A Smart Modeling Method for Combinatorial Optimization Problems

Abstract

This invention discloses an intelligent modeling method for combinatorial optimization problems, comprising: obtaining a demand description in natural language form to generate a disambiguated set of production constraints; constructing and solving an initial scheduling model based on the disambiguated set of production constraints, identifying and supplementing implicit constraints by analyzing abnormal features to form a complete set of production constraints; constructing and repairing a mathematical optimization model based on the complete set of production constraints to obtain a feasible production scheduling model; and solving the feasible production scheduling model to generate a production scheduling execution plan. This invention can improve the automation and intelligence level of modeling, reduce reliance on expert experience, and quickly obtain a feasible optimization model that highly fits the actual business scenario.

Description

Technical Field

[0001] This invention belongs to the field of intelligent modeling, and in particular to an intelligent modeling method for combinatorial optimization problems. Background Technology

[0002] In the development of intelligent manufacturing, how to quickly and accurately transform complex and dynamically changing production demands into solvable mathematical optimization models has become a core bottleneck in improving enterprises' intelligent decision-making capabilities and achieving lean production. Therefore, researching efficient and intelligent modeling methods for combinatorial optimization problems not only has significant theoretical value but also carries practical significance in promoting industrial digital transformation and enhancing core competitiveness. It is a cutting-edge topic of common concern to both academia and industry.

[0003] Currently, the modeling process for combinatorial optimization problems largely relies on the deep involvement of operations research (OR) experts. Mainstream modeling approaches include using algebraic modeling languages ​​(such as AMPL and GAMS) or optimization libraries integrated into general-purpose programming languages ​​(such as Pyomo in Python). These methods require modelers to possess strong mathematical skills, enabling them to accurately translate business logic into mathematical constraints and objective functions. In recent years, with the development of Natural Language Processing (NLP) technology, some research has begun to explore using NLP techniques to automatically extract entities and basic constraints from requirements documents to aid in modeling. These methods are typically based on template matching or keyword recognition, capable of handling some structured and clearly articulated requirements. In specific, mature application scenarios (such as the standardized description of the Vehicle Routing Problem (VRP), they have shown certain automation potential, reducing some of the data entry and processing work for modelers.

[0004] However, existing technologies still face several specific and profound technical challenges in transforming real, original business requirements into high-quality, solvable optimization models. In summary, existing technologies mainly suffer from three major problems: a semantic understanding gap, blind spots in model construction, and a broken chain in conflict resolution. In front-end requirement understanding, it is difficult to effectively bridge the semantic gap between the vague, colloquial natural language of business personnel and the rigorous, precise mathematical forms of optimization models. In middle-stage model construction, there is a lack of proactive review and diagnostic mechanisms, resulting in blind spots in discovering implicit constraints that users may overlook due to habitual usage. In back-end model debugging, the inability to trace mathematical conflicts returned by the solver back to their original business requirements creates a broken chain in the troubleshooting process from error location to root cause analysis. Summary of the Invention

[0005] The purpose of this invention is to provide an intelligent modeling method for combinatorial optimization problems, in order to solve at least one technical problem existing in the prior art.

[0006] Technical solution: An intelligent modeling method for combinatorial optimization problems, comprising:

[0007] Obtain the requirements description in natural language form and generate a disambiguated set of production constraints;

[0008] Implicit constraints are discovered based on the disambiguated production constraint set, forming a complete production constraint set.

[0009] A feasible production scheduling model is obtained by constructing and repairing a mathematical optimization model based on the complete set of production constraints.

[0010] Solve for a feasible production scheduling model and generate a production scheduling execution plan.

[0011] Beneficial effects: This invention can improve the automation and intelligence of modeling, reduce reliance on expert experience, and quickly obtain feasible optimization models that are highly consistent with actual business scenarios. Attached Figure Description

[0012] Figure 1 A flowchart illustrating the steps of an intelligent modeling method for combinatorial optimization problems provided in this application embodiment.

[0013] Figure 2 A flowchart illustrating the steps for forming a complete set of production constraints, provided in an embodiment of this application.

[0014] Figure 3 A flowchart illustrating the steps for identifying abnormal features in scheduling results provided in this application embodiment.

[0015] Figure 4 A flowchart illustrating the steps for reasoning implicit constraints based on abnormal features, provided in an embodiment of this application. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0017] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0018] The research revealed a significant semantic gap between the natural language descriptions used by business users and the rigorous mathematical expressions required for optimizing solvers. Business users frequently use vague terms like "approximately," "as soon as possible," and "around," or omit implicit boundary conditions. Existing NLP technologies often stop at surface entity extraction, lacking mechanisms to effectively clarify deep semantic ambiguities. This introduces uncertainty into model building from the outset, requiring multiple rounds of inefficient communication between modeling experts and business experts to reach a consensus, thus prolonging the modeling cycle.

[0019] The blind spot in model building lies in the fact that existing methods are passive modeling methods, relying entirely on explicit constraints provided by the user. However, in actual production, many key constraints are implicit, rooted in industry practices, unwritten rules within the workshop, or physical dependencies between equipment, which users often overlook due to their familiarity. Existing modeling tools cannot proactively and forward-lookingly discover these overlooked implicit constraints, resulting in initial models that are often out of touch with reality. Solution solutions based on such models will expose various anomalies in actual implementation (such as severe equipment load imbalance and excessive personnel fatigue), lacking practical value.

[0020] The problem of broken chains in conflict resolution is particularly prominent. When multiple constraints contradict each other, rendering the model infeasible, the optimization solver can only return a minimal infeasible subset (IIS) consisting of mathematical expressions. There is a completely broken traceability chain between this code-level conflict and its root cause—the original business layer requirement. Current technology cannot automatically map mathematical conflicts back to specific, contradictory natural language requirement descriptions, making model debugging akin to the blind men and the elephant, requiring extensive manual investigation and logical reasoning by experts from multiple domains, resulting in extremely high costs for locating and fixing conflicts.

[0021] like Figure 1 As shown, an intelligent modeling method for combinatorial optimization problems is proposed, including the following steps:

[0022] Obtain the requirements description in natural language form and generate a disambiguated set of production constraints.

[0023] Specifically, the system first receives a user's requirement description in natural language text format. For example, a description might read: Order A requires 100 units of product P1, which must be completed by Friday. Producing product P1 requires first performing process G1 on equipment M1, and then process G2 on equipment M2. Equipment M1 has a capacity of approximately 20 units per day, and equipment M2 has a capacity of 30 units per day. Operators Xiao Wang and Xiao Li can operate equipment M1, but only Xiao Wang can operate equipment M2. Upon receiving this text, the system uses natural language processing technology for parsing. For example, it uses rule-based named entity recognition technology to identify production element entities such as order A, product P1, equipment M1, process G1, and operator Xiao Wang. For potentially ambiguous statements in the text, such as "complete by Friday" or "capacity approximately 20 units per day," the system initiates an interactive disambiguation process. This process transforms vague statements into precise, unambiguous constraints by asking the user clarifying questions. For example, the system might ask if "complete by Friday" includes Friday itself. Ultimately, all the original, vague requirements are transformed into a precise set of production constraints that are understandable to machines.

