Flexible job shop scheduling method oriented to date of delivery constraint

Abstract

The invention discloses a flexible job shop scheduling method oriented to date of delivery constraints. The method is oriented to date of delivery constraints, takes total tardiness and maximum completion time into account, establishes a model comprising process, machine and sequence constraints, and expresses scheduling as Markov decision; constructing a delivery time perception heterogeneous graph composed of process and machine nodes, and explicitly injecting semantics such as urgency degree, residual processing time, queue and predicted idle time in node and edge features by combining three relations of process sequence, process-machine feasibility and same-machine time sequence; tardiness perception graph attention network coding is adopted, a single actor-double commentator structure is matched, and a decision is made in a feasible action set through mask normalization and temperature sampling; the rewards and the event advance are aligned and calculated according to increments, and PPO + GAE is used for stable optimization in the training stage. The method is stable in performance in the aspects of reducing the total tardiness and controlling the maximum completion time, convergence is faster, good generalization is achieved, and the method is suitable for engineering deployment and online application.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and production scheduling optimization technology, and in particular to a flexible job shop scheduling method oriented towards delivery date constraints. Background Technology

[0002] Flexible job shop scheduling is a typical complex combinatorial optimization problem, involving multiple jobs, multiple processes, and multiple selectable machines, and is subject to industrial constraints such as process sequence, non-parallelism of individual machines, and non-preemption. In production organization centered on delivery time, enterprises need to maximize on-time delivery while balancing overall production cycle time and resource utilization. While common work assignment rules offer advantages such as simplicity and rapid response, they are sensitive to changes in order structure and equipment load, making it difficult to simultaneously and stably improve both maximum completion time and total delay. In offline optimization scenarios, evolutionary and metaheuristic methods can obtain optimal solutions through search, but under dynamic conditions such as order insertion, time fluctuations, and changes in equipment status, frequent recalculations are often required, resulting in high computational costs and strong dependence on parameter tuning, making it difficult to meet the real-time decision-making needs at the shop floor level.

[0003] With the development of learning-based methods, graph representation and reinforcement learning have provided new technical paths for scheduling problems. Modeling processes and machines as heterogeneous nodes and coupling process sequences, selectable machine sets, and competition among machines through relational modeling can better align with actual production structures. However, existing methods still have shortcomings in explicitly characterizing delivery date semantics, stably handling multi-objective trade-offs, and ensuring the inherent feasibility of online decisions: delivery date-related features are difficult to effectively inject into key representation and aggregation stages; multi-objective learning is prone to training instability and transfer distortion due to objective conflicts; and action generation without inherent feasible constraints will lead to ineffective exploration and affect online stability. Furthermore, the lack of unified metrics and implementation standards in the training and inference stages can cause evaluation mismatch and policy degradation. Therefore, for delivery date-driven flexible workshops, there is an urgent need for a workshop scheduling method that combines structured representation, stable multi-objective learning, and inherent constraints on feasible actions. This method should achieve comprehensive improvements in delay and maximum completion time while ensuring low latency and interpretability, and facilitate industrial system integration. Summary of the Invention

[0004] This invention primarily addresses the aforementioned problems by proposing a workshop scheduling method that centers on delivery time indicators while considering both maximum completion time and total delay. This method constructs a heterogeneous graph representing the multiple relationships between tasks and machines, encodes them using a delay-aware graph attention network, and, within a single-actor, dual-commentator reinforcement learning structure, stably absorbs multi-objective learning signals through improved strategy optimization. Furthermore, it natively introduces feasibility masks at the action level to ensure the implementability of online decisions. Compared to existing heuristic, metaheuristic, and undecomposed value learning methods, this invention, without increasing online complexity, better identifies and prioritizes "near-delay orders," continuously reducing total delay under dynamic operating conditions while also considering the maximum completion time.

