Tire intelligent manufacturing vulcanization workshop scheduling method based on improved NSGA-Ⅱ

Abstract

The application provides a kind of based on improved NSGA-Ⅱ tire intelligent manufacturing vulcanization workshop scheduling method and system, it is related to workshop scheduling technical field.The application constructs the model of tire intelligent manufacturing vulcanization workshop scheduling problem, and proposes a kind of based on improved NSGA-Ⅱ tire intelligent manufacturing vulcanization workshop scheduling method, for obtaining EMS trolley and vulcanization machine scheduling scheme, through the reasonable arrangement of tire intelligent manufacturing vulcanization workshop production scheduling scheme, improve production efficiency.Meanwhile, based on batch adding population initialization method and based on the decoding mode of minimum waiting time principle EMS trolley scheduling scheme obtained, not only can quickly search optimal solution, but also can effectively reduce vulcanization machine waiting time in large-scale experiment, thereby reducing the completion time.

Description

Technical Field

[0001] This invention relates to the field of workshop scheduling technology, specifically to a scheduling method and system for a tire intelligent manufacturing vulcanization workshop based on the improved NSGA-II. Background Technology

[0002] Tire manufacturing is a crucial component of the automotive industry and, more importantly, the manufacturing sector as a whole. For tire manufacturing, vulcanization is characterized by its long production time, high energy consumption, and irreversibility, making it a critical step in the tire manufacturing process. Therefore, researching the scheduling of tire vulcanization workshops is beneficial for improving workshop efficiency and promoting the advancement and intelligent development of tire manufacturing processes.

[0003] With the development of intelligent and automated tire vulcanizing workshops, existing intelligent tire manufacturing vulcanizing workshops have introduced EMS (Electrical Monorail System) trolleys for automatically grabbing and transporting tires. However, current research on vulcanizing workshop scheduling mainly focuses on traditional vulcanizing workshops, and the corresponding mathematical models do not consider the EMS trolleys, failing to meet the current development trend of tire manufacturing vulcanizing workshops. Consequently, existing technologies also do not consider the scheduling of EMS trolleys in vulcanizing workshops when solving the vulcanizing workshop scheduling problem.

[0004] However, if the scheduling problem of EMS carts in the tire vulcanizing workshop is not taken into account, the final solution to the scheduling optimization problem of the tire vulcanizing workshop will be inaccurate and not in line with the actual situation, thus failing to provide an accurate reference for the tire vulcanizing process. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a scheduling method and system for tire vulcanization workshops based on the improved NSGA-II, which solves the problem of inaccurate scheduling optimization results in tire vulcanization workshops due to the failure to consider the scheduling problem of EMS carts in existing technologies.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] In a first aspect of the present invention, a scheduling method for a tire intelligent manufacturing vulcanization workshop based on an improved NSGA-II is provided, the method comprising:

[0010] S1. Construct a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes;

[0011] S2. Generate an initial population using a batch addition method, which will serve as the parent population. Set the algorithm parameters: current iteration count gen, maximum iteration count gen. max The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing.

[0012] S3. Randomly select, crossover, and mutate the parent population to obtain a new population, which serves as the offspring population.

[0013] S4. Merge the parent population and the offspring population to form a merged population;

[0014] S5. The merged population is sorted non-dominated using a fast non-dominated sorting method, and individuals in the merged population are decoded based on the minimum waiting time principle to obtain the scheduling scheme and objective function value of each individual; wherein, the minimum waiting time principle means that the idle waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme;

[0015] S6. Based on the elite selection strategy, select individuals from the merged population after the non-dominated sorting is completed to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached.

[0016] S7. Determine if gen ≥ gen max If the condition is met, then obtain the Pareto optimal solution set of the candidate population; otherwise, then gen = gen + 1, and use the candidate population as the parent population, and proceed to S3.

[0017] S8. Use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set, and use it as the final scheduling scheme.

[0018] Optionally, the objective function of the vulcanizing workshop scheduling model includes:

[0019] Minimize the maximum completion time: min C max Among them, C max C represents the maximum completion time. max =max(C l,k); C l,k This indicates the completion time of vulcanizing machine k in production line l; l represents the EMS trolley or production line number, l = 1,...,n; k represents the vulcanizing machine number, k = 1,...,m;

[0020] Minimize the delayed completion time: min NT; where NT represents the delayed completion time;

[0021] Minimize the number of mold changes: min H; where H represents the number of mold changes;

[0022] The constraints of the vulcanizing workshop scheduling model include:

[0023] Constraint 1 Indicates tire O p,q Processing can only be done on one vulcanizing machine; among them,

[0024] Constraint 2 Indicates tire O p,q It can only be transported by one EMS vehicle; among them,

[0025] Constraint 3 This indicates that the number of tires of each specification processed is equal to the total number of tires.

[0026] Constraint 4 Indicates tire O p,q In EMS trolley M l The start time of transportation must not be earlier than the EMS vehicle M l Transporting the previous tire O p',q' The time it takes to return to the origin, and the tire storage device can only hold one tire at a time, tire O p,q In EMS trolley M l The start time of transport is affected by the vulcanizing machine M to which it is sent. l,k The previous tire O p”,q” Limitations on the start vulcanization time;

[0027] Constraint 5 Indicates tire O p,q In EMS trolley M l The delivery time is the sum of the start time of shipment and the shipment time.

[0028] Constraint 6 Indicates EMS cart M l Tire delivery O p,q The time to return to the origin is the delivery time plus the transportation time;

[0029] Constraint 7 Indicates tire Op,q In vulcanizing machine M l,k The start time of vulcanization is affected by the transportation delivery time, M l,k Previous vulcanized tire O p',q' Constraints on vulcanization end time and mold change time; among which...

[0030] Constraint 8 Indicates tire O p,q In vulcanizing machine M l,k The vulcanization end time is the sum of the vulcanization start time and the vulcanization time.

[0031] Constraint 9 The completion time of vulcanizing machine k in production line l is represented by vulcanizing machine M. l,k The vulcanization end time of the last tire;

[0032] Constraint 10 This indicates that the completion time of the p-th specification tire is the vulcanization end time of the last p-th specification tire.

[0033] Constraint 11 This indicates that the delayed completion time is the sum of the completion times of all tire sizes exceeding the latest completion time of that tire size;

[0034] Constraint 12 The mold change count represents the total number of times the vulcanizing tire specification has been changed across all vulcanizing machines.

[0035] Where n represents the number of EMS carts or production lines; m represents the number of vulcanizing machines on each production line; d represents the number of tire specifications; q p This indicates the quantity of tires of the p-th specification; p represents the tire specification number, p = 1, ..., d; O p,q DT represents the q-th tire of the p-th specification; p T represents the latest completion time for the p-th tire specification; p,l,k This indicates that the p-th specification tire is in vulcanizing machine M l,k Processing time on HT i,j,l,k Indicates vulcanizing machine M l,k The preparation time required to switch from model i to model j, where i ≠ j, i ∈ p, j ∈ p; TT k This represents the time it takes for the EMS trolley to travel from the origin to the kth vulcanizing machine; Indicates tire O p,q In EMS trolley M l The start time of delivery; Indicates tire O p,q In EMS trolley M l Delivery time; Indicates EMS cart M l Tire delivery O p,q The time it takes to return to the origin; Indicates tire O p,q In vulcanizing machine M l,k Start processing time; Indicates tire O p,q In vulcanizing machine M l,k The processing end time on C; l,k Indicates vulcanizing machine M l,k Completion time; C max Indicates the maximum completion time of all vulcanizing machines; H represents the number of mold changes required for the vulcanizing machine; RT p NT represents the completion time of the p-th tire specification; NT represents the total delayed completion time.

