Method and system for solving mixed integer linear programming industrial problems using neural network embeddings

Abstract

The application discloses a neural network embedding mixed integer linear programming industrial problem solving method and system. It belongs to the field of industrial problem solving. The method comprises the following steps: obtaining an industrial problem model to be solved, a trained neural network proxy model and closed-loop solving control parameters; converting the proxy model into model recognizable embedded auxiliary constraints, retaining the original physical hard constraints and grouping the embedded constraints; performing risk scoring and hierarchical screening on the constraint groups according to model structure information, solving state and historical check information, solving the simplified model and quickly checking the violation degree, proxy output deviation and target deviation; selectively supplementing the necessary constraint groups, re-optimizing the incremental results of the last round, and updating the historical risk information for iteration when the stop condition is not met. The application can reduce the solving scale and calculation cost of the neural network embedded MILP industrial problem, improve the solving efficiency, and maintain the feasibility of the industrial constraints and the reliability of the results.

Description

Technical Field

[0001] This invention relates to the field of industrial problem-solving technology, and in particular to a method and system for solving mixed-integer linear programming industrial problems oriented towards neural network embedding. Background Technology

[0002] Mixed-integer linear programming (MILP) is one of the most commonly used modeling tools in combinatorial optimization and industrial decision-making. It can uniformly express discrete decisions, continuous variable constraints, and linear objective functions, and is therefore widely used in production scheduling, vehicle routing planning, energy dispatching, resource allocation, and supply chain management. However, with the increasing number of implicit constraints, black-box relationships, and complex nonlinear processes in industrial problems, relying solely on explicit manual modeling often fails to accurately describe the operational patterns of real-world industrial systems. To improve the expressive power of MILP models, researchers typically utilize neural networks to learn the mapping relationships between complex variables from historical data and embed these neural networks as surrogate models into MILP, forming a unified "prediction-optimization" neural network-embedded MILP model corresponding to the industrial problem being solved.

[0003] Existing research and tools have enabled the automatic transformation of trained neural networks into linear or piecewise linear constraints acceptable to MILP, such as modeling ReLU activation functions or network layer propagation processes based on Big-M, indicator variables, and SOS1 methods. These methods significantly lower the barrier to manual derivation and provide crucial support for the integration of machine learning models and mathematical programming models. However, as the number of embedded network layers, neurons, and input dimensions increases, the auxiliary variables and linear constraints derived from the neural network often grow exponentially, leading to a significant "constraint explosion" problem for the solver. A large number of auxiliary constraints not only expand the model size but also disrupt the sparse structure of the original problem, significantly slowing down the branch-and-bound and linear relaxation processes.

[0004] To address the aforementioned issues, existing technologies have attempted to employ network pruning, constraint reduction, or reinforcement learning-driven solution acceleration methods. One type of method reduces the number of weight connections before neural network embedding through amplitude-based unstructured pruning, thereby compressing the size of variables and constraints after embedding. Another type of method, after embedding, heuristically reduces the set of auxiliary constraints or uses graph neural networks, reinforcement learning, and other techniques to identify redundant constraints, thus narrowing the solution space. These methods have achieved some improvement in solution speed, but still suffer from the following significant shortcomings:

[0005] First, existing methods typically handle embedded auxiliary constraints with coarse granularity, often employing uniform thresholds, heuristic scoring of single constraints, or one-time pruning strategies. They lack mechanisms to strictly separate the original physical hard constraints from the neural network embedded auxiliary constraints and manage them in groups according to network layers, neurons, or constraint paths. Furthermore, existing solutions generally lack risk scoring methods that combine static structural characteristics, current solution state, and historical pruning effects. Consequently, it is difficult to accurately identify which constraint groups should be retained and which can be prioritized for pruning, leading to insufficient stability in pruning decisions.

[0006] Second, existing methods, after constraint reduction, often directly accept the solution results of the simplified model or perform only a single static evaluation, lacking a closed-loop control mechanism of "solution-verification-backfilling-re-solution". In particular, existing technologies typically lack rapid verification methods for the violation degree of deleted constraints, surrogate output deviations, and target value deviations, and also lack a mechanism to selectively backfill only high-risk constraint groups after risks are detected. Therefore, excessive reduction can easily lead to fluctuations in solution quality, distortion of surrogate outputs, and even deviations from the feasible region boundary, making it difficult to meet the stability and controllability requirements of engineering applications.

[0007] Therefore, it is necessary to provide an optimization solution method and system for industrial problems involving mixed-integer linear programming with embedded neural networks. This method should be able to separate, label, group, assess risks, and hierarchically reduce the auxiliary constraints embedded in the neural network while strictly preserving the original physical hard constraints. After obtaining candidate solutions, the impact of the deleted constraints should be quickly verified. When risks are detected, only high-risk constraint groups should be selectively replenished and solved again, thereby achieving a more robust balance between solution efficiency and solution quality.

[0008] In view of this, the present invention is hereby proposed. Summary of the Invention

[0009] The purpose of this invention is to provide a method and system for solving mixed-integer linear programming industrial problems using neural networks, thereby improving the efficiency and quality of solving mixed-integer linear programming industrial problems using neural networks, and thus solving the aforementioned technical problems existing in the prior art.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] A method for solving mixed-integer linear programming industrial problems using neural network embeddings includes:

[0012] Step 1: Obtain the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution;

[0013] Step 2: Transform the trained neural network surrogate model into an embedded auxiliary constraint that can be recognized by the mixed integer linear programming industrial problem model to be solved. Retain the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved. Divide the embedded auxiliary constraints into several constraint groups that can be subsequently filtered and supplemented to obtain the neural network embedded mixed integer linear programming industrial problem model.