[0005] The technical solution adopted by this invention to solve its technical problem is: a flexible job shop scheduling method oriented towards delivery date constraints, comprising the following steps:

[0006] S1: Establish a flexible workshop scheduling model oriented towards delivery time, and determine the basic constraints of operations, processes, and machines;

[0007] S2: Represent the scheduling process as a Markov decision process, defining states, actions, transitions, and rewards;

[0008] S3: Construct a heterogeneous graph representation for delivery time perception, and use a delay perception graph attention network to encode the workshop status and generate a global representation;

[0009] S4: Based on the global representation, set up a single actor-dual critic structure and output action strategies and two types of value assessments;

[0010] S5: At each decision step, apply masked softmax to the set of "ready process - compatible machine" to force the probability of non-actions to zero, normalize within the set of actionable actions and perform greedy selection or temperature sampling.

[0011] S6: An improved proximal policy optimization combined with generalized advantage estimation is used to jointly train the policy and value networks;

[0012] S7: During the deployment phase, online inference and task assignment are performed based on the training strategy to generate scheduling results;

[0013] S8: Implement job shop scheduling using the trained model and output metrics.

[0014] As a preferred embodiment of the above scheme, in step S1, a unified definition and dimensionless processing are adopted for the completion and delivery-related indicators; the comprehensive target uses offline-set weights to controllably balance the maximum completion time and total delay, and maintains a consistent approach during the training and inference phases. The maximum completion time and the work delay are defined as follows:

[0015]

[0016] T j =max(C j -d j ,0)

[0017] Among them, C j Let dj be the completion time of task j, and dj be the delivery date of task j.

[0018] The overall goal is

[0019]

[0020] Where α,β∈[0,1] and α+β=1 are weights set offline. This is the dimensionless result of the corresponding indicator.

[0021] As a preferred embodiment of the above scheme, step S2 employs a delivery-oriented incremental real-time reward system measured by "changes in indicators before and after the action." The reward system penalizes increases in indicators and rewards decreases within the same dimensionless scale. Specifically:

[0022]

[0023] Where t is the decision step, and "after / before" refers to the index values ​​before and after the current action is executed, respectively.

[0024] As a preferred embodiment of the above scheme, in step S3, the heterogeneous graph includes two types of nodes and three types of edges, the two types of nodes being process nodes V. O With machine node V M The three types of edges are process sequence edges E. prec Process - Machine Feasibility (E) feas Same-machine timing / queue edge E que Each of the three types of relationships is configured with independent parameters.

[0025] As a preferred embodiment of the above scheme, in step S3, delivery date-related features are introduced into the state construction, and urgency Slack is used as the core metric. The delivery date-related features are dynamically updated as events progress and are used as node or edge attribute inputs to the graph encoder, where urgency is defined as:

[0026] Slack j =d j -(t+RPT j )

[0027] Where t is the current time, RPT jFor estimating the remaining processing time of job j, delivery time-related features include job-side input features and machine-side input features. Job-side input features include Slack. j RPT j Remaining number of processes, percentage of completed processes, release time, and historical waiting time; machine-side input features include current occupancy status, estimated idle time, queue length, and candidate compatibility count.

[0028] As a preferred embodiment of the above scheme, in step S3, the delay perception graph attention network adopts a multi-head attention and hierarchical readout mechanism. Each attention head aggregates neighborhood information in parallel within different relational subspaces and explicitly injects an embedding mapping of urgency. After multi-layer propagation, mean pooling is performed on the process layer and machine layer respectively, and the results are concatenated into a graph-level representation. The single-head attention scoring and hierarchical readout are represented as follows:

[0029]

[0030] Where u and v are neighboring nodes, h∈{1,...,H} is the attention head index, and x u ,x v ,w h Let h be the learnable parameters of the h-th attention head, where "||" represents vector concatenation, and φ(Slack) is the embedding mapping of urgency-related features; As a shared global representation for subsequent decision-making networks.