[0036] Optionally, the process of generating the initial population using batch addition in step S2 includes:

[0037] S201. The processing status of tires on the machine is encoded based on a real number matrix, and an initial population is generated by batch addition; wherein, the row number in the real number matrix represents the corresponding vulcanizing machine number, the number in the real number matrix represents the tire model, and 0 indicates that no tires are being processed on the vulcanizing machine.

[0038] S202. Convert the encoding form of the initial population into chromosome form.

[0039] Optionally, in step S5, individuals in the merged population are decoded based on the principle of minimum waiting time to obtain the scheduling scheme and objective function value for each individual, including:

[0040] S501. Convert the encoding form in the merged population that is subjected to non-dominated sorting into the form of a real matrix.

[0041] S502. The first tire on each vulcanizing machine is transported according to the principle of proximity. The principle of proximity means that the EMS trolley prioritizes transporting the first tire of the vulcanizing machine with the smaller number on the production line until the first tire of all vulcanizing machines on the production line has been transported. The closer the vulcanizing machine is to the starting point of the EMS trolley, the smaller its number.

[0042] S503. The transportation tasks of EMS vehicles are scheduled using the principle of minimum waiting time to obtain the scheduling scheme and objective function value;

[0043] The formula for calculating the waiting time t is: Indicates tire O p,q In vulcanizing machine M l,k The processing end time on h;p,p' Indicates whether a mold change is needed; 1 indicates yes, 0 indicates no. HT p,p',l,k Indicates vulcanizing machine M l,k Preparation time required to switch from model p to model p'; Indicates tire O p',q' In EMS trolley M l The delivery time is indicated by p'; p' represents the tire model to be shipped; q' represents the tire serial number to be shipped.

[0044] In a second aspect of the invention, a tire intelligent manufacturing vulcanization workshop scheduling system based on the improved NSGA-II is provided, the system comprising:

[0045] The model building module is used to execute S1 and build a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes;

[0046] The initial population generation module is used to execute S2 and generate an initial population as the parent population using a batch addition method. It also sets the algorithm parameters: current iteration count `gen`, and maximum iteration count `gen`. max The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing.

[0047] The offspring population generation module is used to execute S3, which involves random selection, crossover, and mutation of the parent population to obtain a new population, which serves as the offspring population.

[0048] The population merging module is used to execute S4, merging the parent population and the offspring population to form a merged population;

[0049] The decoding module is used to execute S5, perform non-dominated sorting on the merged population using a fast non-dominated sorting method, and decode the individuals in the merged population based on the minimum waiting time principle to obtain the scheduling scheme and objective function value for each individual; wherein, the minimum waiting time principle means that the total waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme;

[0050] The individual selection module is used to execute S6 and select individuals from the merged population after the non-dominated sorting is completed based on the elite selection strategy to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached.

[0051] The first acquisition module is used to execute S7 and determine whether gen ≥ gen. max If the condition is met, the Pareto optimal solution set of the candidate population is obtained; otherwise, gen = gen + 1, and the candidate population is used as the parent population, and the process is transferred to the offspring population generation module to execute step S3.

[0052] The second acquisition module is used to execute S8 and use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set as the final scheduling scheme.

[0053] Optionally, the objective function of the vulcanizing workshop scheduling model includes:

[0054] Minimize the maximum completion time: min C max Among them, C max C represents the maximum completion time. max =max(C l,k ); C l,k This indicates the completion time of vulcanizing machine k in production line l; l represents the EMS trolley or production line number, l = 1,...,n; k represents the vulcanizing machine number, k = 1,...,m;

[0055] Minimize the delayed completion time: min NT; where NT represents the delayed completion time;

[0056] Minimize the number of mold changes: min H; where H represents the number of mold changes;

[0057] The constraints of the vulcanizing workshop scheduling model include:

[0058] Constraint 1 Indicates tire O p,q Processing can only be done on one vulcanizing machine; among them,

[0059] Constraint 2 Indicates tire O p,q It can only be transported by one EMS vehicle; among them,

[0060] Constraint 3 This indicates that the number of tires of each specification processed is equal to the total number of tires.

[0061] Constraint 4 Indicates tire O p,q In EMS trolley M l The start time of transportation must not be earlier than the EMS vehicle M l Transporting the previous tire O p',q'The time it takes to return to the origin, and the tire storage device can only hold one tire at a time, tire O p,q In EMS trolley M l The start time of transport is affected by the vulcanizing machine M to which it is sent. l,k The previous tire O p”,q” Limitations on the start vulcanization time;

[0062] Constraint 5 Indicates tire O p,q In EMS trolley M l The delivery time is the sum of the start time of shipment and the shipment time.

[0063] Constraint 6 Indicates EMS cart M l Tire delivery O p,q The time to return to the origin is the delivery time plus the transportation time;

[0064] Constraint 7 Indicates tire O p,q In vulcanizing machine M l,k The start time of vulcanization is affected by the transportation delivery time, M l,k Previous vulcanized tire O p',q' Constraints on vulcanization end time and mold change time; among which...

[0065] Constraint 8 Indicates tire O p,q In vulcanizing machine M l,k The vulcanization end time is the sum of the vulcanization start time and the vulcanization time.

[0066] Constraint 9 The completion time of vulcanizing machine k in production line l is represented by vulcanizing machine M. l,k The vulcanization end time of the last tire;

[0067] Constraint 10 This indicates that the completion time of the p-th specification tire is the vulcanization end time of the last p-th specification tire.

[0068] Constraint 11 This indicates that the delayed completion time is the sum of the completion times of all tire sizes exceeding the latest completion time of that tire size;

[0069] Constraint 12 The mold change count represents the total number of times the vulcanizing tire specification has been changed across all vulcanizing machines.

[0070] Where n represents the number of EMS carts or production lines; m represents the number of vulcanizing machines on each production line; d represents the number of tire specifications; qp This indicates the quantity of tires of the p-th specification; p represents the tire specification number, p = 1, ..., d; O p,q DT represents the q-th tire of the p-th specification; p T represents the latest completion time for the p-th tire specification; p,l,k This indicates that the p-th specification tire is in vulcanizing machine M l,k Processing time on HT i,j,l,k Indicates vulcanizing machine M l,k The preparation time required to switch from model i to model j, where i ≠ j, i ∈ p, j ∈ p; TT k This represents the time it takes for the EMS trolley to travel from the origin to the kth vulcanizing machine; Indicates tire O p,q In EMS trolley M l The start time of delivery; Indicates tire O p,q In EMS trolley M l Delivery time; Indicates EMS cart M l Tire delivery O p,q The time it takes to return to the origin; Indicates tire O p,q In vulcanizing machine M l,k Start processing time; Indicates tire O p,q In vulcanizing machine M l,k The processing end time on C; l,k Indicates vulcanizing machine M l,k Completion time; C max Indicates the maximum completion time of all vulcanizing machines; H represents the number of mold changes required for the vulcanizing machine; RT p NT represents the completion time of the p-th tire specification; NT represents the total delayed completion time.