[0014] Step 3: Based on the structural information and solution status of the neural network embedded mixed-integer linear programming industrial problem model, output risk scores for each constraint group, and perform hierarchical reduction of several constraint groups under a given budget, in combination with the risk scores, to obtain the reduced simplified neural network embedded mixed-integer linear programming industrial problem model.

[0015] Step 4: Solve the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion, and determine whether the deleted constraint groups need to be reinstated. If yes, proceed to step 5; otherwise, proceed to step 6.

[0016] Step 5: By selectively restoring the deleted necessary constraint groups, an updated neural network embedded mixed-integer linear programming industrial problem model is obtained. The model is then incrementally re-optimized using the previous solution results to obtain new candidate solutions. These new candidate solutions are returned to Step 4 for rapid verification. When the constraint reduction strategy needs to be readjusted, the historical verification information is updated based on the verification results obtained in Step 4 and the restoring records obtained in Step 5. The process then returns to Step 3 for risk scoring and stratified screening. The historical verification information includes one or more of the following: constraint violation rate of the deleted constraint groups, proxy output deviation, target deviation, whether restoring was triggered, number of restoring attempts, and verification results after restoring.

[0017] Step 6: Determine whether the solution termination condition is met. If it is met, end the solution and output the solution result. If it is not met, update the iteration state based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and return to step 3 to re-perform risk scoring and stratified screening to continue iterative solution.

[0018] A system for implementing the neural network embedded mixed-integer linear programming industrial problem solving method of the present invention includes:

[0019] The system comprises the following modules: data and model input module, embedded constraint generation and grouping module, constraint risk assessment and hierarchical screening module, simplified model solution and fast verification module, selective backfilling and incremental re-optimization module, and stopping decision and result output module.

[0020] The data and model input module is connected to the embedded constraint generation and grouping module, and can respectively obtain the mixed integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution;

[0021] The embedded constraint generation and grouping module, connected to the constraint risk assessment and hierarchical screening module, can transform the trained neural network surrogate model obtained by the data and model input module into embedded auxiliary constraints that can be recognized by the mixed integer linear programming industrial problem model to be solved. It retains the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved, and divides the embedded auxiliary constraints into several constraint groups that can be subsequently screened and supplemented, thus obtaining the neural network embedded mixed integer linear programming industrial problem model.

[0022] The constraint risk assessment and hierarchical reduction module is connected to the simplified model solution and fast verification module. It can output risk scores for each constraint group based on the structural information and solution status of the neural network embedded mixed integer linear programming industrial problem model output by the embedded constraint generation and grouping module. Under a given budget, it performs hierarchical reduction on several constraint groups in combination with the risk scores to obtain the reduced simplified neural network embedded mixed integer linear programming industrial problem model.

[0023] The simplified model solving and fast verification module is connected to the selective backfilling and incremental re-optimization module and the stop determination and result output module, respectively. It can solve the simplified neural network embedded mixed integer linear programming industrial problem model after the constraint risk assessment and hierarchical screening module has been reduced, and determine whether the deleted constraint group needs to be backfilled. If so, it is handed over to the selective backfilling and incremental re-optimization module for execution; otherwise, it is handed over to the stop determination and result output module for execution.

[0024] The selective backfilling and incremental re-optimization module is connected to the stopping judgment and result output module and the constraint risk assessment and hierarchical screening module, respectively. It can recover the deleted necessary constraint groups determined by the simplified model solving and fast verification module through selective backfilling, obtain an updated neural network embedded mixed-integer linear programming industrial problem model, and use the previous solution results to perform incremental re-optimization on the updated neural network embedded mixed-integer linear programming industrial problem model to obtain new candidate solutions. The new candidate solutions are then returned to the simplified model solving and fast verification module for fast verification. When it is necessary to readjust the constraint reduction strategy, the historical verification information updated by the backfilling record obtained by the selective backfilling and incremental re-optimization module, based on the verification results obtained by the simplified model solving and fast verification module and the backfilling record obtained by the selective backfilling and incremental re-optimization module, is returned to the constraint risk assessment and hierarchical screening module. The historical verification information includes one or more of the following: constraint violation degree of the deleted constraint group, proxy output deviation, target deviation, whether backfilling was triggered, number of backfilling attempts, and verification results after backfilling.

[0025] The stop determination and result output module is connected to the constraint risk assessment and hierarchical screening module. It can determine whether the solution termination condition is met. If it is met, the solution is terminated and the solution result is output. If it is not met, the iteration state is updated based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and the module returns to the constraint risk assessment and hierarchical screening module to re-perform risk scoring and hierarchical screening in order to continue iterative solution.

[0026] Compared with existing technologies, the neural network embedding method and system for solving mixed-integer linear programming industrial problems provided by this invention has at least the following advantages over existing methods of automatic neural network embedding or one-time pruning:

[0027] First, the method of the present invention is not limited to a certain form of neural network linearization, but plays a role in the solution enhancement stage "after the embedding is completed". It is compatible with different embedding techniques such as Big-M, SOS1, and indicator variables, and therefore has good versatility and engineering transferability.

