A hierarchical response reactivity scheduling method based on buffer adjustment

Abstract

This invention discloses a hierarchical response-based reactive scheduling method based on buffer adjustment. First, a multi-dimensional disturbance quantification evaluation system is constructed, incorporating buffer consumption status, delivery urgency, and time prediction accuracy, to achieve quantitative assessment and hierarchical classification of disturbance intensity. Second, for different levels of disturbance, time window fine-tuning, heuristic local reordering, and global rescheduling strategies are implemented to achieve differentiated dynamic repair. Finally, for the global rescheduling scenario, a multi-strategy uncertainty-aware NSGA-II algorithm is designed. By improving the crossover mutation operator, skip decoding, and dynamic congestion strategy, the optimization performance under complex disturbances is significantly improved. This invention, through a hierarchical response mechanism and collaborative optimization algorithm, achieves an effective trade-off between scheduling stability and responsiveness, effectively reducing plan offset costs and shortening project completion time.

Description

Technical Field

[0001] This invention belongs to the field of complex product assembly scheduling and production control, and particularly relates to a hierarchical response reactive scheduling method based on buffer adjustment. Background Technology

[0002] Aircraft assembly, as a core manufacturing link of large and complex products, is characterized by tight process coupling, strict resource constraints, and high human involvement. During production execution, process times are highly susceptible to various uncertainties such as personnel skills, equipment status, and unforeseen events, leading to frequent accumulation of time deviations and causing the baseline scheduling plan to fail. To address this issue, while proactive scheduling schemes build up a certain level of disturbance resistance during the planning phase, reactive scheduling mechanisms are still needed to dynamically correct the original plan when actual deviations exceed the buffer absorption range.

[0003] However, existing reactive scheduling techniques still have significant shortcomings:

[0004] 1. The response mechanism is crude and lacks hierarchical classification: Existing methods mostly use fixed thresholds or single deviation indicators to trigger rescheduling, which cannot accurately reflect the differences in the propagation range and impact intensity of different disturbances. This can easily lead to over-adjustment under slight disturbances or response lag under severe disturbances.

[0005] 2. Lack of flexibility in response strategy design: A uniform repair method is often adopted for disturbances of different intensities, failing to make full use of the dynamic adjustability of the time buffer, making it difficult for the scheduling system to achieve a balance between stability and recovery efficiency.

[0006] 3. The rescheduling solution algorithm is complex and inefficient: Under severe disturbances, the scheduling scale increases and the solution complexity increases dramatically. Existing optimization algorithms are difficult to achieve fast convergence while ensuring the diversity of solution sets, and are difficult to adapt to the real-time decision-making needs of dynamic production environments. Summary of the Invention

[0007] To address the above problems, this invention provides a hierarchical response reactive scheduling method based on buffer adjustment.

[0008] This invention presents a hierarchical response-responsive scheduling method based on buffer adjustment to address uncertain disturbances during aircraft assembly execution. First, the method constructs a multi-dimensional disturbance quantification evaluation system encompassing buffer consumption status, delivery urgency, and time prediction accuracy, enabling quantitative assessment and hierarchical classification of disturbance intensity. Second, for different levels of disturbance, it implements time window fine-tuning, heuristic local reordering, and global rescheduling strategies to achieve differentiated dynamic repair. Finally, for the global rescheduling scenario, a multi-strategy uncertainty-aware NSGA-II algorithm is designed, improving the optimization performance under complex disturbances by refining the crossover mutation operator, skip decoding, and dynamic congestion strategy.

[0009] Specifically, the following steps are included:

[0010] Step 1: Problem description and assumptions.

[0011] In proactive scheduling facing uncertain working hours, the resilience of the baseline scheduling scheme needs to be enhanced in two ways: firstly, by predicting working hours to improve the accuracy of planned inputs as much as possible; secondly, by allocating time buffers reasonably for relevant processes based on the prediction results to absorb the impact of prediction errors and random disturbances. The essence of time buffering is to embed appropriate redundancy into the planned duration, thereby improving the stability and reliability of the scheduling scheme during the execution phase by sacrificing some time efficiency. Proactive scheduling, by linking predicted working hours, time buffers, and planned durations, forms a baseline scheduling scheme with a certain degree of flexibility, thereby controlling the actual execution deviation within an absorbable range under most disturbance conditions and reducing the chain reaction impact on subsequent processes and the overall duration.

[0012] The following basic assumptions are proposed:

[0013] (1) Assume that preemption is not allowed between processes, that is, once a process starts, it must continue until it is completed.

[0014] (2) Assume that all resources involved are updatable, meaning that their availability remains constant during each scheduling cycle.

[0015] (3) Assume that the preceding relationships of the processes are determined and known, that is, the process logic order between processes is fixed.

[0016] Step 2: Objective function and constraints.

[0017] Objective function: To minimize the total project duration C max Minimize the total buffer sum ∑B i Maximizing scheduling robustness 1-SC / SC max For multi-objective optimization, the mathematical expression is as follows:

[0018] (1)

[0019] (2)

[0020] Constraints:

[0021] (3)

[0022] (4)

[0023] (5)

[0024] (6)

[0025] (7)

[0026] Where sT i represents the start time of activity i in the reactive scheduling phase, sB i represents the start time of activity i in the baseline scheduling scheme of the proactive scheduling phase; n represents the actual number of activities in the project, n+2 represents the total number of activities including virtual start and end nodes; sT n+2 represents the final completion time of the adjusted project. Indicates activity Start time; Indicates activity The immediate preceding set of activities; Represents the virtual start of the activity on resources The demand for it is 0. Indicates activity Resources Demand; These are 0-1 decision variables used to represent the allocation relationship between activities and resources; Indicates at time A collection of activities to be performed.

[0027] Equation (1) is used to measure the magnitude of scheduling adjustment. The smaller the value, the smaller the disturbance of the original plan by the reactive scheduling and the higher the stability of the scheduling scheme. Equation (2) is used to characterize the recovery effect of project completion time under disturbance conditions. There is a certain trade-off between the two objectives: compressing project completion time usually requires a large adjustment to the original work process arrangement, while over-protecting the stability of the scheduling scheme may reduce the system's schedule recovery capability. By optimizing the above two objectives at the same time, a reasonable balance is sought between scheduling stability and recovery efficiency. Equation (3) is the work process priority constraint, which ensures that each work process can only be started after all its immediate predecessor work processes are completed. Considering that the actual work time of the work process is still uncertain before the project starts, the proactive scheduling stage uses the sum of the predicted work time and its corresponding time buffer as the planned schedule d. iEquation (4) is used to generate a baseline scheduling scheme; Equation (4) is a resource constraint condition used to ensure that at any time t, the total demand of all executing processes for the same type of resource k does not exceed the available capacity R of that resource. k To meet the actual characteristics of limited workshop resources; Equation (5) stipulates that the duration of virtual start activities and virtual end activities in the project is 0, which is used to uniformly describe the start and end boundaries of the project; Equation (6) stipulates that virtual start activities and virtual end activities do not consume any resources, so as to avoid additional impact on resource constraints; Equation (7) is a decision variable constraint, which is used to characterize the allocation relationship between activities and resources.