[0071] Optionally, the process of generating the initial population using a batch addition method in the initial population generation module includes:

[0072] S201. The processing status of tires on the machine is encoded based on a real number matrix, and an initial population is generated by batch addition; wherein, the row number in the real number matrix represents the corresponding vulcanizing machine number, the number in the real number matrix represents the tire model, and 0 indicates that no tires are being processed on the vulcanizing machine.

[0073] S202. Convert the encoding form of the initial population into chromosome form.

[0074] Optionally, the decoding module decodes individuals in the merged population based on the principle of minimum waiting time to obtain the scheduling scheme and objective function value for each individual, including:

[0075] S501. Convert the encoding form in the merged population that is subjected to non-dominated sorting into the form of a real matrix.

[0076] S502. The first tire on each vulcanizing machine is transported according to the principle of proximity. The principle of proximity means that the EMS trolley prioritizes transporting the first tire of the vulcanizing machine with the smaller number on the production line until the first tire of all vulcanizing machines on the production line has been transported. The closer the vulcanizing machine is to the starting point of the EMS trolley, the smaller its number.

[0077] S503. The transportation tasks of EMS vehicles are scheduled using the principle of minimum waiting time to obtain the scheduling scheme and objective function value;

[0078] The formula for calculating the waiting time t is: Indicates tire O p,q In vulcanizing machine M l,k The processing end time on h; p,p' Indicates whether a mold change is needed; 1 indicates yes, 0 indicates no. HT p,p',l,k Indicates vulcanizing machine M l,k Preparation time required to switch from model p to model p'; Indicates tire O p',q' In EMS trolley M l The delivery time is indicated by p'; p' represents the tire model to be shipped; q' represents the tire serial number to be shipped.

[0079] In a third aspect of the embodiments of this application, an electronic device is provided, the electronic device including a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus;

[0080] Memory, used to store computer programs;

[0081] When the processor executes the program stored in the memory, it implements any of the steps of the above-described intelligent tire manufacturing vulcanization workshop scheduling method based on the improved NSGA-II.

[0082] In a fourth aspect of this application, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when executed by a processor, the computer program implements the steps of the above-described method for scheduling a tire intelligent manufacturing vulcanization workshop based on the improved NSGA-II.

[0083] (III) Beneficial Effects

[0084] This invention provides a scheduling method and system for intelligent tire manufacturing vulcanization workshops based on an improved NSGA-II. Compared with existing technologies, it has the following advantages:

[0085] This invention not only constructs a model for scheduling problems in the vulcanization workshop of intelligent tire manufacturing, but also proposes a scheduling method for the vulcanization workshop based on an improved NSGA-II, thereby obtaining scheduling schemes for EMS carts and vulcanizing machines. This allows for the rational arrangement of production scheduling schemes in the intelligent tire manufacturing vulcanization workshop, improving workshop efficiency. Furthermore, the use of a population initialization method based on batch addition and a decoding method based on the principle of minimizing waiting time to obtain the EMS cart scheduling scheme not only enables faster search for the optimal solution but also effectively reduces the waiting time of the vulcanizing machines in large-scale experiments, thus reducing completion time. Attached Figure Description

[0086] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0087] Figure 1 A flowchart of a tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II is provided for an embodiment of the present invention;

[0088] Figure 2 A schematic diagram of a cross operation is provided in an embodiment of the present invention;

[0089] Figure 3 A flowchart of a tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II is provided for an embodiment of the present invention;

[0090] Figure 4 An iterative curve of maximum completion time provided for an embodiment of the present invention;

[0091] Figure 5 A Gantt chart of a final scheduling scheme provided in an embodiment of the present invention;

[0092] Figure 6 An improved population initialization comparison curve is provided for an embodiment of the present invention;

[0093] Figure 7 An improved encoding comparison curve is provided for an embodiment of the present invention. Detailed Implementation

[0094] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] This application provides a tire vulcanization workshop scheduling method and system based on the improved NSGA-II, which solves the problem of inaccurate optimization results in tire vulcanization workshop scheduling due to the lack of consideration for EMS trolley scheduling in the prior art. It can not only find the optimal solution faster, but also effectively reduce the waiting time of vulcanizing machines in large-scale experiments, thereby reducing the maximum completion time.

[0096] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0097] See Figure 1 , Figure 1 A flowchart of a tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II, provided as an embodiment of the present invention, is shown below. Figure 1 As shown, the method includes the following steps:

[0098] S1. Construct a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes;

[0099] S2. Generate an initial population using a batch addition method, which will serve as the parent population. Set the algorithm parameters: current iteration count gen, maximum iteration count gen. max The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing.

[0100] S3. Randomly select, crossover, and mutate the parent population to obtain a new population, which serves as the offspring population.

[0101] S4. Merge the parent population and the offspring population to form a merged population;

[0102] S5. The merged population is sorted using a fast non-dominated sorting method, and individuals in the merged population are decoded based on the minimum waiting time principle to obtain the scheduling scheme and objective function value of each individual; wherein, the minimum waiting time principle means that the total waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme;

[0103] S6. Based on the elite selection strategy, select individuals from the merged population after the non-dominated sorting is completed to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached.

[0104] S7. Determine if gen ≥ gen max If the condition is met, then obtain the Pareto optimal solution set of the candidate population; otherwise, then gen = gen + 1, and use the candidate population as the parent population, and proceed to S3.

[0105] S8. Use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set, and use it as the final scheduling scheme.

[0106] Based on the above processing, this invention not only constructs a model for the scheduling problem of the vulcanizing workshop in intelligent tire manufacturing, but also proposes a scheduling method for the vulcanizing workshop based on the improved NSGA-II. This method can obtain scheduling schemes for EMS carts and vulcanizing machines, enabling reasonable arrangement of production scheduling schemes in the intelligent tire manufacturing vulcanizing workshop and improving workshop efficiency. Furthermore, the use of a population initialization method based on batch addition and a decoding method based on the principle of minimizing waiting time to obtain the scheduling scheme for the EMS cart not only finds the optimal solution faster, but also effectively reduces the waiting time of the vulcanizing machine in large-scale experiments, thereby reducing the completion time.

[0107] Regarding the above technical solution, this invention assumes the following: The vulcanization workshop has d types of tires to be processed and n vulcanization production lines. Each line has one EMS trolley and m vulcanizing machines. The EMS trolley transports the tires to be vulcanized to the vulcanizing machine's tire storage container and then returns to its origin. The tire storage container can only hold one tire at a time. Each vulcanizing machine can vulcanize all d types of tires, but each machine can only vulcanize one tire at a time. The vulcanization time for each vulcanizing machine is not exactly the same for different tire specifications. When processing different tire specifications on each vulcanizing machine, a mold needs to be changed. The mold changing time depends on the specifications of the two adjacent tires being switched and the vulcanizing machine itself.