[0028] Second, the method of the present invention divides constraints into original hard constraints and embedded auxiliary constraints, and only performs sieving and replenishment on embedded auxiliary constraints, thereby avoiding the accidental deletion of the original problem's physical rules and improving the security and reliability of the results.

[0029] Third, the method of this invention solves the problem in existing technologies where errors cannot be evaluated and corrected after a one-time reduction through a closed-loop process of "risk scoring - hierarchical reduction - rapid verification - selective replenishment". Especially in complex heterogeneous problems, it can significantly reduce the feasibility loss and target value fluctuation caused by excessive reduction.

[0030] Fourth, the method of this invention adopts a group-level recovery mechanism instead of a full recovery mechanism, and only recovers the high-risk constraint groups that actually cause the deviation, thereby retaining most of the constraint compression benefits while maintaining the solution quality, and achieving a better time-accuracy trade-off.

[0031] Fifth, the method of this invention introduces an incremental re-optimization mechanism, which can reuse the previous round of solution state, feasible solution and search tree information, significantly reducing the redundant calculation overhead in multi-round backfilling scenarios, and making the closed-loop verification scheme feasible in practical engineering.

[0032] Sixth, the method of the present invention can adaptively adjust the reduction intensity and termination conditions according to the error budget and time budget, and is applicable to various industrial scenarios with different requirements for speed and accuracy, and has better robustness and configurability.

[0033] Seventh, the method of the present invention is not only applicable to single static optimization, but also to rolling optimization, batch similar instance solving, and online decision-making systems that require long-term accumulation of screening and reduction experience, and has good prospects for expansion.

[0034] The method of this invention can effectively solve problems such as the surge in the number of auxiliary constraints after neural network embedding, the lack of hierarchical labeling and risk identification in existing screening and reduction strategies, and the lack of closed-loop verification and on-demand replenishment of reduction results. It is applicable to data-driven decision-making scenarios such as urban infrastructure layout, industrial scheduling, energy management, and supply chain optimization. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 A flowchart is provided for an embodiment of the present invention to illustrate a method for solving industrial problems involving hybrid integer linear programming using neural networks.

[0037] Figure 2 A detailed flowchart of a method for solving industrial problems involving hybrid integer linear programming embedded in neural networks is provided for embodiments of the present invention.

[0038] Figure 3 An architecture diagram of a neural network embedded mixed integer linear programming industrial problem solving system is provided for embodiments of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them, and do not constitute a limitation on the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0040] First, the following explanations are provided for the terms that may be used in this article:

[0041] The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0042] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0043] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0044] Unless otherwise explicitly specified or limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this document according to the specific circumstances.

[0045] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “up,” “down,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the current orientation or positional relationship, and are only for the convenience and simplification of description, and do not explicitly or implicitly suggest that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this document.

[0046] The technical solution provided by this invention will be described in detail below. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they shall be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0047] like Figure 1 , Figure 2 As shown, this invention provides a method for solving mixed-integer linear programming industrial problems using neural network embeddings, comprising:

[0048] Step 1: Obtain the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution;

[0049] Step 2: Transform the trained neural network surrogate model into an embedded auxiliary constraint that can be recognized by the mixed integer linear programming industrial problem model to be solved. Retain the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved. Divide the embedded auxiliary constraints into several constraint groups that can be subsequently filtered and supplemented to obtain the neural network embedded mixed integer linear programming industrial problem model.

[0050] Step 3: Based on the structural information and solution status of the neural network embedded mixed-integer linear programming industrial problem model, output risk scores for each constraint group, and perform hierarchical reduction of several constraint groups under a given budget, in combination with the risk scores, to obtain the reduced simplified neural network embedded mixed-integer linear programming industrial problem model.

[0051] Step 4: Solve the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion, and determine whether the deleted constraint groups need to be reinstated. If yes, proceed to step 5; otherwise, proceed to step 6.

[0052] Step 5: By selectively restoring the deleted necessary constraint groups, an updated neural network embedded mixed-integer linear programming industrial problem model is obtained. The model is then incrementally re-optimized using the previous solution results to obtain new candidate solutions. These new candidate solutions are returned to Step 4 for rapid verification. When the constraint reduction strategy needs to be readjusted, the historical verification information is updated based on the verification results obtained in Step 4 and the restoring records obtained in Step 5. The process then returns to Step 3 for risk scoring and stratified screening. The historical verification information includes one or more of the following: constraint violation rate of the deleted constraint groups, proxy output deviation, target deviation, whether restoring was triggered, number of restoring attempts, and verification results after restoring.

[0053] Step 6: Determine whether the solution termination condition is met. If it is met, end the solution and output the solution result. If it is not met, update the iteration state based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and return to step 3 to re-perform risk scoring and stratified screening to continue iterative solution.