[0031] As a preferred embodiment of the above scheme, in step S4, two commentators are used to estimate the value associated with delay and the value associated with maximum completion time, respectively, and calculate the mixed value:

[0032]

[0033] λ1+λ2=1

[0034] λ1,λ2≥0

[0035] in, and These are used to estimate the value associated with delays and the value associated with maximum completion time, respectively.

[0036] For candidate pairings a = (O ji M k Construct action vectors and calculate scores:

[0037]

[0038] g θ (s,a)=f θ (u(s,a))

[0039] Where s is the current state, g θ Let f be the strategy scoring function. θ It is a multilayer perceptron.

[0040] As a preferred embodiment of the above scheme, in step S5, the mask softmax form is:

[0041]

[0042] Where s represents the current state, and a represents the candidate "ready process - compatible machine" pairing action. For indicator functions, g θ Let A(s) be the strategy scoring function, which is the set of actionable actions determined by process sequence constraints, machine availability constraints, and non-preemption constraints to ensure that the strategy is normalized across actionable actions.

[0043] As a preferred embodiment of the above scheme, the calculation and optimization objective in step S6 is:

[0044]

[0045] δ t =r t +γV(s t+1 )-V(s t )

[0046]

[0047] Where λ is the GAE decay factor, γ is the discount factor, ∈ is the pruning threshold, η is the entropy weight, H(·) is the policy distribution entropy, and r t (θ) represents the probability ratio.

[0048] As a preferred embodiment of the above scheme, in step S7, a "mask-greedy priority, temperature sampling as a supplement" decision-making mechanism is adopted to generate scheduling decisions; to adapt to different instance sizes and production cycles, recommended ranges are set for key hyperparameters and maintained at a stable level during deployment; simultaneously, to ensure robust selection among candidates with similar probabilities, online inference adopts an action selection mechanism of "mask-greedy priority, temperature sampling as a supplement":

[0049]

[0050] Where τ is the temperature coefficient, the smaller τ is, the more it is biased towards greedy selection.

[0051] The beneficial effects of this invention are as follows: It forms a closed-loop optimization from measurement metrics to learning signals, based on an integrated approach encompassing "delivery date semantics—structural encoding—value decomposition—feasibility decision-making." At the representation level, delivery date elements such as urgency, remaining processing time, queue size, and expected idle time are directly embedded into attention scoring and hierarchical readout, and dynamically updated as events progress, enabling the strategy to identify and prioritize near-delay orders earlier. At the learning level, it adopts a "unified dimensionless indicator + incremental real-time reward" approach, coupled with dual commentators to perform division of labor modeling and value decoupling of "total delay" and "maximum completion time," significantly mitigating training oscillations caused by target conflicts, improving convergence speed and stability, while retaining interpretability for improvements to different indicators.

[0052] At the decision-making level, by implementing masking normalization and feasibility verification on the "ready process - compatible machine" set, hard constraints are endogenized into the policy distribution, natively guaranteeing action feasibility and significantly reducing invalid exploration and online trial and error. This achieves low-latency inference and industrial-grade robustness, facilitating seamless integration with systems such as MES and APS. In summary, this invention can stably reduce delays while maintaining maximum completion time in dynamic scenarios such as multi-variety, small-batch, order insertion, and fluctuating work hours, adapting to different scale instances and real production line cycles. Simultaneously, it outputs evaluation metrics and policy logs consistent with training, facilitating continuous iteration and maintenance, and possesses significant engineering implementation and promotional value. Attached Figure Description

[0053] Figure 1 This is a flowchart of the SAC2 workflow.

[0054] Figure 2 This is a diagram of the TDGAT network architecture. Detailed Implementation

[0055] The technical solution of the present invention will be further described below through embodiments and in conjunction with the accompanying drawings.