[0024] Implicit constraints are discovered based on the disambiguated production constraint set, forming a complete production constraint set.

[0025] In this embodiment, after obtaining a preliminary, explicit constraint set, the system recognizes that the user may have overlooked some industry practices or potential rules within the workshop, i.e., implicit constraints. To discover these implicit constraints, an initial, potentially incomplete, scheduling model is constructed using the disambiguated production constraint set and solved quickly. The system analyzes possible abnormal patterns in the initial solution. For example, if the initial solution shows that the utilization rate of a certain piece of equipment is much lower than that of other equipment, or that a worker's overtime hours are abnormally concentrated, the system will infer potential implicit constraints based on these abnormal characteristics. For example, an imbalance in equipment utilization may suggest the existence of unstated process dependencies or equipment-specific constraints. The system adds these inferred implicit constraints to the constraint set after confirming them with the user or conducting a confidence assessment based on historical data, thereby forming a more comprehensive and realistic complete set of production constraints.

[0026] A feasible production scheduling model is obtained by constructing and repairing a mathematical optimization model based on the complete set of production constraints.

[0027] In this embodiment, the system automatically converts the complete set of production constraints into standard mathematical expressions. For example, time constraints are converted into linear inequalities, and resource allocation constraints are converted into 0-1 variable constraints. These mathematical expressions together constitute a mathematical optimization model, such as a mixed integer programming (MIP) model. Simultaneously with model construction, the system establishes a constraint traceability graph. This graph records the complete mapping link from the final mathematical constraints to their original natural language requirement descriptions. After model construction is complete, the solver may detect model infeasibility, i.e., all constraints cannot be satisfied simultaneously. At this point, using this infeasibility state, the minimum infeasible subset (IIS) causing the conflict is calculated. With the constraint traceability graph, the system can quickly locate which original requirement descriptions conflict. For example, it may locate a conflict between the original requirement of completing 100 products within 3 days and the equipment's daily capacity of only 20 units. Based on this, remedial suggestions are generated, such as extending the delivery period or adding temporary equipment, and the user-selected remedial strategy is applied to ultimately obtain a mathematically feasible production scheduling model.

[0028] Solve for a feasible production scheduling model and generate a production scheduling execution plan.

[0029] In this embodiment, after obtaining the feasible model, a professional optimization solver (such as Gurobi or CPLEX) is invoked to solve the feasible production scheduling model. The goal of the solution process is usually to optimize one or more key performance indicators (KPIs), such as minimizing total completion time or maximizing equipment utilization. After the solution is completed, the system parses and transforms the mathematical solution (i.e., the values ​​of a series of variables) into a human-readable and directly executable production scheduling plan. This plan is usually presented in the form of a Gantt chart or a work list, detailing in detail which time period, which equipment, and which worker will perform which production task. In addition, an evaluation report is also attached, containing predicted values ​​of key indicators such as equipment utilization, order completion rate, and personnel load balancing, for managers to evaluate and make decisions.

[0030] Optionally, intelligent modeling methods for combinatorial optimization problems can be applied to fields such as industrial manufacturing, logistics scheduling, and resource allocation, and executed through computer programs. For example, they can be deployed on servers or cloud platforms, where users input their production scheduling requirements through a client interface, and the system automatically completes the modeling and solution.

[0031] According to one aspect of this application, a disambiguated set of production constraints is generated, specifically including:

[0032] Calculate the ambiguity score for the constraint statements in the requirement description, and identify ambiguous constraints based on the ambiguity score.

[0033] In this embodiment, after receiving the natural language demand description and extracting the initial constraint statements, the system needs to quantify the semantic uncertainty of each statement. Specifically, for each constraint statement extracted from the text, such as the production capacity of device M1 being approximately 20 units per day, the system encodes it into a high-dimensional semantic vector using a pre-trained industrial domain language model (such as an industry variant of BERT). Simultaneously, the system constructs a candidate interpretation set for this statement, for example, {production capacity ≤ 20 units / day, production capacity < 20 units / day, production capacity ∈ [18, 22] units / day}. Each candidate interpretation is also encoded into a semantic vector. The system calculates the cosine similarity between the vector of the original statement and the vector of each candidate interpretation. Ambiguity score S ambi Defined as: S ambi = 1 - max(cos(V orig V exp1 ), cos(V orig V exp2 ), ...); where V orig It is the semantic vector of the original expression, V expi Let be the semantic vector of the i-th candidate explanation, and cos() represents the cosine similarity calculation. The principle behind this scoring is that if the original expression is highly semantically similar to a candidate explanation (similarity close to 1) but significantly different from other explanations, then the expression is clear, and the ambiguity score is close to 0. Conversely, if the original expression is semantically similar to multiple candidate explanations, resulting in a low maximum similarity, then the expression is ambiguous, and the ambiguity score is high. An ambiguity threshold is set, for example, 0.6. When the S of a certain constraint expression... ambi If the value exceeds this threshold, the constraint is identified as an ambiguous constraint and proceeds to the next processing step.

[0034] Generate a set of candidate interpretations for ambiguity constraints.

[0035] Specifically, a set of multiple possible interpretations is generated for each identified ambiguous constraint. This process can be based on a predefined industry-specific ambiguous pattern library. This library contains common ambiguous types, such as: quantity ambiguity (e.g., approximately, around), which can generate range interpretations based on percentages or absolute values; boundary ambiguity (e.g., before, within), which can generate two interpretations: one including boundary values ​​(≤) and one excluding boundary values ​​(<); and range ambiguity (e.g., between A and B), which can generate interpretations including endpoints and one excluding endpoints. For example, for order A, which requires processing on equipment M1, if the system knowledge base has multiple models of equipment M1 (M1-a, M1-b), then the candidate interpretation set could be {processing on M1-a, processing on M1-b, or processing on either M1-a or M1-b}.

[0036] Calculate an information gain for each ambiguous constraint and select the ambiguous constraint with the maximum information gain to construct a discriminative problem.

