Flexible parallel batch optimization scheduling method for rubber tire production workshop with multi-cavity vulcanization constraints

Abstract

This invention discloses a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints. Specifically, it involves: acquiring basic data of the rubber tire production workshop and establishing a flexible workshop scheduling model with multi-cavity vulcanization constraints; parsing the customer order set to generate order-task-batch data; constructing a scheduling data structure; decoding each candidate scheduling scheme under multiple constraints to generate and evaluate corresponding feasible scheduling schemes; performing iterative optimization to generate and evaluate new candidate scheduling schemes; and selecting the optimal scheduling scheme when a preset termination condition is met. The beneficial effects of this invention are: it can significantly reduce the maximum completion time of rubber tire production workshops under multi-cavity vulcanization constraints, improve equipment utilization and on-time order delivery rate, and maintain good robustness and adaptability when order structure, batch demand, and equipment load change.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and production scheduling technology, and in particular to a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints.

[0002] This production optimization scheduling solution is designed for rubber tire production workshops, specifically targeting the parallel batch processing production scenario in flexible workshops with multi-cavity vulcanization constraints. It aims to solve the comprehensive optimization problem of order delivery time, bottleneck capacity utilization, and production operation efficiency for tire companies under large-scale mixed production conditions. Background Technology

[0003] With the continuous increase in car ownership and the rapid development of the new energy vehicle industry, tire products are characterized by diverse specifications and models, large differences in order batches, and tight delivery deadlines. The tire manufacturing process (such as...) Figure 1 (As shown) It generally includes multiple sequential processes such as raw material preparation, mixing, extrusion, calendering and cutting, molding and vulcanization. The process is long, there are many types of work-in-process, and the equipment is complex. There are significant differences in process parameters and processing cycle between different products, making production organization quite difficult.

[0004] Among the many processes, vulcanization directly determines the mechanical properties and service life of tires, making it a crucial step affecting final product quality and production cycle time. To increase unit equipment capacity, tire manufacturers commonly use multi-cavity vulcanizing machines. These machines employ two, four, or more chambers to process multiple tire blanks simultaneously on the same equipment, enabling significant batch processing and parallel operation. However, multi-cavity vulcanizing machines must simultaneously meet constraints such as different tire specifications, filling combinations, process curves, and cavity capacities. They are also affected by factors such as long mold change times, diverse mold types, and high changeover frequencies. Consequently, the vulcanization process often becomes a bottleneck in the production system.

[0005] Under traditional production management models, some tire companies rely primarily on the experience of dispatchers for manual production scheduling, or use simple first-come, first-served or earliest-delivery-priority rules for sorting. These methods are easy to implement, but they are difficult to achieve optimal overall production scheduling results in complex flexible operating environments and multi-cavity batch processing environments, often resulting in uneven loads on bottleneck equipment, excessive equipment idle time, and congestion in local processes.

[0006] To improve production efficiency, some enterprises and research institutions have introduced optimization methods based on job shop scheduling models or parallel machine scheduling models, such as flexible job shop scheduling, batch processing machine scheduling, and extended models that consider factors such as transportation time and loading time, and use heuristic or metaheuristic algorithms for solving these problems. These methods can achieve certain results under standard operating conditions and general parallel machine environments. However, when faced with the characteristics of tire production, such as "multi-cavity vulcanization, parallel batch processing on the same machine, significant differences in process cycle time, and non-negligible mold change time," existing models often fail to reflect equipment status and process constraints in a timely and accurate manner, and discrepancies still exist between scheduling results and actual production.

[0007] On the other hand, tire production is significantly order-driven, requiring companies to organize production while meeting diverse customer demands and delivery schedule commitments. In current practice, order information is typically input into scheduling systems as load data, with the scheduling process primarily focused on the shop floor level, lacking sufficient coordination with order delivery management and capacity assessment. When order structures are complex and product changes are frequent, problems can easily arise such as scheduling plans becoming disconnected from order delivery plans, repeated order insertions in certain processes to meet deadlines, and disruption of the overall production rhythm, impacting on-time delivery and production stability.

[0008] In summary, in rubber tire production workshops that simultaneously face constraints such as multi-cavity vulcanization, parallel batch processing characteristics, differences in process cycle time, and order delivery requirements, how to coordinate various resources, rationally arrange the processing sequence of different products and batches, and balance bottleneck capacity utilization and order delivery performance while meeting complex process and equipment constraints remains a technical challenge in this field. Summary of the Invention

[0009] To address the challenges in rubber tire production workshops, such as scheduling difficulties, low utilization of bottleneck equipment, and unstable order delivery caused by factors including multi-cavity vulcanization constraints, parallel batch processing characteristics, process cycle time differences, and order delivery deadlines, this invention provides a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints. This method rationally arranges the processing sequence and resource allocation for different orders, products, and batches within the workshop while meeting process and equipment constraints. This shortens the production cycle, improves the utilization rate of bottleneck equipment, enhances the feasibility and stability of the scheduling plan, and improves on-time order delivery capabilities.

[0010] To achieve the above-mentioned objectives, this invention provides a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints. The optimization scheduling method is as follows:

[0011] Step S1: Obtain basic data of the rubber tire production workshop, and establish a flexible operation workshop scheduling model with multi-cavity vulcanization constraints based on the basic data to obtain workshop model data for describing workpiece process priority relationships, equipment capacity constraints and batch processing constraints;

[0012] Step S2: Based on the customer order set and workshop model data obtained in Step S1, the customer order set is parsed, each order is converted into one or more corresponding production tasks, and the production tasks are divided into batches based on the chamber capacity parameters of the multi-cavity vulcanizing equipment and the allowable batch size of each workpiece, generating order-task-batch data containing orders, production tasks and their batch relationships.

[0013] Step S3: Based on the order-task-batch data obtained in Step S2 and the workshop model data in Step S1, construct a scheduling data structure to represent candidate scheduling schemes, generate multiple candidate scheduling schemes according to preset rules, and form a set of candidate scheduling schemes; the scheduling data structure is used to characterize the processing order of each batch in each process and the allocation method on different equipment.

[0014] Step S4: For each candidate scheduling scheme in the candidate scheduling scheme set obtained in step S3, decode it under the premise of satisfying the process route constraints, multi-cavity vulcanization constraints and batch processing constraints in the workshop model data in step S1, determine the start time, completion time and specific equipment allocated to each batch in each process, generate the corresponding feasible scheduling scheme, and evaluate the feasible scheduling scheme according to the preset objective function set in step S1 to obtain the evaluation results of each feasible scheduling scheme;

[0015] Step S5: Based on the evaluation results of each feasible scheduling scheme in Step S4, perform an iterative optimization process on the candidate scheduling scheme set formed in Step S3, select and adjust the candidate scheduling schemes according to the preset update rules, generate new candidate scheduling schemes and return to Step S4 for evaluation; when the preset termination condition is met, select the feasible scheduling scheme with the optimal objective function value as the optimal scheduling scheme according to the evaluation results.

[0016] Preferably, the basic data in step S1 includes process route information for each process within the workshop, operating parameters of various production equipment and the multi-cavity vulcanizing equipment, and a set of customer orders; wherein:

[0017] The process route information includes at least the processing sequence of various workpieces in the raw material preparation, mixing, extrusion, calendering and cutting, forming and vulcanization processes, as well as the corresponding process parameters for each process.

[0018] The operating parameters of the various production equipment and the multi-cavity vulcanizing equipment include at least the number of processes that the equipment can perform, the processing capacity per unit time, the planned available time, and the number of chambers and the capacity of each chamber of the multi-cavity vulcanizing equipment.

[0019] The workpiece type and required quantity of each order in the customer order set correspond one-to-one with the process route of the corresponding workpiece in the process route information.