[0056] Example:

[0057] This embodiment presents a flexible job shop scheduling method oriented towards delivery date constraints, applied to a flexible job shop scheduling scenario. It operates within an event-driven dispatching loop and includes the following steps:

[0058] S1: Establish a flexible workshop scheduling model oriented towards delivery time, and determine the basic constraints of operations, processes, and machines;

[0059] S2: Represent the scheduling process as a Markov decision process, defining states, actions, transitions, and rewards;

[0060] S3: Construct a heterogeneous graph representation for delivery date awareness, and use a delay-aware graph attention network (TDGAT) to encode the workshop status and generate a global representation;

[0061] S4: Based on the global representation, set up a single actor-dual critic structure and output action strategies and two types of value assessments;

[0062] S5: At each decision step, a mask is applied to the set of "ready processes - compatible machines" to force the probability of non-actions to zero, and normalizes only within the set of actionable processes and performs greedy selection or temperature sampling.

[0063] S6: An improved proximal policy optimization combined with generalized advantage estimation is used to jointly train the policy and value networks;

[0064] S7: During the deployment phase, online inference and task assignment are performed based on the training strategy to generate scheduling results;

[0065] S8: Implement job shop scheduling using the trained model and output metrics.

[0066] In step S1, a delivery-oriented flexible job shop scheduling mathematical model is established. Let the job set be J, and the process sequence of job j be... The set of machines is M = {M1, ..., M} K}, Process O ji The compatible machine collection is The start and end times of the process are S. ji C ji , in M K The nominal processing time is p ji,k ; Time of completion of work Delivery period d j The delay and maximum completion time are defined as follows:

[0067]

[0068] T j =max(C j -d j ,0)

[0069] The goal is to minimize the weighted sum of the two:

[0070]

[0071] Where α,β∈[0,1] and α+β=1, the target uses offline set weights α,β to make a controllable trade-off between the maximum completion time and the total delay, and maintains a consistent standard during the training and inference phases. To obtain the dimensionless results for the corresponding indicators, dimensionless transformation uses a fixed scale or interval scaling method to map the original values ​​to the [0,1] interval, thus eliminating dimensional differences. A unified dimensionless transformation method is employed...

[0072]

[0073] The disjunctive diagram approach is used to describe the "process-machine" allocation, ensuring no overlap within the same machine. Binary variables are introduced.

[0074]

[0075] Satisfy the constraints of unique allocation, process sequence, and processing time:

[0076]

[0077] For two processes that may be located on the same machine O ji O j′ i ′ Introduce the ordinal variable y (ji),(j′i′),k Let M be a sufficiently large constant, ∈{0,1}:

[0078] S ji ≥C j′i′ -M(1-y (ji),(j′i′),k )

[0079] S j′i′ ≥C ji -My (ji),(j′i′),k

[0080] If necessary, release time, non-preemption, and preparation / replacement clauses can be added, while maintaining consistency in model definitions.

[0081] In step S2, the scheduling process is represented as a Markov decision process (S, A, P, r, γ). State s consists of a set of ready operations, job-side delivery characteristics (urgency, remaining processing time, number of remaining operations, percentage completed, release / waiting time), and machine-side characteristics (occupancy flag, estimated idle time, queue length, compatibility count); action a is to select a pair of "ready operations - compatible machines" from the set of available actions A(s), a = (O... ji M k Immediate rewards are defined incrementally based on changes in metrics before and after an action, strictly aligned with the causal boundaries of event progression: penalties are applied when an action increases total delay or maximum completion time, and rewards are applied when it decreases; increments are cropped or normalized within a uniform scale to suppress the interference of extreme samples on the learning process and reduce variance. Specifically...

[0082] r t =-[αΔC max (t)+βΔTΣ (t)]

[0083]

[0084]

[0085] Where “before / after” refers to the index values ​​measured before and after the action is executed and the process proceeds to the next stable event point; γ∈(0,1] is the discount factor.

[0086] In step S3, a delivery-aware heterogeneous graph is constructed and encoded using TDGAT. The heterogeneous graph G = (V, E) includes two types of nodes and three types of edges. The two types of nodes are process nodes V. O With machine node V M The three types of edges are process sequence edges E. prec Process - Machine Feasibility (E) feas Same-machine timing / queue edge E que Each of the three types of relationships is configured with independent parameters.