[0037] In this embodiment, when multiple ambiguous constraints exist, the system needs to decide which one to clarify first. A preferred strategy is to select the one that, after clarification, brings the greatest certainty to the entire constraint system. This is achieved by calculating information gain. Specifically, the step of calculating an information gain for each ambiguous constraint includes: for each candidate interpretation in the candidate interpretation set, evaluating the degree of reduction in the uncertainty of the constraint system under the condition of adopting the candidate interpretation; and determining the information gain based on the degree of reduction. The formula for calculating information gain I(Q) is: I(Q) = H(C) - Σ a p(a) * H(C|a); where Q represents the clarification question posed for a certain ambiguous constraint; C is the current state set of the entire constraint system; H(C) is the information entropy of the entire constraint system, representing its overall uncertainty, which can be calculated as the sum of the ambiguity scores of all ambiguous constraints; a is a possible answer of the user to question Q (i.e., choosing a candidate interpretation); p(a) is the prior probability of the user choosing answer a, which can be initially assumed to be equal; H(C|a) is the conditional entropy of the remaining uncertainty of the system given that the user's answer is a. In other words, when an ambiguity is clarified, it may also eliminate the ambiguity of other related constraints, thereby reducing the total entropy of the system. The system iterates through all ambiguous constraints to be clarified, calculating the information gain for each constraint. Choosing the ambiguous constraint with the largest I(Q) means that clarifying it can minimize the uncertainty of the entire system. After selecting the constraint, the system analyzes the key differences between its candidate interpretations and constructs a discriminative question. For example, if the candidate interpretation is {x≤100, x<100}, the system will generate the question: When you say no more than 100, does it include the case of equal to 100?

[0038] Obtain user feedback on the distinguishability question, and determine the constraint interpretation from the candidate interpretation set based on the user feedback to form the disambiguated production constraint set.

[0039] Specifically, the system presents the constructed discriminative question to the user through an interface and receives the user's selection or input. The user's feedback directly determines the final accurate interpretation of the ambiguous constraint. This interpretation is then updated in the production constraint set, and its status is marked as confirmed.

[0040] Furthermore, after obtaining user feedback, it also includes:

[0041] Based on user feedback, the system updates the user expression preference model. Specifically, the system records users' selection habits. For example, if a user repeatedly selects an explanation containing boundary values ​​in scenarios not exceeding a certain limit, the system will build or update the user's preference model, recording their tendency to use expressions with non-strict inequalities.

[0042] Among the remaining ambiguous constraints, identify those with similar linguistic structures to the clarified constraints. This can be achieved by analyzing the structural similarity of the dependency syntax trees of the constraint representations.

[0043] By applying a user expression preference model, constraints with similar linguistic structures are automatically interpreted, reducing the number of user interactions. For example, when the system subsequently encounters another constraint, "Inventory not exceeding 50 units," and its linguistic structure is similar to the previously clarified "Production capacity not exceeding 100 units," the system will automatically interpret it as "Inventory ≤ 50 units" using the user preference model, without requiring further user interaction. This disambiguation result propagation mechanism effectively reduces the user's interaction burden and improves modeling efficiency.

[0044] This embodiment calculates the information gain of each ambiguous constraint, prioritizing questions that, once clarified, contribute the most to the determinism of the entire constraint system. This minimizes the overall uncertainty of the system with each user interaction. The user expression preference model established by the system learns users' language habits and automatically infers ambiguities with similar structures. Compared to traditional sequential or random questioning methods, this reduces the number of user interactions, improves modeling efficiency, and further reduces the cognitive burden on users through the disambiguation result propagation mechanism.

[0045] like Figure 2 As shown, according to one aspect of this application, a complete set of production constraints is formed, including:

[0046] Based on the disambiguated production constraint set, an initial scheduling model is constructed and solved, and an initial scheduling scheme is derived.

[0047] Specifically, an initial mathematical optimization model, such as a linear programming or mixed-integer programming model, is constructed using the obtained disambiguated set of production constraints that contains only the explicit constraints specified by the user. In this model, decision variables x[i, j, k] can be defined, representing that order i is processed by worker k on machine j. The objective function can be set as a basic objective, such as minimizing the total completion time of all orders (minimizeΣ completion time). A commercial solver is then invoked to quickly solve this initial model, not necessarily for the optimal solution, but to quickly obtain a baseline initial scheduling scheme. This scheme reflects the theoretical results of production scheduling only under the constraints explicitly stated by the user.

[0048] Analyze the initial scheduling scheme and identify abnormal features in the scheduling results.

[0049] After obtaining the initial scheduling plan, the system performs a multi-dimensional review of its rationality to proactively identify potential problems. In this embodiment, such as... Figure 3 As shown, the abnormal features identified in the scheduling results specifically include:

[0050] Based on the initial scheduling scheme, multi-dimensional anomaly detection indicators are calculated; among them, the multi-dimensional anomaly detection indicators include at least one of resource utilization balance, continuous working time of personnel, and process waiting time.

[0051] As a preferred implementation, the system calculates six types of anomaly detection indicators to form an anomaly feature vector: Resource utilization balance: Calculates the ratio of the standard deviation to the average utilization of all similar resources (such as equipment or personnel): σ(utilization) / μ(utilization). A larger ratio indicates a more unbalanced load, where σ represents the standard deviation, μ represents the average, and utilization represents resource utilization; Continuous working time of personnel: Finds the longest continuous uninterrupted working time among all personnel: max(continuous working hours); Process waiting time: Calculate the proportion of total invalid waiting time between processes for all orders to the total production time: Σ(Inter-process waiting) / Total production time; Order completion time dispersion: Calculate the ratio of the standard deviation to the mean of the completion times of similar or all orders: σ(Completion time) / μ(Completion time), used to measure the stability of delivery; Equipment idle rate: Calculate the ratio of the total idle time to the total available time of critical equipment: Σ(Idle time) / Total available time; Batch changeover frequency: Calculate the number of times the product type is changed on the equipment within the planning period: count(Product changeover) / Total number of batches, where count represents counting operations.

[0052] Multidimensional anomaly detection indicators are compared with preset industry standard thresholds to determine anomaly characteristics.

[0053] Specifically, the system has a built-in configurable library of industry-standard thresholds. For example, if the calculated resource utilization balance is greater than 0.5, it is marked as a load imbalance anomaly; if personnel work continuously for more than 10 hours, it is marked as a fatigue work anomaly; if the idle rate of a critical piece of equipment is greater than 40%, it is marked as a capacity configuration anomaly. For each triggered anomaly, the system also calculates its severity score, for example, severity score = (actual value - threshold) / threshold. This ultimately forms a set of anomaly patterns containing information such as anomaly type, location of occurrence, and severity.

[0054] Implicit constraints are inferred based on abnormal features, and the implicit constraints are merged with the disambiguated production constraint set to generate a complete production constraint set.

[0055] In this embodiment, as Figure 4 As shown, the implicit constraints are inferred based on abnormal features, specifically including:

[0056] An anomaly severity score is determined for the anomaly features; based on the anomaly features, a candidate implicit constraint set is generated by applying a pre-defined anomaly constraint inference rule base; each rule in the anomaly constraint inference rule base is associated with a rule reliability.

[0057] Specifically, the system maintains a rule base for inference, establishing a mapping relationship between abnormal patterns and potentially missing constraints. Each rule is set based on industry knowledge and expert experience, and is accompanied by a rule reliability calculated based on historical verification accuracy. For example, the rule base may contain the following rules: Rule 1: If there is a load imbalance anomaly, and analysis reveals that the utilization rate of certain specific equipment is consistently below 20%, then it is inferred that there may be a missing equipment capacity difference constraint or a specific matching constraint between processes and equipment. Rule 2: If there is a fatigue operation anomaly, then it is inferred that there is a missing daily working time limit constraint or a missing shift system constraint. Rule 3: If the order completion time dispersion is abnormal, and the processing time difference with similar orders exceeds 50%, then it is inferred that there is a missing batch production optimization constraint.