[0028] Step 3: Multidimensional disturbance assessment and graded response mechanism.

[0029] Under slight disturbances, a buffer time window fine-tuning strategy is adopted. Existing time buffers are dynamically reallocated to restore scheduling feasibility without changing the original process sequencing and resource allocation framework. The specific implementation steps are as follows:

[0030] (1) Calculation of the total remaining buffer.

[0031] Calculate the total remaining buffer for all unstarted processes after the disturbance occurs. This total is composed of the original buffer configuration minus the consumed portion and the actual overdue amount, reflecting the scale of time redistribution available.

[0032] (2) Calculation of basic allocation weights.

[0033] The basic allocation weight of each process is calculated based on the predicted working time percentage of the remaining processes. This weight reflects the impact of the process working time scale on buffer demand. The longer the working time of a process, the more buffer is theoretically needed to cope with uncertainty.

[0034] (3) Uncertainty and importance coefficient correction.

[0035] An uncertainty coefficient is introduced to correct the basic weights. This coefficient is obtained by normalizing the process prediction accuracy. Processes with lower prediction accuracy are assigned a higher uncertainty coefficient, thus gaining more protection in the buffer allocation. At the same time, an importance coefficient is introduced to further adjust the allocation weights. This coefficient is based on the criticality of the process in the network. Processes with higher criticality receive a greater weight gain.

[0036] (4) Comprehensive allocation factor and buffer reallocation.

[0037] A comprehensive allocation factor is constructed by combining the uncertainty coefficient and the importance coefficient, and the remaining buffer amount is allocated proportionally according to this factor to obtain the adjusted buffer configuration for each process.

[0038] The mathematical expression of the above process is as follows:

[0039] (8)

[0040] (9)

[0041] (10)

[0042] (11)

[0043] (12)

[0044] (13)

[0045] in, Indicate process Predicted working hours Indicates the weight of the uncertainty level coefficient; The normalized uncertainty coefficient is used to quantify uncertainty and correct the basic allocation weights in a buffer time window fine-tuning strategy for minor perturbations. Indicate process Key weights; Indicate process The proportion of the predicted working hours to the total predicted working hours of all remaining unstarted processes; Indicate process The criticality of intermediate quantities; The basic weight representing the process itself.

[0046] Equations (8) and (9) determine the remaining buffer size and its proportional structure, buffersize' i The adjusted time buffer size for process i, buffersize i For the original buffer configuration of process i, B total e represents the original buffer amount for all processes that have not yet started after the disturbance process. true,i Δ' is the latest completion time calculated according to the rules for disturbance process i. i The comprehensive allocation factor for process i; Equations (10) and (11) are obtained through Vp' i With β' i Uncertainty and structural importance are quantified and normalized, N remain S*remain(i) is the set of remaining unstarted processes; Equation (12) reflects the impact of key nodes on buffer absorption capacity; Equation (13) eliminates the dimensional interference between projects of different sizes through relative proportions, and S*remain(i) is the set of all subsequent processes of process i.

[0047] Step 4: Heuristic rule scheduling for intermediate disturbances.

[0048] In the hierarchical response framework, when the disturbance develops to the moderate stage, the time buffer configured in the proactive stage is no longer sufficient to fully absorb the time deviation, but the overall system resource structure and process network remain stable. At this time, it is necessary to perform limited reconfiguration of the scheduling sequence of processes that have not yet been executed, under the premise of satisfying process priority relationships and resource constraints.

[0049] (1) Identification of disturbance-dominant constraints.

[0050] To identify the dominant constraints of disturbances, three indicators are introduced: delivery urgency (TU), resource stress (RC), and network complexity (NC). RC describes the deviation between peak resource demand and supply capacity, while NC measures the amplification potential of network connection density on disturbance propagation. The formula is:

[0051] (14)

[0052] (15)

[0053] In formula (14), K is the total number of resource types, including all updatable resource types such as equipment, tooling, and personnel; T is the set of all time points within the scheduling cycle; Rdemand k(t) represents the instantaneous demand of the k-th type of resource at time t, that is, the sum of the demand of all activities executed at that time for this type of resource; Ravai k represents the total available amount of the k-th type of resource, which is determined by the project resource configuration; in formula (15), E is the total number of edges in the project network, that is, the number of predecessor and successor relationships; and N is the total number of processes.

[0054] (2) Prioritize situations based on time urgency.

[0055] When time urgency (TU) dominates, the main risk of the system is the continuous deviation of the project completion time. A hybrid sorting mechanism is constructed by selecting the maximum position weight rule (GRPW) and the shortest process priority rule (SPT). The resource intensity rule (RI) is introduced as an auxiliary constraint to suppress resource conflicts that may be caused by time-oriented sorting.

[0056] (3) The order of resource tension as the dominant factor.

[0057] When resource stress (RC) is the dominant factor, the system bottleneck is mainly manifested as an imbalance between resource supply and demand. The maximum resource demand rule (GRD) and the SPT rule are combined. GRD prioritizes the processes with higher resource demand, while SPT accelerates the release of resources by prioritizing shorter processes.

[0058] (4) Structural coupling-dominated case reordering.

[0059] When network complexity (NC) dominates, the disturbance risk mainly comes from the enhanced coupling of the process network structure and the delay propagation effect. The rule with the most subsequent processes (MIS) and the rule with the fewest subsequent processes (LNS) are combined to control the influence range of critical nodes and reduce network tail backlog.

[0060] Step 5: Two-stage reactive scheduling based on multi-strategy uncertainty-aware NSGA-II.

[0061] When the disturbance level develops to a severe level, the existing time buffer can no longer absorb the actual execution deviation, and the critical path structure and resource allocation relationship are substantially changed. Here, while retaining the basic evolutionary framework of NSGA-II, a multi-strategy uncertainty perception mechanism is introduced to construct the MUA-NSGA-II algorithm to reconstruct the remaining unfinished processes as a whole.

[0062] (1) Design of cross operator with uncertainty perception.

[0063] By introducing an uncertainty perception index, the process structure that contributes significantly to scheduling stability is selectively retained during the crossover process, thus constructing two core indicators: process start time stability and adjustment cost impact.