[0020] The flexible job shop scheduling model with multi-cavity vulcanization constraints adopts a flexible job shop scheduling model with batch processing and multi-cavity vulcanization constraints. The maximum completion time of all workpieces in the shop is used as the optimization objective, and workpiece process optimization constraints, equipment capacity constraints, and batch processing constraints are set under this optimization objective.

[0021] Preferably, step S2 specifically involves: based on the customer order set and workshop model data obtained in step S1, calculating the sum of processing times for each process and the earliest delivery date among all relevant orders for each workpiece type, obtaining a comprehensive priority index combining the shortest processing time rule (SPT) and the earliest delivery date rule (EDD), using the order decomposition mapping (OTDM) strategy to decompose the customer order set into multiple production tasks and sorting them according to the comprehensive priority index to form a production task list, and based on the production task list, using equal batching and prime number correction strategies according to the required quantity of each production task to generate batch division results that satisfy the allowable batch size constraints of the workpiece and the capacity constraints of the multi-cavity vulcanizing equipment.

[0022] Preferably, the scheduling data structure in step S3 adopts a two-layer coding structure, including sub-batch scheduling allocation coding and process sorting coding, wherein:

[0023] The sub-batch scheduling allocation code is used to record the batch division results corresponding to each production task in step S2. The sub-batch quantity is determined according to the pre-determined equal batching and prime number correction results for the required quantity of each production task, and the corresponding workpiece quantity and production task identifier are recorded for each sub-batch.

[0024] The process sorting code encodes the processes within each batch according to the hierarchical structure of "production task-batch-process". Each process sorting code unit includes at least an index field for representing the production task number, batch number, and process number, which is used to indicate the production task, batch, and processing order of the process. When the process is a vulcanization process, the equipment identifier of the target multi-cavity vulcanization equipment is further recorded in the process sorting code unit to indicate that the vulcanization process is carried out on the corresponding multi-cavity vulcanization equipment.

[0025] Each of the process sorting and encoding units is also associated with a set of process parameter vectors. The process parameter vectors include at least: the number of candidate machines corresponding to the process, the target machine number determined according to the preset greedy machine selection rule, and the loading time, processing time and unloading time of the batch on the target machine, which are used to determine the specific start time and completion time of the process on the target machine in the subsequent decoding process.

[0026] The candidate scheduling scheme is generated by instantiating and combining the sub-batch scheduling allocation code and the process sorting code to form the candidate scheduling scheme set.

[0027] When generating the candidate scheduling scheme set in step S3, a population mixing initialization strategy is adopted, specifically including:

[0028] Based on the order-task-batch data obtained in step S2 and the workshop model data obtained in step S1, some candidate scheduling schemes are constructed according to preset heuristic rules. In the process sorting and coding, the coding units involving the vulcanization process are sorted according to the combination value of vulcanization time and mold change time to determine the key processing path containing the vulcanization process, and the corresponding candidate scheduling scheme is generated accordingly.

[0029] Other candidate scheduling schemes are constructed by randomly perturbing and randomly generating the scheduling data structure, so that the set of candidate scheduling schemes simultaneously includes candidate scheduling schemes constructed based on heuristic rules and scheduling schemes based on random generation, thereby improving population diversity and enhancing search capabilities in a large-scale solution space.

[0030] Preferably, the decoding of the candidate scheduling scheme in step S4 specifically includes:

[0031] (1) Establish a work processing station and decode it according to sub-batch:

[0032] In the decoding stage, a worktable is established, and the workpiece type, batch number, processing machine, processing start time, and processing end time corresponding to each process are recorded. According to the process sorting code obtained in step S3, the processes in each batch are read sequentially in units of sub-batches, and each process is written into the worktable. When there are two or more processes with overlapping times on the same machine, the start time of the later-written process is postponed so that the same machine corresponds to only one process at any given time.

[0033] (2) Decoding the overlapping of execution processes:

[0034] Under the premise of satisfying the process route constraints in step S1, for non-vulcanization processes, based on the processing time of the process and its predecessor processes and the idle time of the corresponding machine, determine whether the workpieces that have been partially completed in the predecessor processes should enter the process before they are fully completed, and record the start and end times of the corresponding processes in the work processing table.

[0035] For the vulcanization process, the number of completed processes from the preceding processes is based on the records in the worktable. With the total quantity of this batch When satisfied When the vulcanization process is in progress, the mold change preparation time is inserted into the work processing table, and the corresponding vulcanization processing time is arranged after the mold change preparation is completed.

[0036] Preferably, in step S4, when determining the specific processing equipment for each process in each batch, a dynamic greedy machine selection strategy is adopted, specifically including:

[0037] (1) For the process of assigning machines during the decoding process j Based on the workshop model data established in step S1, determine the set of selectable machines. In the current decoding state, for any candidate machine Calculate the completion time of process j on this machine. The completion time satisfies:

[0038]

[0039] in, For workpiece type i process j In the machine m The start time on For the previous process of the same workpiece in the machine m Completion time on For process j in the candidate machine k Processing time;

[0040] (2) Selecting the target machine based on the candidate set in segments:

[0041] Based on the current scheduling status and sulfur batch processing constraints, the candidate machines are divided into sets. and set The target machine for process j is determined according to the following segmentation relationship. :

[0042]

[0043] in, To make the process j Assigned to candidate machines kThe maximum completion time obtained thereafter; the target machine As a process j The specific processing equipment in the corresponding feasible scheduling scheme, and in accordance with This is the end time of the process on the worktable.

[0044] Preferably, in the iterative optimization process of step S5, when updating the candidate scheduling scheme set, the two-layer coding structure constructed in step S3 is perturbed by the crossover operator and the mutation operator respectively. The crossover operator, for the sub-batch scheduling allocation code, recombines the batch division scheme of the corresponding production task from the two parent chromosomes according to the preset crossover position. The batch information of parent one in the crossover interval is retained in the original order, and the remaining batches in parent two are filled into the empty positions in order of their relative order in the parent. The process chain integrity check is performed on the recombined batch sequence. If the continuity constraint of the same tire batch is not met, the crossover operation is re-executed. The mutation operator, under the premise of satisfying the process route constraint and equipment capacity constraint, performs neighborhood perturbation on the sub-batch scheduling allocation code and process sorting code, including randomly selecting the target sub-batch or process code and changing its arrangement order in the chromosome by position swapping, insertion or local rearrangement to generate a new candidate scheduling scheme.

[0045] The beneficial effects of this invention are as follows: Under multi-cavity vulcanization constraints, this invention can significantly reduce the maximum completion time in rubber tire production workshops, improve equipment utilization and on-time order delivery rates, and maintain good robustness and adaptability when order structure, batch demand, and equipment load change. By uniformly considering process routes, equipment capabilities, and batch processing characteristics, the scheduling results obtained by this invention under real workshop operating conditions are closer to actual production, reducing inter-process waiting and bottleneck process congestion. Furthermore, this invention utilizes order decomposition and batching strategies to structure customer needs, making task allocation more balanced when different orders are issued to the workshop; it adopts a dual-layer encoding and decoding strategy to coordinate batch division and process sequence optimization, reducing invalid switching and idle time; combined with a multi-layer adaptive iterative optimization mechanism, it enables the scheduling scheme to achieve a dynamic balance between global search and local convergence, thus achieving excellent scheduling results even in large-scale problem scenarios. Attached Figure Description

[0046] Figure 1 This is a flowchart of tire production in the background art of this invention.

[0047] Figure 2 This is a schematic diagram of the overall process of the optimized scheduling method provided in Embodiment 2 of the present invention.

[0048] Figure 3 This is a schematic diagram of the order parsing and batch division process in Embodiment 2 of the present invention.