[0087] Delivery-related features are introduced into the state construction, with urgency (Slack) as the core metric. These features are dynamically updated as events progress and are used as node or edge attributes input to the graph encoder. At the current time t, the remaining processing time estimate and urgency of job j are defined as follows:

[0088]

[0089] Slack j =d j -(t+RPT j )

[0090] RPT j For estimating the remaining processing time of job j, delivery time-related features include job-side input features and machine-side input features. Job-side input features include Slack. j RPT j Remaining number of processes, percentage of completed processes, release time, and historical waiting time; machine-side input features include current occupancy status, estimated idle time, queue length, and candidate compatibility count.

[0091] Procrastination perception graph attention network, such as Figure 1 As shown, a multi-head attention and hierarchical readout mechanism is adopted, in which each attention head aggregates neighborhood information in parallel within different relational subspaces, and explicitly injects urgency Slack. j Embedding mapping φ(Slack) jTo highlight near-expiry orders; after multi-layer propagation during the readout phase, mean pooling is performed on both the process layer and the machine layer, and then they are sequentially concatenated to form a graph-level representation for subsequent strategy and value network input; different edge types are configured with independent linear projection and attention parameters, and residuals and normalization can be used between layers to improve training stability. The scoring, normalization, and aggregation of the h-th attention head in the l-th layer on the relation τ∈{prec,feas,que} are as follows:

[0092]

[0093] Layered reading uses a "process average ⊕ machine average" concatenation method:

[0094]

[0095] Where u and v are neighboring nodes, h∈{1,...,H} is the attention head index, and x u ,x v ,w h Let h be the learnable parameters of the h-th attention head, where "||" represents vector concatenation, and φ(Slack) is the embedding mapping of urgency-related features; As a shared global representation for subsequent decision-making networks.

[0096] In step S4, the single-actor-dual-critic structure is as follows: Figure 2 As shown, actors output policy distributions on the set of possible actions; two critics learn values ​​related to total delay and maximum completion time, respectively, or regress a dimensionless combination of the two, for advantage estimation and signal decomposition to alleviate gradient conflicts in multi-objective training and improve convergence stability and interpretability. The mixed value is represented as:

[0097]

[0098] λ1+λ2=1

[0099] λ1,λ2≥0

[0100] in, and These are used to estimate the value associated with delays and the value associated with maximum completion time, respectively.

[0101] For candidate pairings a = (O ji M k Construct action vectors and calculate scores:

[0102]

[0103] g θ (s,a)=f θ (u(s,a))

[0104] Where s is the current state, g θ Let f be the strategy scoring function. θ It is a multilayer perceptron.

[0105] In step S5, the set of actionable actions is generated by hard constraints such as process sequence, machine availability, and non-preemption. The set of actionable actions is as follows:

[0106]

[0107] The masking mechanism forces the probability of pairing actions that do not meet the constraints to zero, and only performs normalized sampling or greedy selection on the available actions; when the machine is in the processing state, only pairings whose expected idle time is no later than the candidate start time are allowed to enter the set, thus avoiding invalid exploration from the source.

[0108] The strategy performs mask normalization within the set of possible actions:

[0109]

[0110] In step S6, the dominance term is calculated using generalized dominance estimation:

[0111]

[0112] δ t =r t +γV(s t+1 )-V(s t )

[0113] To balance bias and variance, and to optimize the target by using a pruning proximal policy, the magnitude of each policy update is limited, while entropy regularization is used to maintain moderate exploration; the value network uses mean squared error regression to target return.

[0114]

[0115] Where λ is the GAE decay factor, γ is the discount factor, ∈ is the pruning threshold, η is the entropy weight, H(·) is the policy distribution entropy, and r t (θ) represents the probability ratio. Recommended ranges for hyperparameters are: λ∈[0.8,1.0], γ∈[0.05,0.2], γ∈(0,1], c2∈[10...]. -4 10 -2 The training samples are derived from multi-instance rolling simulations, and slight perturbations can be injected into the processing time or release time to enhance generalization, but no external targets unrelated to delivery time are introduced.

