are shown in Table 1. The solution time of small-scale scheduling instances on the Gurobi solver increases with the increase in the number of tasks, work centers, and workers, but the optimal solution can be obtained within a reasonable time. Specifically, the solution time of instance s'01-8-3-8 is 6.1 seconds, while the solution time of instance s'06-15-5-12 is 484.4 seconds. The results show that the Gurobi solver can effectively process small-scale scheduling instances in a shorter time and ensure the optimality of the solution.

[0116] Table 1 Small-scale scheduling examples solved by Gurobi solver

[0117]

[0118]

[0119] For solving large-scale scheduling instances, the present invention adopts a hybrid particle swarm optimization algorithm, the number of iterations of the algorithm is 300 times, and the population size is 30. In order to reduce the experimental error, all experiments are run independently 10 times, and then the average value is taken as the final experimental result. The experimental results are shown in Table 2. The algorithm is used to solve large-scale scheduling instances. The results show that the algorithm exhibits good solution effect and low standard deviation, indicating that the results obtained by the algorithm are more stable. In addition, the average solution time is relatively short, indicating that the algorithm can quickly converge to a better solution. Specifically, the average solution time of instance l'01-20-3-6 is short. As the number of tasks and resources increases, the solution time increases, but it is still within a reasonable range.

[0120] Table 2. Examples of large-scale scheduling solved by hybrid particle swarm optimization algorithm

[0121]

[0122] In summary, the present invention proposes an unrelated parallel machine scheduling model for rocket tank assembly processes that takes into account variable resources for multi-variety and small-batch rocket tank assembly tasks. On this basis, the Gurobi solver is used to optimize and solve small-scale scheduling instances, and the hybrid particle swarm optimization algorithm is used to optimize and solve large-scale scheduling instances. The simulation experimental results show the effectiveness and feasibility of the proposed scheduling method. Through the method proposed in the present invention, it is possible to ensure a reasonable match between tasks, work centers and workers, improve the utilization rate of work centers and the collaboration efficiency of workers, and effectively shorten the completion time of assembly tasks.

[0123] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0124] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for scheduling unrelated parallel machines for rocket tank assembly processes considering variable resources, characterized in that: The specific steps include: S1. Conduct detailed task analysis for multi-variety, small-batch rocket tank assembly tasks to identify the processing time of each task and its specific requirements for worker combinations; S2. Record the skill set and proficiency data of each worker; the skill set is the specific tasks that each worker can perform, and the proficiency data is the skill proficiency of each worker in completing these tasks; S3. Comprehensively consider the impact of workers' skill constraints, skill proficiency and the collaborative efficiency of worker combinations on scheduling optimization, and construct an unrelated parallel machine scheduling model for rocket tank assembly processes that takes variable resources into consideration with the goal of minimizing completion time; the skill constraints are the specific tasks that workers can perform; the scheduling model is represented by a three-field representation, specifically: Among them, R m Indicates that the machine environment is an unrelated parallel machine environment; m i∈ a T xC i It represents the maximum finishing time of all tasks, which is used to evaluate the optimization goal; is a constraint condition; In the above constraints, i and j represent tasks and workers respectively; f ij represents the proficiency coefficient of worker j for task i, s ij is a parameter used to evaluate whether worker j is competent for task i; W is the set of workers, α ij is a decision variable used to evaluate whether task i is assigned to worker j; r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i; The optimization goal of the scheduling model is: in, is the objective function of the scheduling model, C i is the end processing time of task i, T is the task set, i is the index to represent a single task; the optimization goal is to minimize the maximum end processing time of all tasks; The constraints of the scheduling model include: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) In the above constraint formula, the task set T = {1,2,…,n t }, with index i or i' representing a single task, and the work center set M = {1,2,…,n m }, with index k representing a single work center, and the worker set W = {1,2,…,n w }, with index j representing a single worker; n t 、n m 、n w are the number of tasks, work centers, and workers, respectively; Constraint (1) ensures that each operation is completed in only one work center, β ik is a 0-1 decision variable. If task i is completed at work center k, then β ik =1, otherwise 0; Constraint (2) ensures that workers are assigned to tasks only if they are competent for the task, α ij is a 0-1 decision variable. If task i is assigned to worker j to complete, then α ij =1, otherwise 0; s ij is the parameter, s ij =1 means worker j is competent for task i, otherwise 0; Constraints (3) and (4) ensure that the number of workers assigned to a task is within the corresponding interval, where r i is the upper bound of the number of workers for task i; l i is the lower bound for the number of workers for task i; Constraint (5) ensures that each worker is assigned at least one task; Constraints (6) to (8) ensure that each task has a reasonable completion time; where u i represents the inverse of the number of workers who have completed task i; f ij represents the proficiency coefficient of worker j for task i, and its value range is 0.5 to 1.