[0064] (16)

[0065] Among them, s i,p sbase i,p represents the start time of process i in the p-th parent chromosome, and sbase i,p represents the start time of this process in the baseline scheme generated by proactive scheduling. p=1,2 correspond to two parent individuals respectively. The value range of this index is (0,1], and the larger the value, the more stable the start time of the process.

[0066] (17)

[0067] Among them, 𝑤 𝑖 The process weight is 2 when process 𝑖 is on the critical path of any parent individual; otherwise, it is 1. |Succ(𝑖)| represents the number of successor activities of process 𝑖. The more successor activities there are, the greater the chain reaction of the change in the order of the process on subsequent processes, and the higher the adjustment cost.

[0068] (18)

[0069] in, and These represent the impact of normalized start time stability and adjustment cost, respectively. 𝛼 and 𝛽 are weighting coefficients used to adjust the relative importance of scheduling stability and adjustment cost in cross-decision-making.

[0070] (19)

[0071] (2) Design of uncertainty-aware permutation mutation operator.

[0072] The uncertainty of the work process is quantified using the coefficient of determination R² of the work time prediction model. The process is divided into three levels: high, medium, and low, and assigned decreasing variation probabilities. A feasible region-restricted permutation mechanism is designed, defining the feasible permutation variation interval [L] for process j. j U j ]for:

[0073] (20)

[0074] Where pos(·) represents the position index of the process in the current chromosome, and Pred(j) and Succ(j) represent the sets of the immediate predecessor and immediate successor processes of process j, respectively.

[0075] (3) Skip-type SSGS decoding.

[0076] Based on the classic SSGS, a skip-style SSGS decoding strategy is designed. This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to key time points where resource status may change, thereby improving computational efficiency while keeping the scheduling generation logic unchanged.

[0077] (4) Dynamic congestion setting.

[0078] Differentiated crowding assignment rules are used based on the location attributes of individuals in the Pareto front, including a boundary individual protection mechanism and an intermediate individual adaptive calculation mechanism; boundary individuals are assigned an infinitely large crowding distance.

[0079] (twenty one)

[0080] For the intermediate individual, their contribution to crowding on this dimension is:

[0081] (twenty two)

[0082] The total crowding distance of an individual can be obtained by summing the crowding contributions of each objective dimension.

[0083] (twenty three)

[0084] This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to key time points where resource status may change, thereby improving computational efficiency while keeping the scheduling generation logic unchanged.

[0085] The beneficial technical effects of this invention compared to the prior art are as follows:

[0086] (1) This invention constructs a refined hierarchical response mechanism, which effectively solves the problem of over-adjustment or response lag caused by the "one-size-fits-all" response method in traditional reactive scheduling. By incorporating buffer adequacy, delivery risk and prediction uncertainty into the quantitative evaluation system, it achieves precise matching between disturbance level and response strategy. It not only effectively ensures production stability under slight disturbances, but also restores scheduling feasibility through global repair under severe disturbance scenarios, thus achieving a balance between stability and recovery capability.

[0087] (2) This invention designs a multi-strategy uncertainty-aware NSGA-II algorithm, which is deeply compatible with the complex constraints of reactive scheduling. By introducing a stability score-based perceptual crossover operator and a hierarchical mutation mechanism, high-quality genetic information is effectively preserved, avoiding blind search in large-scale rescheduling. By adopting a skip-style SSGS decoding and dynamic congestion strategy, redundant computational overhead is greatly reduced while improving the coverage and convergence speed of the solution set on the Pareto front, ensuring that the system can output high-quality dynamic repair solutions in real time under large-scale complex perturbation environments. Attached Figure Description

[0088] Figure 1 This is a logic diagram for hierarchical response reactive scheduling based on buffer adjustment.

[0089] Figure 2 Example of designing a crossover operator for uncertainty awareness.

[0090] Figure 3 This is a schematic diagram illustrating the definition of the variation range of process substitution.

[0091] Figure 4 This is a schematic diagram of the skip-type SSGS decoding logic.

[0092] Figure 5 Radar chart showing the overall performance of four typical algorithms under multiple computational scales.

[0093] Figure 6 A bar chart comparing the mutual coverage (C value) of the solution sets of the MUA-NSGA-II algorithm.

[0094] Figure 7 This is a performance comparison chart of different reactive scheduling strategies under multiple instance scales. Detailed Implementation

[0095] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0096] This invention addresses the challenges of diverse disturbance types, significantly varying impact levels, and high organizational and coordination costs during aircraft assembly execution. With the objective function of minimizing scheduling adjustment costs and maximizing project completion stability, it establishes a reactive scheduling method based on multi-dimensional quantitative assessment and graded response. By constructing a multi-dimensional assessment system encompassing buffer consumption, delivery urgency, and prediction accuracy, it achieves graded determination of disturbance intensity. Differentiated response strategies, such as time window fine-tuning, heuristic local reordering, and optimized algorithm rescheduling, are designed to achieve targeted dynamic repair. Ultimately, a closed-loop scheduling framework covering disturbance monitoring, graded assessment, and graded execution is established. This ensures the feasibility of production plans while minimizing plan oscillations and resource waste caused by disturbances, providing efficient dynamic decision support for production execution in complex assembly environments.

[0097] The present invention provides a hierarchical response reactive scheduling method based on buffer adjustment, the logic of which is as follows: Figure 1 As shown, this method demonstrates the complete triggering process from disturbance monitoring and multi-dimensional state assessment to three response strategies (fine-tuning, rescheduling, and global reconstruction), covering the entire process of disturbance classification, strategy matching, and solution output. First, it constructs a multi-dimensional disturbance quantification assessment system that includes buffer consumption status, delivery urgency, and time prediction accuracy, enabling quantitative assessment and classification of disturbance intensity. Second, for different levels of disturbance, it implements time window fine-tuning, heuristic local reordering, and global rescheduling strategies to achieve differentiated dynamic repair. Finally, for the global rescheduling scenario, a multi-strategy uncertainty-aware NSGA-II algorithm is designed, improving the optimization performance under complex disturbances by refining the crossover mutation operator, skip decoding, and dynamic congestion strategy.

[0098] Specifically, the following steps are included:

[0099] Step 1: Problem description and assumptions.

[0100] Because work hours are uncertain, scheduling schemes based solely on deterministic durations often struggle to remain stable during actual execution. When actual work hours deviate from planned values, existing scheduling arrangements are prone to problems such as plan deviations, resource conflicts, and even project delays. Therefore, proactive scheduling for uncertain work hours requires enhancing the resilience of the baseline scheduling scheme in two ways: firstly, by predicting work hours to maximize the accuracy of planned inputs; secondly, by allocating appropriate time buffers for relevant processes based on the prediction results to absorb the impact of prediction errors and random disturbances. The essence of time buffering is to embed appropriate redundancy into the planned project duration, sacrificing some time efficiency to improve the stability and reliability of the scheduling scheme during the execution phase. Proactive scheduling, by linking predicted work hours, time buffers, and planned project durations, forms a relatively flexible baseline scheduling scheme, thereby controlling actual execution deviations within an absorbable range under most disturbance conditions and reducing the cascading impact on subsequent processes and the overall project duration.