[0049] Figure 4 This is a schematic diagram of the two-layer encoding of the scheduling data structure in Embodiment 2 of the present invention.

[0050] Figure 5 This is a schematic diagram of the process decoding and process overlap processing in Embodiment 2 of the present invention.

[0051] Figure 6 This is a schematic diagram of the batch processing strategy crossover in Embodiment 2 of the present invention.

[0052] Figure 7 This is a schematic diagram of the scheduling strategy crossover in Embodiment 2 of the present invention.

[0053] Figure 8 This is a schematic diagram of the mutation operator in Embodiment 2 of the present invention.

[0054] Figure 9 This is a schematic diagram of the structure of the multi-layer adaptive selection mechanism in an embodiment of the present invention.

[0055] Figure 10 The following are the response surface analysis results of the key parameters of the scheduling algorithm in the test example of this invention: (a) is a three-dimensional response surface plot between the objective function value and the key parameters; (b) is a contour plot of the objective function value; (c) is a comparison plot of predicted values ​​and experimental values; (d) is a residual analysis plot; and (e) is a residual normality test plot.

[0056] Figure 11 This is an adaptive kernel density distribution diagram showing the relationship between the number of different batches and fitness values ​​in the test examples of this invention.

[0057] Figure 12 This is the scheduling Gantt chart of the standard calculation example S01 in the test examples of the present invention under the scheduling method of the present invention.

[0058] Figure 13 The following is a statistical result graph comparing the performance of various algorithms in the test examples of this invention, where (a) is a curve comparing the standard deviation of each algorithm in multiple runs; and (b) is a radar graph of the quality index of the optimal solution of each algorithm.

[0059] Figure 14 This is a distribution chart of order completion times in a real dataset from a tire production workshop, used in the test examples of this invention.

[0060] Figure 15 This is a Gantt chart showing the scheduling of a typical order across multiple devices in real factory data from the test examples of this invention. Detailed Implementation

[0061] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0062] Example 1

[0063] This invention provides a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints. The optimization scheduling method is as follows:

[0064] Step S1: Obtain basic data of the rubber tire production workshop, and establish a flexible workshop scheduling model with multi-cavity vulcanization constraints based on the basic data to obtain workshop model data for describing the priority relationship of workpiece processes, equipment capacity constraints and batch processing constraints; wherein: the basic data includes process route information of each process in the workshop, operating parameters of various production equipment and multi-cavity vulcanization equipment, and customer order set.

[0065] The process route information should include at least the processing sequence of various workpieces in the raw material preparation, mixing, extrusion, calendering and cutting, forming and vulcanization processes, as well as the corresponding process parameters for each process.

[0066] The operating parameters of various production equipment and multi-chamber vulcanizing equipment shall include at least the number of processes that the equipment can perform, the processing capacity per unit time, the planned available time, and the number of chambers of the multi-chamber vulcanizing equipment and the capacity parameters of each chamber.

[0067] The workpiece type and required quantity of each order in the customer order set correspond one-to-one with the process route of the corresponding workpiece in the process route information.

[0068] The flexible job shop scheduling model with multi-cavity vulcanization constraints adopts a flexible job shop scheduling model with batch processing and multi-cavity vulcanization constraints. The maximum completion time of all workpieces in the shop is used as the optimization objective, and workpiece process optimization constraints, equipment capacity constraints, and batch processing constraints are set under this optimization objective.

[0069] Step S2: Based on the customer order set and workshop model data obtained in Step S1, the customer order set is parsed, and each order is converted into one or more corresponding production tasks. Considering the chamber capacity parameters of the multi-cavity vulcanizing equipment and the allowable batch size of each workpiece, the production tasks are batched to generate order-task-batch data containing orders, production tasks, and their batch relationships. Specifically, Step S2 includes the following steps: Based on the customer order set and workshop model data obtained in Step S1, the sum of the processing time of each process and the earliest delivery date among all related orders are calculated for each workpiece type. A comprehensive priority index combining the shortest processing time rule (SPT) and the earliest delivery date rule (EDD) is obtained. The customer order set is decomposed into multiple production tasks using the Order Decomposition Mapping (OTDM) strategy and sorted according to the comprehensive priority index to form a production task list. Based on the production task list, an equal batching and prime number correction strategy is used to generate batch division results that meet the allowable batch size constraints of the workpiece and the capacity constraints of the multi-cavity vulcanizing equipment according to the demand quantity of each production task.

[0070] Step S3: Based on the order-task-batch data obtained in Step S2 and the workshop model data in Step S1, construct a scheduling data structure to represent candidate scheduling schemes, generate multiple candidate scheduling schemes according to preset rules, and form a set of candidate scheduling schemes; the scheduling data structure is used to characterize the processing order of each batch in each process and the allocation method on different equipment.

[0071] The scheduling data structure adopts a two-layer coding structure, including sub-batch scheduling allocation coding and process sorting coding, specifically:

[0072] The sub-batch scheduling allocation code is used to record the batch division results corresponding to each production task in step S2. The sub-batch quantity is determined according to the pre-determined equal batching and prime number correction results for the required quantity of each production task, and the corresponding workpiece quantity and production task identifier are recorded for each sub-batch.

[0073] The process sequencing code encodes the processes within each batch according to the hierarchical structure of "production task-batch-process". Each process sequencing code unit includes at least an index field to represent the production task number, batch number, and process number, which is used to indicate the production task, batch, and processing order of the process. When the process is a vulcanization process, the equipment identifier of the target multi-cavity vulcanization equipment is further recorded in the process sequencing code unit to indicate that the vulcanization process is processed on the corresponding multi-cavity vulcanization equipment.

[0074] Each process sorting and encoding unit is also associated with a set of process parameter vectors. The process parameter vectors include at least: the number of candidate machines corresponding to the process, the target machine number determined according to the preset greedy machine selection rules, and the loading time, processing time and unloading time of the batch on the target machine. These are used to determine the specific start time and completion time of the process on the target machine during the subsequent decoding process.

[0075] Candidate scheduling schemes are generated by instantiating and combining sub-batch scheduling allocation codes and process sorting codes to form a set of candidate scheduling schemes.

[0076] In step S3, when generating the candidate scheduling scheme set, the population mixing initialization strategy adopted is as follows: based on the order-task-batch data obtained in step S2 and the workshop model data in step S1, some candidate scheduling schemes are constructed according to preset heuristic rules. In the process sorting and coding, the coding units involving the vulcanization process are sorted according to the combination value of vulcanization time and mold change time to determine the key processing path containing the vulcanization process, and the corresponding candidate scheduling scheme is generated accordingly. The remaining candidate scheduling schemes are constructed by randomly perturbing and randomly generating the scheduling data structure, so that the candidate scheduling scheme set contains both candidate scheduling schemes constructed based on heuristic rules and scheduling schemes based on random generation, so as to improve population diversity and enhance the search capability in the large-scale solution space.

[0077] Step S4: For each candidate scheduling scheme in the candidate scheduling scheme set obtained in Step S3, decode it under the premise of satisfying the process route constraints, multi-cavity vulcanization constraints and batch processing constraints in the workshop model data in Step S1, determine the start time, completion time and specific equipment allocated to each batch in each process, generate the corresponding feasible scheduling scheme, and evaluate the feasible scheduling scheme according to the preset objective function set in Step S1 to obtain the evaluation results of each feasible scheduling scheme.

[0078] Decoding the candidate scheduling scheme specifically includes:

[0079] (1) Establish a work processing station and decode it according to sub-batch:

[0080] In the decoding stage, a worktable is established, and the workpiece type, batch number, processing machine, processing start time, and processing end time corresponding to each process are recorded. According to the process sorting code obtained in step S3, the processes in each batch are read sequentially in units of sub-batches, and each process is written into the worktable. When there are two or more processes with overlapping times on the same machine, the start time of the later-written process is postponed so that the same machine corresponds to only one process at any given time.