[0058] By combining the anomaly severity score and rule reliability, a confidence score is calculated for each candidate implicit constraint in the candidate implicit constraint set, and the implicit constraint is determined based on the confidence score.

[0059] In this embodiment, in order to evaluate the value of each candidate constraint and avoid introducing unnecessary constraints, the system calculates a confidence score C for it. score :C score = W s * S severe + W r * R rule + W c * C context ; where C score It is the final confidence score; S severe It is the severity score of the abnormality; R rule It is the reliability of the rule that triggers this reasoning; C context It is contextual relevance, calculated by analyzing whether there are relevant clues in the original problem description; W s W r W cThese are the weighting coefficients of the three factors, which sum to 1. For example, they can be set to 0.4, 0.4, and 0.2 respectively. The system will select candidate constraints with confidence scores higher than a certain threshold (e.g., 0.7) as high-value implicit constraints to be confirmed.

[0060] This embodiment constructs an initial scheduling model and calculates a six-dimensional anomaly feature vector (resource utilization balance, continuous working hours of personnel, process waiting time, etc.), enabling it to infer implicit constraints not explicitly expressed by the user from anomaly patterns in scheduling results. Compared to traditional methods relying on predefined rule bases, it can discover unique constraint requirements in specific production scenarios. For example, when the system detects a pattern where most workers' daily working hours are abnormally concentrated, it automatically infers the lack of a daily working time limit constraint, avoiding unreasonable scheduling schemes caused by insufficient user experience or oversights in expression. This improves the accuracy and completeness of implicit constraint discovery while reducing reliance on domain experts.

[0061] Optionally, before merging the set of high-confidence implicit constraints with the disambiguated production constraints, a verification and calibration process is also included:

[0062] Based on the received user feedback, implicit constraints are classified into hard constraints that must be met and soft constraints that can be violated but are subject to penalties.

[0063] Specifically, the system will present high-confidence candidate implicit constraints to users in a visual manner. For example, it can highlight excessively long working hours caused by the lack of a daily working hour limit constraint on a Gantt chart. Users can label each constraint as: must be met (hard constraint), try to meet (soft constraint), or not needed.

[0064] For soft constraints, obtain the strength of user preferences.

[0065] Specifically, for soft constraints that users mark as something to be satisfied as much as possible, the system will further ask users to give a preference strength score of 1-10. This score represents the user's level of acceptability of violating the constraint, with a higher score indicating a greater unwillingness to have it violated.

[0066] Sensitivity analysis of soft constraints is performed to quantify the impact of soft constraints on the objective function of the initial scheduling model and obtain sensitivity indices.

[0067] In this embodiment, sensitivity analysis is performed using the parameter perturbation method. For example, to ensure that the daily working hours are not more than 10 hours under the soft constraint, the system will test the rate of change of the model's overall objective function value when this upper limit is perturbed within ±20% (e.g., 8 to 12 hours). Sensitivity index S sense Calculated as: S sense= ΔObjective / ΔParameter; where ΔObjective is the change in the objective function value, and ΔParameter is the change in the constraint parameters. sense The larger the absolute value of the soft constraint, the greater its influence on the final solution.

[0068] By combining user preference intensity and sensitivity indicators, penalty weights are determined for soft constraints.

[0069] Specifically, the penalty weight W is used to penalize violations of soft constraints in the objective function of the final mathematical model. The formula for calculating the penalty weight is: W penalty = I pref * S norm * W base ; where I pref It is the strength of the preference given by the user (e.g., 1-10 points); S norm It is a normalized sensitivity index, ensuring its value is within the range [0, 1]; W base It is a baseline weighting coefficient used to adjust the overall magnitude of all soft constraint penalties. Each implicit constraint is processed in a refined manner; hard constraints are directly added to the model, while soft constraints are added to the objective function as weighted penalty terms, ultimately forming a complete production constraint set with comprehensive constraints and reasonable parameter calibration.

[0070] This embodiment combines user preference intensity scores, normalized sensitivity indices derived from sensitivity analysis, and baseline weights to automatically calculate penalty weights for soft constraints. Traditional qualitative preferences (such as minimizing overtime) are transformed into precise numerical parameters in the optimization model. Sensitivity analysis accurately assesses the impact of constraints on the objective function through parameter perturbations, enabling the optimization solver to find the optimal balance between completing production tasks and satisfying soft constraints. Compared to manually setting weights, this improves the overall satisfaction of the scheduling scheme while avoiding solution bias problems caused by improper weight settings.

[0071] According to one aspect of this application, a feasible production scheduling model is obtained, including:

[0072] Based on the complete set of production constraints, a mathematical optimization model and a constraint traceability graph are constructed; the constraint traceability graph records the mapping relationship between the mathematical constraints in the mathematical optimization model and the original requirement descriptions of the mathematical constraints.

[0073] Specifically, the system reads the complete set of production constraints and converts each constraint into standard mathematical form. For example, the time constraint is converted to Σ(x[i,j,k] * t[i,j])≤T max Where t[i,j] is the task processing time, and T maxThis represents the maximum allowed completion time. Capacity constraint: transformed into Σx[i,j,k]≤Cap[j], where Cap[j] is the upper limit of the capacity of device j. Skill matching constraint: transformed into x[i,j,k]≤skill[k,i], where skill[k,i] is a 0-1 parameter indicating whether worker k possesses the skills required to execute order i. These mathematical constraints, together with the objective function F = αΣ completion time + βΣ delay penalty + γΣ soft constraint violation penalty, which includes a soft constraint penalty term, constitute the complete mixed-integer programming model, where α, β, and γ represent different weighting coefficients.

[0074] Preferably, constructing a constraint traceability map includes:

[0075] For each mathematical constraint in the mathematical optimization model, a three-layer mapping structure is established, consisting of a semantic layer, a model layer, and a code layer. The semantic layer is associated with the original requirement description, the model layer is associated with the decision variables and parameters of the mathematical constraint, and the code layer is associated with the mathematical expression of the mathematical constraint.

[0076] Specifically, the system creates a unique identifier (CID) for each constraint in the model. A hash table structure is then built around this CID to store its three-layer mapping information: Code Layer: Records the internal identifier of the constraint in the solver and its standard mathematical expression. For example: <CID_101, C1, x1+x2≤10>. Model Layer: Records the set of decision variables, parameter set, and constraint type (e.g., equality, inequality) associated with the constraint. For example: <CID_101, {x1, x2}, {10}, upper bound constraint>. Semantic Layer: Records the original natural language description, disambiguation history, and generation timestamp corresponding to the constraint. For example: <CID_101, The total output of product A and product B cannot exceed 10, user confirmed 'not exceeding' includes 'equal to', 2025-07-30 07:00:00>.