[0101] The following basic assumptions are proposed:

[0102] (1) Assuming that preemption is not allowed between processes, that is, once a process starts, it must continue until it is completed. In the actual scenario of aircraft assembly, due to the continuity of assembly process and the complexity of resource coordination, interrupting the ongoing process will result in extremely high restart costs and quality risks.

[0103] (2) Assume that all resources involved are updatable, meaning that their availability remains constant during each scheduling cycle. For example, assembly stations and general tools can be released and used for other processes after they are occupied during a certain period.

[0104] (3) Assume that the preceding relationships of the processes are determined and known, that is, the process logic order between processes is fixed.

[0105] Step 2: Objective function and constraints.

[0106] Objective function: To minimize the total project duration C max Minimize the total buffer sum ∑B i Maximizing scheduling robustness 1-SC / SC max For multi-objective optimization, the mathematical expression is as follows:

[0107] (1)

[0108] (2)

[0109] Constraints:

[0110] (3)

[0111] (4)

[0112] (5)

[0113] (6)

[0114] (7)

[0115] Where sT i represents the start time of activity i in the reactive scheduling phase, sB i represents the start time of activity i in the baseline scheduling scheme of the proactive scheduling phase; n represents the actual number of activities in the project, n+2 represents the total number of activities including virtual start and end nodes; sT n+2 represents the final completion time of the adjusted project. Indicates activity Start time; Indicates activity The immediate preceding set of activities; Represents the virtual start of the activity on resources The demand for it is 0. Indicates activity Resources Demand; These are 0-1 decision variables used to represent the allocation relationship between activities and resources; Indicates at time A collection of activities to be performed.

[0116] Equation (1) is used to measure the magnitude of scheduling adjustment. The smaller the value, the smaller the disturbance of the original plan by the reactive scheduling and the higher the stability of the scheduling scheme. Equation (2) is used to characterize the recovery effect of project completion time under disturbance conditions. There is a certain trade-off between the two objectives: compressing project completion time usually requires a large adjustment to the original work process arrangement, while over-protecting the stability of the scheduling scheme may reduce the system's schedule recovery capability. By optimizing the above two objectives at the same time, a reasonable balance is sought between scheduling stability and recovery efficiency. Equation (3) is the work process priority constraint, which ensures that each work process can only be started after all its immediate predecessor work processes are completed. Considering that the actual work time of the work process is still uncertain before the project starts, the proactive scheduling stage uses the sum of the predicted work time and its corresponding time buffer as the planned schedule d. i Equation (4) is used to generate a baseline scheduling scheme; Equation (4) is a resource constraint condition used to ensure that at any time t, the total demand of all executing processes for the same type of resource k does not exceed the available capacity R of that resource. kTo meet the actual characteristics of limited workshop resources; Equation (5) stipulates that the duration of virtual start activities and virtual end activities in the project is 0, which is used to uniformly describe the start and end boundaries of the project; Equation (6) stipulates that virtual start activities and virtual end activities do not consume any resources, so as to avoid additional impact on resource constraints; Equation (7) is a decision variable constraint, which is used to characterize the allocation relationship between activities and resources.

[0117] Step 3: Multidimensional disturbance assessment and graded response mechanism.

[0118] When the disturbance level is low and the predicted completion time still has a safety margin, the disturbance does not change the original critical path structure and resource allocation relationship. Its main impact is the erosion of the time buffer by local time deviations. Under slight disturbance conditions, a buffer time window fine-tuning strategy is adopted to restore scheduling feasibility by dynamically reallocating the existing time buffer without changing the original process sequencing and resource allocation framework. The specific implementation steps are as follows:

[0119] (1) Calculation of the total remaining buffer.

[0120] Calculate the total remaining buffer for all unstarted processes after the disturbance occurs. This total is composed of the original buffer configuration minus the consumed portion and the actual overdue amount, reflecting the scale of time redistribution available.

[0121] (2) Calculation of basic allocation weights.

[0122] The basic allocation weight of each process is calculated based on the predicted working time percentage of the remaining processes. This weight reflects the impact of the process working time scale on buffer demand. The longer the working time of a process, the more buffer is theoretically needed to cope with uncertainty.

[0123] (3) Uncertainty and importance coefficient correction.

[0124] An uncertainty coefficient is introduced to correct the basic weights. This coefficient is obtained by normalizing the process prediction accuracy. Processes with lower prediction accuracy are assigned a higher uncertainty coefficient, thus gaining more protection in the buffer allocation. At the same time, an importance coefficient is introduced to further adjust the allocation weights. This coefficient is based on the criticality of the process in the network. Processes with higher criticality receive a greater weight gain.

[0125] (4) Comprehensive allocation factor and buffer reallocation.

[0126] A comprehensive allocation factor is constructed by combining the uncertainty coefficient and the importance coefficient, and the remaining buffer amount is allocated proportionally according to this factor to obtain the adjusted buffer configuration for each process.

[0127] The mathematical expression of the above process is as follows:

[0128] (8)

[0129] (9)

[0130] (10)

[0131] (11)

[0132] (12)

[0133] (13)

[0134] in, Indicate process Predicted working hours Indicates the weight of the uncertainty level coefficient; The normalized uncertainty coefficient is used to quantify uncertainty and correct the basic allocation weights in a buffer time window fine-tuning strategy for minor perturbations. Indicate process Key weights; Indicate process The proportion of the predicted working hours to the total predicted working hours of all remaining unstarted processes; Indicate process The criticality of intermediate quantities; The basic weight representing the process itself.

[0135] Equations (8) and (9) determine the remaining buffer size and its proportional structure, buffersize' i The adjusted time buffer size for process i, buffersize i For the original buffer configuration of process i, B total e represents the original buffer amount for all processes that have not yet started after the disturbance process. true,i Δ' is the latest completion time calculated according to the rules for disturbance process i. i The comprehensive allocation factor for process i; Equations (10) and (11) are obtained through Vp' i With β' i Uncertainty and structural importance are quantified and normalized, N remain S*remain(i) is the set of remaining unstarted processes; Equation (12) reflects the impact of key nodes on buffer absorption capacity; Equation (13) eliminates the dimensional interference between projects of different sizes through relative proportions, and S*remain(i) is the set of all subsequent processes of process i.