[0081] (2) Decoding the overlapping of execution processes:

[0082] Under the premise of satisfying the process route constraints in step S1, for non-vulcanization processes, based on the processing time of the process and its predecessor processes and the idle time of the corresponding machine, determine whether the workpieces that have been partially completed in the predecessor processes should enter the process before they are fully completed, and record the start and end times of the corresponding processes in the work processing table.

[0083] For the vulcanization process, the number of completed processes from the preceding processes is based on the records in the worktable. With the total quantity of this batch When satisfied When the vulcanization process is in progress, the mold change preparation time is inserted into the work processing table, and the corresponding vulcanization processing time is arranged after the mold change preparation is completed.

[0084] The dynamic greedy machine selection strategy employed specifically includes:

[0085] (1) For the process of assigning machines during the decoding process j Based on the workshop model data established in step S1, determine the set of selectable machines. In the current decoding state, for any candidate machine Calculate the completion time of process j on this machine. The completion time meets the following requirements:

[0086]

[0087] in, For workpiece type i process j In the machine m The start time on For the previous process of the same workpiece in the machine m Completion time on For process j in the candidate machine k Processing time;

[0088] (2) Selecting the target machine based on the candidate set in segments:

[0089] Based on the current scheduling status and sulfur batch processing constraints, the candidate machines are divided into sets. and set The target machine for process j is determined according to the following segmentation relationship. :

[0090]

[0091] in, To make the process j Assigned to candidate machines kThe maximum completion time obtained later; the target machine As a process j The specific processing equipment in the corresponding feasible scheduling scheme, and in accordance with This is the end time of the process on the worktable.

[0092] Step S5: Based on the evaluation results of each feasible scheduling scheme in Step S4, perform an iterative optimization process on the candidate scheduling scheme set formed in Step S3. Select and adjust the candidate scheduling schemes according to the preset update rules, generate new candidate scheduling schemes, and return to Step S4 for evaluation. When the preset termination condition is met, select the feasible scheduling scheme with the optimal objective function value as the optimal scheduling scheme based on the evaluation results.

[0093] Example 2

[0094] This invention provides a flexible parallel batch optimization scheduling method for rubber tire production workshops with multi-cavity vulcanization constraints, such as... Figure 2 As shown, the method includes the following steps:

[0095] First, obtain basic data of the rubber tire production workshop, and establish a flexible workshop scheduling model with multi-cavity vulcanization constraints based on the basic data to obtain workshop model data for describing workpiece process priority relationships, equipment capacity constraints and batch processing constraints.

[0096] The basic data includes process route information for each step in the workshop, operating parameters of various production equipment, including multi-cavity vulcanizing equipment, and a collection of customer orders; among which:

[0097] The process route information should include at least the processing sequence of various workpieces in the raw material preparation, mixing, extrusion, calendering and cutting, forming and vulcanization processes, as well as the corresponding process parameters for each process.

[0098] The operating parameters of various production equipment and multi-chamber vulcanizing equipment shall include at least the number of processes that the equipment can perform, the processing capacity per unit time, the planned available time, and the number of chambers of the multi-chamber vulcanizing equipment and the capacity parameters of each chamber.

[0099] The workpiece type and required quantity of each order in the customer order set correspond one-to-one with the process route of the corresponding workpiece in the process route information.

[0100] The flexible job shop scheduling model with multi-cavity vulcanization constraints adopts a flexible job shop scheduling model with batch processing and multi-cavity vulcanization constraints. The optimization objective is the maximum completion time of all workpieces within the shop, and under this objective, workpiece process optimization constraints, equipment capacity constraints, and batch processing constraints are set. Details:

[0101] The flexible job shop scheduling model with multi-cavity vulcanization constraints established in Step 1 is based on mixed-integer programming, with the optimization objective being to minimize the maximum completion time. The objective function is set as follows: for:

[0102]

[0103] And this objective must include at least the following constraints:

[0104] (1) Process route and process priority constraints:

[0105] For the workpiece set N Each workpiece i process set N i , No. j Each process is recorded as Each process The corresponding set of available machines is Its start time on machine m is The feeding time is The processing time is The next process is in the machine. The start time is ,satisfy:

[0106] , ;

[0107] (2) Unique constraint for machine selection:

[0108] In the flexible workshop scheduling model, each process is... Set machine allocation variables This ensures that each process can be assigned to only one available machine, satisfying the following constraints:

[0109]

[0110] (3) Equipment capacity and multi-cavity vulcanization constraints:

[0111] For machine set M Any machine m At any time t The number of processing steps is determined by the time indicator variable. This means that the following conditions are met:

[0112]

[0113] For the vulcanizing equipment subset The workpiece is introduced into the vulcanizing machine. s Occupancy indicator variable of each cavity and maximum parallel processing capability parameters ,satisfy:

[0114]

[0115] (4) Constraint that the number of batch processing groups remains constant:

[0116] Let the batch set be B ,batch b The number of workpieces inside is When workpiece i is assigned to batch b, the variable is assigned. Otherwise, it is 0, workpiece type The total number of items is Then, for the same type of workpiece, the number of groups in each process can vary but the total number remains constant, satisfying:

[0117]

[0118] (5) Integer constraint on the number of workpieces within a sub-batch:

[0119] For each batch Number of workpieces It must be a positive integer not less than 1, satisfying:

[0120] , .

[0121] The operating parameters of the multi-cavity vulcanizing equipment include the start time of the batch process. Completion Time and workpiece allocation variables Processing time of batch processes on the machine In the scheduling model, batches are defined using the following formula. b The j Completion time of each process:

[0122]

[0123] The workpiece type is determined based on the batch process completion time. i Production task completion time and orders k Actual completion time ,satisfy:

[0124] , .

[0125] 2. Based on the customer order set and workshop model data obtained in Step 1, the customer order set is parsed, and each order is converted into one or more corresponding production tasks. Considering the chamber capacity parameters of the multi-cavity vulcanizing equipment and the allowable batch size of each workpiece, the production tasks are divided into batches to generate order-task-batch data containing orders, production tasks, and their batch relationships. Figure 3 The specific steps are as follows:

[0126] (1) Based on the customer order set obtained in step one, perform a search on the orders contained in the order set. Each workpiece type i Calculate its earliest delivery date The earliest delivery date is determined using the following formula:

[0127]

[0128] in, For orders k Delivery deadline, For orders k Does it include workpiece type? i The indicator variable, when orders k The requirements include workpiece type i hour Otherwise, it is 0;

[0129] (2) Use preset weighting coefficients w 1 and w 2 pairs of SPT priority components and EDD priority components Perform weighted calculations for each workpiece type. i Comprehensive priority index ,

[0130] ;

[0131] And based on the comprehensive priority index Construct an Order Decomposition Mapping (OTDM) set for each order. ,definition:

[0132]

[0133] in, For orders k Medium workpiece type i The demand quantity is used to map each quadruple in the OTDM set to a production task, ensuring that each production task is associated with at least one workpiece type, the corresponding demand quantity, the delivery deadline, and a comprehensive priority index, and then sorted according to the comprehensive priority index. The production tasks are sorted to obtain a production task list;

[0134] (4) Based on the production task list, candidate equal batching schemes are generated according to the required quantity of each production task and the chamber capacity parameters of the multi-chamber vulcanizing equipment. When the required quantity of a certain production task is a prime number, the required quantity is corrected to a prime number and then the equal batching scheme is regenerated. The scheme that satisfies the allowable batch constraints of each workpiece and the capacity constraints of the multi-chamber vulcanizing equipment is selected from the candidate equal batching schemes as the final batch division result of the production task, so as to form order-task-batch data.

