A method for optimizing forging production scheduling based on dynamic demand perception

Abstract

This invention relates to the field of production scheduling optimization technology, and particularly to a forging production scheduling optimization method based on dynamic demand perception. The method includes: collecting workshop data and discretizing and classifying it; combining an order dwell time exponential compensation factor and an equipment temperature recovery time exponential penalty factor to construct a comprehensive priority weight for each order; initializing a discrete particle swarm optimization (PSO) population based on this; employing a process proximity segmentation crossover operator controlled by the population fitness variance and order weights during iteration; supplemented by neighborhood recombination based on mold sharing rate and nonlinear inertia weighting based on information entropy to update position and velocity; and performing weighted repair on illegal sequences before outputting a scheduling scheme after furnace merging verification. This invention overcomes the limitation of scheduling easily getting trapped in local optima under complex thermodynamic constraints, achieving multi-dimensional coordination of delivery rigidity, mold change efficiency, and energy consumption costs, thus reducing equipment idling and overall order delay rates in real-world scenarios.

Description

Technical Field

[0001] This invention relates to the field of production scheduling optimization technology, and in particular to a forging production scheduling optimization method based on dynamic demand perception. Background Technology

[0002] As the market rapidly evolves towards multi-variety, small-batch, and customized production, the order demands received by the forging workshop exhibit high dispersion in terms of delivery urgency, process complexity, and batch size. The significant differences in order attributes mean that failure to scientifically categorize and represent these orders can easily lead to delays in urgent orders or disruptions to the workshop's production rhythm. Furthermore, the forging process is highly sensitive to temperature conditions, and equipment temperature recovery time and furnace loading constraints directly impact production continuity. If scheduling fails to balance order waiting times with equipment thermodynamic constraints, it will result in equipment idling, energy waste, and prolonged order backlogs, ultimately weakening the overall operational efficiency of the workshop.

[0003] Chinese patent document CN110597218B discloses a scheduling optimization method based on flexible scheduling, including the following steps: Customer orders are processed using a time-based decomposition method, with the CR value used as the convergence formula for particle swarm optimization to find the optimal solution; the optimized particle swarm is embedded into an artificial immune algorithm based on process decomposition and mathematical model structure decomposition to obtain an initial production scheduling sequence; a multi-objective optimization model is established; the bottleneck process and the most efficient process are calculated; complementary product models of the bottleneck and most efficient processes are matched, and the original solution is mutated using artificial immune optimization to generate multiple scheduling sequences; the affinity of multiple scheduling sequences is calculated to filter solutions, ultimately generating the optimal scheduling sequence.

[0004] Introducing swarm intelligence optimization algorithms, such as Discrete Particle Swarm Optimization (DPO), into the scheduling process allows for the construction of a scheduling model that combines workshop resource constraints and order attributes. Through iterative optimization, a reasonable processing sequence and furnace arrangement can be obtained. Existing order weight allocation often employs a static linear weighting mechanism, lacking dynamic compensation for order dwell time and failing to incorporate equipment temperature recovery time as a decay penalty factor in weight calculation, leading to priority allocation deviating from actual working conditions. When traditional DPO algorithms handle high-constraint forging scheduling, position updates and crossover operators are often arbitrary, making it difficult to determine the crossover operator segment length based on population fitness variance and weight information. Furthermore, it is difficult to introduce a recombination mechanism based on mold sharing rate and nonlinear inertial weights based on information entropy, easily leading to local optima. Moreover, illegal solution repair often relies on random strategies, making it difficult to perform targeted weighted fusion repair based on demand priority, thus limiting the algorithm's optimization efficiency. Existing furnace merging mechanisms often only perform basic condition checks, failing to integrate the geometric mean of weights within a batch with the logarithmic gain of the merged quantity to construct a comprehensive evaluation system, making it difficult to generate a better scheduling scheme that balances delivery time and energy efficiency under forging constraints. Summary of the Invention

[0005] To enhance the multi-variety, small-batch customized production capacity of forging workshops, this invention provides a forging production scheduling optimization method based on dynamic demand perception, employing the following technical solution: S1. Collect workshop data and discretize and classify order demands according to delivery urgency, process complexity and batch size to obtain a discrete demand classification matrix. Based on the discrete demand classification matrix, construct a weight allocation function, embed an order dwell time exponential compensation factor on the basis of weighted summation, and map the equipment temperature recovery time to an exponential decay penalty factor after the temperature recovery penalty coefficient is mapped to the weight calculation to obtain the comprehensive priority weight of each order. S2 initializes the discrete particle swarm optimization (PSO) population using the order processing sequence as the particle position and comprehensive priority weights. It then updates the position using a segmented crossover operator based on process proximity, with the segment length determined by the normalized value of the population fitness variance and the normalized value of the mean weights of orders with weights greater than the mean. If the fitness variance is below a threshold, it triggers neighborhood reorganization based on mold sharing rate. In the speed update, the inertia weight is replaced with a nonlinear mapping value based on the information entropy of the population fitness distribution. For conflicting or missing illegal particles, a sequence repair operation based on demand priority weighted fusion is used. S3, based on the furnace merging rule to verify the feasibility of the solution, merge orders of the same material and temperature range and whose total weight does not exceed the rated load of the heating furnace into a joint batch. The weight of the joint batch is the product of the geometric mean of the weights within the batch and the logarithmic gain correction term of the number of merged orders; iteratively output the scheduling scheme.

[0006] The technical advantages of this invention are as follows: Compared with existing scheduling methods that use static linear weighting and fixed algorithm parameters, which easily lead to delays in urgent orders, frequent mold changes, and equipment idling, this invention reconstructs the comprehensive priority weight by combining a discrete demand hierarchical matrix with a dynamic compensation penalty factor. While taking into account the rigidity of delivery time, it effectively avoids long-term order delays and high-energy-consuming equipment operation. Furthermore, through adaptive segment length crossover, neighborhood reorganization based on mold sharing rate, and linkage optimization based on information entropy inertial weights, it breaks the limitation of traditional swarm intelligence algorithms that are prone to getting trapped in local optima under complex forging constraints. At the same time, a furnace merging mechanism with geometric mean and logarithmic gain correction is introduced at the decoding end, which significantly improves the global optimization capability and resource allocation rationality of scheduling in practical application scenarios, and effectively achieves a flexible trade-off between delivery time rigidity, resource fairness, and equipment energy consumption costs.