[0077] Based on a three-layer mapping structure, the dependencies between mathematical constraints are recorded and incorporated into the constraint tracing graph.

[0078] In this embodiment, the system analyzes all constraints, identifies their dependencies, and constructs a directed graph G=(V, E), where nodes V represent constraints and edges E represent dependencies. Dependency types can include: variable dependency: two constraints share the same decision variable; parameter dependency: a parameter of one constraint (such as a right-hand side term) is the result of the calculation of another constraint; logical dependency: the effectiveness of one constraint depends on the fulfillment of another constraint, for example, a process sequence constraint depends on an equipment allocation constraint. This entire system, comprising a three-layer mapping structure and a dependency graph, constitutes a queryable and traceable constraint traceability graph.

[0079] When the mathematical optimization model is detected to be infeasible, the minimum infeasible subset (IIS) is identified, and the original requirement description corresponding to the mathematical constraints within the minimum infeasible subset is located using the constraint tracing graph.

[0080] Specifically, when the solver returns an "infeasible" state, it means that there are conflicts in the constraints of the model. The system will automatically call the solver's built-in IIS algorithm. This algorithm can identify the smallest subset of conflicting constraints that cause the overall model to be infeasible. A model may contain multiple IISs. For each conflicting constraint in an IIS, the system uses a constraint tracing graph to trace from the code layer all the way to the semantic layer, thereby accurately locating which of the original, user-proposed natural language requirements are contradictory. For example, the system can generate a conflict source analysis report, pointing out that the three original requirements of working 8 hours a day, completing 100 products in 3 days, and each product taking 2 hours to complete are the reasons for the conflict.

[0081] Based on the identified original demand descriptions, a repair strategy is generated and applied to obtain a feasible production scheduling model.

[0082] This embodiment establishes a three-layer mapping structure (semantic, model, and code layers) for each mathematical constraint and constructs a dependency graph between constraints, achieving complete tracing from solver-level errors to the original natural language requirements. When a mixed-integer programming model becomes infeasible, the system can quickly and accurately locate the source of the conflict through the constraint tracing graph. For example, when the IIS algorithm identifies conflicting constraints, the system can immediately trace back to the original conflict between production quantity requirements and equipment capacity limitations. This shortens the time-consuming manual troubleshooting process in traditional methods, while improving the accuracy of error location, enabling non-professional users to understand and resolve model conflict problems.

[0083] Preferably, generating and applying a repair strategy includes:

[0084] For each conflict constraint identified by the original requirement description, the cost of remediation is calculated by evaluating its semantic deviation, model impact, and implementation difficulty.

[0085] Furthermore, the cost of repair is calculated as follows:

[0086] Calculate the semantic deviation, model impact, and implementation difficulty of the conflict constraints separately; and determine the cost of remediation by combining the semantic deviation, model impact, and implementation difficulty.

[0087] In this embodiment, the repair cost C repair The calculation formula is: C repair = w1 * D sem + w2 * I mod +w3 * D imp ; where D sem (Semantic deviation) measures the degree of deviation between the corrected constraints and the user's original intent, and can be calculated by the cosine similarity of the semantic vectors of the two statements before and after modification; I mod (Model impact) measures the extent to which modifying a constraint affects other constraints and the objective function in the model, and can be evaluated by its out-degree in the constraint dependency graph; D imp (Implementation Difficulty) To assess the difficulty of implementing the modification in actual production, users can pre-set difficulty coefficients for different types of modifications (such as extending working hours or adding equipment); w1, w2, and w3 are the weight coefficients of the three, and their sum is 1. For example, they can be set to 0.4, 0.3, and 0.3 respectively.

[0088] Based on the repair cost, repair suggestions are generated and arranged in ascending order of repair cost to form a hierarchical repair suggestion sequence.

[0089] Specifically, the tiered remediation suggestion sequence includes at least one of the following levels: Parameter fine-tuning level suggestions: used to adjust the numerical parameters of the conflicting constraints; this is the lowest-cost modification, for example, relaxing the 8-hour daily workday limit to 9 hours. Constraint relaxation level suggestions: used to change the constraint type of the conflicting constraints or add slack variables to the conflicting constraints; for example, changing the equality constraint that device M1 must exclusively use to a soft constraint that device M1 has priority in using. Structural adjustment level suggestions: used to increase production resources or adjust delivery deadlines; this is the highest-cost modification, for example, adding a piece of equipment to the process or extending the order delivery period by 2 days. The system generates remediation suggestions containing these three levels for each IIS and follows the C... repair Arranged in ascending order.

[0090] Select and apply a repair strategy from the tiered repair recommendation sequence.

[0091] Specifically, the system presents the sorted repair suggestions to the user. After the user selects a suggestion, the system automatically modifies the model accordingly. For example, if the user selects parameter fine-tuning, the system modifies the corresponding parameter values; if the user selects constraint relaxation, the system changes the constraint type or adds slack variables and sets penalty terms. After modification, the system resolves the model. If the model becomes feasible, the repair is successful, and a feasible production scheduling model is output; if it is still infeasible, the system backtracks to the previous step, prompting the user to try the next repair suggestion until a feasible solution is obtained.

[0092] This embodiment calculates the repair cost of each conflicting constraint and generates a sequence of repair suggestions encompassing three levels: parameter fine-tuning, constraint relaxation, and structural adjustment. It fully considers three dimensions: semantic deviation, model impact, and implementation difficulty, ensuring that the repair solution with the lowest cost is prioritized. For example, when faced with a conflict between time constraints and delivery date constraints, the system will prioritize suggesting parameter fine-tuning rather than changing the production structure. This improves the success rate of model repair while reducing repair costs, effectively enhancing the practicality and economy of modeling, and making production scheduling schemes more closely aligned with actual executability.

[0093] In a specific embodiment, assume the production scenario is as follows: Order information: An urgent order O1 requires the production of 120 products. Resource information: Only one available worker W1 and one available machine M1. Production capacity: Worker W1's efficiency in producing this product on machine M1 is 10 units / hour. Original constraint: Order O1 must be completed. Based on the above original constraints, the system constructs an initial model with the objective of minimizing the total completion time of order O1. Solving this model yields the most direct initial scheduling scheme: Worker W1 must work continuously on machine M1 for 120 units / 10 units / hour = 12 hours to complete the order. The system then reviews the rationality of this initial scheme. The continuous working time index for workers is calculated, and the value is 12 hours. Assuming the system's preset industry standard threshold is 10 hours, since 12 hours > 10 hours, the system identifies fatigue work anomaly. Based on this anomaly, the anomaly-constraint reasoning rule is applied to infer candidate implicit constraints: There is an upper limit to the daily working time of workers.

