Dyeing vat scheduling method and system based on genetic algorithm for multi-order dynamic scheduling

Abstract

The application discloses a dye vat scheduling method and system based on a genetic algorithm, and relates to the field of artificial intelligence.The method comprises the following steps: collecting order and resource data, determining a dye vat allocation and sequencing problem; constructing a constraint-oriented data code, and converting original data into a composite feature vector; adopting a hypergraph clustering and hierarchical coding strategy to form a double-layer chromosome structure of cluster arrangement and intra-cluster sequencing; constructing a multi-objective dynamic weighted fitness function; executing adaptive crossover and mutation based on the cluster structure, and outputting a multi-order dynamic scheduling scheme.The application effectively compresses the search space by embedding inventory constraints and color conflicts into coding and genetic operations, avoids premature convergence, significantly reduces cleaning costs and order delays during the scheduling process, and improves the utilization rate of dye vat equipment.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a dyeing vat scheduling method and system based on a genetic algorithm for dynamic scheduling of multiple orders. Background Technology

[0002] With increasingly fierce global market competition and the personalization of consumer demands, the textile printing and dyeing production model is gradually shifting from traditional large-batch, low-variety production to small-batch, high-variety production with short lead times. This transformation has brought unprecedented challenges to production scheduling in dyeing and finishing workshops. As the core bottleneck equipment in the printing and dyeing production process, the quality of the dyeing vat's scheduling directly determines the efficiency, cost, and order delivery capability of the entire production system.

[0003] The main shortcomings of existing technologies are as follows: Existing methods often only use delivery dates as the sorting criterion when handling dyeing vat scheduling, ignoring the dynamic impact of work-in-process inventory levels on production priority. This leads to the repeated production of high-inventory orders while delaying truly urgent orders. Furthermore, the handling of color switching costs is rather crude, typically only considering whether colors are identical, failing to quantify the impact of similarity differences between different colors on cleaning costs. Traditional genetic algorithms directly encode the order sequence, ignoring the multidimensional feature relationships between orders. This results in a factorial increase in the search space and generates numerous invalid solutions that violate dyeing vat capacity constraints or incur huge cleaning costs during the evolutionary process. The algorithm is inefficient and struggles to handle hundreds or thousands of orders in actual production. Conventional multi-objective optimization methods often use fixed weight coefficients, failing to adapt to dynamic changes in the production environment. For example, when work-in-process inventory accumulates, the priority of related orders should be reduced, but existing methods lack this dynamic adjustment mechanism. Simultaneously, traditional tournament selection strategies use a fixed scale, making it difficult to adaptively balance convergence speed and population diversity at different stages of population evolution. The crossover and mutation operations in existing genetic algorithms are mostly random operations, which can easily destroy the excellent gene blocks accumulated through evolution (such as order sequences with similar colors and urgency). They lack the utilization of knowledge of the problem domain, and when the population gets stuck in local optima, they lack effective monitoring and escape mechanisms, which leads to premature convergence of the algorithm and the quality of the final solution is difficult to meet the actual production needs. Summary of the Invention

[0004] To address the technical problems in the prior art, this invention provides a dyeing vat scheduling method and system based on dynamic scheduling of multiple orders using a genetic algorithm.

[0005] This invention is achieved through the following technical solution: A dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders includes: The problem of order scheduling data collection and optimization is defined; the data collection includes order information, resource status information, and process knowledge information; the optimization problem is to allocate appropriate dyeing vat resources to each order to be scheduled under the constraints, and to determine the processing sequence of all orders on the same dyeing vat; Production task data preprocessing and constraint coding; including using constraint-oriented data coding methods to transform raw order data into composite feature vectors containing time windows, resource requirements, and conflict coefficients; Feature mining and chromosome coding; including a hypergraph-based clustering and hierarchical coding strategy to perform feature mining and clustering on orders, and to encode within and between clusters; the coding is fitness-oriented chromosome coding; Determine the fitness function and parent selection; this includes constructing a multi-objective dynamic weighted fitness function, incorporating resource constraint penalty terms, and designing an adaptive tournament selection strategy. Genetic operations and convergence strategy optimization; including genetic operations using adaptive crossover and mutation operators based on cluster structure, and dynamically adjusting operation probabilities in combination with population evolution state; Dye vat scheduling optimization for dynamic production scheduling of multiple orders; including taking order data, resource status data and process knowledge data collected at the current scheduling time as input to form a dynamic production scheduling scheme for multiple orders.

[0006] Furthermore, the constraint encoding includes transforming the original order data into a composite feature vector containing time windows, resource requirements, and conflict coefficients; the conflict coefficients include color conflicts, which are quantified based on the construction of a color conflict matrix to determine the cleaning difficulty between any two order colors, and are used as a penalty term for gene block recombination in the genetic algorithm.

[0007] Furthermore, the hierarchical coding strategy employs a two-layer coding structure for hierarchical chromosome coding. The first layer is the cluster arrangement layer, which encodes the production order of each cluster to obtain the cluster arrangement layer coding. The second layer is the intra-cluster sorting layer, which encodes the specific processing order of orders within each cluster.

[0008] Furthermore, the hypergraph clustering group orders with similar urgency and low color conflict into one category.

[0009] Furthermore, the multi-objective dynamic weighted fitness function combines total delay penalty, total cleaning cost, cylinder utilization balance, and process path continuity, and introduces a dynamic weight adjustment mechanism based on the current work-in-process level.

[0010] Furthermore, the adaptive tournament selection strategy balances selection pressure by dynamically adjusting the tournament size.

[0011] Furthermore, the adaptive crossover based on the cluster structure includes adaptively adjusting the crossover probability according to the similarity between two parent individuals; the higher the similarity, the lower the crossover probability.

[0012] Furthermore, the mutation operator, combined with color conflict information, guides the mutation direction toward low-conflict regions.

[0013] This invention also provides a dyeing vat scheduling system based on a genetic algorithm for dynamic scheduling of multiple orders, which, based on the above-described dyeing vat scheduling method for dynamic scheduling of multiple orders using a genetic algorithm, includes: The order scheduling data collection and optimization problem identification module is used to collect order information, resource status information, and process knowledge information, and to identify problems such as allocating dyeing vat resources and determining the processing sequence of all orders on the same dyeing vat. The production task data preprocessing and constraint coding module is used to transform the original order data into a composite feature vector by adopting a constraint-oriented data coding method oriented towards the dyeing vat scheduling characteristics, thereby realizing the feature representation of the order data; The feature mining and chromosome coding module is used to perform feature mining and clustering of orders using hypergraph clustering and hierarchical coding strategies, and to encode them within and between clusters respectively. The fitness function and parent selection module are determined, which is used to construct a multi-objective dynamic weighted fitness function and adopt an adaptive tournament selection strategy based on fitness ranking and population diversity in the parent selection stage. The genetic operation module includes adaptive crossover and mutation operators based on cluster structure, and dynamically adjusts the operation probability according to the population evolution state, while introducing local search and population restart mechanisms. The dyeing vat scheduling optimization module for dynamic scheduling of multiple orders is used to form a dynamic scheduling plan for multiple orders by taking the order data, resource status data and process knowledge data collected at the current scheduling time as input.

[0014] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium storing program instructions for a dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm. The program instructions for the dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm can be executed by one or more processors to implement the steps of the dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm as described above.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Construct a constraint-oriented data encoding method for dyeing vat scheduling characteristics. By introducing an urgency factor that includes an inventory suppression mechanism and a color conflict matrix based on HSV color space and same color system penalty, the original order data is transformed into a composite feature vector with physical meaning. Thus, dynamic inventory constraints and color switching costs of the production site are embedded in the data preprocessing stage.