[0007] Preferably, the method for obtaining the discrete demand grading matrix is ​​as follows: Calculate the difference between the delivery deadline of each order and the current scheduling date in the system to obtain the remaining days, match the remaining days to a preset arithmetic threshold interval, and map them as the first discrete level parameter; extract the processing operation steps from the process file corresponding to the order, add the processing operation steps to the number of times the mold needs to be changed for continuous processing, and map the result to the second discrete level parameter based on the preset scaling interval; multiply the standard weight of a single product in the order by the total number of units required to obtain the total order weight, divide the total weight by a preset baseline weight scale value and round down to obtain the initial batch level, and map the initial batch level to the third discrete level parameter; arrange and combine the first discrete level parameter, the second discrete level parameter, and the third discrete level parameter of all orders to be scheduled vertically to construct the discrete demand grading matrix.

[0008] The technical advantage of this invention is that, in contrast to the difficulty in scientifically classifying and representing differences in order attributes in existing technologies, this invention addresses the customized production characteristics of multi-variety, small-batch production in forging workshops by transforming delivery urgency, process execution complexity, and batch size into precisely mapped discrete level parameters. This not only achieves quantitative dimensionality reduction and normalization of complex order attribute dimensions but also accurately reflects the volume and heat load of orders in the heating furnace, laying a scientific and reliable data foundation for subsequent efficient scheduling and weight allocation.

[0009] Preferably, before calculating the comprehensive priority weight of each order, the following steps are taken: retrieving historical temperature recovery time data of the same series of processing operations for candidate heating equipment, and determining the equipment temperature recovery time by combining the current furnace temperature of the candidate heating equipment with the target process temperature of the order; the equipment temperature recovery time is multiplied by the temperature recovery penalty coefficient to form a negative exponential term, and the exponential decay penalty factor is calculated with the natural constant as the base; statistically analyzing the order dwell time data within the historical scheduling cycle and calculating the moving average of the order dwell time, using the sum of the moving average of the order dwell time and the preset dwell time constant to obtain the adjustment coefficient of the exponential compensation factor; obtaining the dwell time of each order from the time the plan is issued to the current system scheduling time, and using the ratio of the dwell time to the adjustment coefficient as the exponent of the natural logarithm base to calculate the exponential compensation factor.

[0010] The technical advantage of this invention is that, compared to the existing technology which struggles to balance order waiting times with equipment thermodynamic constraints during scheduling, it utilizes historical equipment heating recovery time to construct a negative exponential decay penalty and combines it with the historical dwell time moving average to construct an adjustment coefficient to generate an exponential compensation factor. This allows the scheduling priority of long-term dwell orders to be exponentially compensated, while effectively suppressing the insertion of orders that require high-energy-consuming heating operations. As a result, it greatly reduces equipment waiting time and energy waste in actual production.

[0011] Preferably, the method for obtaining the comprehensive priority weight of each order is as follows: the method for obtaining the comprehensive priority weight of each order is as follows: calculate the initial weighting value based on the parameters of each level of the discrete demand grading matrix, and multiply the initial weighting value, the exponential compensation factor and the exponential decay penalty factor to obtain the comprehensive priority weight of each order.

[0012] The technical advantage of this invention is that, compared with the traditional single linear weighting method, by multiplying and integrating the initial weighting value with the exponential term representing residence time compensation and heating energy consumption penalty, a comprehensive priority weight evaluation system that dynamically evolves with production conditions is constructed. This makes the priority allocation fully fit the actual dynamic fluctuations of the business flow characteristics of the forging workshop, and further strengthens the scheduling algorithm's flexible balancing ability between delivery guarantee and energy consumption control.

[0013] Preferably, the crossover operator segment length is jointly determined by the normalized value of the population fitness variance and the normalized value of the mean weight of orders with weights greater than the mean. This includes: calculating the variance of the fitness values ​​of all particles in the current iteration population and dividing the variance by the initial population fitness variance to obtain the normalized variance value; selecting a set of orders with a comprehensive priority weight greater than the average weight of the population from all orders corresponding to the current population, calculating the arithmetic mean of the order weights in the set, and dividing the arithmetic mean by the maximum weight of all orders to obtain the normalized weight mean value; multiplying the normalized variance value and the normalized weight mean value by the total number of orders, and rounding the product down to obtain the crossover operator segment length used for position updates in the discrete particle swarm optimization algorithm, and limiting the crossover operator segment length to be no less than 1 and no greater than the total number of orders.

[0014] The technical advantage of this invention is that, compared to the problem of blindly truncating crossover operations in traditional discrete particle swarm optimization algorithms, which leads to the destruction of superior gene fragments, this invention adaptively and dynamically adjusts the segment length of the crossover operator by linking the variance normalization value, which reflects the diversity of the population space, and the weight mean normalization value, which reflects the aggregation intensity of high-value tasks. This allows the algorithm to allow large-block gene recombination and transition when the global solution space has not converged and high-value orders are dense, while truncating fragments at the end of the population evolution to enhance the precise search capability of the local neighborhood, thereby improving the optimization accuracy and convergence efficiency of the algorithm in complex solution spaces.

[0015] Preferably, if the fitness variance is lower than a threshold, neighborhood recombination based on mold sharing rate is triggered, including: when it is detected that the fitness variance of the current population is lower than a set stagnation threshold for a consecutive preset number of generations, traversing the position sequence of the current best particle; in the position sequence, searching for order gene fragments with the same forging mold number but not adjacent sequence positions; performing a position convergence recombination operation on the found order gene fragments to generate a new neighborhood solution, and evaluating the fitness of the new neighborhood solution; if the fitness score of the new neighborhood solution is higher than the fitness score of the worst particle in the population, then replacing the worst particle with the new neighborhood solution.

[0016] The technical advantage of this invention is that, compared to existing scheduling optimization methods that often cause production downtime due to frequent mold changes, this invention, when detecting that the algorithm is stuck in a local extreme value stagnation, specifically triggers a neighborhood recombination operation with clear workshop constraints. By bringing together orders of the same mold scattered in different process positions, it actively eliminates invalid process barriers from the gene recombination level, thereby improving the continuous processing efficiency of the equipment.