[0116] In step S7, online inference employs a selection mechanism of "mask greedy priority, temperature sampling as a supplement": when the probabilities of candidate actions are close, the policy distribution is softened by temperature to avoid a deadlock of equal probabilities; otherwise, the action with the highest probability is directly selected, balancing stability and response speed. That is, when the difference between the optimal and suboptimal probabilities is less than the threshold δ, the policy distribution is softened by temperature only within A(s).

[0117]

[0118] The system uses an event-driven approach to advance until all processes are completed, outputting a work order sequence and a Gantt chart.

[0119] In step S8, following the same statistical and dimensionless standards as the training phase, delivery-related indicators are output and archived, including maximum completion time, total delay, and delay rate:

[0120]

[0121] T j =max(C j -d j ,0)

[0122]

[0123] It also records key states, actions, and reward trajectories along with strategy logs, facilitating playback and version iteration.

[0124] The flexible job shop scheduling method oriented towards delivery date constraints in this embodiment constructs an end-to-end deep reinforcement learning framework for joint decision-making on "process sequencing-machine allocation" in flexible job shops. The method accurately characterizes the shop state (three types of relationships: process node and machine node, process sequence / process-machine feasibility / simultaneous machine timing) using a heterogeneous graph model, and extracts dynamic features (including urgency, remaining processing time, queues, and idle time) based on a delivery date-aware graph attention network (TDGAT). At the decision layer, a single-actor-dual-commentator structure is used to determine the "maximum completion time C". max "and "total delay ∑T j Value decomposition is performed, and optimal selection is achieved within the "ready process - compatible machine" set using actionable action masks. The reward function is designed based on the incremental changes in indicators before and after the action, strictly aligned with the event progression boundary. During the training phase, PPO+GAE is used for stable optimization, and the target weights are set and fixed offline (after unification and dimensionlessness, C...). max With ∑T j(Weighted) to avoid the uncertainty brought about by online weighting; through multi-instance rolling simulation and consistent feature, mask and index archiving, the model can efficiently learn the delivery-oriented dispatch strategy and show good generalization ability and scheduling efficiency on complex dual-objective scenarios and large-scale public datasets. Compared with traditional heuristic and reinforcement learning methods without value decomposition, it has a stable advantage in the indicators of delay rate and completion time.

[0125] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for due date constraint oriented flexible job shop scheduling, applied to a flexible job shop scheduling scenario, characterized in that, The method comprises the following steps: S1: establishing a delivery period oriented flexible job shop scheduling model to determine the basic constraints of jobs, processes and machines; S2: describing the scheduling process as a Markov decision process, defining states, actions, transitions and rewards; S3: constructing a delivery period aware heterogeneous graph representation, using a tardiness aware graph attention network to encode the state of the workshop and generate a global representation; S4: setting a single actor-double critic structure based on the global representation, outputting action strategies and two types of value evaluation; S5: at each decision step, implementing a masked softmax on the "ready process-compatible machine" set, forcing the probability of non-actionable actions to zero, normalizing within the actionable set and performing greedy selection or temperature sampling; S6: using an improved proximal policy optimization combined with generalized advantage estimation to jointly train the policy and value networks; S7: in the deployment stage, online inference and dispatching are performed according to the trained strategy to generate scheduling results; S8: using the trained model to implement job shop scheduling and output indicators.

2. The due-date-constrained flexible job shop scheduling method according to claim 1, characterized in that: In step S1, the delivery and delivery period related indicators are uniformly defined and dimensionless processed; the comprehensive target uses the offline set weight to controllably balance between the maximum completion time and the total tardiness, and the same caliber is maintained in the training and inference stages, and the maximum completion time and job tardiness are defined as: T j = max(C j -d j , 0) wherein C j is the completion time of job j, and dj is the due date of job j. The comprehensive target is wherein, wherein, a, b ∈ [0, 1] and a + b = 1 are weights set offline, is the dimensionless result of the corresponding indicator.