[0016] 2. A chromosome expression strategy based on hypergraph clustering and hierarchical coding is adopted. By constructing a multimodal feature hypergraph of orders, orders are clustered according to urgency similarity, low color conflict and process path consistency. Then, a two-layer coding structure of cluster arrangement and intra-cluster sorting is adopted to effectively compress the search space of combinatorial optimization and reduce the probability of invalid solutions.

[0017] 3. A multi-objective dynamic weighted fitness function and adaptive selection mechanism are adopted. This function not only integrates four conflicting indicators such as delay penalty, cleaning cost, equipment balance and process continuity, but also dynamically adjusts the weight of each objective based on real-time status such as work-in-process inventory level and clustering effect. At the same time, the scale of tournament selection is dynamically adjusted using population diversity indicators, thus balancing the development and exploration capabilities of the algorithm.

[0018] 4. An adaptive genetic operation and convergence strategy based on cluster structure and color conflict information is adopted, including a two-layer crossover probability dynamically adjusted according to parent similarity, a taboo mutation operator that guides the mutation direction toward low-conflict regions, and an elite restart mechanism based on population entropy monitoring. This effectively avoids premature convergence of the algorithm and enhances the global search capability in complex constraint spaces. Attached Figure Description

[0019] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic flowchart of a dyeing vat scheduling method based on a genetic algorithm for dynamic scheduling of multiple orders, according to an embodiment of this application. Figure 2 This is an urgency factor distribution diagram according to an embodiment of this application; Figure 3 It is a priority distribution diagram based on traditional methods; Figure 4 This is an order clustering result diagram based on urgency factor and color conflict coefficient according to an embodiment of this application; Figure 5 This is a diagram showing the impact of crossover probability and mutation probability on the fitness of the production scheduling scheme according to embodiments of this application. Detailed Implementation

[0020] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0021] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0022] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. The illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the shape, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0023] See Figure 1 A dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders includes the following steps: S1. Identification of data collection and optimization issues for dynamic scheduling of multiple orders. In scenarios involving dynamic scheduling of multiple orders, the production system needs to respond in real time to the arrival of new orders, fluctuations in work-in-process inventory, and changes in the status of dyeing equipment, in order to formulate an efficient and feasible scheduling plan under the constraint of limited production resources. The first step is to systematically collect multi-source heterogeneous data from the production site and to precisely formally define the optimization problem.

[0024] The data collection scope covers three levels: order information, resource status information, and process knowledge information. Order information mainly includes the unique identifier of each order awaiting production, dyeing color code, unit weight, compatible dyeing vat type code, customer-required delivery date timestamp, customer priority level, complete dyeing process path code, order quantity in kilograms, order arrival timestamp in the production system, and indicators of any special processing requirements. Resource status information requires real-time acquisition of the equipment number, vat type, maximum capacity, current occupancy status, and estimated release time of all currently available dyeing vats, as well as the work-in-process inventory corresponding to each color code, i.e., the quantity of semi-finished products that have been put into production but not yet completed. Process knowledge information covers the cleaning difficulty coefficient between different color combinations, the fixed preparation time and unit processing time required for different process paths, the additional cleaning cost coefficient when switching vats, and chemical compatibility rules. By standardizing and integrating the above data, a complete dataset reflecting the current production status is constructed.

[0025] The dyeing vat scheduling problem for dynamic production scheduling of multiple orders is defined as a multi-objective, strongly constrained combinatorial optimization problem: under the premise of satisfying constraints such as dyeing vat capacity limits, order delivery time windows, chemical compatibility, and process path continuity, appropriate dyeing vat resources are allocated to each order to be scheduled, and the processing sequence of all orders on the same dyeing vat is determined, so as to simultaneously optimize multiple conflicting production performance indicators, including minimizing the total delay penalty of all orders, minimizing the total cleaning cost caused by color switching and vat type switching, maximizing the utilization balance among dyeing vats to improve the overall equipment efficiency, and maximizing the continuity of the process path to reduce unnecessary preparation time.

[0026] Because order arrivals are dynamic and work-in-process inventory and equipment status change continuously during the production process, this optimization problem requires a rolling time-domain or event-triggered dynamic scheduling mode. At each scheduling decision point, the optimization solution is re-solved based on the currently collected real-time data, thereby ensuring that the production scheduling plan is always closely aligned with actual production, and providing clear problem boundaries and optimization guidance for subsequent data preprocessing, feature mining, and genetic algorithm optimization.

[0027] S2. Data Preprocessing and Constraint Coding for Multiple Order Production Tasks The dyeing vat scheduling problem is characterized by multiple varieties, small batches, and strong constraints. The order data not only includes conventional attributes such as order number, color, weight, and vat type, but also complex constraints such as delivery urgency, customer priority, and dyeing process path.

[0028] This invention employs a constraint-oriented data encoding method based on the scheduling characteristics of dye vats. It transforms raw order data into a composite feature vector containing time windows, resource requirements, and conflict coefficients, thereby achieving a characteristic representation of the order data and extracting key features such as urgency factors and color conflict coefficients. The specific steps are as follows: 1) Define the original order dataset To perform feature engineering and constraint coding, the original production order data needs to be defined in a structured way; Specifically, there are N orders awaiting production, each containing M original attributes. This data is defined as the original order dataset, represented as: ; In the formula, This represents the original order dataset, which consists of the original information of all orders to be scheduled for production. It is a set, and each element corresponds to the attribute vector of an order. This represents the index of the first order, with a value range of 1 to... ; Indicates the first The attribute vector of an order is a collection of... A vector of elements used to store the multiple original attribute values ​​of the order; This represents the total number of orders awaiting production; it is a positive integer, with an example value of 200. This represents the total number of original attributes for each order; the example value is 10. Indicates the first The first order One original attribute value, Indicates the first The first order One original attribute value; This represents the attribute index, with a value range of 1 to... .

[0029] In one embodiment, the original order dataset Each order's attribute vector is a 10-dimensional vector, corresponding to 10 order attributes, including: Corresponding order quantity (unit: kilograms). Corresponding color code (integer color code, no unit). Corresponding process path code (integer, representing a specific process combination, unitless). Corresponding delivery date (Unix timestamp, in hours, e.g., 1735689600 represents 2025-01-01 00:00:00). Customer priority (integer 1-5, the larger the value, the higher the priority, no unit). Corresponding weight (in grams per square meter). Corresponding cylinder type (integer code, such as 1 for large cylinder, 2 for small cylinder, no unit). Corresponding material type (integer code, e.g., 1=cotton, 2=polyester, no unit). Corresponding order arrival time (Unix timestamp, in hours). Special requirements are indicated by the flag (0 / 1, where 0 indicates no special requirements and 1 indicates yes).

[0030] 2) Calculation of urgency factor based on dynamic time window Considering that the proximity of the order's delivery date to the current decision-making time has a decisive impact on the production scheduling order, using only the absolute delivery date as the sorting basis can easily overlook the dynamic changes in production load; This invention employs a dynamic urgency factor, combining current work-in-process inventory with the available time window of the cylinder, to quantify the true urgency of each order, expressed as: ; In the formula, Indicates the first The urgency factor of an order is a dimensionless real number that ranges from 0 to 1. The larger the value, the more urgent the order is, and the higher the probability that the order will be prioritized in the initial population generation. The timestamp representing the current production scheduling decision moment, in hours, is obtained in real time by the production scheduling system; Indicates the first The estimated processing time for each order, in hours, is based on its process path. and order volume Calculations show that, in one implementation method, the calculation method is as follows: , Indicates process path Fixed preparation time (in hours). Indicates process path The unit processing time (in hours / kg), for example, if the process path correspond Hour, hour / kg, order quantity If the weight is kilograms, then the estimated processing time is... Hour; Indicates the first The process path code for each order, from the original attributes Obtain directly; Indicates the first The order quantity of each order, from the original attributes Obtain directly; Represents the natural constant; Indicates the first The delivery date for each order is a timestamp, derived from the original attributes. Obtain directly; The steepness coefficient represents the urgency curve. It is a positive real number used to adjust the sensitivity of urgency to time difference. The larger the value, the more drastic the impact of time difference changes on urgency. An example value is 0.1. Indicates the color code corresponding to the current time. The work-in-process inventory, in units consistent with the order quantity, is provided in real time by the production management system; This indicates the maximum safety stock level allowed for this color, used to control inventory levels. Exceeding this value will suppress urgency to avoid overproduction. An example value is 1000 kg. Indicates the first The color code for each order, from the original attributes Obtain directly the color used to identify the order.