[0017] Preferably, in the velocity update, the inertia weight is replaced with a nonlinear mapping value based on the population fitness distribution information entropy, including: extracting the fitness values ​​of all particles in the current population, calculating the probability distribution of the fitness values ​​in different preset intervals; calculating the fitness distribution information entropy based on the probability distribution; substituting the fitness distribution information entropy into a preset Sigmoid nonlinear mapping function to calculate the output value, and using the output value as the inertia weight of the current iteration step.

[0018] The technical advantage of this invention is that, compared to the problem of conventional swarm intelligence algorithms using fixed constants or linearly decreasing inertial weights that make it difficult to balance global and local searches, this invention introduces Shannon information entropy, which is based on fitness distribution information, as input. Combined with a nonlinear mapping function, the inertial weights are adaptively adjusted in real time. This enhances the global search to explore new solution spaces when the population is dispersed, and smoothly switches to local search with smaller step sizes when the population gradually gathers. This gives the algorithm a stronger ability to escape local optima and greater stability in finding deep solution spaces.

[0019] Preferably, the sequence repair operation using demand priority weighted fusion involves the following steps: locating duplicate and missing orders using dictionary mapping; extracting the comprehensive priority weight of each missing order and determining the repair order from high to low according to the comprehensive priority weight; for each missing order, using the location of the duplicate order and other allowed insertion positions as candidate insertion positions; determining the selection probability of each candidate insertion position based on the comprehensive priority weight of the order corresponding to the candidate insertion position or its adjacent orders; and sequentially inserting the missing order into the candidate insertion positions and replacing the duplicate order according to the repair order until there are no duplicate or missing orders in the particle sequence.

[0020] The technical advantage of this invention is that, compared to the problem of low scheduling quality after repair caused by the blind random insertion strategy when repairing illegal solutions in traditional methods, it guides sequence repair through a weighted fusion mechanism based on demand priority. After accurately locating missing and duplicate orders using a dictionary, it strictly arranges the repair order from high to low according to the comprehensive weight, and implements selective insertion based on the weight distribution probability of orders around the candidate insertion position. This not only ensures the absolute legality of the particle sequence, but also continues the rigidity principle of delivery time in the repair stage, greatly improving the scheduling quality of the overall iterative output of the algorithm.

[0021] Preferably, the steps for merging orders of the same material, within the same temperature range, and whose total weight does not exceed the rated load capacity of the heating furnace into a joint batch are as follows: extract orders sequentially according to the particle sequence, and verify whether the orders meet the requirements of having the same material number and that the heating process temperature requirements are within the same allowable temperature range; group orders that continuously meet the merging conditions into the same joint batch; if the total weight exceeds the rated load capacity of the heating furnace after adding the current order, end the current joint batch, and use the current order as the starting order for the next joint batch to re-accumulate the weight.

[0022] Preferably, the step of updating the position using a segmented crossover operator based on process adjacency is as follows: calculate the number of process switching, mold consistency, and process temperature difference between two adjacent orders; calculate the process adjacency based on the number of process switching, mold consistency, and process temperature difference; wherein, the process adjacency is negatively correlated with the number of process switching and negatively correlated with the process temperature difference; retain the continuous order segment with the highest process adjacency, i.e., the fewest number of process switching, the most consistent mold, and the smallest process temperature difference, to update the position of the offspring particles.

[0023] The present invention has the following technical effects: By integrating order delay index compensation and equipment temperature recovery penalty, a dynamic comprehensive priority weight system was constructed. Deep optimization strategies, including adaptive segmented crossover, premature neighborhood reorganization based on mold sharing rate, and inertial weighting based on information entropy nonlinear mapping, were embedded into the discrete particle swarm algorithm. A batch weight gain correction furnace merging verification rule was also implemented. Its main application value lies in breaking through the bottleneck of traditional scheduling easily falling into local optima under complex thermodynamic constraints, achieving a multi-dimensional trade-off between delivery rigidity, mold changing efficiency, and energy consumption costs. This reduces equipment idling rate and overall delay rate, improving the overall flexible operation efficiency of customized forging production. Attached Figure Description

[0024] Figure 1 This is a flowchart of a forging production scheduling optimization method based on dynamic demand perception, according to the present invention.

[0025] Figure 2 This is a schematic diagram of the discretization mapping of the delivery urgency parameter of the present invention using the arithmetic threshold interval.

[0026] Figure 3 This is a grayscale diagram showing the comparison of scheduling evaluation indicators for different schemes of the present invention. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] This invention discloses a forging production scheduling optimization method based on dynamic demand perception, referring to... Figure 1 This includes the following steps: S1. Collect workshop data and discretize and classify order demands according to delivery urgency, process complexity, and batch size to obtain a discrete demand classification matrix. Based on the discrete demand classification matrix, construct a weight allocation function, embed an order dwell time exponential compensation factor on the basis of weighted summation, and map the equipment temperature recovery time to an exponential decay penalty factor after the temperature recovery penalty coefficient is mapped to the weight calculation to obtain the comprehensive priority weight of each order.

[0029] The system connects to the Manufacturing Execution System (MES) and Programmable Logic Controller (PLC) via Industrial Ethernet protocol to acquire workshop data in real time, extracting attributes such as order delivery dates, process flow routes, and planned production quantities. Using a quantile strategy, preset threshold ranges, or baseline weight scale values, delivery urgency, process complexity, and batch size are mapped to discrete integer levels within a preset range. The number of levels for each feature dimension can be set according to the workshop order size and scheduling accuracy requirements, and are uniformly normalized to the same numerical range before participating in weight calculation. Delivery urgency is inversely encoded according to the remaining days, so that the fewer the remaining days, the higher the discrete level. A two-dimensional numerical array containing all discrete level feature dimensions of the orders is constructed, namely the discrete demand grading matrix. When constructing the weight allocation function, the discrete level parameters of delivery urgency, process complexity, and batch size are first normalized according to the preset level upper limit or the maximum level value of the current batch for each feature dimension, obtaining normalized level parameters in the range of 0 to 1. Then, fixed basic linear weights are assigned to delivery urgency, process complexity, and batch size, and an initial weighted sum is calculated using vector inner product. The difference between the current time and the order placement time is calculated as the order dwell time. The order dwell time is divided by the adjustment coefficient of the exponential compensation factor to obtain the dimensionless ratio. The exponent of the dimensionless ratio is calculated using the natural logarithm base to obtain the order dwell time exponential compensation factor. The adjustment coefficient of the exponential compensation factor is the sum of the moving average of the historical order dwell time and the preset dwell time constant.