[0135] Third, based on the order-task-batch data obtained in step two and the workshop model data in step one, construct a scheduling data structure to represent candidate scheduling schemes, generate multiple candidate scheduling schemes according to preset rules, and form a set of candidate scheduling schemes; the scheduling data structure is used to characterize the processing order of each batch in each process and the allocation method on different equipment.

[0136] The mentioned scheduling data structure adopts a two-layer coding structure, including sub-batch scheduling allocation coding and process sorting coding, such as Figure 4 As shown, where:

[0137] The sub-batch scheduling allocation code is used to record the batch division results corresponding to each production task in step two. The sub-batch quantity is determined according to the pre-determined equal batching and prime number correction results for the required quantity of each production task, and the corresponding workpiece quantity and production task identifier are recorded for each sub-batch.

[0138] The process sequencing code encodes the processes within each batch according to the hierarchical structure of "production task-batch-process". Each process sequencing code unit includes at least an index field to represent the production task number, batch number, and process number, which is used to indicate the production task, batch, and processing order of the process. When the process is a vulcanization process, the equipment identifier of the target multi-cavity vulcanization equipment is further recorded in the process sequencing code unit to indicate that the vulcanization process is processed on the corresponding multi-cavity vulcanization equipment.

[0139] Each process sorting and encoding unit is also associated with a set of process parameter vectors. The process parameter vectors include at least: the number of candidate machines corresponding to the process, the target machine number determined according to the preset greedy machine selection rules, and the loading time, processing time and unloading time of the batch on the target machine. These are used to determine the specific start time and completion time of the process on the target machine during the subsequent decoding process.

[0140] Candidate scheduling schemes are generated by instantiating and combining sub-batch scheduling allocation codes and process sorting codes to form a set of candidate scheduling schemes.

[0141] The population mixing initialization strategy used in this step to generate the candidate scheduling scheme set specifically includes:

[0142] Based on the order-task-batch data obtained in step two and the workshop model data obtained in step one, some candidate scheduling schemes are constructed according to preset heuristic rules. In the process sorting and coding, the coding units involving the vulcanization process are sorted according to the combination value of vulcanization time and mold change time to determine the key processing path containing the vulcanization process, and the corresponding candidate scheduling scheme is generated accordingly.

[0143] The remaining candidate scheduling schemes are constructed by randomly perturbing and randomly generating the scheduling data structure, so that the candidate scheduling scheme set includes both candidate scheduling schemes constructed based on heuristic rules and scheduling schemes based on random generation, thereby improving population diversity and enhancing search capabilities in large-scale solution spaces.

[0144] Fourth, for each candidate scheduling scheme in the set of candidate scheduling schemes obtained in step three, decode it under the premise of satisfying the process route constraints, multi-cavity vulcanization constraints and batch processing constraints in the workshop model data in step one, determine the start time, completion time and specific equipment allocated to each batch in each process, generate the corresponding feasible scheduling scheme, and evaluate the feasible scheduling scheme according to the preset objective function set in step one to obtain the evaluation results of each feasible scheduling scheme.

[0145] It should be noted that decoding candidate scheduling schemes includes the following two aspects, such as... Figure 5 As shown:

[0146] (1) Establish a work processing station and decode it according to sub-batch:

[0147] During the decoding phase, a worktable is established, recording the workpiece type, batch number, processing machine, processing start time, and processing end time corresponding to each process. According to the process sorting code obtained in step three, the processes in each batch are read sequentially in units of sub-batches, and each process is written into the worktable. When there are two or more processes with overlapping times on the same machine, the start time of the later-written process is postponed so that the same machine corresponds to only one process at any given time.

[0148] (2) Decoding the overlapping of execution processes:

[0149] Under the premise of satisfying the process route constraints in step one, for non-vulcanization processes, based on the processing time of the process and its predecessor processes and the idle time of the corresponding machine, determine whether the workpieces that have been completed in the predecessor processes should enter the process before they are fully completed, and record the start and end times of the corresponding processes in the work processing table.

[0150] For the vulcanization process, the number of completed processes from the preceding processes is based on the records in the worktable. With the total quantity of this batch When satisfied When the vulcanization process is in progress, the mold change preparation time is inserted into the work processing table, and the corresponding vulcanization processing time is arranged after the mold change preparation is completed.

[0151] When determining the specific processing equipment for each batch and each process, the dynamic greedy machine selection strategy employed includes the following steps:

[0152] (1) For the process of assigning machines during the decoding process j Based on the workshop model data established in step one, determine the set of selectable machines. In the current decoding state, for any candidate machine Calculate the completion time of process j on this machine. The completion time meets the following requirements:

[0153]

[0154] in, For workpiece type i process j In the machine m The start time on For the previous process of the same workpiece in the machine m Completion time on For process j in the candidate machine k Processing time;

[0155] (2) Selecting the target machine based on the candidate set in segments:

[0156] Based on the current scheduling status and sulfur batch processing constraints, the candidate machines are divided into sets. and set The target machine for process j is determined according to the following segmentation relationship. :

[0157]

[0158] in, To make the process j Assigned to candidate machines k The maximum completion time obtained later; the target machine As a process j The specific processing equipment in the corresponding feasible scheduling scheme, and in accordance with This is the end time of the process on the worktable.

[0159] V. Based on the evaluation results of each feasible scheduling scheme in step four, an iterative optimization process is performed on the candidate scheduling scheme set formed in step three. The candidate scheduling schemes are selected and adjusted according to preset update rules, generating new candidate scheduling schemes and returning to step four for evaluation. When the preset termination condition is met, the feasible scheduling scheme with the optimal objective function value is selected as the optimal scheduling scheme based on the evaluation results. The iterative optimization process employs a multi-layer adaptive selection mechanism, the overall structure of which is as follows: Figure 9 As shown, each iteration includes the following steps:

[0160] (1) Calculate the fitness variance and determine the evolutionary stage:

[0161] Fitness statistics are performed on the population formed by the feasible scheduling schemes obtained in step four, and the fitness values ​​of each feasible scheduling scheme are used. f i Based on this, calculate the average fitness of the population. and fitness variance Among them, fitness variance The calculation formula is:

[0162]

[0163] in, P s For population size, f i For the first i The fitness of an individual The average fitness of the population;

[0164] 2) Calculate diversity measures:

[0165] In the current population, with a given partition width along the fitness axis. Based on this, the fitness density function is calculated for the fitness of each individual. The calculation formula is:

[0166]

[0167] in, For indicator functions, The preset fit window width;

[0168] Divide the fitness axis into There are several intervals, and the proportion of individuals within the i-th interval is denoted as . Calculate information entropy H :

[0169]

[0170] Genotype sequences of any two candidate scheduling schemes , Calculate edit distance And construct a similarity matrix based on the maximum edit distance. The formula for calculating the similarity matrix is ​​as follows:

[0171]

[0172] in, To make the sequence Minimum number of editing operations required The maximum edit distance between any two individuals in the current population;

[0173] (3) Construct a dynamic selection pressure function:

[0174] Depends on the current iteration number t Total number of iterations T Get the selection pressure function value of the current iteration :

[0175]

[0176] in, and These are the preset minimum and maximum selectable pressure parameters, when... t Approaching 0 To enhance global search capabilities, when t near T hour near To accelerate convergence;

[0177] (4) Perform hierarchical selection based on multi-level adaptive rules:

[0178] Using the fitness density function obtained in step (2) Information entropy H and similarity matrix The population was statistically analyzed and divided into elite, superior, ordinary, and improvement-needed layers; based on this, the selection pressure function obtained in step (3) was used. A hierarchical selection process is performed on the candidate scheduling schemes, with an elite retention ratio of approximately 30%, a selection ratio based on diversity metrics of approximately 30%, and an adaptive competition selection ratio of approximately 40%, to obtain a new set of candidate scheduling schemes for evaluation in step four of the next iteration.