[0108] In some embodiments, the objective function of the vulcanizing workshop scheduling model includes:

[0109] Minimize the maximum completion time: min C max Among them, C max C represents the maximum completion time. max =max(C l,k ); C l,k This indicates the completion time of vulcanizing machine k in production line l; l represents the EMS trolley or production line number, l = 1,...,n; k represents the vulcanizing machine number, k = 1,...,m;

[0110] Minimize the delayed completion time: min NT; where NT represents the delayed completion time;

[0111] Minimize the number of mold changes: min H; where H represents the number of mold changes;

[0112] The constraints of the vulcanizing workshop scheduling model include:

[0113] Constraint 1 Indicates tire O p,q Processing can only be done on one vulcanizing machine; among them,

[0114] Constraint 2 Indicates tire O p,q It can only be transported by one EMS vehicle; among them,

[0115] Constraint 3 This indicates that the number of tires of each specification processed is equal to the total number of tires.

[0116] Constraint 4 Indicates tire O p,q In EMS trolley M l The start time of transportation must not be earlier than the EMS vehicle M l Transporting the previous tire O p',q' The time it takes to return to the origin, and the tire storage device can only hold one tire at a time, tire O p,q In EMS trolley M l The start time of transport is affected by the vulcanizing machine M to which it is sent. l,k The previous tire O p”,q” Limitations on the start vulcanization time;

[0117] Constraint 5 Indicates tire O p,q In EMS trolley M l The delivery time is the sum of the start time of shipment and the shipment time.

[0118] Constraint 6 Indicates EMS cart M l Tire delivery O p,q The time to return to the origin is the delivery time plus the transportation time;

[0119] Constraint 7 Indicates tire O p,q In vulcanizing machine M l,k The start time of vulcanization is affected by the transportation delivery time, M l,k Previous vulcanized tire O p',q' Constraints on vulcanization end time and mold change time; among which...

[0120] Constraint 8 Indicates tire O p,q In vulcanizing machine M l,k The vulcanization end time is the sum of the vulcanization start time and the vulcanization time.

[0121] Constraint 9 The completion time of vulcanizing machine k in production line l is represented by vulcanizing machine M. l,k The vulcanization end time of the last tire;

[0122] Constraint 10 This indicates that the completion time of the p-th specification tire is the vulcanization end time of the last p-th specification tire.

[0123] Constraint 11 This indicates that the delayed completion time is the sum of the completion times of all tire sizes exceeding the latest completion time of that tire size;

[0124] Constraint 12 The mold change count represents the total number of times the vulcanizing tire specification has been changed across all vulcanizing machines.

[0125] Where n represents the number of EMS carts or production lines; m represents the number of vulcanizing machines on each production line; d represents the number of tire specifications; q p This indicates the quantity of tires of the p-th specification; p represents the tire specification number, p = 1, ..., d; O p,q DT represents the q-th tire of the p-th specification; p T represents the latest completion time for the p-th tire specification; p,l,k This indicates that the p-th specification tire is in vulcanizing machine M l,k Processing time on HT i,j,l,k Indicates vulcanizing machine M l,k The preparation time required to switch from model i to model j, where i ≠ j, i ∈ p, j ∈ p; TT k This represents the time it takes for the EMS trolley to travel from the origin to the kth vulcanizing machine; Indicates tire Op,q In EMS trolley M l The start time of delivery; Indicates tire O p,q In EMS trolley M l Delivery time; Indicates EMS cart M l Tire delivery O p,q The time it takes to return to the origin; Indicates tire O p,q In vulcanizing machine M l,k Start processing time; Indicates tire O p,q In vulcanizing machine M l,k The processing end time on C; l,k Indicates vulcanizing machine M l,k Completion time; C max Indicates the maximum completion time of all vulcanizing machines; H represents the number of mold changes required for the vulcanizing machine; RT p NT represents the completion time of the p-th tire specification; NT represents the total delayed completion time.

[0126] For step S2, the process of generating the initial population using batch addition includes:

[0127] S201. The processing status of tires on the machine is encoded based on a real number matrix, and an initial population is generated by batch addition; wherein, the row number in the real number matrix represents the corresponding vulcanizing machine number, the number in the real number matrix represents the tire model, and 0 indicates that no tires are being processed on the vulcanizing machine.

[0128] S202. Convert the encoding form of the initial population into chromosome form.

[0129] Since different models of tires require mold changing during the vulcanization process, and considering that mold changing consumes a lot of manpower and resources, the above-mentioned batch addition population initialization method can minimize the number of mold changes in the early processing stage of the algorithm.

[0130] In practical applications, assuming there are two production lines, each with two machines, the total number of vulcanizing machines is four. The tire specifications and quantities to be processed are J = {1:3, 2:2, 3:2, 4:3}. Tires of the same model are designated by the same number. The rows of matrix M represent vulcanizing machines. Matrix M can be used to represent the tire processing status on the machines as follows:

[0131]

[0132] In matrix M, rows 1 to 4 represent vulcanizing machines 1 to 4. Vulcanizing machines 1 and 2 are transported by the first EMS cart, while vulcanizing machines 3 and 4 are transported by the second EMS cart. Vulcanizing machine 1 processes one tire of type 1 and two tires of type 2; vulcanizing machine 2 processes one tire of type 4, one tire of type 3, and one tire of type 1; vulcanizing machine 3 processes one tire of type 1 and one tire of type 3; and vulcanizing machine 4 processes two tires of type 4. A value of 0 indicates that no tire is processed on that vulcanizing machine. To satisfy subsequent operations in the algorithm, the matrix needs to be transformed into chromosome form, introducing the integer "0" as a marker for the interval between each machine. Matrix M is then transformed into M = [1 2 2 0 4 3 1 0 1 3 0 4 4].

[0133] In some embodiments, the process of generating individuals for the initial population by batch addition includes: treating each tire model as a whole, randomly selecting a vulcanizing machine, adding all tires of that model to the vulcanizing machine in batches, and repeating the operation until all tire models are assigned to the vulcanizing machine for processing.

[0134] In some embodiments, the process of performing random selection, crossover, and mutation operations on the parent population in step S3 to obtain a new population as the offspring population includes:

[0135] S301. Perform a random selection operation on the offspring population. First, generate Pop_size random integers between [1, Pop_size], where Pop_size represents the maximum number of individuals in the population. Then, use these integers as indices for the individuals to be selected, and group the individuals at these index positions in the parent population into a single population for the next step.

[0136] S302. Perform a crossover operation on the above population: based on a preset crossover probability P. c Perform a crossover operation. The process of the crossover operation can be found in [link to relevant documentation]. Figure 2 This includes the following steps:

[0137] Step a: Randomly select two parent chromosomes, create two blank offspring chromosomes, and copy the position of "0" in the parent chromosome to the corresponding position in the offspring chromosome.

[0138] Step b: Randomly select the scheduling task on one of the vulcanizing machines in the parent chromosome and fill it into the corresponding position in the two offspring chromosomes.