[0030] When historical order dwell time data is insufficient, a preset dwell time scale is used to replace the moving average of historical order dwell time, and this is added to a preset dwell time constant to obtain the adjustment coefficient. The moving average of the order dwell time series within the historical scheduling period is calculated, and the moving average is added to the preset dwell time constant as the adjustment coefficient of the exponential compensation factor.

[0031] Obtain the expected heating and cooling time required for the current device to switch to the temperature required for the next order, i.e., the device temperature recovery time. When there are multiple candidate heating devices, select the minimum temperature recovery time among the candidate devices or the temperature recovery time after weighting the device availability probability as the device temperature recovery time corresponding to the order. Construct an exponential decay penalty term using the negative power of the natural logarithm base. Multiply the initial weighted sum by the order dwell time exponential compensation factor, and then multiply by the exponential decay penalty term of the device temperature recovery time to output a comprehensive priority weight vector in one-dimensional floating-point array format.

[0032] In some embodiments, order demands are discretized and classified according to delivery urgency, process complexity, and batch size to obtain a discrete demand classification matrix, including: The difference between the delivery deadline for each order and the current scheduling date in the system is used to obtain the remaining days. The remaining days are then matched to a preset arithmetic threshold range and mapped to a first discrete level parameter representing the urgency of the delivery date. Extract the number of processing steps from the process file corresponding to the order, add the number of processing steps to the number of times the mold needs to be changed for continuous processing, and map the result to a second discrete level parameter representing the process complexity based on the preset calibration interval. The total order weight is obtained by multiplying the standard weight of a single product by the total number of products required. The total weight is then divided by the preset baseline weight scale value and rounded down to obtain the initial batch level. The initial batch level is then limited to between the preset minimum level and the preset maximum level, and mapped to the third discrete level parameter representing the batch size. The first, second, and third discrete level parameters of all orders to be scheduled are arranged vertically to construct a discrete demand hierarchy matrix.

[0033] The order's delivery deadline and current scheduling date are obtained through the ERP data interface. The remaining days are calculated by subtracting the order's date in calendar days, with a preferred step size of 5 days for the arithmetic threshold interval. For example, the left-closed, right-open intervals are set to [0, 5), [5, 10), [10, 15), and [15, +∞), respectively, with the first discrete level parameter assigned values ​​of 4, 3, 2, and 1. If an order has 7 days remaining, it falls into the second interval, and the first discrete level parameter is mapped to 3. A larger value indicates a stronger urgency in the delivery deadline. Figure 2As the remaining days decrease, the urgency of order delivery increases progressively, with the discrete level parameter monotonically increasing from 1 to 4, representing the quantitative grading logic of order delivery attributes. The process BOM file in the Manufacturing Execution System is parsed to count the number of processing steps such as heating, drawing, and upsetting, and to obtain the theoretical number of mold replacements required in the process chain. Assuming a flange forging has 5 processing steps and 2 mold replacements, the algebraic sum is 7. This feature value is input into a preset calibration interval, such as setting [1, 4], [5, 8], and [9, 12] to correspond to levels 1, 2, and 3 respectively, and the second discrete level parameter is mapped to 2, thus completing the quantitative dimensionality reduction of the forging process execution complexity. Furthermore, when representing batch size, the standard weight of a single piece as indicated on the CAD drawing is extracted and multiplied by the total number of pieces in the production order to obtain a total weight of 12500 kg. The preferred baseline weight scale value is set to 2000 kg. Dividing the total weight by this scale value yields a floating-point number of 6.25. After rounding down, the third discrete level parameter is 6. If the preset maximum level is 5, the initial batch level is truncated to 5. Alternatively, the initial batch level of 6 is divided by the maximum batch level of the current batch to obtain a normalized batch size parameter before participating in the weight calculation, thus representing the volume and heat load of the order in the heating furnace. For the N orders to be scheduled in the current batch, the first, second, and third discrete level parameters generated for each order are stacked vertically as row vectors, outputting a discrete demand hierarchy matrix with dimension N×3.

[0034] In some embodiments, an order dwell time exponential compensation factor is embedded on the weighted summation basis. The equipment temperature recovery time is mapped to an exponential decay penalty factor through a temperature recovery penalty coefficient and then associated with the weight calculation to obtain the comprehensive priority weight of each order, including: Retrieve historical temperature recovery time data for the same series of processing operations of the candidate heating equipment, and combine the current furnace temperature of the candidate heating equipment with the target process temperature of the order to determine the equipment temperature recovery time; the equipment temperature recovery time is multiplied by the temperature recovery penalty coefficient to form a negative exponential term, and the exponential decay penalty factor is calculated with the natural constant as the base; The order dwell time data within the historical scheduling period is statistically analyzed and the moving average of the order dwell time is calculated. The adjustment coefficient of the index compensation factor is obtained by using the sum of the moving average of the order dwell time and the preset dwell time constant. Obtain the dwell time of each order from the time the plan is issued to the current system scheduling time, and use the ratio of the dwell time to the adjustment coefficient as the exponent of the natural logarithm base to calculate the exponential compensation factor; The initial weighted value is calculated based on the parameters of each level of the discrete demand grading matrix. The product of the current equipment's required temperature recovery time and the temperature recovery penalty coefficient is used as the negative exponent of the natural logarithm base to calculate the exponential decay penalty factor. The initial weighting, the exponential compensation factor, and the exponential decay penalty factor are multiplied together to obtain the overall priority weight of each order.

