A parallel machine scheduling method for railway wagon body spraying operation

Abstract

The application discloses a kind of parallel machine scheduling methods of railway wagon body spraying operation, it is related to spraying operation technical field, establishes parallel machine scheduling model, to minimize maximum completion time objective model is established model objective function, designs a kind of based on Tadpole sea colony algorithm to solve this model;Tadpole sea colony algorithm has high robustness, parameter is simple and easy to operate, to incompatible operation family adopts a new population initialization mode, improves initial overall quality, uses multiple neighborhood search strategies, further improves the quality of solution, accelerates the convergence speed of algorithm;When spraying operation is carried out by the obtained scheduling method, the efficiency of automatic spraying machine spraying and character spraying quality can be improved, and the intervention of human resources is reduced.

Description

Technical Field

[0001] This invention belongs to the field of spray painting technology, specifically relating to a parallel scheduling method for spray painting operations on railway freight cars. Background Technology

[0002] The Parallel Machine Scheduling Problem (PMSP) is a typical high-complexity problem in actual production processes. It can be described as processing n jobs on m machines, with each job requiring only one processing cycle on each machine. The goal is to find the optimal batch size to minimize the total processing time. Similar to shop floor scheduling, once processing begins, jobs cannot be added or removed from the batch.

[0003] The painting process for truck bodies is complex and involves numerous steps, making it a crucial step in the truck body manufacturing process. The quality and efficiency of this painting directly impact the overall production capacity of the truck industry chain. Many constraints exist during the painting process, such as the number and type of characters, the surface roughness of the truck body, and the number of tools required. Furthermore, the painting parameters of the automatic painting machine affect the quality of the painting process. Parameters such as the air intake of the nozzle air pump and the distance between the nozzle and the truck body can be automatically adjusted by built-in software. However, due to the limitations of automatic painting, when painting characters on different ends or with different sizes, the automatic painting machine needs to be moved and the painting parameters reset, still requiring manual intervention and introducing many uncertainties to the scheduling plan. Therefore, while improving the painting efficiency of the automatic painting machine, it is crucial to improve the quality of character painting and reduce human intervention. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a parallel scheduling method for railway freight car body painting operations. The objective function of the model is established by minimizing the maximum completion time, and a solution based on the tunica swarm optimization algorithm is designed to solve this model. The tunica swarm optimization algorithm has high robustness, simple parameters, and is easy to operate. A new population initialization method is used for incompatible job families to improve the initial overall quality. Multiple neighborhood search strategies are employed to further improve the quality of the solution and accelerate the convergence speed of the algorithm.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for scheduling parallel machines in railway freight car body painting operations includes the following steps:

[0007] S1. Establish a parallel machine scheduling model based on the characteristics of the truck painting process. The scheduling model includes:

[0008] 1.1 Make reasonable assumptions about the scheduling model;

[0009] 1.2 Set parameters and decision variables;

[0010] 1.3 Construct the objective function of the scheduling model;

[0011] S2. Optimize the objective function based on the tunic group algorithm;

[0012] 2.1 Collect the data to be processed, and treat each font size with sprayed characters as a processing task, and treat different models of spray guns as different spraying machines;

[0013] 2.2 The above-mentioned data to be processed is transformed by adopting a two-layer coding method of process coding OS and machine coding MS, and the above scheduling model is transformed into a mathematical model, that is, transformed into a mathematical problem that can be calculated.

[0014] 2.3 Set the parameters of the tunicate group algorithm and initialize the population according to the encoding method in step 2.2;

[0015] 2.4 Calculate and rank the fitness values ​​of the salps population, select the one with the best fitness as the leader, and the others as followers;

[0016] 2.5 The leader performs neighborhood search, and the followers perform follow-up movements, reordering the population and completing the update and iteration of individuals;

[0017] 2.6 Repeat step 2.5 until the maximum number of iterations is reached to obtain the optimal solution for the current population, which is the optimal solution of the mathematical model, i.e., the optimal solution of the scheduling model, and also the optimal solution of the objective function of the scheduling model;

[0018] S3. Compare and verify the effectiveness of the scheduling model and algorithm. Specifically, compare with the scheduling scheme based on the minimum processing time principle, where all processes are processed on the machine with the shortest processing time, i.e., the MS part of each process is determined, and the processing scheme is obtained by optimizing its process arrangement; then compare with the scheduling method obtained in this invention to verify its effectiveness.