5. A value of 1 means that the worker can complete the task according to the standard time. The higher the proficiency, the higher the proficiency coefficient f ij The lower the value, the i represents the average proficiency coefficient of workers who complete task i; S i represents the start processing time of task i; p ik represents the standard processing time of task i in work center k; the actual collaborative processing time of task i The standard processing time p of the work center ik and the average skill coefficient v of the combination of workers who complete the task i Joint decision making; Constraint (9) stipulates that the same work center cannot start the next task before completing the previous task, so as to ensure that the work center can only process one task at a time; i' represents the start processing time of task i'; N represents a sufficiently large positive number; x ii'k is a 0-1 decision variable; if task i and task i' are adjacent and completed on work center k, and task i precedes task i', then x ii'k =1, otherwise 0; Constraint (10) stipulates that the same worker cannot start the next task before completing the previous task, so as to ensure that the worker can only perform one task at a time; ii'k is a 0-1 decision variable. If task i and task i' are completed by worker j one after another, and task i precedes task i', then y ii ' k =1, otherwise 0; Constraints (11) to (15) ensure that the decision variables are within the feasible range; S4, solving the scheduling model constructed in step S3 to obtain an optimal scheduling solution, and applying the scheduling solution to the rocket tank assembly process to improve assembly efficiency; specifically: The Gurobi solver is used to optimize and solve small-scale scheduling, and the hybrid particle swarm optimization algorithm is used to optimize and solve large-scale scheduling; the hybrid particle swarm optimization algorithm specifically includes the following steps: P1, initialize parameters and use the three-dimensional coding scheme to initialize the population; P2, calculate the fitness of particles in the population; P3, update individual historical optimal position and global optimal position; P4, execute genetic operators to update particle positions; P5. Determine whether the iteration stop condition is met. If so, output the optimal scheduling plan, otherwise return to P2.

2. The method for scheduling unrelated parallel machines for rocket tank assembly processes considering variable resources according to claim 1 is characterized in that: Initializing the population using the three-dimensional encoding scheme described in step P1 specifically includes: Each particle contains task sequence, work center and worker allocation information; the length of each dimension is the total number of tasks; the first dimension encodes the task sequence, and the value is the task number; the second dimension encodes the work center, and the value is the work center number that completes the task; the third dimension encodes the worker allocation, and the value is the combination of workers that completes the task; The order in which tasks are processed by the work center and the order in which workers perform tasks are determined by the corresponding task number sequence in the first dimension.

3. The method for scheduling unrelated parallel machines for rocket tank assembly processes considering variable resources according to claim 1, characterized in that: Step P4 is specifically as follows: P41, take each particle in the population as the current particle and execute the mutation operator first; P42. Generate a random number r between 0 and 1. If r<0.5, select the best position gbest among all particles and perform the crossover operator with the current particle. Otherwise, select the historical best position pbest obtained by the current particle and perform the crossover operator with the current particle.

4. The method for scheduling unrelated parallel machines for rocket tank assembly processes taking into account variable resources according to claim 3 is characterized in that: The execution of the mutation operator in step P41 specifically includes: P411, randomly select two different columns of the current particle A; P412, exchange the elements of the two selected columns; P413. Recombine the exchanged third-dimensional worker allocation information to form a new worker combination.

5. The method for scheduling unrelated parallel machines for rocket tank assembly processes considering variable resources according to claim 3 is characterized in that: The execution of the cross calculation in step P42 specifically includes: P421, particle A is the basic particle, and particle B is the inserted particle; P422, randomly generate a 0-1 vector with the same length as the particle; P423. According to the 0-1 vector, the columns corresponding to 1 in the basic particle are retained in the new particle in the original position order; P424, insert the columns of the remaining tasks in the inserted particle into the new particle in order; P425. Exchange the roles of particle A and particle B, repeat steps P424 and P425, and generate another new particle.

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