[0139] Step c: Mark the genes in parent chromosome 2 that are identical to those in offspring chromosome 1 and are not "0" as "-1"; mark the genes in parent chromosome 1 that are identical to those in offspring chromosome 2 and are not "0" as "-1". The number of marked genes must be equal to the number of genes extracted in the previous step.

[0140] Step d: Copy the genes that are not "0" and "-1" in the parent chromosome 2 from left to right to the empty positions in the offspring chromosome 1; copy the genes that are not "0" and "-1" in the parent chromosome 1 from left to right to the empty positions in the offspring chromosome 2.

[0141] S303. Perform mutation calculations on the above population: based on the mutation rate P. m Perform mutation operations.

[0142] The methods for mutation operations include the following:

[0143] Method 1: Randomly select two gene loci for exchange, including: First, the two selected genes are workpieces processed on the same vulcanizing machine, and only the processing order of the workpieces is changed; Second, the two selected genes are not on the same vulcanizing machine or one of the selected genes is "0", and the allocation of workpieces on the machine and the processing order are changed.

[0144] Method 2: Select two groups of "0" genes to exchange, so as to swap the workpieces on the two vulcanizing machines, while keeping the workpiece processing order unchanged.

[0145] Method 3: Combine Method 1 and Method 2 to simultaneously change the order of the workpieces and their distribution on the machine.

[0146] For step S5, the following steps are included:

[0147] S501. Transform the encoding form in the merged population that is undergoing non-dominated sorting into the form of a real matrix.

[0148] S502. The first tire on each vulcanizing machine is transported according to the principle of proximity. The principle of proximity means that the EMS trolley prioritizes transporting the first tire of the vulcanizing machine with the smaller number on the production line until the first tire of all vulcanizing machines on the production line has been transported. The closer the vulcanizing machine is to the starting point of the EMS trolley, the smaller its number.

[0149] S503. The transportation tasks of the EMS vehicle are scheduled using the principle of minimum waiting time to obtain the scheduling scheme and objective function value.

[0150] The formula for calculating the waiting time t is: Indicates tire O p,q In vulcanizing machine Ml,k The processing end time on h; p,p' Indicates whether a mold change is needed; 1 indicates yes, 0 indicates no. HT p,p',l,k Indicates vulcanizing machine M l,k Preparation time required to switch from model p to model p'; Indicates tire O p',q' In EMS trolley M l The delivery time is indicated by p'; p' represents the tire model to be shipped; q' represents the tire serial number to be shipped.

[0151] Regarding step S502, in practical applications, the proximity principle can be understood as follows: Assuming there are 2 production lines, each production line has 2 vulcanizing machines, then the total number of vulcanizing machines is 4. The EMS carts are numbered 1 and 2, and the vulcanizing machines are numbered 1, 2, 3, and 4. By default, the vulcanizing machine with the smaller serial number on each production line is closer to the origin of the EMS cart. Therefore, EMS cart 1 will first transport the first tire to vulcanizing machine 1, then to vulcanizing machine 2, and EMS cart 2 will first transport the first tire to vulcanizing machine 3, then to vulcanizing machine 4.

[0152] For step S503, the process of scheduling the EMS cart's transportation tasks using the minimum waiting time principle includes: after calculating the idle waiting time of each vulcanizing machine on each production line, sorting the waiting times, and issuing EMS cart tasks according to the minimum waiting time principle. After each transportation, the waiting time of the vulcanizing machine is updated, and scheduling is then performed according to the updated waiting time until all tires have been transported.

[0153] In some embodiments, the fast non-dominated sorting method performs a non-dominated sorting of the merged population, including:

[0154] S401. Assign two key quantities to each solution p (i.e., the individual in this invention): the number n of solutions that dominate p and the set S of solutions dominated by p.

[0155] S402. Set i = 1 and assign individuals with n = 0 to the solution set Q_i; where i represents the non-dominant level.

[0156] S403. For the individual in the current Q_i, iterate through the S of each solution p, and decrement n by 1 for each solution in S.

[0157] S404, i = i + 1, assign the solution n = 0 to Q_i (i = 2, 3, ...);

[0158] S405. Repeat steps S403 and S404 until all individuals in the solution set are assigned to a certain Q_i (i = 1, 2, ...). The smaller i is, the lower the non-dominant level of the population in Q_i.

[0159] For step S6, the elite strategy selection process includes the following steps:

[0160] S601. According to the order of non-dominance level from low to high, put the entire population of a certain layer into a blank new population until it is impossible to put an entire individual of a certain layer into a certain layer.

[0161] S602. Calculate the crowding degree of individuals in this layer using a preset crowding degree formula. Sort the individuals with the highest crowding degree from highest to lowest, and sequentially select individuals with the highest crowding degree to enter the new population until the population size is reached. The crowding distance between the first and last individuals is set to infinity. Where k is the number of objective functions. The preset crowding degree formula is: Among them, D p For individual crowding, f k (p+1), f k (p-1) represents the kth objective function value of the two adjacent volumes p+1 and p-1, respectively.

[0162] Step S8, the process of obtaining the optimal solution in the Pareto optimal solution set using the TOPSIS method based on entropy weight, includes:

[0163] S801. Calculate the Pareto optimal solution set using the entropy weight method to obtain the weights of each objective function.

[0164] S802. Select the optimal solution from the Pareto solution set using the TOPSIS method based on entropy weight.

[0165] In one implementation, step S801 includes the following:

[0166] S80101. Transform the objective function values ​​of the Pareto solution set into a matrix; where each row in the matrix represents a scheme, i.e., a solution, and each column represents an index, i.e., the objective function value in this invention.

[0167] S80102. Since the objective functions are all very small indicators, they need to be positiveized to transform them into very large indicators.

[0168] S80103, Based on Formula The matrix is ​​standardized. Here, m is the number of indices, i.e., the number of objective functions, and n is the number of solutions, i.e., the number of Pareto solutions; z ij This represents the proportion of the j-th objective function value under the i-th scheme to the sum of the squares of the objective function values ​​of all schemes; x ij This represents the numerical value of the matrix before standardization, i.e., the objective function value of the Pareto solution set.

[0169] S80104, Based on Formula Calculate the probability matrix. Where p ijThis represents the proportion of the value of the j-th objective under the i-th scheme to the sum of the values ​​of that objective under all schemes.

[0170] S80105, Based on Formula Calculate the information entropy for each indicator. Where e j The information entropy represents the value of the j-th objective function.

[0171] S80106, Based on formula d j =1-e j Calculate the information utility value. Where d j The information utility value represents the j-th objective function value.

[0172] S80107, Based on Formula Calculate the entropy weight. Where w j The weight represents the information entropy of the j-th objective function value.

[0173] In one implementation, step S802 includes the following steps:

[0174] S80201. Calculate the distance score. Based on the standardized matrix obtained in step S801 and the calculated entropy weights, obtain the optimal solution z for each index in the standardized matrix. + And the worst solution z - The distance between the i-th solution and the optimal solution is:

[0175] in, Let represent the Euclidean distance between the i-th solution and the optimal solution.