[0019] It can be compared with a processing scheme based on the principle of shortest processing time, which means that the processing machine for each process is selected from the available machines with the shortest processing time.

[0020] Reasonable assumptions about the scheduling model in step 1.1 include:

[0021] ① Each character and font size has its own independent painting task, which is not affected by other painting tasks;

[0022] ② Spraying operations on the same end face will not exceed the working space of the automatic spraying machine;

[0023] ③Each job task can be processed by at most one parallel machine;

[0024] ④ Each batch of products can only be processed once on the parallel machine;

[0025] ⑤ Consider the time required to move the automatic spraying machine when spraying characters on different end faces;

[0026] ⑥ Consider the time required for the automatic spraying machine software to change parameters when spraying different font sizes;

[0027] ⑦ In static workshop scheduling, assuming four spray guns of different calibers are used to spray 64 characters of different sizes, the machines and workpieces in the workshop need to meet the following constraints:

[0028] (1) Pre-specify the workpiece processing steps;

[0029] (2) The machine can only process one workpiece at a time;

[0030] (3) Unless there are special circumstances, each workpiece has equal priority in processing.

[0031] (4) The pre-specified processing time and machine shall not be changed.

[0032] The parameters and decision variables in step 1.2 include:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] The objective function in step 1.3 is:

[0039] minC max =min[max(C j (1)

[0040]

[0041] The constraints are:

[0042]

[0043]

[0044] C ijk ≤S ghk +M(1-γijghk (5)

[0045] Equation (1) indicates that the maximum completion time of the workpiece is the minimum, that is, the completion time of the last completed process is the minimum; Equation (2) indicates that the time for manual movement of the trolley in the scheduling is the minimum, that is, the amount of human resources used is the minimum. For the automatic spraying process, the input of human resources is its variable cost and is the main direction of enterprise cost control; Equation (3) indicates that a process can only be processed by one machine; Equation (4) indicates that the next process of the workpiece can only be started after the previous process of the workpiece is completed; Equation (5) indicates that a machine can only be occupied by one process at a time.

[0046] The steps in 1.1-1.3 above describe the process of establishing a parallel machine scheduling model. Parameters, decision variables, constraints, and objective functions together constitute this parallel machine scheduling model.

[0047] In step 2.2, the first-level process coding scheme is as follows:

[0048] The initial individuals are sorted using the Logistic chaotic mapping iterative equation to obtain the process codes. Chaos is an unstable phenomenon that spontaneously arises in deterministic systems; it can experience all states within a certain range without repetition. Utilizing chaotic variables for optimization search is superior to blind random search. The Logistic chaotic mapping iterative equation...

[0049] The equation is: y(k+1)=μy(k)(1-y(k)),k=1,2...n (6)

[0050] x j =u j +z nj (v j -u j (7)

[0051] In equation (6), y(k) is the value of the chaotic variable in the k-th iteration, k is the iteration number, and μ is the parameter. When the parameter μ is 4, the Logistic mapping is in a completely chaotic state and can achieve better results.

[0052] In equation (7), v j and u j These are the upper and lower bounds of the j-th dimension variable, x. j This represents the value of the j-dimensional component;

[0053] Define the individual dimension as m, the population size as N, and randomly generate an m-dimensional initial sequence z1 = (z 11 ,z 12 ,...,z 1mThe initial chaotic sequence matrix is ​​obtained by iterating through each component of the initial sequence using formula (6); the initial chaotic sequence matrix is ​​then transformed onto the variable interval of the target problem using formula (7) to complete the initial chaotic mapping; a set of random variables is generated, and a chaotic vector is obtained after multiple iterations using formula (6); the chaotic vector is then mapped onto the display code using formula (7) to obtain the individual's OS part code x = (x1, x2, ..., x...). m ).

[0054] The generation rules for population initialization are demonstrated by applying the Logistic chaotic mapping iterative equation to an example of 3 workpieces and 3 processes, as shown in the table below.