[0054] Preferably, in step 1 of the above method, the mixed-integer linear programming industrial problem model to be solved is a mixed-integer linear programming model that includes an objective function, continuous decision variables, integer decision variables, original physical hard constraints, and upper and lower bound information; wherein, the original physical hard constraints are derived from the business rules of the industrial problem corresponding to the mixed-integer linear programming industrial problem model to be solved, and the business rules include at least one of: production scheduling rules, capacity limits, supply and demand balance, equipment logic, and service radius;

[0055] The acquired trained neural network proxy model is a multilayer perceptron or a feedforward neural network with ReLU activation function;

[0056] The control parameters required for the closed-loop solution include one or more of the following: embedding method selection parameters, pruning threshold, constraint grouping granularity, risk scoring model parameters, upper limit of constraint reduction ratio, constraint violation threshold, proxy output deviation threshold, target deviation threshold, maximum number of iterations, maximum solution time, and re-optimization switch parameters;

[0057] The industrial problems corresponding to the mixed-integer linear programming industrial problem model to be solved include any one of the following: production scheduling problem, vehicle routing problem, energy dispatching problem, resource allocation problem, supply chain management problem, urban facility layout optimization problem, public service facility site selection problem, workload scheduling problem, computing resource allocation problem, and industrial park energy management optimization problem.

[0058] Preferably, in step 2 of the above method, the trained neural network surrogate model is converted into embedded auxiliary constraints that can be recognized by the mixed-integer linear programming industrial problem model to be solved, including:

[0059] When transforming the forward propagation process of the trained neural network surrogate model into the constraints of the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model is subjected to equivalent linear processing to obtain a set of auxiliary variables and linear constraints describing the neuron states of the neural network surrogate model, which serve as embedded auxiliary constraints that the mixed-integer linear programming industrial problem model to be solved can recognize.

[0060] In step 2, the embedded auxiliary constraints are divided into several constraint groups that can be subsequently filtered and replenished, as follows:

[0061] The embedded auxiliary constraints are grouped in at least one of the following ways to form a constraint group set. ,include:

[0062] (231) Grouping by network layer with embedded auxiliary constraints;

[0063] (232) Grouping neurons according to embedded auxiliary constraints;

[0064] (233) Grouping according to the linearized constraint clusters corresponding to the individual neurons with embedded auxiliary constraints;

[0065] (234) Group the output channels according to embedded auxiliary constraints;

[0066] (235) Group by local subnetworks or paths with embedded auxiliary constraints;

[0067] (236) Grouped by the sparse pattern of the constraint coefficients of the embedded auxiliary constraints or the similarity of the activation intervals.

[0068] Preferably, in step 3 of the above method, risk scores are output for each constraint group based on the structural information and solution status of the neural network-embedded mixed-integer linear programming industrial problem model, and hierarchical reduction is performed on several constraint groups under a given budget, in conjunction with the risk scores, to obtain a reduced simplified neural network-embedded mixed-integer linear programming industrial problem model, including:

[0069] Step 31: Extract features from each constraint group based on the model structure information and solution status:

[0070] For each constraint group, extract at least one of the following types of features:

[0071] (311) Static structural characteristics: network layer, number of neurons, number of constraints, number of non-zero coefficients, proportion of variable types, input-output connectivity, intra-group coefficient norm, and theoretical activation boundary;

[0072] (312) Dynamic solution state characteristics: variable values, constraint relaxation, dual value, pseudo cost, branch depth, constraint activity frequency and historical node statistics in the current linear relaxation solution;

[0073] (313) Historical verification characteristics: the degree of violation, proxy output deviation, number of times the constraint group was deleted in past rounds, and the effect after the replacement;

[0074] Step 32: Construct a risk scoring model based on the features extracted in Step 31, and use the risk scoring model to score the risk of each constraint group. The risk scoring model is as follows:

[0075] ;

[0076] in, This represents the risk score for the k-th constraint group. After normalization, it satisfies 0 ≤ ≤1; The scoring function is implemented using any of the following: graph neural network, reinforcement learning policy network, supervised learning model, or heuristic rule. This represents the static structural feature of the k-th constraint group; This indicates the characteristics of the current solution state. This represents historical verification features; a first risk threshold τ1 and a second risk threshold τ2 are preset, and 0≤τ1<τ2≤1, when... When τ1 ≥ τ2, the k-th constraint group is confirmed as unsuitable for deletion; when τ1 ≤ r_k < τ2, the k-th constraint group is confirmed as a priority retention constraint group; when When < τ1, the k-th constraint group is confirmed as a candidate deletable constraint group;

[0077] Step 33: Based on the risk scores of each constraint group obtained in Step 32 All constraint groups are divided according to a preset first risk threshold τ1 and a second risk threshold τ2, where 0 ≤ τ1 < τ2 ≤ 1: when When τ1 ≥ τ2, the k-th constraint group is designated as a mandatory constraint group; when τ1 ≤ τ2, the k-th constraint group is designated as a mandatory constraint group. When <τ2, the k-th constraint group is assigned as the priority retention constraint group; when When <τ1, the kth constraint group is divided into candidate deletable constraint groups; when performing constraint reduction, only constraint groups are deleted from the candidate deletable constraint groups in order of risk score from low to high, and the number of constraint groups or constraints deleted does not exceed the preset constraint reduction budget.

[0078] Under the premise of satisfying the constraint reduction budget, low-risk constraint groups are removed first from the candidate deletable constraint groups to obtain a simplified embedded auxiliary constraint set. The simplified embedded auxiliary constraint set is combined with the original physical hard constraint set to form a simplified neural network embedded mixed integer linear programming industrial problem model.