[0176] The distance to the worst solution is:

[0177] in, Let represent the Euclidean distance between the i-th solution and the worst solution.

[0178] The score for the i-th solution is:

[0179] Among them, S i This represents the score of the i-th solution.

[0180] S80202. Rank the scores of each solution, and the solution with the highest score is the optimal solution.

[0181] See Figure 3 , Figure 3 A flowchart illustrating another intelligent tire manufacturing vulcanization workshop scheduling method based on the improved NSGA-II, provided as an embodiment of the present invention. Furthermore, as... Figure 4 , Figure 5 As shown, Figure 4An iterative curve of maximum completion time provided for an embodiment of the present invention; Figure 5 This is a Gantt chart of a final scheduling scheme provided in an embodiment of the present invention.

[0182] The applicant conducted experiments to verify the technical solution provided by this invention, the details of which are as follows:

[0183] The specific parameter settings and experimental data are shown below:

[0184] Table 1 Parameter Settings

[0185]

[0186]

[0187] Table 2 Specifications and Quantities of Tires to be Vulcanized

[0188] Specification 1 2 3 4 5 6 7 quantity 3 2 2 3 4 3 2

[0189] Table 3 Latest Tire Completion Time / h

[0190] Specification 1 2 3 4 5 6 7 quantity 3 3 3.5 3.5 3.3 4.3 3.5

[0191] Table 4. Vulcanization schedule / h

[0192] schedule 1 2 3 4 5 6 7 1 0.52 0.55 0.63 0.48 0.50 0.60 0.58 2 0.58 0.53 0.67 0.45 0.52 0.63 0.55 3 0.56 0.54 0.60 0.50 0.53 0.62 0.59 4 0.55 0.52 0.65 0.49 0.48 0.65 0.53

[0193] Table 5 Vulcanizing Machine 1 Die Change Schedule (h)

[0194] Vulcanizing machine 1 1 2 3 4 5 6 7 1 0 0.50 0.60 0.50 0.62 0.65 0.55 2 0.50 0 0.60 0.50 0.52 0.60 0.50 3 0.55 0.62 0 0.65 0.50 0.62 0.48 4 0.45 0.50 0.60 0 0.60 0.58 0.52 5 0.60 0.53 0.52 0.60 0 0.60 0.50 6 0.62 0.65 0.60 0.55 0.62 0 0.55 7 0.60 0.50 0.45 0.50 0.55 0.60 0

[0195] Table 6 Vulcanizing Machine 2 Mold Change Schedule (h)

[0196] Vulcanizing machine 2 1 2 3 4 5 6 7 1 0 0.50 0.55 0.50 0.60 0.62 0.58 2 0.45 0 0.48 0.52 0.50 0.55 0.56 3 0.65 0.55 0 0.62 0.55 0.60 0.50 4 0.50 0.50 0.65 0 0.60 0.55 0.55 5 0.65 0.50 0.55 0.58 0 0.62 0.52 6 0.60 0.60 0.62 0.52 0.60 0 0.58 7 0.60 0.55 0.48 0.50 0.53 0.55 0

[0197] Table 7 Vulcanizing Machine 3 Mold Change Schedule (h)

[0198]

[0199]

[0200] Table 8 Vulcanizing Machine 4 Mold Change Schedule (h)

[0201] Vulcanizing machine 4 1 2 3 4 5 6 7 1 0 0.50 0.62 0.55 0.60 0.62 0.58 2 0.50 0 0.60 0.52 0.50 0.60 0.55 3 0.52 0.62 0 0.60 0.52 0.65 0.50 4 0.48 0.50 0.60 0 0.62 0.55 0.55 5 0.65 0.55 0.60 0.58 0 0.62 0.45 6 0.65 0.62 0.58 0.60 0.65 0 0.55 7 0.60 0.55 0.60 0.52 0.52 0.55 0

[0202] Table 9 EMS cart transportation time / h

[0203]

[0204] Using the technical solution provided by this invention for modeling and calculation, the Pareto optimal solution set is obtained as shown in Table 10, where the iterative curve of the objective function for the maximum completion time is shown in the figure. Figure 4 As shown, the scheme of this invention selects the final solution from the Pareto optimal solution set and decodes it to obtain the Gantt chart of the scheduling scheme, as shown below. Figure 4 As shown, where Figure 4 In the vertical axis, M1, M2, M3, and M4 are the vulcanizing machine numbers, W1, W2, W3, and W4 are the tire storage device numbers corresponding to the vulcanizing machines, and AGV1 and AGV2 represent the EMS trolley numbers.

[0205] Table 10 Pareto optimal solution set

[0206]

[0207] This invention also provides a tire intelligent manufacturing vulcanization workshop scheduling system based on the improved NSGA-II, the system comprising:

[0208] The model building module is used to execute S1 and build a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes;

[0209] The initial population generation module is used to execute S2 and generate an initial population as the parent population using a batch addition method. It also sets the algorithm parameters: current iteration count `gen`, and maximum iteration count `gen`. max The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing.

[0210] The offspring population generation module is used to execute S3, which involves random selection, crossover, and mutation of the parent population to obtain a new population, which serves as the offspring population.

[0211] The population merging module is used to execute S4, merging the parent population and the offspring population to form a merged population;

[0212] The decoding module is used to execute S5, perform non-dominated sorting on the merged population using a fast non-dominated sorting method, and decode the individuals in the merged population based on the minimum waiting time principle to obtain the scheduling scheme and objective function value for each individual; wherein, the minimum waiting time principle means that the total waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme;

[0213] The individual selection module is used to execute S6 and select individuals from the merged population after the non-dominated sorting is completed based on the elite selection strategy to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached.

[0214] The first acquisition module is used to execute S7 and determine whether gen ≥ gen. max If the condition is met, the Pareto optimal solution set of the candidate population is obtained; otherwise, gen = gen + 1, and the candidate population is used as the parent population, and the process is transferred to the offspring population generation module to execute step S3.

[0215] The second acquisition module is used to execute S8 and use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set as the final scheduling scheme.

[0216] It is understood that the tire intelligent manufacturing vulcanization workshop scheduling system based on the improved NSGA-II provided in this embodiment of the invention corresponds to the tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II described above. The explanations, examples, and beneficial effects of the relevant content can be referred to the corresponding content in the tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II, and will not be repeated here.

[0217] In another embodiment of the present invention, a computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, implements the steps of any of the above-described intelligent tire manufacturing vulcanization workshop scheduling methods based on the improved NSGA-II.

[0218] In another embodiment of the present invention, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute any of the above embodiments of the tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II.

[0219] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated.

[0220] The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0221] In summary, compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0222] 1. This invention proposes a model for the scheduling problem in the vulcanization workshop of intelligent tire manufacturing and designs NSGA-Ⅱ to solve this problem. It can obtain the scheduling scheme of EMS trolley and vulcanizing machine, and make reasonable arrangements for the production scheduling scheme in the vulcanization workshop of intelligent tire manufacturing, thereby improving the workshop efficiency.