[0136] Step 4: Heuristic rule scheduling for intermediate disturbances.

[0137] In the hierarchical response framework, when the disturbance develops to the moderate stage, the time buffer configured in the proactive stage is no longer sufficient to fully absorb the time deviation, but the overall system resource structure and process network remain stable. At this time, it is necessary to perform limited reconfiguration of the scheduling sequence of processes that have not yet been executed, under the premise of satisfying process priority relationships and resource constraints.

[0138] (1) Identification of disturbance-dominant constraints.

[0139] To identify the dominant constraints of disturbances, three indicators are introduced: delivery urgency (TU), resource criticality (RC), and network complexity (NC). RC describes the deviation between peak resource demand and supply capacity, while NC measures the amplification potential of network connection density on disturbance propagation. The formula is:

[0140] (14)

[0141] (15)

[0142] In formula (14), K is the total number of resource types, including all updatable resource types such as equipment, tooling, and personnel; T is the set of all time points within the scheduling cycle; Rdemand k(t) represents the instantaneous demand of the k-th type of resource at time t, that is, the sum of the demand of all activities executed at that time for this type of resource; Ravai k represents the total available amount of the k-th type of resource, which is determined by the project resource configuration; in formula (15), E is the total number of edges in the project network, that is, the number of predecessor and successor relationships; and N is the total number of processes.

[0143] (2) Prioritize situations based on time urgency.

[0144] When time urgency (TU) dominates, the main risk of the system is the continuous deviation of the project completion time. A hybrid sorting mechanism is constructed by selecting the maximum position weight rule (GRPW) and the shortest process priority rule (SPT). The resource intensity rule (RI) is introduced as an auxiliary constraint to suppress resource conflicts that may be caused by time-oriented sorting.

[0145] (3) The order of resource tension as the dominant factor.

[0146] When resource stress (RC) is the dominant factor, the system bottleneck is mainly manifested as an imbalance between resource supply and demand. The maximum resource demand rule (GRD) and the SPT rule are combined. GRD prioritizes the processes with higher resource demand, while SPT accelerates the release of resources by prioritizing shorter processes.

[0147] (4) Structural coupling-dominated case reordering.

[0148] When network complexity (NC) dominates, the disturbance risk mainly comes from the enhanced coupling of the process network structure and the delay propagation effect. The rule with the most subsequent processes (MIS) and the rule with the fewest subsequent processes (LNS) are combined to control the influence range of critical nodes and reduce network tail backlog.

[0149] Step 5: Two-stage reactive scheduling based on multi-strategy uncertainty-aware NSGA-II.

[0150] When the disturbance level develops to a severe level, the existing time buffer can no longer absorb the actual execution deviation, and the critical path structure and resource allocation relationship are substantially changed. Here, while retaining the basic evolutionary framework of NSGA-II, a multi-strategy uncertainty perception mechanism is introduced to construct the MUA-NSGA-II algorithm to reconstruct the remaining unfinished processes as a whole.

[0151] (1) Design of cross operator with uncertainty perception.

[0152] By introducing an uncertainty perception index, the process structure that contributes significantly to scheduling stability is selectively retained during the crossover process, thus constructing two core indicators: process start time stability and adjustment cost impact.

[0153] (16)

[0154] Among them, s i,p sbase i,p represents the start time of process i in the p-th parent chromosome, and sbase i,p represents the start time of this process in the baseline scheme generated by proactive scheduling. p=1,2 correspond to two parent individuals respectively. The value range of this index is (0,1], and the larger the value, the more stable the start time of the process.

[0155] (17)

[0156] Among them, 𝑤 𝑖 The process weight is 2 when process 𝑖 is on the critical path of any parent individual; otherwise, it is 1. |Succ(𝑖)| represents the number of successor activities of process 𝑖. The more successor activities there are, the greater the chain reaction of the change in the order of the process on subsequent processes, and the higher the adjustment cost.

[0157] (18)

[0158] in, and These represent the impact of normalized start time stability and adjustment cost, respectively. 𝛼 and 𝛽 are weighting coefficients used to adjust the relative importance of scheduling stability and adjustment cost in cross-decision-making.

[0159] (19)

[0160] Examples of uncertainty-aware crossover operator design Figure 2 As shown, based on process topology and elite activity selection, by comparing the activity sequences of parents p1 and p2 with offspring d and s, the crossover mechanism that preserves a highly stable process structure is intuitively presented, which effectively improves the quality of genetic search.

[0161] (2) Design of uncertainty-aware permutation mutation operator.

[0162] The uncertainty of the work process is quantified using the coefficient of determination R² of the work time prediction model. The process is divided into three levels: high, medium, and low, and assigned decreasing variation probabilities. A feasible region-restricted permutation mechanism is designed, defining the feasible permutation variation interval [L] for process j. j U j ]for:

[0163] (20)

[0164] Where pos(·) represents the position index of the process in the current chromosome, and Pred(j) and Succ(j) represent the sets of the immediate predecessor and immediate successor processes of process j, respectively.

[0165] The definition of the variation range of process substitution is as follows: Figure 3 As shown, the “displaceable range” of process 5 between the preceding and succeeding activity sets clearly delineates the dynamic permutation boundary that satisfies process priority constraints, ensuring that the variation operation is carried out within the feasible domain.

[0166] (3) Skip-type SSGS decoding.

[0167] A jump-SSGS decoding strategy is designed based on the classic SSGS. This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to critical time points where resource states may change, thereby improving computational efficiency while maintaining the scheduling generation logic. The jump-SSGS decoding logic is as follows: Figure 4 As shown, the display illustrates the resource status changes and skip-time node selection of the process along the timeline. Compared to the traditional unit-by-unit-time scanning and event-driven skip mechanism, it intuitively highlights the elimination of computational redundancy and the improvement in efficiency. The pseudocode for skip-based SSGS decoding is shown in Table 1.

[0168] Table 1. Pseudocode of the skip-style SSGS decoding algorithm

[0169]

[0170] (4) Dynamic congestion setting.

[0171] Differentiated crowding assignment rules are used based on the location attributes of individuals in the Pareto front, including a boundary individual protection mechanism and an intermediate individual adaptive calculation mechanism; boundary individuals are assigned an infinitely large crowding distance.

[0172] (twenty one)

[0173] For the intermediate individual, their contribution to crowding on this dimension is:

[0174] (twenty two)

[0175] The total crowding distance of an individual can be obtained by summing the crowding contributions of each objective dimension.

[0176] (twenty three)

[0177] This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to key time points where resource states may change, thereby improving computational efficiency while maintaining the scheduling generation logic. Unlike traditional methods, Jump-SSGS does not examine consecutive time points one by one, but instead constructs a set of resource change time points and selects candidate times from this set for scheduling decisions.