[0031] It should be noted that, The term uses the Sigmoid function to calculate the time difference. Mapped to The interval, when the estimated completion time is... Beyond delivery period When the urgency level is low, the value is close to 1 (high urgency); conversely, if the urgency level is low, it is close to 0 (low urgency) if the urgency level is low. Its smoothness ensures that the urgency level changes continuously over time, avoids sudden changes caused by hard thresholds, facilitates the calculation of fitness gradients in genetic algorithms, and enables the algorithm to dynamically adjust order priorities according to the urgency of delivery dates, thus achieving flexible scheduling.

[0032] It should also be noted that high inventory levels generally warrant lowering production priority, and production should be suppressed to avoid overstocking. This item reflects the constraint that "high inventory inhibits production." This item represents the proportion of current inventory to the maximum safety stock. When inventory is high, If the ratio of the terms is close to 1, then The item is close to 0, thus reducing the urgency factor. This suppresses the production priority of the order to avoid overproduction and backlog; conversely, if the urgency is not suppressed, production is encouraged.

[0033] 3) Constraint preprocessing based on color conflict matrix The core difficulty in dyeing vat scheduling lies in color conflict, that is, when switching to different colors, the dyeing vat needs to be cleaned, which incurs time and resource costs. If colors are treated as independent labels, it is impossible to quantify the differences in cleaning costs caused by the similarity between colors. This invention quantifies the cleaning difficulty between any two order colors by constructing a color conflict matrix, and uses it as a penalty term for gene block recombination in a genetic algorithm, expressed as: ; In the formula, Represents the color conflict matrix Corresponding color code and The element value is a real number, and its value range is 1. , indicating from the order Switch to order after production The conflict coefficient for cleaning required for production. The higher the value, the higher the cleaning cost. 1 indicates that complete cleaning is required, and 0 indicates that no cleaning is required. Indicates order Color codes are derived from the original attributes. Obtain directly Indicates the first The first order A raw attribute value used to identify the color of the order; Indicates order Color codes are derived from the original attributes. Obtain directly Indicates the first The first order A raw attribute value used to identify the color of the order; Indicates the second order index; Indicates the third order index; Indicates color In the HSV color space, the hue value ranges from 0 to 360 degrees and is obtained by converting the color code through the color space. Indicates color In the HSV color space, the hue value ranges from 0 to 360 degrees and is obtained by converting the color code through the color space. This represents the maximum possible difference in the tone space, used for normalization calculations; the default value is 360. This represents the hue difference weighting coefficient, which is a positive real number used to adjust the degree of influence of hue difference on the conflict coefficient. An example value is 0.8. Indicates the characteristic function, when an order Colors and orders The value is 1 when the colors belong to the same color family but have different specific color numbers, otherwise it is 0. This is used to capture complex situations of color switching within the same family during production. For example, dark blue and light blue may have similar hues but may still need to be cleaned. This represents the homochromatic color penalty weighting coefficient, which is a positive real number used to adjust the influence of the indicator function on the conflict coefficient. An example value is 0.5. This function represents the minimum value between 1 and the value within the parentheses, ensuring that the conflict coefficient does not exceed 1.

[0034] It should be noted that this is achieved by constructing a color conflict matrix. The model can pre-evaluate the cleaning costs that may arise when any two orders are arranged adjacently, and the color conflict matrix. Direct quantification from orders Color switch for orders The cleaning difficulty required for the color is indicated by the value, and the higher the value, the higher the cleaning cost (such as time, water resources, etc.). Therefore, when two orders are adjacent in the production scheduling sequence, their cleaning cost can be directly given by the corresponding matrix element, so that the potential cost of any order pair can be evaluated before production scheduling.

[0035] In one embodiment, the effectiveness of the urgency factor calculation formula proposed in this invention is verified. By comparing it with the traditional priority ranking method based solely on delivery date, the optimization effect of the inventory suppression mechanism on production scheduling is highlighted. The experiment uses a combination of scatter plots and bubble charts, such as... Figure 2 As shown, this is the distribution of the urgency factor generated by the present invention. Figure 3The figure shows the priority distribution of the traditional method. The horizontal axis represents "estimated completion time minus delivery time" in hours, with negative values ​​indicating that the order can be completed ahead of schedule and positive values ​​indicating possible delays. The vertical axis represents the urgency factor of this invention or the priority of the traditional method, both being dimensionless values ​​between 0 and 1. In the first figure, each bubble represents an order, and the size of the bubble indicates the proportion of work-in-process inventory of the corresponding color for that order, i.e., the current inventory is the percentage of the maximum safety stock. The larger the bubble, the higher the inventory. As can be seen from the scatter distribution, the urgency factor of this invention not only increases with the degree of delay (Sigmoid curve trend), but is also suppressed by the inventory ratio: when the inventory ratio is high, even if the delay is severe, the urgency factor is relatively low, which is reflected in the upper right area of ​​the figure where the bubbles are large (high inventory) but light in color (low urgency value). The traditional method is based solely on the delivery time, and its priority is determined only by the degree of delay, presenting a single Sigmoid shape, completely unaffected by inventory. This leads to high-inventory orders still being given high priority, which may cause overproduction.

[0036] S3, Order Feature Mining and Fitness-Oriented Chromosome Coding After the original order data is converted into a feature set with time and conflict attributes, conventional genetic algorithms directly encode the order sequence, ignoring the multidimensional feature similarity between orders, such as orders with similar colors or delivery dates. This can easily lead to a huge search space and a high proportion of invalid solutions that violate the cylinder's capacity constraints.

[0037] This invention employs a hypergraph clustering and hierarchical coding strategy to perform feature mining and clustering of orders, followed by encoding within and between clusters to compress the search space while maintaining the feasibility of solutions. The specific steps are as follows: 1) Construct a multimodal feature hypergraph of orders To uncover deeper connections between orders beyond color, each order is treated as a node in a hypergraph. Hyperedges connecting multiple orders are constructed using order features (including urgency factors, color conflict matrices, and process path codes). These hyperedges are defined by a weight function, which quantifies the overall similarity of order pairs within a hyperedge by calculating its weight. Then, a hypergraph clustering algorithm is used to optimize the hyperedge weights, resulting in order clusters with high intrinsic similarity or low switching costs. The weight function is expressed as: ; In the formula, Indicates the superedge The weight is a real number. The larger the weight value, the higher the overall similarity between orders within the superedge or the lower the switching cost, meaning that they are more suitable to be classified into the same order cluster. In the hypergraph, the first... Each hyperedge is a subset consisting of multiple order nodes; This represents the superedge index, which is the index of the order cluster, and its value ranges from 1 to... ; This represents the total number of order clusters obtained after hypergraph clustering; Indicates the fourth order index; Indicates the first The urgency factor of each order. Indicates the first The urgency factor of each order; This represents a very small positive number, used to avoid the denominator being zero. Examples of its values ​​are: ; The weight coefficient representing urgency similarity is a positive real number used to adjust the contribution of urgency similarity to the hyperedge weight. An example value is 0.3. The weight coefficient representing low color conflict is a positive real number used to adjust the contribution of the low color conflict term to the hyperedge weight. An example value is 0.5. The weighting coefficient representing process path consistency is a positive real number used to adjust the contribution of the process path consistency term to the hyperedge weight. An example value is 0.2. This represents the corresponding color code in the color conflict matrix. and The element value; Indicates the first The color code for each order is derived from the original attribute. Obtain; Indicates the first The color code for each order is derived from the original attribute. Obtain; Represents the characteristic function of process path consistency, when the first... The process path for each order With the The process path for each order The value is 1 when they are exactly the same, and 0 otherwise, which is used to encourage the aggregation of orders with the same process path; Indicates the first The process path for each order. Indicates the first The process path for each order.