[0223] 2. The improved NSGA-II proposed in this invention uses a batch-addition population initialization method, enabling the algorithm to find the optimal solution more quickly. For example... Figure 6 As shown, the method used in this invention approaches the optimal solution faster than the method of initializing the population in a random manner.

[0224] 3. This invention employs a decoding method based on the principle of minimizing waiting time to schedule the EMS trolley. In large-scale experiments, this effectively reduces the waiting time of the vulcanizing machine, thereby reducing the completion time. Figure 7 As shown, by increasing the number of machines on each production line in Example 1 to 6, it can be seen that the decoding method of this invention based on the principle of minimizing waiting time enables the algorithm to find the optimal solution faster, and the optimal solution obtained is better than the optimal solution obtained by randomly allocating EMS carts.

[0225] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0226] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A scheduling method for a tire intelligent manufacturing vulcanization workshop based on an improved NSGA-II, characterized in that, The method includes: S1. Construct a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes; S2. Generate an initial population using a batch addition method, which will serve as the parent population. Set the algorithm parameters: current iteration count (gen) and maximum iteration count. The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing. S3. Randomly select, crossover, and mutate the parent population to obtain a new population, which serves as the offspring population. S4. Merge the parent population and the offspring population to form a merged population; S5. The merged population is sorted using a fast non-dominated sorting method, and individuals in the merged population are decoded based on the minimum waiting time principle to obtain the scheduling scheme and objective function value of each individual; wherein, the minimum waiting time principle means that the idle waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme; S6. Based on the elite selection strategy, select individuals from the merged population after the non-dominated sorting is completed to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached. S7, Judgment If the condition is met, then obtain the Pareto optimal solution set of the candidate population; otherwise, The selected population is then used as the parent population and transferred to S3; S8. Use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set, and use it as the final scheduling scheme. In step S5, individuals in the merged population are decoded based on the principle of minimum waiting time to obtain the scheduling scheme and objective function value for each individual, including: S501. Convert the encoding form in the merged population that is subjected to non-dominated sorting into the form of a real matrix. S502. The first tire on each vulcanizing machine is transported according to the principle of proximity. The principle of proximity means that the EMS trolley prioritizes transporting the first tire of the vulcanizing machine with the smaller number on the production line until the first tire of all vulcanizing machines on the production line has been transported. The closer the vulcanizing machine is to the starting point of the EMS trolley, the smaller its number. S503. The transportation tasks of EMS vehicles are scheduled using the principle of minimum waiting time to obtain the scheduling scheme and objective function value; Among them, the waiting time is calculated. t The formula is: ; Indicates tires In the vulcanizing machine The processing end time; This indicates whether a mold change is needed; 1 indicates yes, and 0 indicates no. Indicates vulcanizing machine From Model changed to Preparation time required for the model; Indicates tires In EMS cart Delivery time; Indicates the model of the tires to be transported; This indicates the tire number that is about to be transported.

2. The method according to claim 1, characterized in that, The objective function of the vulcanization workshop scheduling model includes: Minimize the maximum completion time: ;in, This indicates the maximum completion time for all vulcanizing machines. ; Indicates production line l medium vulcanizing machine k Completion time; Indicates the EMS cart or production line number. ; Indicates the vulcanizing machine number. ; Minimize the delay in completion time: ;in, Indicates the total delayed completion time; Minimize the number of model changes: ;in, Indicates the number of mold changes; The constraints of the vulcanizing workshop scheduling model include: Constraint 1 , indicating tires Processing can only be done on one vulcanizing machine; among them, ; Constraint 2 , indicating tires It can only be transported by one EMS vehicle; among them, ; Constraint 3 This indicates that the number of tires of each specification processed is equal to the total number of tires. Constraint 4 , indicating tires In EMS cart The start time of transportation must not be earlier than that of the EMS vehicle. Transport the last tire The time it takes to return to the starting point, and the fact that the tire storage device can only hold one tire, and the tire... In EMS cart The start time of transport is affected by the vulcanizing machine to which it is sent. The previous tire Limitations on the start vulcanization time; Constraint 5 , indicating tires In EMS cart The delivery time is the sum of the start time of shipment and the shipment time. Constraint 6 This indicates the EMS cart. Tire delivery The time to return to the origin is the delivery time plus the transportation time; Constraint 7 , indicating tires In the vulcanizing machine The start time of vulcanization is affected by the transportation and delivery time. Previous vulcanized tire Constraints on vulcanization end time and mold change time; Constraint 8 , indicating tires In the vulcanizing machine The vulcanization end time is the sum of the vulcanization start time and the vulcanization time. Constraint 9 This indicates that the completion time of vulcanizing machine k in production line l is vulcanizing machine The vulcanization end time of the last tire; Constraint 10 , indicating that the completion time of the p-th specification tire is the vulcanization end time of the last p-th specification tire; Constraint 11 This indicates that the total delayed completion time is the sum of the completion times of all tire sizes exceeding the latest completion time of that tire size; Constraint 12 This indicates that the mold change count is the total number of times the vulcanizing tire specification has been changed across all vulcanizing machines; where, ; in, Indicates the number of EMS carts or production lines; This indicates the number of vulcanizing machines on each production line; Indicates the quantity and specifications of the tires; Indicates the first The quantity of tires of various specifications; Indicates the tire specification number. ; Indicates the first The first of the specifications q One tire; Indicates tires Is it vulcanizing machine? Processing; Indicates the first The latest completion time for this type of tire specification; Indicates the first Tires of various specifications in vulcanizing machine vulcanization time; This represents the transportation time of the EMS trolley from the origin to the k-th vulcanizing machine; Indicates tires In EMS cart Start time of shipment; Indicates tires In EMS cart Delivery time; Indicates EMS cart Tire delivery The time it takes to return to the origin; Indicates tires In the vulcanizing machine The start time of vulcanization; Indicates tires In the vulcanizing machine vulcanization completion time; Indicates the number of mold changes required for the vulcanizing machine; Indicates the first p Completion time for various tire specifications; Indicates the total delayed completion time. Indicates EMS cart Transport the last tire The time it takes to return to the origin, Indicates the previous tire In the vulcanizing machine The start time of vulcanization Indicates tires Was it sent by EMS car? transportation, Indicates the previous tire In the vulcanizing machine vulcanization completion time, Indicates vulcanizing machine From Model changed to Preparation time required for the model; Indicates vulcanizing machine The value is 1 if the vulcanized tire specification has been changed from model i to model j, and 0 otherwise.

3. The method according to claim 1, characterized in that, The process of generating the initial population using batch addition in step S2 includes: S201. The processing status of tires on the machine is encoded based on a real number matrix, and an initial population is generated by batch addition; wherein, the row number in the real number matrix represents the corresponding vulcanizing machine number, the number in the real number matrix represents the tire model, and 0 indicates that no tires are being processed on the vulcanizing machine. S202. Convert the encoding form of the initial population into chromosome form.