[0094] The proposed implicit constraint, suggesting a daily workday limit for worker W1 (currently 12 hours, recommended to be no more than 10 hours), was presented to the production supervisor. The production supervisor responded that, given the urgent order, appropriate overtime was acceptable if additional manpower couldn't be added, but it was still desirable to minimize overtime. Therefore, this constraint was categorized as a soft constraint, to be satisfied as much as possible. The supervisor was then asked to rate the importance of this soft constraint. The supervisor assigned a user preference strength I. pref= 8 (scoring range 1-10, higher scores indicate less likelihood of violation). To quantify the impact of violating this soft constraint on the overall production plan quality, the system performs a sensitivity analysis. Here, quality is represented by the objective function value of the final optimization model. The system uses the soft constraint parameter T... limit (Daily working hours limit) is used as a disturbance variable; analyze its impact on the final model objective function value. Assume the final objective function includes a penalty for excessive working hours, in the form F... total = F base + W penalty * max(0, T) work -T limit ), where F base It is the basic cost related to production time, T work This refers to the actual working hours. The goal of sensitivity analysis is to determine W. penalty The reasonable value. Execution parameter perturbation and re-solution: Perturbation point A (tightening constraint): The system temporarily sets the soft constraint limit value to T. limit_A = 9 hours. Under these conditions, to complete 12 hours of work, workers must work for two days (e.g., 9 hours on the first day and 3 hours on the second day), which will lead to an extension of the total completion time and an increase in related costs. The system re-solves this model to obtain the comprehensive objective function value, such as Z. A =150. Disturbance point B (relaxed constraint): The system temporarily sets the soft constraint limit value to T. limit_B = 11 hours. Under these conditions, the worker can complete the task in one day, but still needs to work 1 hour overtime. The system re-solves this model to obtain the comprehensive objective function value, such as Z. B = 110. Calculate the sensitivity index S. sense :S sense =|ΔObjective / ΔParameter| = |(Z A - Z B ) / (T limit_A - T limit_B Substitute the value: S sense = |(150 - 110) / (9 - 11)| = |40 / (-2)| = 20. This result indicates that within this parameter range, tightening the upper limit of working time by 1 hour will lead to an increase of 20 units in the overall target (which can be understood as cost).

[0095] After obtaining the sensitivity index, the system calculates the final penalty weight by combining it with the strength of user preferences. To eliminate the influence of dimensions, the system needs to... sense Normalization is performed. Assuming that through historical data or analysis of multiple constraints, the system knows the maximum possible value S of the sensitivity index in this scenario.max It is approximately 50. Therefore, the normalization sensitivity S norm For: S norm = S sense / S max = 20 / 50 = 0.4. The system sets the global baseline weight W. base This is used to adjust the overall magnitude of all soft constraint penalty terms, ensuring that they are numerically comparable to other terms in the objective function (such as production costs and delay penalties). Here, W is set... base = 100. Calculate the final penalty weight W. penalty W penalty = I pref * S norm * W base Substitute the value: W penalty = 8 * 0.4 * 100 = 320.

[0096] Through the above steps, the initially vague user preference worker was successfully and reproducibly quantified into a specific penalty weight value of 320 in this embodiment, minimizing the workload. In the final constructed mathematical optimization model, the objective function will include the penalty term +320 * max(0, T). work - 10). During the solution process, the optimization solver, due to the existence of this penalty term, will proactively seek a more humane and reasonable scheduling scheme that can both complete the production task and minimize worker overtime, rather than simply making workers work continuously for 12 hours. This fully demonstrates the effectiveness and operability of this embodiment in handling and quantifying complex and fuzzy real-world constraints.

[0097] According to one aspect of this application, calculating an ambiguity score for a constraint statement includes:

[0098] Each candidate explanation in the candidate explanation set constraining the expression is encoded as a semantic vector to construct a candidate explanation vector matrix; based on the similarity between the semantic vectors in the candidate explanation vector matrix, the ambiguity score is calculated.

[0099] In this embodiment, a pre-trained language model based on deep learning is used to generate semantic vectors, such as a BERT-wwm-ext model trained on a massive Chinese corpus. When a vector needs to be generated for a sentence (whether the original expression or a candidate interpretation), the system first constructs the sentence into the format [CLS] + sentence text + [SEP]. This constructed sequence is then input into the BERT model for forward propagation computation. The model outputs the hidden layer state vector corresponding to each token. In this embodiment, the output vector (usually with a dimension of 768) corresponding to the special token [CLS] in the last hidden layer is preferably used as the semantic vector representing the global semantics of the entire sentence. For an identified ambiguous constraint, it is assumed that it has N candidate interpretations. The system generates a corresponding D-dimensional semantic vector (e.g., D=768) for each of these N candidate interpretations. These N D-dimensional vectors are stacked to form an N×D matrix, which is the candidate interpretation vector matrix. This matrix completely stores the quantified semantic information of all possible interpretations of an ambiguous constraint.

[0100] According to one aspect of this application, constraints with similar linguistic structures are identified, including:

[0101] Dependency trees are generated for ambiguous constraints and clarified constraints respectively; and constraints with similar language structures are identified by comparing the similarity of the dependency trees.

[0102] In this embodiment, the system can call mature natural language processing toolkits (such as spaCy, Stanza, or Baidu DDParser) to analyze the constrained text and generate its corresponding dependency syntax tree. The nodes of this tree are words, and the edges are the syntactic relations between words (such as subject-verb, verb-object, modifier-please, etc.). Preferably, the Tree EditDistance algorithm is used to quantify the structural similarity between two dependency syntax trees. This algorithm calculates the minimum number of edit operations required to transform one tree T1 into another tree T2. Basic edit operations are defined as: Insertion: inserting a new node into T1; Deletion: deleting a node from T1; Substitution: replacing the label (i.e., word or part-of-speech) of a node in T1 with the label of the corresponding node in T2. ​​Each operation is assigned a cost (usually 1). The edit distance between the two trees is the minimum total cost. The smaller the distance, the more similar the structures of the two trees. The system can set a distance threshold. When the edit distance between the dependency syntactic trees of two constraints is less than the threshold, they are determined to have similar language structures.

[0103] According to one aspect of this application, the contextual relevance C in the confidence score calculation formula... contextThis aims to measure the relevance between a candidate constraint and the complete requirement description text input by the user. A feasible calculation method is as follows: The complete requirement description text input by the user is taken as a long document D; the core entity words (device M1, specificity) in the candidate implicit constraint to be evaluated (e.g., the specificity constraint exists for device M1) are extracted as query Q; the relevance score between query Q and document D is calculated. Specifically, the word vectors of each word in query Q and the word vectors of all words in document D can be obtained first. The final vector V of query Q is then calculated. Q Defined as the average of all word vectors in it; the final vector V of document D is... D Defined as the average of all word vectors within it. Calculate V. Q and V D The cosine similarity between them, and the similarity score is C. context The value of the candidate constraint is 1. The closer the score is to 1, the higher the correlation between the candidate constraint and the original context.