[0055] Table 1 Process Code

[0056]

[0057] The processing order obtained by decoding the encoded sequence shown in Table 1 is O. 11 O 12 O 31 O 21 O 32 O 22 O 23 O 33 O 13 Among them, O ij In this context, 'i' represents the workpiece, and 'j' represents the process. ij The process j representing workpiece i is being processed in this sequence.

[0058] In step 2.2, the second-layer machine coding scheme is as follows: the machine selection part of the initial individuals adopts a hybrid mechanism, in which 50% of the individuals are generated according to formulas (6) and (7), and 50% of the individuals are selected according to the principle of shortest processing time, based on the mechanism with the shortest processing time in the machine table, which is used to encode the MS part of the machine selection. The above ratio can be arbitrary, and orthogonal experiments can be added to verify the influence of different parameters on the convergence speed of the algorithm to find the optimal ratio.

[0059] Taking the 3×3 shop floor scheduling problem as an example, as shown in the figure below: the OS part represents the order in which workpieces appear, with the j-th appearance of workpiece i representing a process, and the position of the corresponding MS part represents its machine order within its selectable range. This encoding method can guarantee all constraints of the model and is widely used in solving the FJSP problem.

[0060] OS part

[0061]

[0062] MS section

[0063] Example of coding a 3×3 problem

[0064] In step 2.3, the parameters of the tunic group algorithm include the maximum number of iterations T. max The maximum number of iterations and population size for variable neighborhood search, etc.

[0065] In step 2.4, minimizing the maximum completion time and maximum human resources are used as optimization objectives. When calculating the fitness value of individual tunicates, the end faces of the preceding and following processing steps on the same machine are considered to calculate the required human interference. The Pareto sorting method is used to handle the multi-objective problem, obtaining a set of approximate optimal solutions. All non-dominated solutions in the Pareto solution set are designated as leaders, and other solutions as followers. The Pareto-based multi-objective approach can provide decision-makers with a set of approximate optimal solutions, effectively improving optimization efficiency.

[0066] In step 2.5, POX crossover and four neighborhood search operators are introduced to complete the iterative update of the tunicate population; the POX crossover method is as follows:

[0067] (1) For the two parent individuals that cross each other, randomly generate a proper subset Ω of the workpiece code type;

[0068] (2) Remove the element belonging to Ω from one of the parent generations to form a new child generation. Insert the elements belonging to the set from the other parent generation into the new child generation in the order of their arrangement in the parent generation to form the crossed individuals.

[0069] (3) Perform the same operation on another parent generation according to the method in (2) above; specifically, remove the elements belonging to Ω in another parent generation to form another new child generation, and insert the elements belonging to the set in one of the parent generations in (2) into the other new child generation in the order of their arrangement in the parent generation to form the crossed individuals;

[0070] The MS part then moves in position following the OS part;

[0071] The four domain search structures are as follows:

[0072] (1) Domain structure N1: Two-point flip, select any two points and flip the elements between the two points;

[0073] (2) Domain structure N2: Two-point swap, arbitrarily choose two points and swap the elements of the two points;

[0074] (3) Domain structure N3: Single point insertion. Select any point and insert the point and the elements thereafter before the first element.

[0075] (4) Domain structure N4: Critical path movement. The critical path refers to the processing operation on the machine with the longest completion time. The target value is optimized by changing the processing machine of these operations or swapping the positions of operations on other machines.

[0076] For the leader of the salps population, perform the four search strategies mentioned above, retain the best individual and add it to the population; for other followers, perform POX cross-selection with the salps ranked one Pareto level above them, select the remaining individuals, and then perform one of the four neighborhood search strategies mentioned above to select the best individual as the next generation, thus obtaining the iterative salps population, and sorting it to select a new leader and the order of the salps.

[0077] First, a parallel machine scheduling model is established. The parallel machine scheduling model describes the characteristics of this problem through simple parameters and formulas, but it cannot be solved directly. Then, the model is converted into a mathematical model through the above encoding and decoding methods, which becomes a mathematical problem that can be calculated. Finally, the tunic algorithm is used to solve this mathematical problem.