[0079] In step 3, the following protection rules are set to avoid excessive reduction of constraint groups, including:

[0080] (341) Set the minimum retention ratio for each network layer;

[0081] (342) Set the minimum retention ratio for each output channel;

[0082] (343) Force the retention of constraint groups that are highly coupled with key objective variables;

[0083] (344) Statistical analysis of any constraint group The number of times a deletion was triggered in the most recent L iterations. Where L is a preset positive integer; when ≥M or When / L≥ρ, determine the constraint group. For constraint groups that frequently trigger retracement, M is a preset retracement count threshold, and ρ is a preset retracement frequency threshold where 0 < ρ ≤ 1; the risk score for the frequently triggered retracement constraint group is then calculated. Adjust to max( Alternatively, they can be directly classified into constraint groups that must be retained to increase the retention priority of frequently triggered constraint replenishment groups.

[0084] Preferably, in step 4 of the above method, the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion is solved in the following manner, and it is determined whether the deleted constraint groups need to be reinstated, including:

[0085] Step 41: Call the solver to solve the simplified neural network embedded mixed integer linear programming industrial problem model to obtain candidate solutions. The candidate solutions are any one of the following: integer feasible solution, optimal solution, current best solution under time truncation, and approximate solution that meets the given tolerance.

[0086] Step 42, evaluate the violation of the deleted constraint in the following ways, including:

[0087] For each constraint in the deleted constraint group, select candidate solutions. Substitute back into the original embedded expression to calculate the violation index, if the constraint is This violates the degree index. Defined as:

[0088] ;

[0089] For a certain set of constraints Calculate group-level verification indicators for:

[0090] ;

[0091] in, To find the function with the maximum value;

[0092] Step 43, after evaluating the violation of the deleted constraints, also evaluates the deviation of the proxy output from the target, including:

[0093] Step 431: Fix the original decision variable values ​​in the candidate solution, perform forward computation using the unreduced complete neural network surrogate model or its complete embedding expression to obtain the complete surrogate output corresponding to the candidate solution; compare the complete surrogate output with the surrogate output obtained in the process of solving the simplified neural network embedded mixed integer linear programming industrial problem model, and calculate the surrogate output deviation; wherein, this step 431 is used to verify the output consistency of the candidate solution, and is not to re-solve the original complete neural network embedded mixed integer linear programming industrial problem model;

[0094] Step 432: Fix the original decision variable values ​​in the candidate solution, substitute the original decision variables into the complete evaluation expression containing the original physical hard constraints and the unreduced embedded auxiliary constraints, calculate the objective function value corresponding to the candidate solution under the complete model, and compare it with the objective function value obtained by solving the simplified neural network embedded mixed integer linear programming industrial problem model or the previous round's benchmark objective function value to obtain the objective deviation; when the complete objective function value cannot be directly calculated, estimate the objective deviation based on the output of the complete neural network surrogate model and the original objective function expression; here, this step 432 is used to evaluate the objective consistency of the candidate solution, and is not to re-solve the original complete neural network embedded mixed integer linear programming industrial problem model;

[0095] Step 433: In a multi-output scenario, the proxy output deviation obtained in step 431 is further decomposed by output channel; for the q-th output channel, the channel output deviation Δy is calculated. q =|y q ^full-y q ^red|, where y q ^full represents the output of the q-th channel obtained using the undone full neural network surrogate model or the full embedding expression, where y q^red represents the q-th channel output in the simplified model; step 433 is used to identify the output channels that have a significant impact on the feasibility of the objective function or constraints, and its result, together with the proxy output deviation in step 431 and the target deviation in step 432, serves as the input for constructing the group-level verification index in step 44; a sensitivity coefficient s is preset for each output channel. q And 0 ≤ s_q ≤ 1; s q It can be determined by normalizing the channel's weight in the objective function, its participation in the original physical hard constraints, and its historical backfill contribution. When s q When ≥σ, the q-th output channel is defined as a high-sensitivity channel, where σ is a preset sensitivity threshold and 0 < σ ≤ 1; a more stringent output deviation threshold ε is set for the high-sensitivity channel. y ,q=β·ε y , where ε y β is the normal output deviation threshold, and β is the tightening coefficient with 0 < β < 1;

[0096] Step 44, based on the group-level violation degree obtained in step 42 and the proxy output deviation obtained in step 43 and target deviation Construct the group-level verification index for the k-th constraint group. ,for:

[0097] ;

[0098] in, Represents a constraint group Historical risk information; Preset weights;

[0099] If group-level verification indicators If the risk exceeds the preset risk threshold, the constraint group is determined to need to be replenished.

[0100] Preferably, in step 5 of the above method, the updated neural network embedded mixed-integer linear programming industrial problem model is obtained by selectively restoring the deleted necessary constraint groups in the following manner, and the updated neural network embedded mixed-integer linear programming industrial problem model is incrementally re-optimized using the solution results of the previous round, including:

[0101] Step 51, selective replenishment:

[0102] The set of constraint groups that trigger risk thresholds is used to construct a set of back constraint groups. The embedded auxiliary constraints corresponding to all constraint groups in the set of back constraint groups are restored to the neural network embedded mixed integer linear programming industrial problem model to obtain the updated neural network embedded mixed integer linear programming industrial problem model.