[0035] From the manufacturing execution system or scheduling database, backtrack the historical scheduling cycle to calculate the moving average of the dwell time data for each order from the time the plan is issued to the time it enters the schedule. Input a preset dwell time constant, preferably within the range of 0.001 min to 0.05 min. If precisely set to 0.01 min, add the 45-minute moving average to this preset dwell time constant to obtain an adjustment coefficient of 45.01 min for the exponential compensation factor. Monitor in real time the accumulated dwell time of each order from the time the plan is issued by the ERP system to the time the current scheduling calculation is triggered, in minutes. For example, if a backlogged order has been dwelling for 180 minutes, divide this dwell time by the adjustment coefficient 45.01 min to obtain a dimensionless characteristic ratio of approximately 4.0. Calculate the exponential function of this ratio. This generates an exponential compensation factor that expands non-linearly with waiting time, thereby exponentially compensating for the scheduling priority of long-delayed orders.

[0036] In the multi-dimensional weight integration stage, the discrete level parameters of delivery urgency, process complexity, and batch size are first divided by the preset maximum level value of the corresponding dimension to obtain normalized level parameters. Then, a normalized weight vector is pre-assigned to the discrete demand grading matrix, such as 0.5 for delivery, 0.3 for complexity, and 0.2 for scale. The weighted sum of the weighted vector and the specific level value of the target order is then performed to obtain an initial weighted benchmark value of 0.78.

[0037] Based on the thermodynamic temperature difference between the current actual furnace temperature and the target process temperature obtained by the real-time temperature control probe, the expected temperature recovery time required is calculated and multiplied by a pre-set temperature recovery penalty coefficient. The dimension of the temperature recovery penalty coefficient is the reciprocal of time, and the preferred range is [0.01, 0.1]. For example, take the calibration value of 0.05. The exponential decay independent variable is 3.0, resulting in a negative exponent of -3.0. The negative exponential function is then calculated. An exponential decay penalty factor is obtained to reduce the insertion of orders that require high-energy-consuming heating operations. As the temperature recovery time base value increases, the exponential decay penalty factor decays rapidly, achieving priority suppression for orders with high temperature switching costs. Simultaneously, an exponential compensation factor for order dwell time can prioritize long-waiting orders, thus creating a flexible trade-off between delivery time rigidity, resource fairness, and equipment energy consumption costs. Multiplying the initial weighted value, the exponential compensation factor, and the exponential decay penalty factor together, the overall priority weight value for this order is approximately 2.12, achieving a flexible trade-off between delivery time rigidity, resource fairness, and equipment energy consumption costs in scheduling.

[0038] S2 initializes the discrete particle swarm optimization (PSO) population using the order processing order as the particle position and comprehensive priority weights. It then updates the position using a segmented crossover operator based on process proximity, with the segment length determined by the normalized value of the population fitness variance and the normalized value of the mean weights of orders with weights greater than the mean. If the fitness variance is below a threshold, it triggers neighborhood reorganization based on mold sharing rate. In the speed update, the inertia weight is replaced with a nonlinear mapping value based on the information entropy of the population fitness distribution. For conflicting or missing illegal particles, a sequence repair operation based on demand priority weighted fusion is used.

[0039] A discrete particle swarm optimization (DSO) algorithm framework is constructed, treating the permutation index sequence of multiple orders as particle position vectors in a multi-dimensional discrete space. In the DSO algorithm, particle velocity represents the probability set of order position swapping, fragment insertion, or crossover update operations. Inertia weight is used to adjust the retention ratio of the previous generation's position change trend in the current update. When randomly generating the initial particle swarm permutation, the orders are sorted in descending order according to the comprehensive priority weight obtained in the previous step. The positions of 20% of the elite particles in the population are initialized according to this sequence, and the remaining particles are randomly generated. The variance of the fitness value of the entire population under the current iteration is calculated, and the variance is divided by the initial population fitness variance to obtain the normalized value of the population fitness variance. The fitness value is the scheduling comprehensive evaluation score; the larger the value, the better the scheduling scheme. The scheduling comprehensive evaluation score is calculated inversely based on the normalized penalty values ​​of maximum completion time, delay rate, number of mold changes, and equipment waiting time; it can also be linearly normalized based on the historical iteration variance sequence.

[0040] Select a subset whose weights are greater than the average weight of all orders, calculate the arithmetic mean of the weights of this subset and perform normalization on it, multiply the two normalization indices above by the total length of the particle dimension and round down to obtain the segment length parameter of the segmented cross operator, and limit the segment length to an integer range that is not less than 1 and not greater than the total number of orders. The parent particle's continuous order segments are extracted using this length, and the segment combination with the highest corresponding process adjacency (i.e., the fewest process switching times, the lowest mold change cost, or the lowest process transfer cost) is retained to update the child particle's position. Process adjacency is calculated based on the number of process switching times between two adjacent orders, whether the molds are consistent, and the process temperature difference. The fewer the number of process switching times, the more consistent the molds, and the smaller the process temperature difference, the higher the process adjacency. When the population fitness variance is detected to be lower than the set premature convergence warning threshold in real time, the order sequence of the current best particle is traversed to find order segments with the same mold number but not adjacent sequence positions. If the mold sharing rate between such orders reaches a preset threshold, a position-converging neighborhood reorganization is performed, moving orders with the same mold to adjacent or nearby positions. Optionally, in one embodiment, the mold sharing rate is the ratio of the total number of orders using the same mold in the current sequence to the total index span of the first to last occurrence of such orders in the sequence.

[0041] In the particle velocity update stage, the fitness values ​​of all particles in the current swarm are extracted and their discrete probability distributions are calculated. The Shannon information entropy of this distribution is then calculated, and the information entropy value is nonlinearly mapped to replace the fixed constant inertial weight in the standard particle swarm velocity update formula. After each position update, the particle sequence is traversed to check for conflicting entries caused by duplicate orders or missing entries caused by unincluded orders. For particles deemed invalid, duplicate and missing orders are located using dictionary mapping, and the comprehensive priority weight of each missing order is extracted. The repair order is then determined according to the weight from high to low. For each missing order, the position of the duplicate order and other allowed insertion positions are considered as candidate insertion positions. The selection probability of each candidate insertion position is determined based on the normalized value of the comprehensive priority weight of the corresponding order or its adjacent orders. Missing orders are inserted into candidate positions sequentially according to the repair order, replacing duplicate orders, until no duplicate or missing orders remain in the particle sequence.