[0078] Salicylia are marine invertebrates, completely transparent, feeding on plankton and resembling jellyfish. They pump water into their bodies for propulsion. In the deep ocean, salicylia move forward in a chain-like manner, with individuals linked end-to-end to form a "chain." Half of the salicylia in the chain act as leaders, and the other half as followers. The leaders guide the followers forward, gradually finding food sources with each iteration. Because the followers move strictly according to a "hierarchical system," only influenced by the behavior of the preceding salicylia, salicylia possess strong global search and local exploitation capabilities. The standard salicylia swarm algorithm is as follows:

[0079] (1) Population initialization

[0080] X D×N =lb+rand(D,N)×(ub-lb) (1-1)

[0081] Let the search space be a D*N Euclidean space, where D represents the dimension of the space and N represents the population size. In formula (1-1), ub = [ub1, ub2, ... ub D ] represents the upper limit of the search space, lb = [lb1, lb2, ... lb] D The search space is defined by the lower bound of the search space. `rand(D,N)` represents a uniformly distributed random number between 0 and 1 in rows D and columns N. During population initialization, a matrix is ​​generated as shown in formula (1-2). The j-th tunicate individual can be represented as...

[0082]

[0083] (1) Leader position update

[0084] During the movement and food-finding process of the salver chain, the leader's position is updated using the following formula:

[0085]

[0086] Where c1, c2, and c3 are control parameters, F d This represents the current position of the food in d-dimensional space. As can be seen from formula (1-3), the leader's position change depends only on the position of the food. c2 and c3 are random numbers obtained within the interval [0, 1]. c2 determines the step size, c3 determines the leader's direction of movement, and c1 is the most important parameter, directly determining the search and development capabilities of the tunic swarm optimization algorithm throughout the entire iteration process. The formula for calculating c1 is shown below:

[0087]

[0088] Where t represents the current algebra number and T represents the maximum number of iterations.

[0089] (3) Follower position update

[0090] During the movement of the salver chain, the followers move forward in a chain-like manner, influenced by the individuals in front and behind, following the position of the leader. Based on the structural characteristics of the salver, the position update of the followers conforms to Newton's laws of motion, that is, the position of the salver depends only on the individual's initial velocity (v0), acceleration (a), and movement time (t). * This relates to the position of followers. Therefore, the formula for follower position is as follows:

[0091]

[0092] The standard Salicornia algorithm is designed to solve discrete problems. Its iterative movement process is applicable to discrete problem structures and cannot directly handle shop floor scheduling problems. Therefore, it needs to be improved based on the original algorithm.

[0093] Compared with existing technologies, the beneficial effects of this invention are as follows: The objective function of the model is established by minimizing the maximum completion time, and a solution based on the tunic group algorithm is designed to solve the model. The tunic group algorithm has high robustness, simple parameters, and is easy to operate. A new population initialization method is adopted for incompatible job families to improve the initial overall quality. Multiple neighborhood search strategies are employed to further improve the quality of the solution and accelerate the convergence speed of the algorithm. When the obtained scheduling method is used for spraying operations, the spraying efficiency of the automatic spraying machine and the quality of character spraying can be improved, while reducing human intervention. Attached Figure Description

[0094] Figure 1 This is the complete optimal scheduling Gantt chart in a preferred embodiment of the present invention;

[0095] Figure 2 A Gantt chart for scheduling based on the principle of minimizing processing time;

[0096] Figure 3 This is a comparison chart of processing times in a preferred embodiment of the present invention;

[0097] Figure 4 This is the Pareto solution set in the last iteration of the preferred embodiment of the present invention;

[0098] Figure 5 This is a GWO flowchart drawn according to the operation steps of the tunic algorithm in a preferred embodiment of the present invention;

[0099] Figure 6 This is the analysis process for dynamic spraying in a preferred embodiment of the present invention; Detailed Implementation

[0100] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0101] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0102] The present invention will be further described below with reference to specific embodiments, but these are not intended to limit the scope of the invention.