[0038] In practical implementation, the hyperedge weights are optimized using a hypergraph clustering algorithm (such as hypergraph segmentation) to ultimately obtain... A cluster of orders, denoted as Orders within each cluster have high intrinsic similarity or low switching costs, among which This represents the k-th order cluster.

[0039] In practice, hypergraph clustering is typically implemented by optimizing hyperedge weights. First, initialization... The system generates several random clusters, then iteratively calculates the correlation between each order and each cluster, and reassigns the orders to the cluster with the highest correlation until convergence.

[0040] It should be noted that, This measure assesses the similarity in urgency between orders; the closer the urgency (...), the better. The smaller the value, the larger this value, which encourages orders with similar urgency to be clustered together, thus making orders within the same cluster have similar delivery pressure. This facilitates the unified arrangement of production rhythm during scheduling and avoids production interruptions or resource conflicts caused by excessive differences in urgency.

[0041] It should also be noted that, This item reflects the cost of color switching; the less color conflict, the lower the cost. The smaller the value (the closer this value is to 1), the more it encourages grouping orders of similar colors together, directly reducing the number of cleaning cycles and costs required for color changes during production. The technical benefit is reduced total cleaning time, increased equipment utilization, and avoidance of resource waste caused by frequent cleaning.

[0042] It should also be noted that a hyperedge is an edge in a hypergraph that connects multiple nodes, where each node represents an order. In the hypergraph, the first... A hyperedge is a subset consisting of several orders, for example... This indicates that these three orders are grouped into the same superedge, and they have a high degree of similarity.

[0043] 2) Hierarchical chromosome coding Based on the hypergraph clustering results, this invention employs a two-layer coding structure for hierarchical chromosome coding; The first layer is the cluster arrangement layer, which encodes the production order of each cluster, resulting in the cluster arrangement layer code; the second layer is the intra-cluster sorting layer, which encodes the specific processing order of each order within each cluster. Chromosomes are composed of two gene strings spliced ​​together. This hierarchical encoding method ensures that, during evolution, order clusters with low switching costs tend to be arranged consecutively, thereby effectively reducing the probability of generating invalid solutions. This can be represented as: ; In the formula, Representing a complete chromosome code, corresponding to a complete birth scheduling plan, it is a vector composed of multiple sub-vectors. By parsing the chromosome, first according to... Traverse the clusters, then by each By iterating through the orders within the cluster, we can obtain the processing sequence for all orders, for example: , , , The final sequence is This refers to a complete production scheduling plan; This indicates the cluster arrangement layer encoding, which is of length . The vector represents The production order of each order cluster is represented by a vector that is a permutation of cluster indices. For example, [3,1,2] indicates that cluster 3 is produced first, then cluster 1, and finally cluster 2. Indicates the first The intra-cluster sorting layer encoding of the i-th cluster is a variable-length vector representing the i-th cluster. Order cluster The processing order of all orders within a cluster is represented by a vector that is a permutation of the order indices within the cluster. For example, for a cluster containing orders {5,2,8}, the permutation [2,8,5] indicates that order 2 is processed first, then order 8, and finally order 5.

[0044] It should be noted that in the complete chromosome coding, It is placed at the first position because it determines the global order of the cluster. The subsequent ordering layers within each cluster correspond to the internal order of each cluster. For example, if there are 3 clusters... This means that cluster 2 will be produced first, then cluster 1, and finally cluster 3. If cluster 2 contains orders... Its internal order The actual processing order is: orders 3, 1, 4 (from cluster 2), then orders from cluster 1, and finally orders from cluster 3.

[0045] It should also be noted that hierarchical coding decomposes the original problem into two levels: inter-cluster sorting ( The arrangement of individual clusters and the intra-cluster sorting (the arrangement of orders within each cluster), due to Much smaller than the total number of orders Furthermore, the number of orders within a cluster is relatively small, therefore the search space is limited. Downgraded to Meanwhile, hypergraph clustering ensures that orders within a cluster have high similarity (such as similar colors and similar urgency), making it easier to maintain the feasibility of solutions during the evolution process by adjusting the local order within the cluster (such as avoiding color conflicts), thereby reducing the generation of invalid solutions and greatly improving search efficiency.

[0046] In one embodiment, such as Figure 4 As shown, order feature clustering visualization is performed, displaying the order clustering results based on urgency factor and color conflict coefficient to verify the effectiveness of the hypergraph clustering strategy. In the figure, the horizontal axis represents the urgency factor (dimensionless, ranging from 0 to 1), and the vertical axis represents the average color conflict coefficient (dimensionless, ranging from 0 to 1). Each point represents an order, and the color of the point indicates the cluster label (three clusters in total) assigned by the clustering algorithm. The scatter distribution shows that the three clusters have relatively clear boundaries on the plane, with red pentagrams marking the center of each cluster. Experimental results demonstrate that this invention, by constructing a multimodal feature hypergraph of orders, can automatically cluster orders with similar urgency and low color conflict into one category, thus laying the foundation for subsequent hierarchical coding.

[0047] S4. Computational Resource Constraints, Fitness Function, and Parent Selection The dyeing vat scheduling problem is characterized by multiple resources and strong constraints. Conventional fitness functions are difficult to comprehensively evaluate delays, cleaning costs, equipment balance, and process continuity, and they also ignore the uncertainties in the dynamic production environment.