[0179] It should be noted that in the iterative optimization process of step five, when updating the candidate scheduling scheme set, the two-layer coding structure constructed in step three can be perturbed using crossover and mutation operators respectively. The crossover operator assigns codes to sub-batch scheduling, and the specific process is as follows: Figure 6 As shown, the batch division scheme corresponding to the production task is recombined from the two parent chromosomes according to the preset crossover position. The batch information of parent one within the crossover interval is retained in its original order, and the remaining batches in parent two are filled into the empty positions in order of their relative order in the parent generation. The completeness of the process chain is checked on the recombined batch sequence. If the continuity constraint of the same tire batch is not met, the crossover operation is re-executed. When the parent batch processing strategy is consistent, the process sorting code is recombined using the scheduling strategy crossover operator, as illustrated in the diagram. Figure 7 As shown. Under the premise of satisfying process route constraints and equipment capacity constraints, the mutation operator performs neighborhood perturbation on the sub-batch scheduling allocation code and process sequencing code. The specific mutation method is as follows: Figure 8 As shown, this involves randomly selecting target sub-batch or process codes and changing their arrangement order in the chromosome through position swapping, insertion, or local rearrangement to generate new candidate scheduling schemes.

[0180] Test case

[0181] To verify the effectiveness and superiority of the flexible parallel batch optimization scheduling method for a rubber tire production workshop with multi-cavity vulcanization constraints in Embodiment 2 of the present invention, simulation experiments were conducted using standard examples and actual factory data. By supplementing the data, the required data structure for the model was completed, and parameters were selected. Simultaneously, comparisons with other algorithms were made to verify feasibility and effectiveness. Finally, actual verification was performed using production data from a rubber tire company in Qingdao. Experiments were conducted based on the above data, and all experiments were completed on a personal computer with a Windows 10 operating system, a 3.5GHz CPU, and 16GB of RAM.

[0182] 1. Data Preprocessing

[0183] To verify the effectiveness of the algorithm, this study constructed the FJSP-BV test set based on the MK01-MK10 benchmark cases, selected 6 types of PT (Precipitation Temperature Coefficient) and designed 6 standard process flows, of which the first 5 are conventional processing and the 6th is a vulcanization process. Incomplete process configurations were completed using cyclic mapping of parameters from the same instance. The process parameters were set according to actual production, with a loading and unloading time of U(1,10) minutes; mold changing and vulcanization parameters are shown in Table 1; and the delivery time constraint was U(100,800) minutes. The relevant data for this test set has been uploaded to the Zenodo platform, DOI 10.5281 / zenodo.17587885, and is publicly available for access and reuse.

[0184] Table 1. Parameters of vulcanization equipment in test examples.

[0185]

[0186] 2. Response Surface Method Parameter Analysis

[0187] To analyze the impact of key parameters on the performance of the genetic algorithm, this test uses the Response Surface Methodology (RSM) to construct a continuous mathematical model between the parameters and the objective function, and quantitatively describes the interaction between parameters using a second-order polynomial model. Four core factors were selected: Ps, number of iterations (Gen), crossover probability (Cp), and mutation probability (Mr), as shown in Table 2. A Box-Behnken experimental design was used to construct the experimental matrix. This design requires 29 experimental points (including 24 edge points and 5 center points). For each parameter combination, the algorithm was run 10 times on four representative instances: Mk01, Mk05, Mk09, and Mk10, with the average value... As the response variable, the experimental data were used to fit a second-order response surface model containing linear, quadratic, and interaction terms.

[0188]

[0189] in For response variables, For the encoded factor variables, For regression coefficients, This is random error.

[0190] Table 2 Selection of Orthogonal Experiment Parameters

[0191]

[0192] RSM (Response Surface Methodology) demonstrated excellent fitting accuracy in this test. See also Figure 10 Scatter plot of experimental and predicted values ​​( Figure 10 The results in (a) show a high degree of overlap, with a model determination coefficient R² of 0.962, indicating that the model can explain 96.2% of the response variation. Residual analysis further validated the reliability of the model: the residuals are randomly distributed near zero. Figure 10 In (b), the fluctuation range was controlled within ±10, the relative error was about 2.5%, and no systematic deviation was found; the residual normality test ( Figure 10 In (c), all points are close to the reference line, satisfying the normality assumption. Parameter sensitivity analysis ( Figure 10 (d) shows that Ps has the most significant impact on performance, followed by Mr, while Gen and Cp have relatively smaller effects. (Contour plot) Figure 10(e) reveals a significant interaction between Ps and Gen, with the optimal region located near the encoded value of 0, corresponding to actual values ​​of Ps=600 and Gen=325. The three-dimensional response surface ( Figure 10 Figure (f) shows that Cp and Mr jointly affect the target performance, with optimal ranges of (0.85-0.90) and (0.30-0.35) respectively. Finally, the optimal parameter combination obtained based on RSM optimization is Ps=672, Gen=348, Cp=0.89, Mr=0.34.

[0193] 3. The impact of batch quantity on adaptability

[0194] To systematically evaluate the practical effect of the batching strategy in parallel batch scheduling of tire vulcanization, this test constructed a verification environment based on the MK standard test suite, containing 30 typical scenarios, covering small-scale... medium-sized large-scale Three categories. Based on the characteristics of the vulcanization process, four batching strategies were designed: small batches... Medium batch large batches and mixed batches A genetic algorithm was used to conduct 50 independent and repeated experiments for each strategy, with parameter P. s =672, G en =348, C p =0.89, M r =0.34. A multi-dimensional evaluation was conducted using three key indicators: batch size, fitness value, and batch utilization. Experimental data show that different batching strategies have a significant impact on scheduling performance. Figure 11 The adaptive kernel density distribution shows a clear non-linear correlation between batch size and fitness value. The high fitness region is concentrated in the medium batch size range (8-12), which confirms the existence of a clear optimal batch configuration window. Specifically, while the small batch strategy improves equipment utilization (average 85.2%), it leads to an excessive number of batches and increases mold changeover time; the large batch strategy reduces the number of mold changeovers, but the excessively large batch size causes equipment utilization to drop to 72.3%.

[0195] Furthermore, the impact of batching strategies becomes more significant as the problem scale increases. In small instances (Mk01, Mk03, Mk05), the performance differences between strategies are relatively small (fitness fluctuation range ≤4.2%), and the optimal batch size is distributed in the range (5-12). However, in large instances (Mk07, Mk09, Mk10), the performance gap between strategies widens to 11.7%, and the optimal batch size rises to the range (8-14). Notably, the hybrid batching strategy performs best in large instances, with its fitness value increasing by an average of 6.3% compared to the fixed strategy, which verifies the necessity of dynamically adjusting batch capacity in complex scenarios. Batch utilization analysis further shows that the medium batching strategy achieves the best balance between equipment utilization and mold change frequency, with an average utilization of 88.6% and a stable fitness value in the high range (0.82-0.85).