[0103] Step 52, Incremental Re-optimization:

[0104] After obtaining the updated neural network embedded mixed-integer linear programming industrial problem model, the updated neural network embedded mixed-integer linear programming industrial problem model is solved using incremental re-optimization based on the solution results of the previous round. The incremental re-optimization method includes at least one of the following methods:

[0105] (521) Use the candidate solutions from the previous round as the initial feasible solutions;

[0106] (522) Use initial values ​​for variables, basic variables, or slack variables;

[0107] (523) Use historical nodes, boundary changes, or re-optimization tree information in the branch and bounding tree;

[0108] (524) Adopt the historically feasible solution pool;

[0109] (525) Candidate solutions are generated using local search and heuristics;

[0110] Step 53, adjust the dynamic deletion ratio:

[0111] Let α be the candidate elimination ratio in round t. t And preset the minimum reduction ratio as α min The maximum deletion ratio is α. max Decrease step size δ down Increase step size δ up , Replenishment ratio threshold ρ restore and the threshold R for the number of consecutive rounds passed, where 0 ≤ α min ≤α t ≤α max ≤1; After the t-th round of verification, calculate the replenishment ratio p. t =|G restore ^t| / |G del ^t|, where G restore ^t represents the set of constraint groups that trigger backfilling in round t, G del ^t represents the set of constraint groups that are deleted and participate in the validation in round t;

[0112] When p t ≥ρ restore If the current round of replenishment is deemed to have triggered too frequently, the candidate reduction ratio for the next round will be adjusted to α. {t+1} =max(α min ,α t -δ down When all deleted constraint groups pass the verification in R consecutive rounds and p t When =0, the candidate elimination ratio for the next round will be adjusted to α. {t+1} =min(αmax ,α t +δ up ); otherwise, keep α {t+1} =α t .

[0113] Preferably, in step 6 of the above method, the solution termination condition is met, the iteration is terminated, and the result is output when any of the following conditions are satisfied:

[0114] (61) All deleted constraint groups passed the validation, that is, for any deleted constraint group ∈ All satisfy ≤ ;in, This represents the set of constraint groups that have been deleted and require validation in the current round. This indicates the k-th deleted constraint group. This represents the group-level verification index calculated based on the group-level violation rate, proxy output deviation, target deviation, and historical risk information of the constraint group. This represents the preset risk threshold corresponding to the k-th constraint group, where k represents the constraint group number; if all deleted constraint groups satisfy... ≤ If so, then all deleted constraint groups are deemed to have passed the validation.

[0115] (62) The feasibility and objective deviation of the current candidate solution to the mixed-integer linear programming industrial problem model embedded in the complete neural network meet the error budget;

[0116] (63) The maximum number of iterations is reached;

[0117] (64) The maximum allowable solution time is reached;

[0118] (65) The solution yield is lower than the preset threshold for several consecutive rounds;

[0119] In step 6, the output of the solution results after the solution is completed includes:

[0120] (66) The results of the optimal or near-optimal decision variables after verification;

[0121] (67) The final set of constraint groups to be retained and replenished;

[0122] (68) Solving time, deletion ratio, replenishment ratio and verification log;

[0123] (69) Historical risk information and screening strategy records that can be reused for subsequent similar instances.

[0124] See Figure 3The present invention also provides a system for implementing the above-described method for solving mixed-integer linear programming industrial problems using neural network embeddings, comprising:

[0125] The system comprises the following modules: data and model input module, embedded constraint generation and grouping module, constraint risk assessment and hierarchical screening module, simplified model solution and fast verification module, selective backfilling and incremental re-optimization module, and stopping decision and result output module.

[0126] The data and model input module is connected to the embedded constraint generation and grouping module, and can respectively obtain the mixed integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution;

[0127] The embedded constraint generation and grouping module, connected to the constraint risk assessment and hierarchical screening module, can transform the trained neural network surrogate model obtained by the data and model input module into embedded auxiliary constraints that can be recognized by the mixed integer linear programming industrial problem model to be solved. It retains the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved, and divides the embedded auxiliary constraints into several constraint groups that can be subsequently screened and supplemented, thus obtaining the neural network embedded mixed integer linear programming industrial problem model.

[0128] The constraint risk assessment and hierarchical reduction module is connected to the simplified model solution and fast verification module. It can output risk scores for each constraint group based on the structural information and solution status of the neural network embedded mixed integer linear programming industrial problem model output by the embedded constraint generation and grouping module. Under a given budget, it performs hierarchical reduction on several constraint groups in combination with the risk scores to obtain the reduced simplified neural network embedded mixed integer linear programming industrial problem model.

[0129] The simplified model solving and fast verification module is connected to the selective backfilling and incremental re-optimization module and the stop determination and result output module, respectively. It can solve the simplified neural network embedded mixed integer linear programming industrial problem model after the constraint risk assessment and hierarchical screening module has been reduced, and determine whether the deleted constraint group needs to be backfilled. If so, it is handed over to the selective backfilling and incremental re-optimization module for execution; otherwise, it is handed over to the stop determination and result output module for execution.

[0130] The selective backfilling and incremental re-optimization module is connected to the stopping judgment and result output module and the constraint risk assessment and hierarchical screening module, respectively. It can recover the deleted necessary constraint groups determined by the simplified model solving and fast verification module through selective backfilling, obtain an updated neural network embedded mixed-integer linear programming industrial problem model, and use the previous solution results to perform incremental re-optimization on the updated neural network embedded mixed-integer linear programming industrial problem model to obtain new candidate solutions. The new candidate solutions are then returned to the simplified model solving and fast verification module for fast verification. When it is necessary to readjust the constraint reduction strategy, the historical verification information updated by the backfilling record obtained by the selective backfilling and incremental re-optimization module, based on the verification results obtained by the simplified model solving and fast verification module and the backfilling record obtained by the selective backfilling and incremental re-optimization module, is returned to the constraint risk assessment and hierarchical screening module. The historical verification information includes one or more of the following: constraint violation degree of the deleted constraint group, proxy output deviation, target deviation, whether backfilling was triggered, number of backfilling attempts, and verification results after backfilling.