[0104] Furthermore, to achieve O(1) time complexity for querying constraint information, the system uses a hash table (dict in Python, HashMap in Java) for storage. The hash table data structure is as follows: Key: A unique identifier (CID) for each constraint, which is a string or integer generated when the constraint is created, such as constraint_001; Value: A JSON object containing complete information about the constraint or a custom class instance. This object contains at least three attributes, corresponding to a three-layer mapping structure: semantic_layer: Stores an object containing fields such as original_text and disambiguation_history; model_layer: Stores an object containing fields such as variables (list of decision variables involved), parameters (related parameters), and type (constraint type); code_layer: Stores an object containing fields such as solver_id (internal name in the solver) and expression (mathematical expression string). All traceability information for the constraint can be retrieved at once using hashtable[CID].

[0105] In an optional embodiment, the construction process of the anomaly constraint inference rule base preferably incorporates the following methods:

[0106] Association rule mining based on historical data: The system can perform offline analysis on historical production data accumulated by enterprises. Data sources include historical scheduling records from the Production Planning System (MES), problem reports, and the final execution plans adjusted manually. Through data preprocessing, the abnormal characteristics of the initial plan (such as the utilization rate of certain equipment being consistently below 30%) and the constraints added in the final plan (such as adding specific material matching constraints for these devices) are treated as transaction items. Applying association rule mining algorithms (such as Apriori or FP-Growth), strong association rules of the form {Abnormality A, Abnormality B} => {Constraint C} can be discovered. These mined rules form the basis of the rule base.

[0107] Knowledge engineering based on expert knowledge: This involves conducting structured interviews with domain experts (such as senior production managers and schedulers) to transform their tacit knowledge into explicit, machine-readable rules. For example, the interviews could revolve around the question, "When you see... in the scheduling results, what rules or constraints do you usually suspect are missing?" The collected expert experience is formatted as IF-THEN rules, and the experts subjectively assess the reliability of an initial set of rules.

[0108] Rule validation and iteration: The rule set obtained through the two methods described above is tested on an independent validation dataset. The reliability parameters of each rule are objectively calibrated and updated by evaluating its prediction accuracy, recall, and F1 score on the validation set. Rules with low reliability may be corrected or removed to ensure the quality and effectiveness of the rule base.

[0109] According to one aspect of this application, a visualization interface is provided for the interactive impact of constraints. Specifically, the interactive interface can be a web-based application. The front-end can use mainstream JavaScript frameworks, such as Vue.js or React, to achieve component-based development and efficient state management. The data visualization portion, particularly the rendering of the Gantt chart, can utilize powerful charting libraries such as ECharts, D3.js, or dedicated Gantt chart components. The back-end can be implemented using any language capable of handling data and providing APIs (such as Python or Java). When user confirmation of candidate constraints is required, the back-end first encapsulates the current scheduling scheme (containing the IDs of all tasks, start and end times, allocated resources, etc.) and the list of candidate constraints to be confirmed (containing the constraint text, confidence level, and a list of task IDs primarily affected by the constraint) into a JSON object. This JSON object is sent to the front-end via a RESTful API (e.g., POST / api / constraints / validate). After receiving the JSON data, the front-end calls the charting library to render the Gantt chart of the scheduling scheme. The frontend iterates through the candidate constraint list, finds the corresponding task bar in the Gantt chart based on the task ID list affected by each constraint, and highlights it (e.g., changing its color to orange or adding a blinking border). When the user hovers their mouse over a highlighted task bar, a tooltip is displayed, showing the corresponding constraint text and its confidence score (e.g., suggesting adding the constraint: each worker's daily working hours ≤ 9 hours (confidence: 0.85)). When the user clicks on a highlighted area, a modal dialog box pops up, providing three options: Must satisfy (hard constraint), Try to satisfy (soft constraint), and Do not need. After the user clicks one of the buttons, the frontend sends the user's selection (along with the constraint ID being operated on) back to the backend via another API (e.g., PUT / api / constraints / confirm). The backend updates the status of the constraint based on the user's selection and continues the subsequent process.

[0110] According to one aspect of this application, after solving the feasible production scheduling model and extracting the values ​​of each decision variable from the solution results, and parsing out the processing equipment, responsible workers, start time, and end time for each order, the system solves the feasible production scheduling model and generates a production scheduling execution plan. The process is as follows:

[0111] The goal of refining the scheduling scheme to consider practical factors is to transform the solver's output, which only considers the core logic, into an execution scheme that more closely reflects actual workshop operations by supplementing it with necessary auxiliary operation time. Specifically, this involves: traversing the optimized scheduling scheme and executing task pairs sequentially on the same machine. If the product mold or tooling required for the later task differs from the earlier task, the system will query the corresponding mold change time from the preset machine mold change time database. A non-production task of mold change type with the appropriate duration will be inserted between the two production tasks. The system will also check the first production task of each machine in each shift. If the machine's attributes (recorded in the machine information table) indicate that it requires preheating before starting work, the system will query the required preheating time and insert a non-production task of preheating type with the appropriate duration before the first production task begins. By inserting these necessary buffer times, the generated production scheduling execution scheme has higher practical executability.

[0112] Before generating the final report, the system conducts a comprehensive feasibility check on the refined plan to proactively identify potential execution risks. Specifically, it performs a continuity check to ensure the timeline between different processes within the same order is reasonable; for example, the start time of a subsequent process must be later than the end time of a preceding process. It also performs a resource conflict check to verify that no equipment or personnel are simultaneously assigned to two or more tasks at any given time. Finally, it performs a load balancing check, calculating the resource utilization rate of key equipment or personnel at different times and analyzing its fluctuations, such as calculating the standard deviation of utilization. Through these checks, the system can identify high-risk points. For example, if the check finds that the planned utilization rate of a key piece of equipment exceeds 95% within a consecutive two-hour period, the system will generate a risk warning, indicating that there is a lack of buffer for handling emergencies (such as temporary equipment failures or material delays) during that period, classifying it as a high-risk plan.

[0113] Integrating all analysis results, a structured scheduling scheme evaluation report is automatically generated. The specific format and content of this report may include: Final Execution Scheme: Presenting the final production scheduling execution scheme in an intuitive format. For example: Generating a work plan for each workstation: This table, in hourly units, clearly indicates the order number, product specifications, quantity, and process requirements that the workstation needs to process within each time period; Generating a personal work schedule for each worker: This table details the equipment that the worker needs to operate and the specific processing tasks they are responsible for in each work period. Key Performance Indicator (KPI) Quantitative Analysis: The core part of the report calculates a series of key performance indicators based on the simulated execution results of the scheduling scheme, and can compare them with the baseline values ​​before optimization to quantify the improvement effect brought by this method. These metrics preferably include: Overall Equipment Utilization (OEE): calculated as: OEE = Σ(Actual Processing Time) / Σ(Available Time); On-Time Delivery Rate (OTD): calculated as: OTD = (Number of Orders Completed on Time) / (Total Number of Orders); Load Balancing (LB): calculated as: LB = 1 - (Standard Deviation of Work Hours σ) / (Average Work Hours μ). Risk Warnings and Improvement Suggestions: The report will clearly list all risk warning information. For these risk points, the report can also provide corresponding improvement suggestions based on a pre-set rule base. For example, for high load risks, it is recommended to consider diverting some tasks to off-peak hours or outsourcing processing.