[0178] Example:

[0179] 1. Experimental Design

[0180] To verify the effectiveness of the proposed method, the experimental hardware environment consisted of an Intel(R) Core(TM) i5-9400 CPU with a clock speed of 2.90 GHz, 8 GB of memory, and Windows 10 operating system. The algorithm was implemented using Python 3.8. All comparison algorithms were run under the same hardware environment and parameter settings to ensure the fairness and comparability of the experiment. The parameter settings for the reactive scheduling phase are shown in Table 2.

[0181] Table 2 Algorithm parameter settings for the reactive scheduling phase

[0182]

[0183] Regarding the test data, the experimental examples selected standard examples of four sizes from the PSPLIB example library: J30, J60, J90, and J120. Since the process times in the original PSPLIB examples are deterministic, while this invention studies dynamic scheduling problems that consider time uncertainty, the examples need to be modified to convert the deterministic time times into stochastic time times.

[0184] In terms of evaluation metrics, this invention comprehensively evaluates the algorithm's performance from two aspects: MUA-NSGA-II optimization performance and reactive scheduling application performance, to fully reflect the differences in performance of different methods in terms of solution set quality and scheduling execution. First, regarding multi-objective optimization performance, the experiment uses defined AC and Makespan as dual optimization objectives, and evaluates the algorithm's performance based on these. To measure the convergence and distribution uniformity of the algorithm in the objective space, this invention selects three commonly used multi-objective optimization evaluation metrics to comprehensively measure the algorithm's performance. Among them, the Mean Ideal Distance (MID) measures the closeness of the algorithm's solution set to the ideal solution, reflecting the algorithm's convergence performance; the Spacing (SNS) metric characterizes the distribution uniformity of the solution set in the objective space, thus evaluating the diversity of the solution set; and the Rate of Achievement of Objectives (RAS) comprehensively evaluates the overall effectiveness of the algorithm in multi-objective optimization. These metrics have been widely used in research on multi-objective resource-constrained project scheduling problems. The calculation methods for each evaluation metric are shown below.

[0185] (twenty four)

[0186] (25)

[0187] (26)

[0188] Where n represents the number of solutions in the Pareto front; f 1i and f 2i f1 and f2 represent the values ​​of the i-th solution on the two objective functions AC and Makespan, respectively; f1 and f2 represent the ideal values ​​(optimal values) of the two objectives, respectively.

[0189] 2. Algorithm Result Comparison and Solution Demonstration

[0190] The experiment aimed to minimize AC and Makespan as dual optimization objectives. Under uniform test cases and consistent parameter settings, multiple independent runs were performed on test cases of different sizes, and the performance results of each algorithm were calculated based on evaluation metrics. The average differences in comprehensive performance of each algorithm across MID, SNS, and RAS metrics are shown in Table 3. Radar charts of the comprehensive performance of four typical algorithms under multiple test case scales are shown below. Figure 5 As shown, the performance differences between MUA-NSGA-II and GABMA, TS-EP-NSGA-II, and MOPSO were compared through three dimensions: MID (convergence), SNS (diversity), and RAS (overall performance).

[0191] Table 3. Overall performance differences of different algorithms across MID, SNS, and RAS metrics.

[0192]

[0193] Experimental data show that, across four test scales (J30, J60, J90, and J120), the algorithm of this invention achieves the minimum value in the MID metric, indicating superior solution set convergence compared to the comparative algorithms. In the SNS metric, the algorithm of this invention also exhibits a lower spacing level, suggesting a more uniform distribution of the obtained solution set and better diversity characteristics. In the RAS metric, the algorithm of this invention maintains a high or optimal level overall, reflecting its stable advantage in multi-objective comprehensive optimization. As the test scale increases, the performance differences of the comparative algorithms further amplify, while the algorithm of this invention still maintains a relatively balanced performance across the three metrics. Combining the tabular data and graphical results, it can be seen that the MUA-NSGA-II algorithm proposed in this invention achieves simultaneous improvement in the quality and stability of the scheduling solution without significantly increasing computational complexity, verifying its effectiveness and engineering application potential in complex RCPSP scenarios.

[0194] Table 4 shows the average C-values ​​of MUA-NSGA-II and the comparison algorithms for different scale examples. The comparison bar chart is shown below. Figure 6 As shown, the Pareto solution set generated by the algorithm of this invention dominates the solution sets of other comparative algorithms under different scale examples from J30 to J120, clarifying its dominant advantage in high-dimensional complex spaces.

[0195] Table 4. Average C-values ​​of MUA-NSGA-II and the comparison algorithms under different scale examples.

[0196]

[0197] The results show that, across the four problem sizes (J30, J60, J90, and J120), MUA-NSGA-II maintains a consistently high level of solution set coverage compared to GAMBA, TS-EP-NSGA-II, and MOPSO. At the J120 scale, MUA-NSGA-II's coverage of GAMBA, MOPSO, and TS-EP-NSGA-II is 0.757784, 0.776623, and 0.556429, respectively, all significantly higher than the reverse coverage. This indicates that the solution set of the algorithm from this invention exhibits a clear dominance on the Pareto front, covering approximately 55%–78% of the solutions from the comparison algorithms, while its own solution set is dominated by very few solutions. Furthermore, it can be observed that as the problem size increases from J30 to J120, the algorithm's dominance over other algorithms remains stable or even improves, while the mutual coverage among the comparison algorithms is generally low and fluctuates significantly, reflecting limitations in its solution set distribution. The aforementioned dominance relationship fully demonstrates that MUA-NSGA-II not only exhibits superior convergence when dealing with large-scale uncertain scheduling problems, but also demonstrates greater diversity of solution sets and closer proximity to the Pareto front. This enables decision-makers to provide a higher-quality set of non-dominated solutions, thereby better balancing the two objectives of completion time and scheduling stability in engineering practice.

[0198] Performance comparison of different reactive scheduling strategies at multi-instance scales Figure 7 As shown, by using three subplots—average completion time, average adjustment cost, and average response time—the TAB, RR, GR-MUA, and HR-DA (tiered response) strategies were compared horizontally, systematically verifying the synergistic optimization effect of the HR-DA strategy in terms of stability and real-time response capability. The experimental results of the tiered response mechanism's effectiveness are shown in Table 5.