[0042] In some embodiments, a segmented crossover operator based on process adjacency is used to update the position. The segment length is jointly determined by the normalized value of the population fitness variance and the normalized value of the mean weight of orders with weights greater than the mean, including: Calculate the variance of the fitness values ​​of all particles in the current iteration population, and divide the variance by the initial population fitness variance to obtain the variance normalization value; among all orders corresponding to the current population, select the order set whose comprehensive priority weight is greater than the population average weight, calculate the arithmetic mean of the order weights in the set, and divide the arithmetic mean by the maximum weight of all orders to obtain the weight mean normalization value; multiply the variance normalization value and the weight mean normalization value by the total number of orders, and round down the product to obtain the crossover operator segment length used for position update in the discrete particle swarm optimization algorithm, and limit the crossover operator segment length to be no less than 1 and no greater than the total number of orders.

[0043] In the generational evolution of the Discrete Particle Swarm Optimization (DPO) algorithm, the fitness values ​​of all individuals in the current generation t are extracted, and the population statistical variance of 100 floating-point fitness data is calculated. The baseline variance of the initial generation 0 population residing in system memory is retrieved, and a division operation is performed to obtain a variance normalization value of 0.25. This ratio maps the degree of diversity reduction caused by local convergence of the current population in the solution space; the ratio typically decreases as iterations deepen. To incorporate the attribute differences between orders in the workshop workflow into the algorithm's operator layer, the entire task queue under the current scheduling snapshot is traversed, and the global arithmetic mean of the comprehensive priority weights of the 80 orders is calculated. A conditional filtering pipeline is constructed to filter out a subset of high-priority tasks with priority weights exceeding 5.5. The arithmetic mean of the weight features of these 25 core orders is calculated, and the arithmetic mean is divided by the absolute maximum weight peak value scanned among all 80 orders in this batch. This yields a weight mean normalization parameter of 0.8. When executing coordinated decision-making, the normalized variance value representing spatial diversity, the normalized mean value representing the clustering intensity of high-value tasks, and the total number of integer orders are subjected to continuous scalar multiplication to obtain a theoretical control baseline value of 16.0. After applying the floor function to the control baseline value, the crossover operator segment length L=16 is obtained. When the global solution space is not converged and high-value orders are dense, large gene segments are allowed to recombine and jump, while when the population is highly homogenized at the end, the segments are truncated to single digits, which enhances the algorithm's ability to perform precise local neighborhood search.

[0044] In some embodiments, if the fitness variance is lower than a threshold, neighborhood recombination based on mold sharing rate is triggered, including: when it is detected that the fitness variance of the current population is lower than a set stagnation threshold for a consecutive preset number of generations, traversing the position sequence of the current best particle; in the position sequence, searching for order gene fragments with the same forging mold number but not adjacent sequence positions; performing a position convergence recombination operation on the found order gene fragments to generate a new neighborhood solution, and evaluating the fitness of the new neighborhood solution; if the fitness score of the new neighborhood solution is higher than the fitness score of the worst particle in the population, then replacing the worst particle with the new neighborhood solution.

[0045] At the end of each evolutionary cycle, the control unit deploys state monitoring probes to record the trajectory of the population fitness variance in real time. A local extremum stagnation monitoring window generation number and a stagnation threshold to characterize the population's convergence stagnation state are pre-injected. When the monitoring probes report that the normalized value of the population fitness variance is lower than the preset stagnation threshold for 15 consecutive generations, the optimization process is determined to have fallen into local convergence. At this point, regular iterations are interrupted, and the global elite particle carrying the best fitness is extracted from memory. Then, the one-dimensional order sequence encapsulated within this particle is decoded and traversed from left to right, using scheduling nodes as units. During the feature gene screening and comparison process, the production BOM process file bound to each order is retrieved position by position, specifically searching for scattered order genes carrying completely consistent forging die coding features but whose index intervals in the current sequence array exceed the tolerance limit. Once an inefficient scheduling segment with the same mold but separated by unrelated processes is matched, a reorganization operation is activated. The target order segment from the original sequence is extracted, and lagging orders with the same mold are shifted left and moved forward within the array. Adjacent orders with the same mold are reassembled and inserted; for example, the order at index 28 is moved and inserted after the order at index 9, thus generating a new neighborhood sequence solution with a higher mold sharing rate. The factory digital twin evaluation component is called to calculate the fitness index of the total time saved by the new neighborhood solution due to reduced mold changes. The fitness value is represented by the scheduling comprehensive evaluation score; a higher value indicates a better scheduling solution. If the evaluation uses a scheduling cost function, the scheduling cost function is first converted into a fitness score where a higher score is better before comparison. If the fitness score of the new neighborhood solution is higher than the fitness score of the worst particle in the population, the new neighborhood solution replaces the worst particle, thus completing particle replacement and reducing production downtime caused by ineffective mold changes.

[0046] In some embodiments, replacing the inertia weight with a nonlinear mapping value based on fitness distribution information entropy in velocity updates includes: extracting the fitness values ​​of all particles in the current population, calculating the probability distribution of fitness values ​​in different preset intervals, calculating the fitness distribution information entropy based on the probability distribution, substituting the fitness distribution information entropy into a preset Sigmoid nonlinear mapping function to calculate the output value, and using the output value as the inertia weight of the current iteration step.