[0114] According to one aspect of this application, an intelligent modeling system for combinatorial optimization problems includes an information summarization module, a mathematical modeling module, an encoding module, and an evaluation module. The information summarization module, during the initial generation process, is responsible for extracting structured information from the problem, including three parts: naming and structured extraction of coefficients, description of constraints, and description of the objective function. This process requires the explicit extraction of auxiliary constraints (e.g., the relationship between integer variables and their corresponding binary variables) and hidden constraints (e.g., decision variables being non-negative integers). The essence of coefficient extraction is numerical mapping, which facilitates subsequent tasks where the module focuses on logical relationships and avoids numerical errors. During error correction, information is re-extracted based on prompts from the evaluation module. The mathematical modeling module, during the initial generation process, needs to model each of the extracted constraints and objective function. In this process, Retrieval-Enhanced Generation (RAG) is used to retrieve examples most relevant to the current constraints to assist in modeling. During error correction, erroneous modeling parts need to be remodeled based on prompts from the evaluation module. The encoding module is responsible for code generation and execution. During the initial generation process, the corresponding Gurobipy code (commercial solver) is generated based on the modeling provided by the mathematical modeling module. During the error correction process, the erroneous code is modified based on the prompts from the evaluation module. The evaluation module is primarily responsible for analyzing errors that occur during code execution and feeding back the diagnostic results to the relevant modules for correction. In this process, rules derived from error statistics effectively narrow down the range of possible error causes, improving the efficiency of problem diagnosis and accelerating the problem-solving process. Furthermore, when the user provides a specific problem description, the information summarization module summarizes structured information; the mathematical modeling module constructs corresponding mathematical expressions for each constraint and objective function in the structured information based on RAG technology; after summarizing all mathematical expressions, the coding module uses the summarized mathematical modeling to generate the corresponding solver code; the evaluation module runs the code; if the code runs normally, the algorithm terminates; if an error occurs, it analyzes possible error prompts based on rules, uses the prompts and the current code error, and the coding module points out the parts that need modification and the module responsible for executing those modifications. The designated module then corrects the corresponding errors based on the prompts from the coding module and passes the improved information to the next module. The process will run in a loop a specified number of times, and the guidance code will no longer report errors.

[0115] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. An intelligent modeling method for combinatorial optimization problems, characterized in that, include: Obtain the requirements description in natural language form and generate a disambiguated set of production constraints; Implicit constraints are discovered based on the disambiguated production constraint set, forming a complete production constraint set. A feasible production scheduling model is obtained by constructing and repairing a mathematical optimization model based on the complete set of production constraints. Solve for a feasible production scheduling model and generate a production scheduling execution plan; This forms a complete set of production constraints, including: Based on the disambiguated production constraint set, an initial scheduling model is constructed and solved to derive the initial scheduling scheme. Analyze the initial scheduling scheme and identify abnormal features in the scheduling results; Implicit constraints are inferred based on abnormal features and then merged with the disambiguated set of production constraints to generate a complete set of production constraints.

2. The method according to claim 1, characterized in that, Identify anomalous features in scheduling results, including: Based on the initial scheduling scheme, multi-dimensional anomaly detection indicators are calculated; among them, the multi-dimensional anomaly detection indicators include at least one of resource utilization balance, continuous working time of personnel, and process waiting time. Multidimensional anomaly detection indicators are compared with preset industry standard thresholds to determine anomaly characteristics.

3. The method according to claim 1, characterized in that, Implicit constraints are derived based on anomalous features, including: Determine the severity score of the anomalous features; Based on the abnormal features, a set of candidate implicit constraints is generated by applying a pre-defined rule base for abnormal constraint inference; each rule in the rule base for abnormal constraint inference is associated with a rule reliability. By combining the anomaly severity score with the rule reliability, a confidence score is calculated for each candidate implicit constraint in the candidate implicit constraint set, and the implicit constraint is determined accordingly.

4. The method according to claim 1, characterized in that, Before merging the implicit constraints and the disambiguated set of production constraints, the following is also included: Based on the received user feedback, implicit constraints are classified into hard constraints that must be met and soft constraints that can be violated but must be penalized. For soft constraints, obtain the strength of user preferences; Sensitivity analysis of soft constraints is performed to quantify their impact on the objective function of the initial scheduling model and obtain sensitivity indices. By combining user preference intensity and sensitivity indicators, penalty weights are determined for soft constraints.

5. The method according to claim 1, characterized in that, Obtain a feasible production scheduling model, including: Based on the complete set of production constraints, a mathematical optimization model and a constraint traceability graph are constructed; the constraint traceability graph records the mapping relationship between the mathematical constraints in the mathematical optimization model and their original requirement descriptions. When the mathematical optimization model is detected to be infeasible, the smallest infeasible subset is identified, and the original requirement description corresponding to the mathematical constraints within the smallest infeasible subset is located using the constraint tracing graph. Based on the identified original demand descriptions, a repair strategy is generated and applied to obtain a feasible production scheduling model.

6. The method according to claim 5, characterized in that, Constructing a constraint traceability graph includes: For each mathematical constraint in the mathematical optimization model, a three-layer mapping structure is established, consisting of a semantic layer, a model layer, and a code layer. The semantic layer is associated with the original requirement description, the model layer is associated with the decision variables and parameters of the mathematical constraint, and the code layer is associated with the mathematical expression of the mathematical constraint. Based on a three-layer mapping structure, the dependencies between mathematical constraints are recorded and incorporated into the constraint tracing graph.

7. The method according to claim 5, characterized in that, Generate and apply remediation strategies, including: For each conflicting constraint identified by the original requirement description, the cost of remediation is calculated by evaluating its semantic deviation, model impact, and implementation difficulty. Based on the repair cost, repair suggestions are generated and arranged in ascending order of repair cost to form a hierarchical repair suggestion sequence; Select and apply a repair strategy from the tiered repair recommendation sequence.

8. The method according to claim 7, characterized in that, The graded repair recommendation sequence includes at least one of the following levels: Parameter fine-tuning level suggestions are used to adjust the numerical parameters of conflict constraints; Constraint relaxation level suggestions are used to change the constraint type of conflicting constraints or add slack variables to them; Structural adjustment recommendations are provided to increase production resources or adjust delivery deadlines.

9. The method according to claim 7, characterized in that, Calculate the cost of repair, including: Calculate the semantic deviation, model impact, and implementation difficulty of conflict constraints respectively; The cost of remediation is determined by considering the semantic deviation, the impact of the model, and the difficulty of implementation.

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