[0103] A method for scheduling parallel machines in railway freight car body painting operations includes the following steps:

[0104] S1. Establish a parallel machine scheduling model based on the characteristics of the truck painting process. The scheduling model includes:

[0105] 1.1 Make reasonable assumptions about the scheduling model;

[0106] 1.2 Set parameters and decision variables;

[0107] 1.3 Construct the objective function of the scheduling model;

[0108] The steps in 1.1-1.3 above describe the process of establishing a parallel machine scheduling model. Parameters, decision variables, constraints, and objective functions together constitute this parallel machine scheduling model.

[0109] S2. Optimize the objective function based on the sea tunic group algorithm;

[0110] 2.1 Collect the data to be processed, and treat each font size with sprayed characters as a processing task, and treat different models of spray guns as different spraying machines;

[0111] 2.2 By adopting a two-layer coding system of process coding (OS) and machine coding (MS), the above scheduling model is transformed into a mathematical model, that is, into a computable mathematical problem;

[0112] 2.3 Set the parameters of the tunicate group algorithm and initialize the population according to the rules in step 2.2;

[0113] 2.4 Calculate and rank the fitness values ​​of the salps population, select the one with the best fitness as the leader, and the others as followers;

[0114] 2.5 Complete the individual update and iteration;

[0115] 2.6 Repeat step 2.5 until the maximum number of iterations is reached, and obtain the optimal solution for the current population as the optimal solution, which is the optimal solution of the mathematical model, that is, the optimal solution of the scheduling model, and also the optimal solution of the objective function of the scheduling model.

[0116] The parallel machine scheduling model describes the characteristics of this problem through simple parameters and formulas, and cannot be solved directly. Then, the above encoding and decoding methods are used to convert the model into a computable mathematical problem, and the tunic algorithm is used to solve this mathematical problem.

[0117] The specific parameters and decision variables include:

[0118]

[0119]

[0120]

[0121]

[0122] The objective function is:

[0123] minC max =min[max(C j (1)

[0124]

[0125] Equation (1) indicates that the maximum completion time of the workpiece is the minimum, that is, the completion time of the last completed process is the minimum; Equation (2) indicates that the time for manual movement of the trolley in the scheduling is the minimum, that is, the amount of human resources used is the minimum. For the automatic spraying process, the input of human resources is its variable cost and is the main direction of enterprise cost control.

[0126] The constraints are:

[0127]

[0128]

[0129] C ijk ≤S ghk +M(1-γ ijghk (5)

[0130] Equation (3) indicates that a process can only be processed by one machine; Equation (4) indicates that the next process can only begin after the previous process of the workpiece has been completed; Equation (5) indicates that a machine can only be occupied by one process at a time.

[0131] Taking a batch painting operation at a truck painting factory as an example, such as... Figure 1-6 :

[0132] Step 1: Based on the data obtained from the survey of the truck painting factory, the original machining schedule and the corresponding machining schedule are obtained, as shown in Table 2 and Table 3.

[0133] Table 2 Processing Machines

[0134]

[0135]

[0136] Table 3 Processing Schedule

[0137]

[0138] Step 2: From the data in Step 1, we can see that there are a total of 69 painting tasks. According to the description of the double-layer coding above, each individual has a double-layer coding, namely process ordering and machine selection. The coding rules for the process ordering part are shown in Table 1 above. Codes 1-69 represent process ordering, and codes 70-138 represent machine selection. The machine selection part code means the sequence number of the machines that can be selected for that process. For example, if the set of machines that can be selected for a certain process is [1 3 4], and the corresponding machine selection part code is 2, then that process will be processed by machine 3 during decoding. That is, the length of an individual tunicate in the algorithm is 138, where the first 69 bits of the code represent the processing order of 39 workpieces, and the last 69 bits of the code represent the machine selection of 69 processing tasks. According to the generation rules of the machine selection part above, 50% of the individuals select the machine with the shortest processing time from the available machines for the task, and the other 50% of the individuals randomly select a machine from the available machine set according to the chaotic vector, resulting in the following coding example table. The ratio mentioned above can be arbitrary. Orthogonal experiments can be added to verify the impact of different parameters on the convergence speed of the algorithm in order to find the optimal ratio.