[0131] The stop determination and result output module is connected to the constraint risk assessment and hierarchical screening module. It can determine whether the solution termination condition is met. If it is met, the solution is terminated and the solution result is output. If it is not met, the iteration state is updated based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and the module returns to the constraint risk assessment and hierarchical screening module to re-perform risk scoring and hierarchical screening in order to continue iterative solution.

[0132] In summary, the solution method of this invention improves the safety and reliability of the results by dividing constraints into original hard constraints and embedded auxiliary constraints, and performing sieving and replenishment only on embedded auxiliary constraints, thus avoiding the accidental deletion of original problem physical rules. Through a closed-loop process of "risk scoring - hierarchical reduction - rapid verification - selective replenishment," it solves the problem in existing technologies where errors cannot be evaluated and repaired after a one-time reduction. Especially in complex heterogeneous problems, it can significantly reduce feasibility losses and target value fluctuations caused by excessive reduction. Employing a group-level replenishment mechanism instead of a full recovery mechanism, it only restores high-risk constraint groups that truly cause deviations, thereby retaining most of the constraint compression benefits while maintaining solution quality, achieving a better time-accuracy trade-off. The incremental re-optimization mechanism reuses the previous round's solution state, feasible solutions, and search tree information, significantly reducing the redundant computational overhead in multi-round replenishment scenarios, making the closed-loop verification scheme practically feasible in engineering.

[0133] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the solution provided by the embodiments of the present invention is provided with reference to specific examples.

[0134] Example 1

[0135] like Figure 1 , Figure 2 As shown, this embodiment provides a method for solving mixed-integer linear programming industrial problems using neural networks. This method is an optimization solution for mixed-integer linear programming industrial problems using neural networks, and it employs the following mechanism:

[0136] (1) Hierarchical labeling and risk scoring mechanism for embedded auxiliary constraints:

[0137] This invention first distinguishes between original physical hard constraints and neural network embedded auxiliary constraints in MILP, allowing only the filtering and reduction of embedded auxiliary constraints to fundamentally avoid compromising the physical feasibility of the original problem. Building upon this, the invention further groups the embedded auxiliary constraints according to network layers, neurons, activation intervals, output channels, or constraint paths, constructing a "constraint group"—a processing unit more suitable for industrial solutions. Subsequently, by jointly utilizing static structural features, solution state features, and historical verification features, a risk score or retention priority is output for each constraint group, providing a basis for subsequent adaptive reduction. Compared to existing one-time, item-by-item constraint deletion methods, this invention can more precisely distinguish between constraints that must be retained, constraints that should be preferentially retained, and candidate constraints that can be deleted, improving the stability and interpretability of the reduction decision.

[0138] (2) A closed-loop constraint screening and reduction mechanism integrating verification and replenishment:

[0139] To address the shortcomings of existing methods that "directly accept the result after a one-time deletion," this invention proposes a closed-loop control mechanism integrating verification and restoration. Specifically, candidate embedding constraints are first removed hierarchically from low to high risk scores, yielding candidate solutions for a simplified model. Then, these candidate solutions are substituted back into the set of deleted constraints, and their violation rate, proxy output bias, objective function bias, and historical risk of the constraint group are rapidly evaluated. If some constraint groups are found to exceed a set error threshold, only the corresponding high-risk constraint groups are restored and solved again, rather than restoring all deleted constraints. This mechanism enables the system to dynamically adjust the constraint retention scale under precision and time budget constraints, achieving a closed-loop optimization process of "fast first, accurate later, and restoration as needed."

[0140] In the method of this invention, the industrial problem corresponding to the mixed integer linear programming industrial problem model to be solved includes any one of the following: production scheduling problem, vehicle routing problem, energy scheduling problem, resource allocation problem, supply chain management problem, urban facility layout optimization problem, public service facility site selection problem, workload scheduling problem, computing resource allocation problem, and industrial park energy management optimization problem.

[0141] The method of this invention focuses on "enhanced closed-loop solution after neural network embedding," and revolves around steps such as embedded auxiliary constraint identification, risk scoring, hierarchical reduction, fast verification, selective backfilling, and incremental solution. Specifically, the solution method of this invention includes the following steps:

[0142] Step 1: Obtain the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution.

[0143] In step 1, the obtained mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution are as follows:

[0144] (11) Obtain the original mixed-integer linear programming industrial problem model to be solved. It is a mixed-integer linear programming model that includes objective function, continuous decision variables, integer decision variables, original physical hard constraints, and upper and lower bound information. The original physical hard constraints of this model can be derived from business rules such as production scheduling rules, capacity limits, supply and demand balance, equipment logic, and service radius. It is the core constraint set that is always retained in this invention.

[0145] (12) The acquired trained neural network proxy model is preferably a multilayer perceptron (MLP) or a feedforward neural network with ReLU activation function. This neural network is used to approximate complex nonlinear relationships in the original problem that are difficult to analyze explicitly, such as the mapping of facility layout to resident satisfaction, the mapping of scheduling parameters to cost or quality indicators, and the mapping of energy scheduling decisions to loss or load response.