[0199] Table 5 Experimental results on the effectiveness of the graded response mechanism

[0200]

[0201] The experimental results show that under small-scale cases (J30, J60), the differences in completion time and adjustment cost among the strategies are relatively small. This is because the problem scale is small, resource conflicts and network coupling are limited, and even simple strategies can achieve feasible scheduling schemes. However, in terms of response time, TAB and RR have a clear advantage due to their simple computational process, while GR-MUA has a relatively long response time due to the need to perform multi-objective optimization. As the case scale increases to J90 and J120, the performance differences among the strategies gradually become apparent. In terms of completion time, both GR-MUA and HR-DA show better optimization capabilities, but HR-DA can further reduce adjustment costs while maintaining a better completion time in most cases. This indicates that the hierarchical response mechanism has an advantage in avoiding excessive rescheduling and helps improve the stability of the scheduling scheme. In terms of response time, the computational cost of GR-MUA increases significantly with the increase of problem scale, while HR-DA effectively controls the overall computational cost by only calling the optimization algorithm under high-intensity perturbations and using rule or time adjustment strategies in low-intensity perturbation stages. In contrast, while RR has a faster response speed, it is difficult to maintain good scheduling performance under large-scale complex disturbances.

[0202] Analysis of the three indicators reveals that the HR-DA strategy exhibits relatively balanced performance across different scales. Its advantage lies in its ability to dynamically select the most suitable response method based on perturbation characteristics, thereby avoiding performance imbalances caused by a single strategy in different situations. Especially in large-scale computational examples, this strategy significantly reduces response time while ensuring scheduling quality, demonstrating good scalability and practicality.