[0048] This invention constructs a multi-objective dynamic weighted fitness function, incorporates a resource constraint penalty term, and designs an adaptive tournament selection strategy to balance the development and exploration capabilities of the population. The specific steps are as follows: 1) Construction of multi-objective dynamic weighted fitness function To quantify the overall performance of the production scheduling scheme, four key indicators are considered: total delay penalty, total cleaning cost, cylinder utilization balance, and process path continuity. A dynamic weight adjustment mechanism based on the current work-in-process level is introduced. The fitness function is defined as an exponentially decaying sum of the weighted sums of the indicators to transform cost-related indicators into a fitness maximization problem. An exponential smoothing term is added to enhance discriminative power, expressed as: ; In the formula, Represents the fitness function. Indicates chromosome coding The fitness value of the corresponding production scheduling scheme is a dimensionless positive real number, taking values ​​in the range of... The larger the value in the interval, the better the solution. This represents the natural exponential function, used to map a linearly weighted sum to... The differences between the intervals and the amplification schemes are amplified; The dynamic weighting coefficient representing the total delay penalty is a dimensionless positive real number. It links the weight of the total delay penalty to the current total work-in-process inventory level. When inventory is high, the weight increases, strengthening the penalty for delays and encouraging priority production of urgent orders to reduce inventory. When inventory is low, the weight decreases, appropriately relaxing delay requirements and balancing production. The calculation method is expressed as follows: ; The dynamic weighting coefficient representing the total cleaning cost is a dimensionless positive real number. It correlates the weight of the total cleaning cost with the clustering effect. If the average number of orders per cluster is high (i.e., the order clustering degree is high), the cleaning cost weight decreases because the colors within a cluster are similar, resulting in low switching costs. Conversely, if the clusters are small, the weight increases, guiding the algorithm to reduce cleaning. The calculation method is expressed as follows: ; The dynamic weighting coefficient representing the cylinder utilization balance is a dimensionless positive real number. It dynamically changes the weight of cylinder utilization balance as the current time approaches the average delivery date. Approaching or exceeding When the load is balanced, the weight increases to emphasize balanced equipment load and avoid overloading of a particular dyeing vat near the delivery date; conversely, the weight decreases to allow for some imbalance. The calculation method is expressed as follows: ; The dynamic weighting coefficient representing the continuity of the process path is a dimensionless positive real number. It correlates the weight of the process path continuity with the proportion of orders with special requirements. When the proportion of orders with special requirements is high, the weight decreases to avoid forcing continuity and thus failing to meet special requirements. When the proportion is low, the weight increases to encourage process path continuity and reduce setup time. The calculation method is expressed as follows: ; Representing the total delay penalty, it is a dimensionless non-negative real number used to quantify the severity of delays for all orders. The calculation method is expressed as follows: ; The total cleaning cost is a dimensionless, non-negative real number used to quantify the cleaning expenses incurred due to order switching during the production process. The calculation method is expressed as follows: ; The utilization balance of dyeing vats is represented by a dimensionless, non-negative real number, used to measure the degree of load imbalance among dyeing vats over time. The calculation method is expressed as follows: ; Representing process path continuity, it is a dimensionless, non-negative real number used to quantify the additional setup time caused by process path switching. Its calculation method is expressed as follows: ; The baseline weighting coefficient for the total delay penalty is a preset dimensionless positive real number, with an example value of 0.4. The baseline weighting coefficient representing the total cleaning cost is a preset dimensionless positive real number, with an example value of 0.3. The benchmark weighting coefficient, which represents the balance of cylinder utilization, is a preset dimensionless positive real number, with an example value of 0.2. The baseline weighting coefficient representing the continuity of the process path is a preset dimensionless positive real number, with an example value of 0.1. This represents the total maximum safety stock for all colors, with the unit consistent with the order quantity. Indicates the first The number of orders within an order cluster is a positive integer. The time sensitivity coefficient is a positive real number used to adjust the dynamic weighting coefficient. Sensitivity to the difference between the current time and the average delivery time, with examples of possible values. ; This represents the average delivery time for all orders, expressed in hours, and is obtained by taking the arithmetic mean of the delivery times for all orders. Indicates a characteristic function with special requirements, when the first... This order has special requirements ( When the value is ) Otherwise take ; Indicates the first The customer priority for each order is a dimensionless integer, derived from the original attributes. Directly retrieve the value; example values ​​are shown below. arrive The higher the integer value, the higher the priority. This indicates the number of chromosomes analyzed. The estimated completion time for each order, in hours, is obtained through simulation scheduling based on the order order sequence obtained from chromosome decoding and dyeing vat allocation rules (such as the earliest available machine rule). For example, for each order, it is assigned to the earliest available dyeing vat of the corresponding type according to its vat type. The start time is the maximum value of the available time of the dyeing vat and the current time (or the end time of the previous order), and the cleaning time between adjacent orders is taken into account (if the colors of the previous and subsequent orders are different, the cleaning time can be obtained by multiplying the color conflict coefficient by the unit cleaning time). Indicates the first The arrival time of each order is a timestamp, derived from the original attributes. Obtain directly; This represents the position index in the processing sequence, with a value range of 1. arrive ; Indicates the first step in the processing sequence The order index for each location is obtained by decoding the chromosome, which is arranged in clusters. and the sorting layer within each cluster It is pieced together; when decoding, first press... Traverse the clusters, then by each Traversing the orders within the cluster, the resulting order constitutes the complete processing sequence. The order index corresponding to each position is... ; Indicates the first step in the processing sequence Order index for each location; Indicates the first The color code for each order; Indicates the first The color code for each order; This represents the cylinder type switching penalty coefficient, a dimensionless positive real number used to quantify the additional cleaning costs incurred due to different cylinder types. An example value is shown below. ; Indicative function for cylinder type mismatch, when order and orders cylinder type (from original properties) (Get) different values ​​at the same time Otherwise take ; Indicates the first The cylinder type code for each order is obtained directly from the original attribute (the 7th attribute) of that order; This represents the dye vat index, with a value range of [value missing]. arrive ; This represents the total number of dye vats; it is a positive integer and is obtained from the production system. Indicates the first The total time occupied by each dyeing vat within the scheduling cycle, in hours, is calculated based on the chromosome scheduling scheme. The scheduling is simulated based on the chromosome scheduling scheme, and the sum of the processing times of all orders on the dyeing vat and the sum of the cleaning times between adjacent orders are calculated. This indicates the total duration of the scheduling cycle, in hours. It is set by the production plan and is pre-set by the production plan. For example, a shift is 8 hours or a day is 24 hours, and it is a fixed value. The average utilization rate is a dimensionless real number used to calculate the variance between the utilization rate of each dyeing vat and the average value, measuring the load balance. The calculation method is expressed as follows: ; Represents the characteristic function of process path consistency, when the first... The process path for each order With the The process path for each order When they are exactly the same, the value is taken as Otherwise take ; Indicates the first Process path code for each order; Indicates the first Process path code for each order; Indicates process path Fixed preparation time, in hours; This represents the maximum fixed setup time across all process paths, expressed in hours.

[0049] 2) Feasibility penalty based on multiple resource constraints Because dye vat scheduling has strict resource constraints, directly generated chromosomes may violate these constraints. A feasibility penalty term quantifies the degree of constraint violation as a reduction in fitness, thereby guiding the algorithm to search the feasible solution space. This feasibility penalty term integrates three typical violations: capacity constraints, time window constraints, and chemical compatibility constraints, and is expressed as follows: ; In the formula, The feasibility penalty term is a dimensionless non-negative real number used to quantify the degree to which a chromosome violates resource constraints. It is subtracted from the fitness to reduce the fitness of infeasible solutions and guide the algorithm to search for feasible solutions. The larger the value, the more severe the degree of constraint violation. This represents the capacity constraint penalty coefficient, a positive real number used to adjust the intensity of the penalty for exceeding capacity limits. An example value is shown below. ; Indicates assignment to the first The total order quantity of all orders for a dyeing vat, with the unit consistent with the order quantity, is calculated based on the chromosome production scheduling plan, summing the order quantities of all orders allocated to that dyeing vat. Indicates the first The maximum capacity of each dyeing vat, with the unit consistent with the order quantity, is a preset value determined by the physical properties of the dyeing vat (such as vat type); This represents the time window constraint penalty coefficient, a positive real number used to adjust the penalty strength for exceeding the start time limit. An example value is shown below. ; Indicates the first The planned start time for each order, in hours, is calculated based on the chromosome scheduling scheme, which is the moment when the order will begin processing on the corresponding dyeing vat. Indicates the first The latest allowed start time for each order, in hours, is used for time window constraints. If the start time is later than this value, the order may be delayed. The calculation method is as follows: ; Indicates the first The arrival time of each order is the timestamp from the original attribute. Obtain directly; This represents the penalty coefficient for chemical compatibility constraints. It is a positive real number used to adjust the intensity of the penalty for chemical conflicts. An example value is shown below. ; Represents the chemical conflict indicator function, when an order... Colors and orders When the chemicals required for the color dyeing process are incompatible, the value is taken as... Otherwise take This information needs to be obtained from the process knowledge base.

[0050] 3) Fitness function correction Considering the various resource constraints in actual production, directly optimizing the original fitness function may lead to infeasible solutions. Therefore, a feasibility penalty term is used to modify the fitness function, incorporating the degree of constraint violation into the evaluation, and guiding the algorithm to search for feasible solutions, expressed as: ; In the formula, This represents the modified fitness function. Indicates chromosome coding If the calculated result of the corrected fitness value of the corresponding production scheduling plan is negative, it will be forcibly set to [value missing]. , indicating an infeasible solution.