3. The due-date-constrained flexible job shop scheduling method according to claim 1, characterized in that: In step S2, the tardiness oriented incremental immediate reward is measured by the "change of indicators before and after action", the reward is punished for the increase of indicators and rewarded for the decrease of indicators in the same dimensionless scale, which is: Where t is the decision step, "after / before" refers to the indicator value before and after the current action.

4. The due-date-constrained flexible job shop scheduling method according to claim 1, characterized in that: The isomerism graph includes two types of nodes and three types of edges, the two types of nodes are process nodes V O and machine nodes V M , the three types of edges are process sequence edges E prec , process-machine feasible edges E feas and same-machine time sequence / queue edges E que , and the three types of relations are respectively configured with independent parameters.

5. The due-date constrained flexible job shop scheduling method according to claim 4, characterized in that: In step S3, the delivery period related features are introduced in the state construction, and the urgency Slack is used as the core measurement, the delivery period related features are dynamically updated with the event advancing, and are input into the graph encoder as node or edge attributes, wherein the urgency is defined as: Slack j = d j - (t + RPT j ) where t is the current time, RPT j The due-date related features include job-side input features and machine-side input features. The job-side input features include Slack j , RPT j The remaining process number, the finished work ratio, the release time and the historical waiting time. The machine-side input features include the current occupation state, the predicted idle time, the queue length and the candidate compatibility count.

6. The due-date-constrained flexible job shop scheduling method according to claim 1, characterized in that: In step S3, the tardiness aware graph attention network uses multi-head attention and hierarchical reading mechanism, each attention head aggregates neighborhood information in different relationship subspaces in parallel, and explicitly injects embedding mapping of urgency; after multi-layer propagation, the mean pooling is performed on the process layer and the machine layer respectively and spliced into a graph level representation; single head attention scoring and hierarchical reading are represented as: where u, v are neighboring nodes, h e {1,..., H} is the attention head index, x u v h is the learnable parameter of the h-th attention head, "||" denotes vector concatenation, and φ(Slack) is the embedding mapping for the urgency-related features. as shared global representation for the subsequent decision network.​​ 7. The due-date constrained flexible job shop scheduling method according to claim 1, wherein: In step S4, two critics are used to estimate the value related to the tardiness and the value related to the maximum completion time, and the mixed value is calculated: λ1+λ2=1 λ1,λ2≥0 wherein, and are used to estimate the value associated with the delay and the value associated with the maximum completion time, respectively; For each candidate pair a = (O ji ,M k ), construct the action vector and compute the score: g θ (s,a) = f θ (u(s,a)) where s is the current state, g θ is the policy scoring function, f θ is a multi-layer perceptron.

8. The due-date constrained flexible job shop scheduling method according to claim 1, characterized in that In step S5, the masked softmax form is: where s is the current state, a is a candidate "ready process - compatible machine" pair action, is an indicator function, g θ is a policy scoring function, A(s) is the set of actionable actions determined by process precedence constraints, machine availability, and non-preemptable constraints to ensure that the policy is normalized over actionable actions.

9. The due-date constrained flexible job shop scheduling method according to claim 1, wherein: In step S6, the calculation and optimization target is: delta t = r t + gamma * V(s t+1 ) - V(s t ) where λ is the GAE decay factor, γ is the discount factor, ∈ is the clipping threshold, η is the entropy weight, H(·) is the policy distribution entropy, r t (θ) is the probability ratio.

10. The due-date-constrained flexible job shop scheduling method of claim 1, wherein: In step S7, the "masked greedy priority, temperature sampling as auxiliary" decision mechanism is used to generate scheduling decisions: Where τ is the temperature coefficient, the smaller the τ, the more biased to the greedy selection.

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