[0047] When calculating the feedforward control parameters that determine the search step size of microparticles, at the beginning of each iteration cycle, the fitness evaluation value pool of all individuals in the entire population space is extracted in batches, and the global maximum fitness and global minimum fitness in the pool are scanned and located. Using the numerical span formed by these two values ​​as the measurement reference surface, the range of values ​​containing all particles is uniformly divided into a preset number of granularities. The partitioning constant K is preferably set to 10 to 20, for example, dividing it into 10 equidistant fitness container sub-intervals. The absolute count value of particles falling into each independent container interval is counted, and the value is divided by the total scale base of 200, thereby calculating and generating the probability distribution array of population fitness in each discrete interval. For example, the discrete probabilities of the first to third intervals are measured. The values ​​are 0.15, 0.25, and 0.10, respectively. After obtaining the normalized global discrete probability distribution array, the Shannon information entropy calculation formula is input. For each non-zero probability interval container, an information entropy value H that accurately identifies the current population spatial distribution chaos degree and discrete free state is output as the fitness distribution. During the control parameter solution stage, the obtained information entropy H is input into an improved Sigmoid activation mapper with bilateral constraint translation features. The computational model is as follows: The absolute boundary of particle inertial weights; Limit to 0.9 Set to 0.4, curve steepness gain operator The preset value is 2.5, which is the threshold for determining the inflection point of information entropy. The anchor value is 1.5. Through this nonlinear mapping: when the information entropy H remains high due to the relatively dispersed population distribution, the function output value approaches 0.9 to enhance the global search capability; while when the population gradually aggregates with the iteration depth, causing the entropy value to decrease, the output weight smoothly decays along the Sigmoid curve to around 0.4, allowing the algorithm to switch to a local search mode with a smaller step size.

[0048] S3 verifies the feasibility of the solution based on the furnace merging rule, merges orders of the same material and temperature range with a total weight not exceeding the rated load of the heating furnace into a joint batch, and takes the weight of the joint batch as the product of the geometric mean of the weights within the batch and the logarithmic gain correction term of the number of merged orders; iteratively outputs the scheduling scheme and drives the production line to execute the processing task.

[0049] The repaired, legitimate particle sequence undergoes a simulated furnace loading decoding operation. Orders are extracted sequentially based on the particle sequence. Conditional statements are used to verify whether the orders meet the requirements of having the same material number and that the heating process temperature requirements are within the same allowable temperature range. The same allowable temperature range is determined centered on the baseline process temperature of the current joint batch. The baseline process temperature is the target process temperature of the first order in the joint batch. The absolute value of the difference between the target process temperature of the order to be added and the baseline process temperature does not exceed 15℃; or, after adding the order, the difference between the highest and lowest target process temperatures in the joint batch does not exceed 30℃. Only orders that consecutively meet the merging conditions are included in the same joint batch. If the total weight after adding the current order exceeds the rated maximum loading capacity threshold of the heating furnace, the current joint batch is terminated, and the current order is used as the starting order for the next joint batch to re-accumulate weight. The scheduling priority of the successfully merged joint batch is reassessed. The geometric mean of the overall priority weight of all orders in the batch is calculated. The logarithmic gain of the number of orders in the batch is calculated with the natural constant as the base. The sum of 1 and the logarithmic value is used as the logarithmic gain correction term for the number of merged orders. The geometric mean and the logarithmic gain correction term for the number of merged orders are multiplied and assigned to the joint batch as the overall execution weight.

[0050] The above swarm intelligence evolution operation and decoding evaluation are repeated until the preset maximum number of iterations is reached. The furnace sequence corresponding to the global historical best particle and the start and end timestamps of each batch are extracted. The scheduling results are converted into JSON data format that the manufacturing execution system can recognize. The task scheduling instructions are sent to the central control console of the forging workshop and the industrial control computers of each workstation to drive the actuators to start material flow and heating forging operations.

[0051] The test set was a monthly production data set from the forging workshop of a large heavy industry enterprise, containing 1200 forging orders to be scheduled, involving 15 heating furnaces of different power and 40 sets of conventional forging dies. The operating environment was configured as an industrial server with a 64-core processor and 256GB of memory, with an initial population size of 200 particles and a maximum iteration count of 1000 generations. To eliminate random error, all control experiments used the same pseudo-random number seed and were run independently 50 times under the same constraints, recording the arithmetic mean of each scheduling evaluation index.

[0052] Control group 1 uses the basic discrete particle swarm optimization (DSO) scheduling algorithm, with an average maximum completion time of 485.2 hours, a comprehensive delay rate of 18.5%, and an average of 312 mold changes per production cycle. Control group 2 adds a module for order discrete demand grading and comprehensive priority weighting to the basic algorithm, reducing the completion time to 426.8 hours, the delay rate to 9.2%, and the number of mold changes slightly to 305. Control group 3 adds a cross-segmentation length and a neighborhood reorganization mechanism based on mold sharing rate to control group 2, optimizing the completion time to 391.5 hours, the delay rate to 6.4%, and the number of mold changes to 185. The complete solution introduces an inertial weight based on fitness distribution information entropy, compressing the completion time to 374.3 hours, reducing the delay rate to 2.1%, and stabilizing the number of mold changes at 176.

[0053] The comprehensive priority weighting successfully balanced the urgency of delivery with the energy cost of equipment, improving the order delay rate in control group two. The neighborhood recombination mechanism exhibited strong workshop constraint orientation; the decrease in mold change times in control group three confirmed that the clustering operation of orders with the same mold can eliminate equipment downtime caused by ineffective mold changes. The comprehensive index of the complete scheme was the best in the control experiment, indicating that the nonlinear inertial weighting based on information entropy helps alleviate the problem of decreased diversity in the later stages of the population, giving the algorithm stronger ability to escape local optima and higher accuracy in finding deep solution spaces, such as... Figure 3 The scheduling performance comparison results of the four schemes show that, with the sequential superposition of modules such as order grading, neighborhood reorganization, and information entropy inertia weight, the complete scheme has achieved optimization in the three core indicators of completion time, number of mold changes, and delay rate, which verifies the synergistic gain effect of each technical module of the present invention.

[0054] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A forging production scheduling optimization method based on dynamic demand perception, characterized in that, Including the following steps: S1. Collect workshop data and discretize and classify order demands according to delivery urgency, process complexity and batch size to obtain a discrete demand classification matrix. Based on the discrete demand classification matrix, construct a weight allocation function, embed an order dwell time exponential compensation factor on the basis of weighted summation, and map the equipment temperature recovery time to an exponential decay penalty factor after the temperature recovery penalty coefficient is mapped to the weight calculation to obtain the comprehensive priority weight of each order. S2 initializes the discrete particle swarm optimization (PSO) population using the order processing sequence as the particle position and comprehensive priority weights. It then updates the position using a segmented crossover operator based on process proximity, with the segment length determined by the normalized value of the population fitness variance and the normalized value of the mean weights of orders with weights greater than the mean. If the fitness variance is below a threshold, it triggers neighborhood reorganization based on mold sharing rate. In the speed update, the inertia weight is replaced with a nonlinear mapping value based on the information entropy of the population fitness distribution. For conflicting or missing illegal particles, a sequence repair operation based on demand priority weighted fusion is used. S3, based on the furnace merging rule to verify the feasibility of the solution, merge orders of the same material and temperature range and whose total weight does not exceed the rated load of the heating furnace into a joint batch. The weight of the joint batch is the product of the geometric mean of the weights within the batch and the logarithmic gain correction term of the number of merged orders; iteratively output the scheduling scheme.

2. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, The discrete demand grading matrix is ​​obtained as follows: Calculate the difference between the delivery deadline of each order and the current scheduling date in the system to obtain the remaining days. Match the remaining days to a preset arithmetic threshold interval and map them as the first discrete level parameter. Extract the processing steps from the corresponding process file of the order. Add the processing steps to the number of mold changes required for continuous processing. Based on the preset scaling interval of the sum, map it as the second discrete level parameter. Multiply the standard weight of a single product in the order by the total number of units required to obtain the total order weight. Divide the total weight by a preset baseline weight scale value and round down to obtain the initial batch level. Map the initial batch level as the third discrete level parameter. Vertically arrange and combine the first, second, and third discrete level parameters of all orders to be scheduled to construct the discrete demand grading matrix.

3. The forging production scheduling optimization method based on dynamic demand perception according to claim 2, characterized in that, Before calculating the overall priority weight of each order, the following steps are taken: Retrieve historical temperature recovery time data for the same series of processing operations of the candidate heating equipment, and combine this data with the current furnace temperature of the candidate heating equipment and the target process temperature of the order to determine the equipment temperature recovery time; Multiply the equipment temperature recovery time by the temperature recovery penalty coefficient to form a negative exponential term, and calculate the exponential decay penalty factor with the natural constant as the base; Statistically analyze the order dwell time data within the historical scheduling cycle and calculate the moving average of the order dwell time, using the sum of the moving average of the order dwell time and the preset dwell time constant to obtain the adjustment coefficient of the exponential compensation factor; Obtain the dwell time of each order from the time the plan is issued to the current system scheduling time, and use the ratio of the dwell time to the adjustment coefficient as the exponent of the natural logarithm base to calculate the exponential compensation factor.

4. The forging production scheduling optimization method based on dynamic demand perception according to claim 3, characterized in that, The method for obtaining the overall priority weight of each order is as follows: calculate the initial weighting value based on the parameters of each level of the discrete demand grading matrix, and multiply the initial weighting value, the exponential compensation factor and the exponential decay penalty factor to obtain the overall priority weight of each order.

5. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, The crossover operator segment length is jointly determined by the normalized value of the population fitness variance and the normalized value of the mean weight of orders with weights greater than the mean. This includes: calculating the variance of the fitness values ​​of all particles in the current iteration population and dividing the variance by the initial population fitness variance to obtain the normalized variance value; selecting a set of orders with a comprehensive priority weight greater than the population average weight from all orders in the current population, calculating the arithmetic mean of the order weights in the set, and dividing the arithmetic mean by the maximum weight of all orders to obtain the normalized weight mean value; multiplying the normalized variance value and the normalized weight mean value by the total number of orders, and rounding the product down to obtain the crossover operator segment length used for position updates in the discrete particle swarm optimization algorithm, and limiting the crossover operator segment length to be no less than 1 and no greater than the total number of orders.

6. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, If the fitness variance is lower than a threshold, neighborhood recombination based on mold sharing rate is triggered, including: when the fitness variance of the current population is detected to be lower than a set stagnation threshold for a consecutive preset number of generations, traversing the position sequence of the current best particle; in the position sequence, searching for order gene fragments with the same forging mold number but not adjacent sequence positions; performing a position convergence recombination operation on the found order gene fragments to generate a new neighborhood solution, and evaluating the fitness of the new neighborhood solution; if the fitness score of the new neighborhood solution is higher than the fitness score of the worst particle in the population, then replacing the worst particle with the new neighborhood solution.

7. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, In the velocity update, the inertia weight is replaced with a nonlinear mapping value based on the population fitness distribution information entropy, including: extracting the fitness values ​​of all particles in the current population, calculating the probability distribution of the fitness values ​​in different preset intervals; calculating the fitness distribution information entropy based on the probability distribution; substituting the fitness distribution information entropy into the preset Sigmoid nonlinear mapping function to calculate the output value, and using the output value as the inertia weight of the current iteration step.

8. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, The steps of the sequence repair operation based on demand priority weighted fusion are as follows: Duplicate orders and missing orders are located using dictionary mapping; the comprehensive priority weight of each missing order is extracted, and the repair order is determined according to the comprehensive priority weight from high to low; for each missing order, the position of the duplicate order and other allowed insertion positions are taken as candidate insertion positions; the selection probability of each candidate insertion position is determined according to the comprehensive priority weight of the order corresponding to the candidate insertion position or its adjacent orders; missing orders are inserted into candidate insertion positions and duplicate orders are replaced in sequence according to the repair order until there are no duplicate or missing orders in the particle sequence.

9. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, The steps to merge orders of the same material, within the same temperature range, and whose total weight does not exceed the rated load capacity of the heating furnace into a joint batch are as follows: extract orders sequentially according to the particle sequence, and verify whether the orders meet the requirements of having the same material number and that the heating process temperature requirements are within the same allowable temperature range; group orders that continuously meet the merging conditions into the same joint batch; if the total weight exceeds the rated load capacity of the heating furnace after adding the current order, end the current joint batch, and use the current order as the starting order for the next joint batch to re-accumulate the weight.

10. The forging production scheduling optimization method based on dynamic demand perception according to claim 1, characterized in that, The steps for updating the position using a segmented crossover operator based on process adjacency are as follows: calculate the number of process switching, mold consistency, and process temperature difference between two adjacent orders; calculate the process adjacency based on the number of process switching, mold consistency, and process temperature difference; wherein, the process adjacency is negatively correlated with the number of process switching and negatively correlated with the process temperature difference; retain the continuous order segment with the highest process adjacency, i.e., the fewest number of process switching, mold consistency, and process temperature difference, to update the position of the child particle.

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