[0051] 4) Adaptive Tournament Selection Strategy While traditional tournament selection is simple and efficient during the parent selection phase, it can easily lead to premature convergence of the population. This invention employs an adaptive tournament selection strategy based on fitness ranking and population diversity, which balances selection pressure by dynamically adjusting the tournament size. In the In this generation, the number of individuals participating in the tournament is determined by the following formula: ; In the formula, Indicates the first The number of individuals selected for the tournament is a positive integer, ranging from 1 to 2. and The number of individuals selected for the tournament is determined in between, thus regulating selection pressure. The larger the size, the more intense the competition and the greater the selection pressure. It is easier to select individuals with high fitness, but this may reduce diversity. Conversely, the smaller the size, the less selection pressure, which is conducive to maintaining diversity. Represents the generation index, with a value range of 1. arrive ; This represents the maximum number of generations, a positive integer, set according to the problem size and computing resources, typically between 100 and 500. ; Represents the minimum tournament size, and is a positive integer. Examples of possible values ​​are: ; Represents the maximum tournament size, and is a positive integer. Examples of possible values ​​are: ; This represents the tournament size adjustment factor, a positive real number used to control the sensitivity of diversity to the impact of size. Examples of possible values ​​are provided. ; Indicates the first The diversity index of the generation population is a dimensionless non-negative real number used to dynamically adjust the size of the tournament. The calculation method is as follows: ; For the first The standard deviation of the corrected fitness of all individuals in the population; For the first The mean of the corrected fitness of all individuals in the population; It represents the level of diversity of objectives and is a dimensionless positive real number. Examples of its values ​​are: ,when At the time, it was believed that high diversity reduced the pressure of choice. It was believed that low diversity would increase selection pressure in order to balance population development and exploration; This represents the function for rounding up.

[0052] In practical implementation, when population diversity is high, ,but Smaller populations reduce selection pressure and preserve greater diversity; conversely, larger populations with lower diversity increase the tournament size to strengthen selection. During selection, individuals are randomly drawn from the current population. From each individual, the one with the highest fitness is selected to enter the mating pool. Simultaneously, to prevent the loss of superior individuals, an elite retention strategy is employed, keeping the best individuals from each generation... Individuals are directly replicated into the next generation. Represents the number of elite individuals, and is a positive integer. Examples of possible values ​​are: .

[0053] S5. Genetic Operations and Convergence Strategy Optimization For the hierarchical coding structure of the dyeing vat scheduling problem, conventional genetic operations easily destroy superior gene blocks. This invention designs an adaptive crossover and mutation operator based on a cluster structure, and dynamically adjusts the operation probability according to the population evolutionary state. At the same time, it introduces local search and population restart mechanisms to accelerate convergence and avoid getting trapped in local optima. The specific steps are as follows: 1) Adaptive crossover probability based on cluster similarity Crossover is an operation designed to exchange superior gene segments between parent individuals; Since chromosomes are divided into clustered arrangement layers and intra-cluster sorting layers, a two-layer crossover strategy is adopted: first, partial mapping crossover is performed on the clustered arrangement layers, and then sequential crossover is performed on the intra-cluster sorting layers of each cluster. The crossover probability is adaptively adjusted based on the similarity between the two parent individuals; the higher the similarity, the lower the crossover probability, in order to avoid invalid crossovers. Specifically, define two parent chromosomes. and The similarity is: ; In the formula, It represents the similarity between two parent chromosomes. It is a dimensionless non-negative real number. The larger the value, the more similar the two parents are. It is used to quantify the overall similarity between two parent chromosomes in terms of cluster arrangement and intra-cluster order. The larger the value, the more similar the two parents are. Indicates the parent generation , Indicates the parent generation In each generation of the genetic algorithm, two individuals are selected from the current population as parents using a selection strategy (such as adaptive tournament selection) to perform the crossover operation. and This means that the two parent chromosomes selected correspond to two different birth control schemes; Indicates the parent generation The first cluster arrangement layer The cluster index at each position is arrive Integers; Indicates the parent generation The first cluster arrangement layer The cluster index at each position is arrive Integers; This represents the position index within the intra-cluster sorting layer, with a value range of... arrive ; Indicates the parent generation The In the intra-cluster sorting layer, the th The order index for each position is a positive integer; Indicates the parent generation The In the intra-cluster sorting layer, the th The order index for each position is a positive integer; The order sequence characteristic function is represented when The time value is Otherwise take .

[0054] It should be noted that when the similarity between two parents is higher than the average similarity of the current population, it indicates that their genetic structures are similar, and the benefit of crossover to produce new individuals is low. In this case, the crossover probability should be reduced to avoid ineffective gene exchange. Conversely, if the similarity is below the average level, the crossover probability should be increased to promote population diversity. This is the core basis for dynamically adjusting the crossover probability.

[0055] Furthermore, the crossover probability for the current parent pair is calculated. By introducing the population average similarity, the crossover probability is dynamically adjusted. When the parent similarity is higher than the average level, the crossover probability decreases, and vice versa, expressed as: ; In the formula, Indicates the first The crossover probability used for the current parent pair in the generation is a dimensionless real number, with a value ranging from 1 to 2. arrive Between, is the first The probability of performing the crossover operation on the currently selected pair of parent chromosomes in a generation; This represents the maximum crossover probability, which is a dimensionless positive real number. Examples of possible values ​​are: ; This represents the crossover probability adjustment coefficient, a positive real number used to control the degree of influence of similarity differences on the crossover probability. An example value is shown below. ; Indicates the first The average similarity of all parent pairs in the current population is a dimensionless real number, which is obtained by randomly selecting multiple parent pairs from the current population, calculating their similarity, and then averaging the results.

[0056] When the similarity between two parents is higher than average, the crossover probability decreases, and vice versa, thus promoting diversity.

[0057] In practical implementation, probability is used. Perform the crossover operation of the genetic algorithm; otherwise, directly copy the parent generation.

[0058] 3) Taboo mutation operators for color conflict Mutation operations are used to maintain population diversity, but random mutations can easily disrupt the desirable order within a cluster. This invention combines color conflict information to define a tabu mutation operator, guiding the mutation direction towards low-conflict regions. For a selected chromosome, first, a cluster of orders is randomly selected, then two positions within that cluster are randomly selected, and the orders at these two positions are swapped. However, whether the swap is accepted depends on the change in the color conflict increment within the cluster after the swap. The mutation probability is defined as follows: ; In the formula, Indicates the first The mutation probability of the generation is a dimensionless real number, which is the probability of mutation of the th generation. The probability of performing the crossover operation on the currently selected pair of parent chromosomes in a generation, with a value ranging from... and between; Represents the minimum mutation probability, which is a dimensionless positive real number. Examples of its values ​​are: ; Represents the maximum mutation probability, which is a dimensionless positive real number. Examples of possible values ​​are: ; This represents the mutation probability decay coefficient, a positive real number used to control the rate at which the mutation probability decreases with increasing algebraic progression. An example value is shown below. .

[0059] In practice, the mutation operation is implemented through tabu mutation, which makes the mutation tend to reduce color conflicts and improve the quality of the solution. The specific steps are as follows: Calculate the sum of color conflicts between adjacent order pairs within the cluster before the swap. The calculation method is as follows , For the first in the cluster Color codes for orders at each location; Calculate after swap ,like Then accept the exchange, where This represents the sum of color conflicts among all adjacent order pairs within the cluster after swapping two positions, calculated in the same way as... same; Otherwise, based on probability Accept, among which To simulate the annealing temperature, it is a positive real number that decreases with algebraic progression. The calculation method is as follows: , Let be the initial temperature, a positive real number, with examples of possible values. .

[0060] It should be noted that the tabu mutation operator is a mutation operation that combines the idea of ​​local search. It uses color conflict information to guide the mutation direction. By evaluating the change in color conflict within the cluster before and after the swap, it prioritizes the swap that can reduce the conflict and accepts degradation with simulated annealing probability, thereby avoiding getting trapped in local optima. Its neighborhood search and probability acceptance mechanism is similar to the directional perturbation in tabu search, which can effectively improve the quality of the solution.