4. A tire intelligent manufacturing vulcanization workshop scheduling system based on the improved NSGA-II, characterized in that, The system implementing the tire intelligent manufacturing vulcanization workshop scheduling method based on the improved NSGA-II as described in any one of claims 1-3, comprises: The model building module is used to execute S1 and build a vulcanizing workshop scheduling model; wherein, the objective function of the vulcanizing workshop scheduling model includes: minimizing the maximum completion time, minimizing the delayed completion time, and minimizing the number of mold changes; The initial population generation module is used to execute S2 and generate an initial population as the parent population using a batch addition method. It also sets the algorithm parameters: the current iteration count (gen) and the maximum iteration count. The batch addition method involves randomly selecting a vulcanizing machine, adding all tires of the same model to the vulcanizing machine in batches, and repeating the operation until all tires of all models are assigned to the vulcanizing machine for processing. The offspring population generation module is used to execute S3, which involves random selection, crossover, and mutation of the parent population to obtain a new population, which serves as the offspring population. The population merging module is used to execute S4, merging the parent population and the offspring population to form a merged population; The decoding module is used to execute S5, perform non-dominated sorting on the merged population using a fast non-dominated sorting method, and decode individuals in the merged population based on the minimum waiting time principle to obtain the scheduling scheme and objective function value for each individual; wherein, the minimum waiting time principle means that the idle waiting time of the vulcanizing machine is minimized in the scheduling scheme; the objective function value represents the maximum completion time, delayed completion time, and number of mold changes for each individual's scheduling scheme; The individual selection module is used to execute S6 and select individuals from the merged population after the non-dominated sorting is completed based on the elite selection strategy to construct a new population as the population to be selected; wherein, the elite selection strategy means that individuals with lower levels in the fast non-dominated sorting are selected first, and when the levels are the same, individuals with higher crowding are selected first, until the population size is reached. The first acquisition module is used to execute S7 and make judgments. If the condition is met, then obtain the Pareto optimal solution set of the candidate population; otherwise, The selected population is then used as the parent population and transferred to the offspring population generation module to execute step S3. The second acquisition module is used to execute S8 and use the TOPSIS method based on entropy weight to obtain the optimal solution in the Pareto optimal solution set as the final scheduling scheme.

5. The system according to claim 4, characterized in that, The objective function of the vulcanization workshop scheduling model includes: Minimize the maximum completion time: ;in, This indicates the maximum completion time for all vulcanizing machines. ; Indicates production line l medium vulcanizing machine k Completion time; Indicates the EMS cart or production line number. ; Indicates the vulcanizing machine number. ; Minimize the delay in completion time: ;in, Indicates the total delayed completion time; Minimize the number of model changes: ;in, Indicates the number of mold changes; The constraints of the vulcanizing workshop scheduling model include: Constraint 1 , indicating tires Processing can only be done on one vulcanizing machine; among them, ; Constraint 2 , indicating tires It can only be transported by one EMS vehicle; among them, ; Constraint 3 This indicates that the number of tires of each specification processed is equal to the total number of tires. Constraint 4 , indicating tires In EMS cart The start time of transportation must not be earlier than that of the EMS vehicle. Transport the last tire The time it takes to return to the starting point, and the fact that the tire storage device can only hold one tire, and the tire... In EMS cart The start time of transport is affected by the vulcanizing machine to which it is sent. The previous tire Limitations on the start vulcanization time; Constraint 5 , indicating tires In EMS cart The delivery time is the sum of the start time of shipment and the shipment time. Constraint 6 This indicates the EMS cart. Tire delivery The time to return to the origin is the delivery time plus the transportation time; Constraint 7 , indicating tires In the vulcanizing machine The start time of vulcanization is affected by the transportation and delivery time. Previous vulcanized tire Constraints on vulcanization end time and mold change time; Constraint 8 , indicating tires In the vulcanizing machine The vulcanization end time is the sum of the vulcanization start time and the vulcanization time. Constraint 9 This indicates that the completion time of vulcanizing machine k in production line l is vulcanizing machine The vulcanization end time of the last tire; Constraint 10 , indicating that the completion time of the p-th specification tire is the vulcanization end time of the last p-th specification tire; Constraint 11 This indicates that the total delayed completion time is the sum of the completion times of all tire sizes exceeding the latest completion time of that tire size; Constraint 12 This indicates that the mold change count is the total number of times the vulcanizing tire specification has been changed across all vulcanizing machines. ; in, Indicates the number of EMS carts or production lines; This indicates the number of vulcanizing machines on each production line; Indicates the quantity and specifications of the tires; Indicates the first The quantity of tires of various specifications; Indicates the tire specification number. ; Indicates the first The first of the specifications q One tire; Indicates tires Is it vulcanizing machine? Processing; Indicates the first The latest completion time for this type of tire specification; Indicates the first Tires of various specifications in vulcanizing machine vulcanization time; This represents the transportation time of the EMS trolley from the origin to the k-th vulcanizing machine; Indicates tires In EMS cart Start time of shipment; Indicates tires In EMS cart Delivery time; Indicates EMS cart Tire delivery The time it takes to return to the origin; Indicates tires In the vulcanizing machine The start time of vulcanization; Indicates tires In the vulcanizing machine vulcanization completion time; Indicates the number of mold changes required for the vulcanizing machine; Indicates the first p Completion time for various tire specifications; Indicates the total delayed completion time. Indicates EMS cart Transport the last tire The time it takes to return to the origin, Indicates the previous tire In the vulcanizing machine The start time of vulcanization Indicates tires Was it sent by EMS car? transportation, Indicates the previous tire In the vulcanizing machine vulcanization completion time, Indicates vulcanizing machine From Model changed to Preparation time required for the model; Indicates vulcanizing machine The value is 1 if the vulcanized tire specification has been changed from model i to model j, and 0 otherwise.

6. The system according to claim 4, characterized in that, The process of generating the initial population using batch addition in the initial population generation module includes: S201. The processing status of tires on the machine is encoded based on a real number matrix, and an initial population is generated by batch addition; wherein, the row number in the real number matrix represents the corresponding vulcanizing machine number, the number in the real number matrix represents the tire model, and 0 indicates that no tires are being processed on the vulcanizing machine. S202. Convert the encoding form of the initial population into chromosome form.

7. The system according to claim 4, characterized in that, The decoding module decodes individuals in the merged population based on the principle of minimum waiting time to obtain the scheduling scheme and objective function value for each individual, including: S501. Convert the encoding form in the merged population that is subjected to non-dominated sorting into the form of a real matrix. S502. The first tire on each vulcanizing machine is transported according to the principle of proximity. The principle of proximity means that the EMS trolley prioritizes transporting the first tire of the vulcanizing machine with the smaller number on the production line until the first tire of all vulcanizing machines on the production line has been transported. The closer the vulcanizing machine is to the starting point of the EMS trolley, the smaller its number. S503. The transportation tasks of EMS vehicles are scheduled using the principle of minimum waiting time to obtain the scheduling scheme and objective function value; Among them, the waiting time is calculated. t The formula is: ; Indicates tires In the vulcanizing machine The processing end time; This indicates whether a mold change is needed; 1 indicates yes, and 0 indicates no. Indicates vulcanizing machine From Model changed to Preparation time required for the model; Indicates tires In EMS cart Delivery time; Indicates the model of the tires to be transported; This indicates the tire number that is about to be transported.

8. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-3.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method described in any one of claims 1-3.

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