[0196] 4. Algorithm Comparison

[0197] To verify the superior performance of the algorithm, four algorithms were selected for comparative experiments: the conventional batch genetic algorithm (NBGA), the improved genetic algorithm using a parallel processing strategy (SMPGA), the improved genetic algorithm based on an overlap mechanism (BOPGA), the three-layer coding genetic algorithm (OPGA), and the two-layer coding algorithm (FJSP-BV) of this invention. The parameter P was determined according to RSM. s =672, G en =348, C p =0.89, M r =0.34. The test case setup and verification groups S01-S15 are shown in Table 3. Each algorithm in each group was run independently 30 times, and the optimal value was used for horizontal comparison. The small-scale comparative experimental data are shown in Table 4. For the typical case S01, FJSP-BV finally... In minutes, it improved upon SMPGA, BOPGA, OPGA, and NBGA by 34.3%, 51.5%, 55.5%, and 74.2% respectively, compared to SMPGA, BOPGA, OPGA, and NBGA. This represents a 33.3% and 51.6% improvement over SMPGA and BOPGA, respectively. This advantage is even more pronounced in large-scale computations (as shown in Table 5), where L01 achieves... Minutes, far shorter than other algorithms.

[0198] Table 3 Number of comparative experiments

[0199]

[0200] Table 4 Data from a small-scale comparative experiment

[0201]

[0202] Table 5. Data from a large-scale comparative experiment

[0203]

[0204] Furthermore, in terms of scheduling scheme quality, the S01 scheduling Gantt chart ( Figure 12 The results visually demonstrate the superiority of FJSP-BV in the S01 case. This algorithm achieves tight task coordination, significantly reduces equipment idle time, and achieves a final completion time of 144.0 minutes. This efficient scheduling arrangement reflects the practical value of the algorithm in real-world production environments. In terms of computational stability, FJSP-BV exhibits excellent robustness. Figure 13 The standard deviation comparison curve (a) shows that in the S01 case, the standard deviation of FJSP-BV is only 0.8, while the standard deviations of the comparison algorithms NBGA and OPGA are as high as 36.7 and 5.5, respectively. Figure 13 The radar chart in (b) further confirms the balanced performance of the algorithm across all performance metrics, with all metrics located within the optimal region. In contrast, the metrics distribution of the comparison algorithm is discrete, and its stability is clearly insufficient.

[0205] The comprehensive comparative experimental results show that the FJSP-BV algorithm significantly outperforms the comparison algorithms in terms of solution efficiency, scheduling quality, and computational stability. In test cases of different scales, FJSP-BV achieves shorter completion times and higher scheduling compactness, indicating its stronger global optimization capability and adaptability in handling complex batch processing and parallel processing collaborative optimization problems. Furthermore, standard deviation and radar chart analysis show that FJSP-BV exhibits balanced performance across multiple metrics with minimal fluctuations, fully demonstrating the algorithm's robustness and stable convergence characteristics. Overall, FJSP-BV not only excels in computational performance but also demonstrates high engineering application potential in terms of the feasibility of its scheduling scheme.

[0206] 5. Factory Case Verification

[0207] To verify the practical application effect of the algorithm, this study conducted simulation experiments based on real production data from a large tire manufacturing enterprise in Qingdao. The dataset covers six tire products, including ST185 / 65R15 and ST205 / 55R16, with a total output ranging from 28,800 to 158,400 units. The production system consists of 19 general-purpose machines and 4 dedicated vulcanizing machines, covering six processes including mixing and calendering, with the first five processes featuring machine flexibility. Table 6, based on local factory data, shows the quantity, batches, and delivery dates of eight orders. Completion time and minimum completion time These key indicators reflect the differences in production scale and delivery requirements among different orders.

[0208] Table 6 Local Factory Data

[0209]

[0210] Order completion time distribution chart ( Figure 14 The time distribution characteristics of the eight orders are shown, verifying the scheduling performance of the algorithm in a multi-order scenario. The sub-order times exhibit obvious gradient characteristics, reflecting the complex scheduling characteristics of the parallel operation of multiple processes in tire production. All orders meet the delivery date constraints, proving the algorithm's on-time delivery capability. Figure 15 The Gantt chart shows that Order 1 was closely scheduled across 23 machines, with high equipment utilization and a completion time of 72,252.2 minutes.

[0211] Experiments have demonstrated the superiority of this invention in actual production, effectively handling complex manufacturing systems with multiple product varieties and processes, significantly shortening completion time and improving equipment utilization. Performance ratios indicate that most orders are close to their expected delivery dates, reflecting the algorithm's stability; the early completion of some orders demonstrates its resource coordination capabilities. This algorithm provides reliable support for intelligent scheduling in process industries such as tire manufacturing.

[0212] Simulation experiments using the aforementioned standard examples and actual factory data demonstrate that, compared to traditional batch genetic algorithms, parallel improved algorithms, and genetic algorithms based on overlapping processes or multi-layer coding, the scheduling method proposed in this invention exhibits significant advantages in terms of maximum completion time, solution stability, and adaptability to complex production environments. Even with simultaneous constraints such as multi-cavity vulcanization, batch processing, and order delivery dates, the method of this invention achieves a shorter overall production cycle and higher resource utilization, thus verifying the effectiveness and beneficial effects of the technical solution in rubber tire production workshops.