[0061] In one embodiment, the impact of crossover probability and mutation probability on fitness is analyzed to explore the influence of two core hyperparameters (crossover probability and mutation probability) in genetic algorithms on the fitness of scheduling schemes. Figure 5As shown in the heatmap, the horizontal axis represents the crossover probability, the vertical axis represents the mutation probability, and the color intensity represents the fitness value; a higher value indicates a better overall performance of the production scheduling scheme. The graph shows that the fitness value does not change monotonically with the parameters, but rather exhibits a clear peak region. Beyond this region, the fitness gradually decreases, and the rate of decrease is asymmetrical. The optimal parameter region is marked with a red asterisk. Experimental results indicate that a reasonable crossover probability can effectively exchange superior gene blocks, while an appropriate mutation probability helps maintain population diversity and avoid premature maturation; a fine-tuned combination of both is necessary to achieve the best optimization results.

[0062] 4) Convergence strategy based on population entropy and elite restart To determine whether a population is trapped in a local optimum, the concept of population entropy is introduced to measure the diversity of gene loci; When the population entropy falls below a threshold, an elite restart mechanism is triggered: the current best individual is retained, the remaining individuals are reinitialized, and chaotic perturbations are introduced to enhance the search. Specifically, the definition of the first Entropy of a generation of population at the cluster arrangement layer Represented as: ; In the formula, Indicates the first The entropy of a population at the cluster arrangement level measures the diversity of cluster arrangement. The larger the value, the greater the difference between different individuals in the cluster arrangement order, and the higher the diversity. Indicates the first In the population, the cluster arrangement layer is the first Cluster index appears at each location. The number of individuals is an integer used to calculate the frequency distribution; The population size is represented by a positive integer. This represents a logarithmic function, with the default base being the natural constant.

[0063] Similarly, define the first Entropy of the population at the intra-cluster ordering level The calculation method involves summing the entropy of the frequencies of all possible order permutations within each cluster. In practice, the average information entropy is used, expressed as: ; In the formula, Indicates the first The overall entropy of a population is a dimensionless non-negative real number. It is combined with the diversity of the cluster arrangement layer and the intra-cluster sorting layer to determine whether the population is trapped in a local optimum. The weighting coefficients representing the entropy of the cluster arrangement are dimensionless real numbers with a range of values. Example of a value: ; Indicates the first The entropy of a generation population at the ordering level within a cluster is a dimensionless non-negative real number used to measure the diversity of order permutations within each cluster.

[0064] Furthermore, if continuous generation Below the threshold Then execute elite restart: retain the best Individuals, the rest Each individual is regenerated, and the generation method is as follows: ; In the formula, This represents the threshold for stagnation algebra, and is a positive integer. Examples of possible values ​​are: When continuous The overall entropy is lower than the threshold. At that time, the population is considered stagnant, triggering a restart; The entropy threshold is a dimensionless positive real number, with examples of its values. A value below this indicates insufficient diversity; The newly generated chromosome is obtained by subjecting the current optimal chromosome to chaotic perturbation; This represents the current optimal chromosome, which is the optimal chromosome in the current population. This represents a bitwise chaotic perturbation operation, which involves applying a probability to each gene bit of the optimal chromosome. Perform random replacement to generate new individuals; It represents the probability of perturbation, is a dimensionless real number, and its value range is [range missing]. Example of a value: , This represents a chaotic sequence generated based on a Logistic mapping, controlling the probability of each gene locus being perturbed.

[0065] After restarting, the evolution generation counter is reset, and evolution begins again until the maximum evolution generation is reached. Or it meets the convergence condition (such as the optimal solution remaining unchanged for a long time).

[0066] S6. Dye vat scheduling optimization for dynamic production scheduling of multiple orders. The dyeing vat scheduling optimization for dynamic production scheduling of multiple orders ultimately outputs a scheduling scheme that satisfies production constraints and has the best overall performance through iterative evolution of a genetic algorithm. The entire optimization process takes order data, resource status data, and process knowledge data collected at the current scheduling moment as input. First, through data preprocessing and constraint encoding steps, the original order information is transformed into a feature representation containing urgency factors and color conflict coefficients, laying the foundation for subsequent order clustering and chromosome encoding.

[0067] Then, through hypergraph clustering and hierarchical coding strategies, orders are aggregated into multiple order clusters according to urgency similarity, low color conflict, and consistency of process path. A two-layer chromosome structure is used to jointly encode the production order between clusters and the order processing order within clusters, thereby compressing the original huge search space into a hierarchical feasible solution space.

[0068] In the population initialization phase, an initial chromosome set with a certain degree of diversity is generated by combining the urgency factor and color conflict information, ensuring that the initial solution has some optimization potential while satisfying the basic constraints. Then, the core iterative process of the genetic algorithm begins: In each generation, each individual in the population is first evaluated based on the modified fitness function. This function integrates four dynamically weighted objectives: total delay penalty, total cleaning cost, cylinder utilization balance, and process path continuity. It also deducts feasibility penalties for violating capacity constraints, time window constraints, and chemical compatibility constraints, thereby accurately reflecting the actual merits of the production scheduling plan. Then, an adaptive tournament selection strategy is adopted to dynamically adjust the selection pressure according to the diversity of the current population and select high-quality individuals from the parents to enter the mating pool. For the selected parents, crossover operations based on the cluster structure are adaptively performed according to their similarity, including partial mapping crossover of the cluster arrangement layer and sequential crossover of the intra-cluster sorting layer, to generate offspring individuals. Subsequently, the tabu mutation operator oriented towards color conflict is executed on the offspring individuals with adaptive probability. The mutation direction is guided by evaluating the change in color conflict within the cluster before and after the exchange. Mutations that can reduce conflict are given priority, while degraded solutions are accepted with simulated annealing probability to maintain diversity.

[0069] During the evolution process, diversity indicators based on population entropy are continuously monitored. When the comprehensive entropy is lower than the preset threshold for multiple consecutive generations, the elite restart mechanism is triggered. The current best individual is retained and the remaining individuals are subjected to chaotic perturbation and then re-initialized, thereby escaping the local optimum trap.

[0070] Repeat the selection, crossover, mutation, evaluation, and restart steps above until the maximum number of generations is reached or the convergence condition is met. Finally, decode the optimal chromosome obtained through evolution to obtain the precise processing sequence, planned start time, estimated completion time, and assigned dyeing vat number for each order, forming a complete and executable multi-order dynamic scheduling plan.

[0071] In response to the dynamic arrival of orders in actual production, this optimization method can re-execute the above process at each rescheduling trigger point (such as a fixed time period or the arrival time of a new order), and use the updated work-in-process inventory, equipment status and order information to continuously optimize the subsequent production plan, realize the continuous optimization of dyeing vat scheduling for dynamic production of multiple orders, effectively guide workshop production operations, and improve resource utilization efficiency and order delivery satisfaction.

[0072] In this implementation, a constraint-oriented data encoding method based on dyeing vat scheduling characteristics is constructed. By introducing an urgency factor incorporating inventory suppression mechanisms and a color conflict matrix based on the HSV color space and same-color system penalties, the original order data is transformed into a composite feature vector with physical meaning. This embeds dynamic inventory constraints and color switching costs from the production site into the data preprocessing stage. A chromosome-based expression strategy based on hypergraph clustering and hierarchical encoding is adopted. By constructing a multimodal feature hypergraph of orders, orders are clustered according to urgency similarity, low color conflict, and process path consistency. A two-layer encoding structure of cluster arrangement and intra-cluster sorting is then used, effectively compressing the search space for combinatorial optimization and reducing the probability of invalid solutions. A multi-objective dynamic weighted fitness function and adaptive selection mechanism are employed. This function not only integrates four conflicting indicators—delay penalties, cleaning costs, equipment balance, and process continuity—but also dynamically adjusts the weights of each objective based on real-time status such as work-in-process inventory levels and clustering effects. Simultaneously, the scale of the tournament selection is dynamically adjusted using population diversity indicators, balancing the algorithm's development and exploration capabilities. An adaptive genetic operation and convergence strategy based on cluster structure and color conflict information is adopted, including a two-layer crossover probability dynamically adjusted according to parent similarity, a taboo mutation operator that guides the mutation direction toward low-conflict regions, and an elite restart mechanism based on population entropy monitoring. This effectively avoids premature convergence of the algorithm and enhances the global search capability in complex constraint spaces.