[0139] Encoding Example Table

[0140]

[0141]

[0142] According to the table above, the meaning of this code is: O ij In this context, 'i' represents the workpiece, and 'j' represents the process. ij The process j representing workpiece i is processed in this sequence. For example, O 11 M4: The first digit 1 in the OS part represents workpiece 1, and the second digit 1 represents process 1, that is, the first process of workpiece 1. The corresponding 70th digit MS part is 4, which means that the process selects the 4th processing in its machine combination, and so on.

[0143] Step 3: Set the parameters of the tunic algorithm, set the population size to 100, that is, the initial population contains 100 individuals with a length of 138, obtain the initial processing order according to the decoding method above, and calculate the maximum processing time of each individual to update the target value of each individual in the tunic population, and select the non-dominated solution in the Pareto solution set as the leader of the population, and the remaining individuals as followers.

[0144] Step 4: Obtain 4 neighboring individuals for the leader through neighborhood search, and select the best one to return to the population; for the followers, use POX crossover to obtain new individuals with the individual preceding it, and randomly select one of the 4 neighborhood structures for mutation operation on the individuals selected after POX crossover; after all individuals in the population have been updated, reorder them according to their target values ​​and select a new leader.

[0145] Step 5: Repeat step 4. When the maximum accuracy or the maximum number of iterations is reached, the iteration is complete and the output result is the optimal solution. Otherwise, continue to execute the loop.

[0146] in, Figure 1 This is a complete optimal scheduling Gantt chart for this embodiment. The vertical axis represents the automatic spraying machines with nozzle diameters of 0.5mm, 0.6mm, 0.8mm, and 1.0mm, respectively; the horizontal axis represents the time unit of the Gantt chart. The completion time for this scheme is 147, and the machine movement time is 66.

[0147] Figure 2 The Gantt chart shows a scheduling scheme decoded based on the principle of minimum processing time. This scheme has a completion time of 166.7 and a machine movement time of 116. The comparison shows that the scheduling method of this invention is more efficient and can save more human resources.

[0148] Figure 3 The optimal solution for each iteration in the iteration process is recorded. The horizontal axis represents the number of iterations of the algorithm, and the vertical axis represents the values ​​of the two objective values ​​of the objective functions (1) and (2) in each iteration. Here, a solution in the Pareto solution set is taken as the optimal result of this generation. It can be seen that the optimal solution in the initial population takes more than 200 seconds, while the optimal processing path can be found in just over 50 iterations after the above algorithm is used, taking only 147 seconds. The machine movement time is also optimized from 100 at the beginning to 60 at the end, which greatly saves processing time and scheduling time.

[0149] Figure 4 It records all non-dominated solutions in the Pareto solution set of the last iteration. These two solutions are not mutually dominant on either objective, allowing managers to choose according to actual needs.

[0150] The above are merely preferred embodiments of the present invention and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should recognize that any equivalent substitutions and obvious changes made based on the content of this specification should be included within the protection scope of the present invention.