[0213] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A flexible co-scheduling parallel batch optimization method for rubber tire production plant containing multi-cavity vulcanization constraints, characterized in that, The optimization scheduling method is: Step S1: Obtain the basic data of the rubber tire production workshop, establish a flexible job shop scheduling model containing multi-cavity vulcanization constraints based on the basic data, and obtain workshop model data for describing the priority relationship of workpiece processes, device capacity constraints and batch processing constraints; Step S2: According to the customer order set and the workshop model data obtained in step S1, analyze the customer order set, convert each order into one or more corresponding production tasks, and divide the production tasks into batches based on the consideration of the chamber capacity parameters of the multi-cavity vulcanization equipment and the allowable batch quantity of each workpiece, and generate order-task-batch data containing orders, production tasks and batch relationships; Step S3: Based on the order-task-batch data obtained in step S2 and the workshop model data in step S1, a scheduling data structure is constructed to represent the candidate scheduling scheme, and a plurality of candidate scheduling schemes are generated according to the preset rules to form a candidate scheduling scheme set; The scheduling data structure is used to represent the processing order of each batch in each process and the allocation method on different devices; The scheduling data structure adopts a double-layer coding structure, including sub-batch scheduling allocation coding and process sorting coding; Step S4: Decode each candidate scheduling scheme in the candidate scheduling scheme set obtained in step S3 under the premise of meeting the process route constraints, multi-cavity vulcanization constraints and batch processing constraints in the workshop model data in step S1, determine the start time, completion time and specific device allocation of each batch in each process, generate the corresponding feasible scheduling scheme, and evaluate the feasible scheduling scheme according to the preset objective function set in step S1, to obtain the evaluation result of each feasible scheduling scheme; Step S5: Based on the evaluation results of each feasible scheduling scheme in step S4, perform an iterative optimization process on the candidate scheduling scheme set formed in step S3, select and adjust the candidate scheduling scheme according to the preset update rule, generate a new candidate scheduling scheme and return to step S4 for evaluation; When the preset termination condition is met, the feasible scheduling scheme with the optimal objective function value is selected as the optimal scheduling scheme according to the evaluation result; The basic data in step S1 includes process route information of each process in the workshop, operating parameters of various production equipment and multi-cavity vulcanization equipment therein, and a customer order set; wherein: The process route information at least includes the processing order of various workpieces in raw material preparation, mixing, extrusion, calendering and cutting, molding and vulcanization processes, and the process parameters corresponding to each process; The operating parameters of various production equipment and multi-cavity vulcanization equipment therein at least include device executable processes, unit time processing capacity, planned available time, and chamber number and capacity parameters of each chamber of the multi-cavity vulcanization equipment; The workpiece type and quantity of each order in the customer order set correspond one-to-one with the process route of the corresponding workpiece in the process route information; The flexible job shop scheduling model with multi-cavity vulcanization constraints adopts a flexible job shop scheduling model with batch processing and multi-cavity vulcanization constraints, takes the maximum completion time of all workpieces in the workshop as an optimization target, and sets workpiece process optimization constraints, equipment capacity constraints and batch processing constraints under the optimization target; The iterative optimization process in step S5 adopts a multi-layer adaptive selection mechanism, and includes the following steps in each iteration: (1) Calculate the fitness variance and determine the evolution stage: The population of feasible scheduling schemes obtained in step S4 is subjected to fitness statistics, and the fitness values of the respective feasible scheduling schemes are utilized f i Based on this, the population average fitness is calculated and the fitness variance where the fitness variance is calculated according to the formula: wherein, P s is the population size, f i is the fitness of the i th individual, is the population average fitness; 2) Calculate the diversity measure: On the current population, with a given partition width of the fitness axis For each individual, the fitness density function is calculated as a basis for the fitness , with the formula: wherein, is an indicator function, is a predetermined fitness window width; The fitness axis is divided into intervals, and the proportion of individuals in the ith interval is denoted as , and the information entropy is calculated as H : genotype sequences of any two candidate scheduling schemes , edit distance , and construct a similarity matrix based on the maximum edit distance The formula for calculating the similarity matrix is as follows: wherein, is the minimum number of edit operations required to transform the sequence is the minimum number of edit operations required to transform the sequence is the maximum edit distance between any two individuals within the current population; (3) Construct a dynamic selection pressure function: Depend on the current iteration number as t , the total iteration number T Get the selection pressure function value of the current iteration : wherein, and are preset minimum and maximum selection pressure parameters, respectively, when t is close to 0 to enhance the global search ability, when t is close to T is close to is close to to accelerate convergence; (4) Perform hierarchical selection based on multi-layer adaptive rules: using the fitness density function obtained in step (2) , information entropy H , and similarity matrix statistics of the population, the population is divided into elite layer, good layer, ordinary layer and to be improved layer; on this basis, combined with the selection pressure function obtained in step (3) , hierarchical selection is performed on the candidate scheduling scheme according to an elite reservation ratio of about 30%, a selection ratio based on diversity measurement of about 30%, and a self-adaptive competition selection ratio of about 40%, to obtain a new candidate scheduling scheme set for evaluation in step S4 of the next iteration; And, when updating the candidate scheduling scheme set in step S5, the double-layer coding structure constructed in step S3 is disturbed by a crossover operator and a mutation operator, respectively, wherein the crossover operator is for sub-batch scheduling allocation coding, and recombines the batch division scheme of the corresponding production task from two parent chromosomes according to a preset crossover position, retains the batch information in the parent one in the crossover interval in the original order, fills the remaining batches in the parent two into the vacancy positions in the order of their relative order in the parent, and performs process chain integrity checking on the recombined batch sequence, and re-executes the crossover operation when the same tire batch continuity constraint is not met; the mutation operator performs neighborhood disturbance on the sub-batch scheduling allocation coding and the process sequence coding under the premise of meeting the process route constraint and the equipment capacity constraint, including randomly selecting a target sub-batch or process coding, and changing its arrangement order in the chromosome by position exchange, insertion or local rearrangement to generate a new candidate scheduling scheme.

2. The method of claim 1, wherein, The step S2 is specifically: based on the customer order set and the workshop model data obtained in step S1, calculating the sum of the processing time of each workpiece type and its earliest delivery period in all related orders to obtain a comprehensive priority index combining the shortest processing time rule SPT and the earliest delivery period rule EDD, using the order decomposition mapping OTDM strategy to decompose the customer order set into multiple production tasks and sorting them according to the comprehensive priority index to form a production task list, and based on the production task list, using the equal batch and prime correction strategy to generate a batch division result that meets the workpiece allowable batch constraint and the multi-cavity vulcanization equipment capacity constraint according to the demand quantity of each production task.

3. The method of claim 1, wherein, In the step S3, The sub-batch scheduling allocation coding is used to record the batch division result corresponding to each production task in step S2, and the number of sub-batches is determined according to the predetermined equal batch and prime correction result for the demand quantity of each production task, and the corresponding workpiece quantity and the production task identifier of each sub-batch are recorded; The process sequence coding encodes the processes in each batch in a hierarchy of "production task-batch-process", each process sequence coding unit at least includes an index field for indicating production task sequence number, batch sequence number and process sequence number, for indicating the production task to which the process belongs, the batch to which the process belongs and the processing order in the batch, and when the process is a vulcanization process, the equipment identification of the target multi-cavity vulcanization equipment is further recorded in the process sequence coding unit; Each of the process sequence coding units is further associated with a set of process parameter vectors, the process parameter vectors at least include: the number of candidate machines corresponding to the process, the target machine sequence number determined according to a preset greedy machine selection rule, and the loading time, processing time and unloading time of the batch on the target machine; The candidate scheduling scheme is generated by instantiating and combining the sub-batch scheduling allocation coding and the process sequence coding.

4. The method of claim 3, wherein, When the candidate scheduling scheme set is generated in step S3, a population hybrid initialization strategy is adopted, specifically including: Based on the order-task-batch data obtained in step S2 and the workshop model data in step S1, part of the candidate scheduling schemes are constructed according to a preset heuristic rule, in the process sequence coding, the coding units involving vulcanization processes are sorted according to the combination value of vulcanization time and mold changing time, to determine the critical processing path containing the vulcanization process, and the corresponding candidate scheduling scheme is generated accordingly; The remaining candidate scheduling schemes are constructed by randomly disturbing and randomly generating the scheduling data structure, so that the candidate scheduling scheme set contains both the candidate scheduling schemes constructed based on the heuristic rule and the scheduling schemes generated based on the random generation.

5. The method of claim 1, wherein, The decoding of the candidate scheduling scheme in step S4 specifically includes: (1) Establishing a job processing table and decoding by sub-batch: In the decoding phase, a job processing table is established to record the workpiece type, batch number, processing machine, processing start time and processing end time corresponding to each process; according to the process sequence coding obtained in step S3, the processes in each batch are read in turn in units of sub-batch, and each process is written into the job processing table; when there are two or more processes with time overlap on the same machine, the start time of the process written later is postponed, so that the same machine only corresponds to the processing of one process at any time; (2) Perform process overlap decoding: Under the premise of meeting the process route constraints in step S1, for non-vulcanization processes, whether the completed part of the workpiece in the previous process enters the process before all the workpieces are completed is determined according to the processing time of the process and the previous process and the idle time of the corresponding machine, and the start time and end time of the corresponding process are recorded in the job processing table respectively; For the vulcanization process, the number of completed processes in the preceding process recorded in the job processing table and the total number of the batch When the condition is satisfied, the mold change preparation time for the vulcanization process is inserted in the job processing table, and the corresponding vulcanization processing time is scheduled after the mold change preparation ends.

6. The method of claim 1, wherein, When determining the specific processing equipment for each process of each batch in step S4, a dynamic greedy machine selection strategy is adopted, specifically including: (1) For the process of the machine to be allocated in the decoding process j , determine its selectable machine set based on the workshop model data established in step S1 , under the current decoding state, for any candidate machine Calculate the completion time of the process j On this machine , the completion time satisfies: in, For workpiece type i process j In the machine m The start time on For the previous process of the same workpiece in the machine m Completion time on For process j In candidate machines k Processing time; (2) Segment selection of target machine based on candidate set: The candidate machines are divided into sets according to the current scheduling state and the vulcanization batch constraints and sets and the target machine of process j is determined according to the following segmentation relationship : wherein, to assign the process j to the candidate machines k the resulting maximum completion time; the target machine as the process j at the specific processing device in the corresponding feasible schedule, and as the end time of the process at the job processing station.

Images