[0073] This invention also proposes a dyeing vat scheduling system based on a genetic algorithm for dynamic scheduling of multiple orders. The dyeing vat scheduling method based on a genetic algorithm for dynamic scheduling of multiple orders, as described above, includes: The order scheduling data collection and optimization problem identification module is used to collect order information, resource status information, and process knowledge information, and to identify problems such as allocating dyeing vat resources and determining the processing sequence of all orders on the same dyeing vat. The production task data preprocessing and constraint coding module is used to transform the original order data into a composite feature vector by adopting a constraint-oriented data coding method oriented towards the dyeing vat scheduling characteristics, thereby realizing the feature representation of the order data; The feature mining and chromosome coding module is used to perform feature mining and clustering of orders using hypergraph clustering and hierarchical coding strategies, and to encode them within and between clusters respectively. The fitness function and parent selection module are determined, which is used to construct a multi-objective dynamic weighted fitness function and adopt an adaptive tournament selection strategy based on fitness ranking and population diversity in the parent selection stage. The genetic operation module includes adaptive crossover and mutation operators based on cluster structure, and dynamically adjusts the operation probability according to the population evolution state, while introducing local search and population restart mechanisms. The dyeing vat scheduling optimization module for dynamic scheduling of multiple orders is used to form a dynamic scheduling plan for multiple orders by taking the order data, resource status data and process knowledge data collected at the current scheduling time as input.

[0074] Furthermore, this embodiment of the invention also proposes a computer-readable storage medium storing program instructions for a dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm. The program instructions for the dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm can be executed by one or more processors to implement the steps of the dyeing vat scheduling method based on a multi-order dynamic scheduling of dyeing vats using a genetic algorithm as described above.

[0075] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A dyeing vat scheduling method based on multi-order dynamic scheduling using a genetic algorithm, characterized in that, include: The issue of order scheduling data collection and optimization was identified; the data collection included order information, resource status information, and process knowledge information. The optimization problem is to allocate appropriate dyeing vat resources to each pending production order while satisfying constraints, and to determine the processing sequence of all orders on the same dyeing vat. Production task data preprocessing and constraint coding; including using constraint-oriented data coding methods to transform raw order data into composite feature vectors containing time windows, resource requirements, and conflict coefficients; Feature mining and chromosome coding; including hypergraph-based clustering and hierarchical coding strategies, to perform feature mining and clustering of orders, and to encode them within and between clusters respectively; The encoding is a fitness-oriented chromosome encoding; This involves treating each order as a node in a hypergraph, constructing hyperedges connecting multiple orders using order features, defining hyperedges through a weight function, quantifying the overall similarity of order pairs within a hyperedge by calculating its weight, and then optimizing the hyperedge weights using a hypergraph clustering algorithm to obtain order clusters with high intrinsic similarity or low switching costs; the weight function integrates urgency similarity, low color conflict, and process path consistency. Determine the fitness function and parent selection; this includes constructing a multi-objective dynamic weighted fitness function, incorporating resource constraint penalty terms, and designing an adaptive tournament selection strategy. Genetic operations and convergence strategy optimization; including genetic operations using adaptive crossover and mutation operators based on cluster structure, and dynamically adjusting operation probabilities in combination with population evolution state; Dye vat scheduling optimization for dynamic production scheduling of multiple orders; including taking order data, resource status data and process knowledge data collected at the current scheduling time as input to form a dynamic production scheduling scheme for multiple orders.

2. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders as described in claim 1, characterized in that, The constraint encoding involves transforming the original order data into a composite feature vector containing time windows, resource requirements, and conflict coefficients. The conflict coefficient includes color conflicts, which are quantified based on a constructed color conflict matrix to determine the difficulty of cleaning between any two order colors. This color conflict matrix is ​​then used as a penalty term for gene block recombination in the genetic algorithm, as shown in the following expression: ； In the formula, Represents the color conflict matrix Corresponding color code and The element value; Indicates order Color codes; Indicates order Color codes; Indicates color Hue values ​​in the HSV color space; Indicates color Hue values ​​in the HSV color space; Indicates the maximum possible difference in the tone space; This represents the weighting coefficient for hue differences; Indicates characteristic functions; This represents the penalty weighting coefficient for colors within the same color family; This function represents the minimum value between 1 and the value within the parentheses.

3. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 1, characterized in that, The hierarchical coding strategy is to use a two-layer coding structure for hierarchical chromosome coding. The first layer is the cluster arrangement layer, which encodes the production order of each cluster to obtain the cluster arrangement layer coding. The second layer is the intra-cluster sorting layer, which encodes the specific processing order of each order within the cluster.

4. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 3, characterized in that, The hypergraph clustering grouped orders with similar urgency and low color conflict into one category.

5. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 1, characterized in that, The multi-objective dynamic weighted fitness function combines total delay penalty, total cleaning cost, cylinder utilization balance and process path continuity, and introduces a dynamic weight adjustment mechanism based on the current work-in-process level.

6. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 5, characterized in that, The adaptive tournament selection strategy balances selection pressure by dynamically adjusting the tournament size.

7. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 1, characterized in that, The cluster-based adaptive crossover involves adaptively adjusting the crossover probability based on the similarity between two parent individuals; the higher the similarity, the lower the crossover probability.

8. The dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders according to claim 7, characterized in that, The mutation operator, combined with color conflict information, guides the mutation direction toward low-conflict regions.

9. A dyeing vat scheduling system based on genetic algorithm for dynamic scheduling of multiple orders, wherein the dyeing vat scheduling method based on genetic algorithm for dynamic scheduling of multiple orders is described in any one of claims 1 to 8, characterized in that, include: The order scheduling data collection and optimization problem identification module is used to collect order information, resource status information, and process knowledge information, and to identify problems such as allocating dyeing vat resources and determining the processing sequence of all orders on the same dyeing vat. The production task data preprocessing and constraint coding module is used to transform the original order data into a composite feature vector by adopting a constraint-oriented data coding method oriented towards the dyeing vat scheduling characteristics, thereby realizing the feature representation of the order data; The feature mining and chromosome coding module is used to perform feature mining and clustering of orders using hypergraph clustering and hierarchical coding strategies, and to encode them within and between clusters respectively. The fitness function and parent selection module are determined, which is used to construct a multi-objective dynamic weighted fitness function and adopt an adaptive tournament selection strategy based on fitness ranking and population diversity in the parent selection stage. The genetic operation module includes adaptive crossover and mutation operators based on cluster structure, and dynamically adjusts the operation probability according to the population evolution state, while introducing local search and population restart mechanisms. The dyeing vat scheduling optimization module for dynamic scheduling of multiple orders is used to form a dynamic scheduling plan for multiple orders by taking the order data, resource status data and process knowledge data collected at the current scheduling time as input.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program instructions for a dyeing vat scheduling method based on a genetic algorithm for dynamic scheduling of multiple orders. The program instructions for the dyeing vat scheduling method based on a genetic algorithm for dynamic scheduling of multiple orders can be executed by one or more processors to implement the steps of the dyeing vat scheduling method based on a genetic algorithm as described in any one of claims 1 to 8.

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