Claims

1. A method for scheduling parallel machines in railway freight car body painting operations, characterized in that, Includes the following steps: S1. Establish a parallel machine scheduling model based on the characteristics of the truck painting process. The scheduling model includes: 1.1 Make reasonable assumptions about the scheduling model; 1.2 Set parameters and decision variables; 1.3 Construct the objective function of the scheduling model; The objective function in step 1.3 is: (1) (2) Equation (1) indicates that the maximum completion time of the workpiece is the minimum, that is, the completion time of the last completed process is the minimum; Equation (2) indicates that the time for manual movement of the trolley in the scheduling is the minimum, that is, the amount of human resources used is the minimum. For the automatic spraying process, the input of human resources is its variable cost, which is the main direction of enterprise cost control. The constraints are as follows: (3) (4) (5) Equation (3) indicates that a process can only be processed by one machine; Equation (4) indicates that the next process can only begin after the previous process of the workpiece has been completed; Equation (5) indicates that a machine can only be occupied by one process at a time. S2. Optimize the objective function based on the sea tunic group algorithm; 2.1 Collect the data to be processed, and treat each font size with sprayed characters as a processing task, and treat different models of spray guns as different spraying machines; 2.2 The above-mentioned data to be processed is converted using a two-layer coding method of process coding (OS) and machine coding (MS), and the above-mentioned scheduling model is converted into a mathematical model; 2.3 Set the parameters of the tunicate group algorithm and initialize the population according to the encoding method in step 2.2; 2.4 Calculate and rank the fitness values ​​of the salps population, select the one with the best fitness as the leader, and the others as followers; 2.5 The leader performs neighborhood search, and the followers perform follow-up movement to reorder the population and complete the individual update iteration; POX crossover and four neighborhood search operators are introduced to complete the iterative update of the salps population; among them, the four neighborhood search structures are as follows: (1) Neighborhood structure N1: two-point flip; (2) Neighborhood structure N2: two-point exchange; (3) Neighborhood structure N3: single-point insertion; (4) Neighborhood structure N4: critical path movement; the above four search strategies are performed on the leader in the salps population to retain the best individual; for other followers, POX crossover selection is performed with the salps ranked one level above, and one of the above four neighborhood search strategies is used to select the best individual as the next generation; 2.6 Repeat step 2.5 until the maximum number of iterations is reached to obtain the optimal solution for the current population, which is the optimal solution of the mathematical model, i.e., the optimal solution of the scheduling model objective function; In step 2.4, minimizing the maximum completion time and maximum human resources is taken as the optimization objective. When calculating the fitness value of individual tunicates, the end face situation of the preceding and following processing steps on the same machine is judged to calculate the required human interference. The Pareto sorting method is used to process the multi-objective problem and obtain a set of approximately optimal solutions. All non-dominated solutions in the Pareto solution set are regarded as leaders and other solutions are regarded as followers. S3. Compare and verify the effectiveness of the scheduling model and algorithm.

2. The parallel scheduling method for railway freight car body painting operations according to claim 1, characterized in that: Reasonable assumptions about the scheduling model in step 1.1 include: ① Each character and font size has its own independent painting task, which is not affected by other painting tasks; ② Spraying operations on the same end face will not exceed the working space of the automatic spraying machine; ③Each job task can be processed by at most one parallel machine; ④ Each batch of products can only be processed once on the parallel machine; ⑤ Consider the time required to move the automatic spraying machine when spraying characters on different end faces; ⑥ Consider the time required for the automatic spraying machine software to change parameters when spraying different font sizes; ⑦ In static shop floor scheduling, the machines and workpieces in the shop floor need to meet the following constraints: (1) Pre-specify the workpiece processing steps; (2) The machine can only process one workpiece at a time; (3) Each workpiece has equal processing priority; (4) The pre-specified processing time and machine shall not be changed.

3. The parallel scheduling method for railway freight car body painting operations according to claim 1, characterized in that: The parameters and decision variables in step 1.2 include: 。 4. The parallel scheduling method for railway freight car body painting operations according to claim 3, characterized in that: In step 2.2, the first-level process coding scheme is as follows: The initial individuals are sorted using the Logistic chaotic mapping iterative equation, which is: (6) （7） In equation (6), For the first The values ​​of the chaotic variables in each iteration For the number of iterations, For parameters; In equation (7), and The first Upper and lower bounds of the values ​​that a dimensional variable can take. express The values ​​of the dimensional components; Define the individual dimension as Population size is Randomly generated dimensional initial sequence The initial chaotic sequence matrix is ​​obtained by iterating through each component of the initial sequence using formula (6); the initial chaotic sequence matrix is ​​then transformed onto the variable interval of the target problem using formula (7) to complete the initial chaotic mapping; a set of random variables is generated, and a chaotic vector is obtained after multiple iterations using formula (6); the chaotic vector is then mapped onto the display encoding using formula (7) to obtain the individual's OS partial encoding. .

5. The parallel scheduling method for railway freight car body painting operations according to claim 4, characterized in that: In step 2.2, the second-layer machine coding scheme is as follows: the machine selection part of the initial individual adopts a hybrid mechanism. Some individuals are generated according to formulas (6) and (7), and the remaining individuals are selected according to the principle of the shortest processing time, according to the mechanism of the least processing time in the machine table, which is the MS part of the machine selection.

6. The parallel scheduling method for railway freight car body painting operations according to claim 5, characterized in that: In step 2.3, the parameters of the tunic group algorithm include the maximum number of iterations. The maximum number of iterations and population size for variable neighborhood search.

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