Claims

1. A hierarchical response-responsive scheduling method based on buffer adjustment, characterized in that, First, a multi-dimensional disturbance quantification evaluation system was constructed, incorporating buffer consumption status, delivery urgency, and time prediction accuracy, to achieve quantitative assessment and classification of disturbance intensity. Second, for different levels of disturbance, time window fine-tuning, heuristic local reordering, and global rescheduling strategies were implemented to achieve differentiated dynamic repair. Finally, for the global rescheduling scenario, a multi-strategy uncertainty-aware NSGA-II algorithm was designed, improving optimization performance under complex disturbances by refining the crossover mutation operator, skip decoding, and dynamic congestion strategy. Specifically, the following steps are included: Step 1: Problem description and assumptions; In proactive scheduling facing uncertain working hours, the resilience of the baseline scheduling scheme needs to be enhanced in two ways: firstly, by predicting working hours to improve the accuracy of planned inputs as much as possible; secondly, by allocating time buffers reasonably for relevant processes based on the prediction results to absorb the impact of prediction errors and random disturbances. The essence of time buffering is to embed appropriate redundancy into the planned duration, sacrificing some time efficiency to improve the stability and reliability of the scheduling scheme during the execution phase. Proactive scheduling, by linking predicted working hours, time buffers, and planned duration, forms a baseline scheduling scheme with a certain degree of flexibility, thereby controlling the actual execution deviation within an absorbable range under most disturbance conditions and reducing the chain reaction impact on subsequent processes and the overall duration. The following basic assumptions are proposed: (1) Assume that preemption is not allowed between processes, that is, once a process starts, it must continue until it is completed; (2) It is assumed that all resources involved are updatable, that is, their availability remains unchanged in each scheduling cycle; (3) Assume that the preceding relationships of the processes are determined and known, that is, the process logic order between processes is fixed; Step 2: Objective function and constraints; Objective function: To minimize the total project duration C max Minimize the total buffer sum ∑B i Maximizing scheduling robustness 1-SC / SC max For multi-objective optimization, the mathematical expression is as follows: （1） （2） Constraints: （3） （4） （5） （6） （7） Where sT i represents the start time of activity i in the reactive scheduling phase, sB i represents the start time of activity i in the baseline scheduling scheme of the proactive scheduling phase; n represents the actual number of activities in the project, n+2 represents the total number of activities including virtual start and end nodes; sT n+2 represents the final completion time of the adjusted project. Indicates activity Start time; Indicates activity The immediate preceding set of activities; Represents the virtual start of the activity on resources The demand for it is 0. Indicates activity Resources Demand; These are 0-1 decision variables used to represent the allocation relationship between activities and resources; Indicates at time A collection of activities to be performed; Equation (1) is used to measure the magnitude of scheduling adjustment. The smaller the value, the smaller the disturbance of the original plan by the reactive scheduling and the higher the stability of the scheduling scheme. Equation (2) is used to characterize the recovery effect of project completion time under disturbance conditions. There is a certain trade-off between the two objectives: compressing project completion time usually requires a large adjustment to the original work process arrangement, while over-protecting the stability of the scheduling scheme may reduce the system's schedule recovery capability. By optimizing the above two objectives at the same time, a reasonable balance is sought between scheduling stability and recovery efficiency. Equation (3) is the work process priority constraint, which ensures that each work process can only be started after all its immediate predecessor work processes are completed. Considering that the actual work time of the work process is still uncertain before the project starts, the proactive scheduling stage uses the sum of the predicted work time and its corresponding time buffer as the planned schedule d. i Equation (4) is used to generate a baseline scheduling scheme; Equation (4) is a resource constraint condition used to ensure that at any time t, the total demand of all executing processes for the same type of resource k does not exceed the available capacity R of that resource. k To meet the actual characteristics of limited workshop resources; Equation (5) stipulates that the duration of virtual start activities and virtual end activities in the project is 0, which is used to uniformly describe the start and end boundaries of the project; Equation (6) stipulates that virtual start activities and virtual end activities do not consume any resources, so as to avoid additional impact on resource constraints; Equation (7) is a decision variable constraint, which is used to characterize the allocation relationship between activities and resources; Step 3: Multidimensional disturbance assessment and graded response mechanism; Under slight disturbances, a buffer time window fine-tuning strategy is adopted. Existing time buffers are dynamically reallocated to restore scheduling feasibility without changing the original process sequencing and resource allocation framework. The specific implementation steps are as follows: (1) Calculation of the total remaining buffer; Calculate the total remaining buffer for all unstarted processes after the disturbance occurs. This total is composed of the original buffer configuration minus the consumed portion and the actual overdue amount, reflecting the scale of time redistribution available. (2) Calculation of basic allocation weights; The basic allocation weight of each process is calculated based on the predicted working time percentage of the remaining processes. This weight reflects the impact of the process working time scale on buffer demand. The longer the working time of a process, the more buffer is theoretically needed to cope with uncertainty. (3) Uncertainty and importance coefficient correction; An uncertainty coefficient is introduced to correct the basic weights. This coefficient is obtained by normalizing the process prediction accuracy. Processes with lower prediction accuracy are assigned a higher uncertainty coefficient, thus gaining more protection in the buffer allocation. At the same time, an importance coefficient is introduced to further adjust the allocation weights. This coefficient is based on the criticality of the process in the network. Processes with higher criticality receive a greater weight gain. (4) Comprehensive allocation factor and buffer reallocation; A comprehensive allocation factor is constructed by combining the uncertainty coefficient and the importance coefficient, and the remaining buffer amount is allocated proportionally according to this factor to obtain the adjusted buffer configuration for each process. The mathematical expression of the above process is as follows: （8） （9） （10） （11） （12） （13） in, Indicate process Predicted working hours Indicates the weight of the uncertainty level coefficient; The normalized uncertainty coefficient is used to quantify uncertainty and correct the basic allocation weights in a buffer time window fine-tuning strategy for minor perturbations. Indicate process Key weights; Indicate process The proportion of the predicted working hours to the total predicted working hours of all remaining unstarted processes; Indicate process The criticality of intermediate quantities; The basic weight representing the process itself; Equations (8) and (9) determine the remaining buffer size and its proportional structure, buffersize' i The adjusted time buffer size for process i, buffersize i For the original buffer configuration of process i, B total e represents the original buffer amount for all processes that have not yet started after the disturbance process. true,i Δ' is the latest completion time calculated according to the rules for disturbance process i. i The comprehensive allocation factor for process i; Equations (10) and (11) are obtained through Vp' i With β' i Uncertainty and structural importance are quantified and normalized, N remain The remaining unstarted process set; Equation (12) reflects the impact of key nodes on buffer absorption capacity; Equation (13) eliminates the dimensional interference between projects of different sizes through relative proportions, and S* remain(i) is the set of all subsequent processes of process i. Step 4: Heuristic rule scheduling for intermediate disturbances; In the hierarchical response framework, when the disturbance develops to the moderate stage, the time buffer configured in the proactive stage is no longer sufficient to fully absorb the time deviation, but the overall system resource structure and process network remain stable. At this time, it is necessary to perform limited reconfiguration of the scheduling order of the unexecuted processes, under the premise of satisfying the process priority relationship and resource constraints. (1) Identification of disturbance-dominant constraints; To identify the dominant constraints of disturbances, three indicators are introduced: delivery urgency (TU), resource stress (RC), and network complexity (NC). RC describes the deviation between peak resource demand and supply capacity, while NC measures the amplification potential of network connection density on disturbance propagation. The formula is: （14） （15） In formula (14), K is the total number of resource types, including all updatable resource types such as equipment, tooling, and personnel; T is the set of all time points within the scheduling cycle; Rdemand k(t) represents the instantaneous demand of the k-th type of resource at time t, that is, the sum of the demand of all activities executed at that time for this type of resource; Ravai k represents the total available amount of the k-th type of resource, which is determined by the project resource configuration; in formula (15), E is the total number of edges in the project network, that is, the number of predecessor and successor relationships; and N is the total number of processes. (2) Prioritizing situations based on time urgency; When time urgency (TU) dominates, the main risk of the system is the continuous deviation of the project completion time. A hybrid sorting mechanism is constructed by selecting the maximum position weight rule (GRPW) and the shortest process priority rule (SPT). The resource intensity rule (RI) is introduced as an auxiliary constraint to suppress resource conflicts that may be caused by time-oriented sorting. (3) Adjustment of resource scarcity as the dominant factor; When resource stress (RC) is the dominant factor, the system bottleneck is mainly manifested as an imbalance between resource supply and demand. The maximum resource demand rule (GRD) and the SPT rule are combined. GRD prioritizes the processes with higher resource demand, while SPT accelerates the release of resources by prioritizing shorter processes. (4) Sequencing in cases dominated by structural coupling; When network complexity (NC) dominates, the disturbance risk mainly comes from the enhanced coupling of the process network structure and the delay propagation effect. The rule with the most subsequent processes (MIS) and the rule with the fewest subsequent processes (LNS) are combined to control the influence range of critical nodes and reduce network tail backlog. Step 5: Two-stage reactive scheduling based on multi-policy uncertainty-aware NSGA-II; When the disturbance level reaches a severe level, the existing time buffer can no longer absorb the actual execution deviation, and the critical path structure and resource allocation relationship are substantially changed. Here, while retaining the basic evolutionary framework of NSGA-II, a multi-strategy uncertainty perception mechanism is introduced to construct the MUA-NSGA-II algorithm to reconstruct the remaining unfinished processes as a whole. (1) Design of uncertainty-aware crossover operators; By introducing an uncertainty perception index, the process structure that contributes significantly to scheduling stability is selectively retained during the crossover process, thus constructing two core indicators: process start time stability and adjustment cost impact. （16） Among them, s i,p sbase i,p represents the start time of process i in the p-th parent chromosome, and sbase i,p represents the start time of this process in the baseline scheme generated by proactive scheduling. p=1,2 correspond to two parent individuals respectively. The value range of this index is (0,1], and the larger the value, the more stable the start time of the process. （17） Among them, 𝑤 𝑖 The process weight is 2 when process 𝑖 is on the critical path of any parent individual; otherwise, it is 1. |Succ(𝑖)| represents the number of successor activities of process 𝑖. The more successor activities, the greater the chain reaction of the change in the order of the process on subsequent processes, and the higher the adjustment cost. （18） in, and These represent the impact of normalized start time stability and adjustment cost, respectively, with 𝛼 and 𝛽 being weighting coefficients used to adjust the relative importance of scheduling stability and adjustment cost in cross-decision-making; （19） (2) Design of uncertainty-aware permutation mutation operators; The uncertainty of the work process is quantified using the coefficient of determination R² of the work time prediction model. The process is divided into three levels: high, medium, and low, and assigned decreasing variation probabilities. A feasible region-restricted permutation mechanism is designed, defining the feasible permutation variation interval [L] for process j. j U j ]for: （20） Where pos(·) represents the position index of the process in the current chromosome, and Pred(j) and Succ(j) represent the sets of the immediate predecessor and immediate successor processes of process j, respectively; (3) Skip-type SSGS decoding; Based on the classic SSGS, a skip-type SSGS decoding strategy is designed. This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to key time points where resource status may change, thereby improving computational efficiency while keeping the scheduling generation logic unchanged. (4) Dynamic congestion setting; Differentiated crowding assignment rules are used based on the location attributes of individuals in the Pareto front, including a boundary individual protection mechanism and an intermediate individual adaptive calculation mechanism; boundary individuals are assigned an infinitely large crowding distance. （21） For the intermediate individual, their contribution to crowding on this dimension is: （22） The total crowding distance of an individual can be obtained by summing the crowding contributions of each objective dimension. （23） This strategy replaces the time-by-time scanning mechanism with an event-driven mechanism, limiting resource feasibility checks to key time points where resource status may change, thereby improving computational efficiency while keeping the scheduling generation logic unchanged.

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