[0146] (13) The control parameters required for the closed-loop solution include, but are not limited to: embedding method selection parameters, pruning threshold, constraint grouping granularity, risk scoring model parameters, upper limit of constraint reduction ratio, constraint violation threshold, proxy output deviation threshold, target deviation threshold, maximum number of iterations, maximum solution time, and re-optimization switch parameters.

[0147] See Figure 3 The system corresponding to the method of the present invention is equipped with a data input and model building module, which can complete step 1 to obtain the original optimization problem to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution.

[0148] Step 2: Transform the trained neural network surrogate model into an embedded auxiliary constraint that can be recognized by the mixed-integer linear programming industrial problem model to be solved. Retain the original physical hard constraints of the mixed-integer linear programming industrial problem model to be solved, and divide the embedded auxiliary constraints into several constraint groups that can be subsequently filtered and supplemented to obtain the neural network embedded mixed-integer linear programming industrial problem model.

[0149] In step 2, the trained neural network surrogate model is converted into embedded auxiliary constraints that can be recognized by the mixed-integer linear programming industrial problem model to be solved, as follows:

[0150] (21) Embedded auxiliary constraint generation:

[0151] When transforming the forward propagation process of a neural network into MILP constraints, Big-M, SOS1, indicator variables, or other equivalent linearization methods can be used. Taking a network with ReLU activation as an example, the pre-activation value of the i-th neuron in the l-th layer can be written as:

[0152] ;

[0153] The corresponding activation value satisfies:

[0154] ;

[0155] After linearization, a set of auxiliary variables and linear constraints describing the neuron's state can be obtained. This invention does not limit the specific embedding linearization method, but emphasizes that after embedding, these newly added auxiliary constraints should be closed-loop filtered, reduced, and re-optimized.

[0156] (22) Separation marker for hard constraints and embedded auxiliary constraints:

[0157] To ensure the physical feasibility of the original problem, this invention uses binary labeling for the constraints in the model:

[0158] (221) Primitive Physical Hard Constraint Set ;

[0159] (222) Neural network embedding auxiliary constraint set .

[0160] Only the neural network embedding auxiliary constraint set is allowed The constraints in the set are subsequently reduced, verified, and replenished, while the original set of physical hard constraints is... It is retained throughout the entire solution process.

[0161] (23) Embedded constraint grouping:

[0162] Considering that removing constraints one by one is neither stable nor conducive to subsequent recovery, this invention groups the embedded auxiliary constraints in at least one of the following ways to form a constraint group set. :

[0163] (231) Grouped by network layer;

[0164] (232) Grouped by neurons;

[0165] (233) Grouping according to the linearized constraint clusters corresponding to individual neurons;

[0166] (234) Group by output channel;

[0167] (235) Group by local sub-network or path;

[0168] (236) Group by constraint coefficient sparsity pattern or activation interval similarity.

[0169] By grouping the constraints, it is possible to ensure that certain strongly coupled embedded constraints are preserved or restored as a whole, thereby reducing the random perturbation of the solution space boundary caused by the pruning decision.

[0170] See Figure 2 The system corresponding to the method of the present invention is equipped with a neural network embedding constraint generation and constraint grouping module, which can complete step 2 by converting the trained neural network into MILP-recognizable embedding auxiliary constraints and dividing the constraints into several constraint groups suitable for subsequent screening and backfilling processing.

[0171] Step 3: Based on the structural information and solution status of the neural network embedded mixed-integer linear programming industrial problem model, output risk scores for each constraint group, and perform hierarchical reduction of several constraint groups under a given budget, in combination with the risk scores, to obtain the reduced simplified neural network embedded mixed-integer linear programming industrial problem model.

[0172] In step 3, risk scores are output for each constraint group based on the structural information and solution status of the neural network-embedded mixed-integer linear programming industrial problem model. Then, under a given budget, hierarchical reduction is performed on several constraint groups based on the risk scores to obtain a simplified neural network-embedded mixed-integer linear programming industrial problem model, as detailed below:

[0173] (31) Feature extraction:

[0174] For each constraint group Extract at least one of the following types of features:

[0175] (311) Static structural characteristics: network layer, number of neurons, number of constraints, number of non-zero coefficients, proportion of variable types, input-output connectivity, intra-group coefficient norm, theoretical activation boundary, etc.

[0176] (312) Dynamic solution state characteristics: variable values, constraint relaxation, dual value, pseudo cost, branch depth, constraint activity frequency, historical node statistics, etc. in the current linear relaxation solution;

[0177] (313) Historical verification characteristics: the degree of violation, proxy output deviation, number of times to be redone, and effect after redone caused by the deletion of the constraint group in the past rounds.

[0178] (32) Risk scoring model:

[0179] Based on the features extracted above, this invention constructs a risk scoring function:

[0180] ;

[0181] in, This represents the static structural feature of the k-th constraint group. This indicates the characteristics of the current solution state. Indicates historical verification features, The larger the value, the less suitable the constraint group is to be deleted. Scoring function It can be implemented using graph neural networks, reinforcement learning policy networks, supervised learning models, or heuristic rules.

[0182] In a preferred embodiment, the entire MILP can first be transformed into a variable-constraint bipartite graph, and then the high-order topological features of each constraint group can be extracted using a graph neural network to output the retention probability or risk score. In the graph, one type of node represents variables, and the other type of node represents constraints. Edges represent the participation relationship and coefficient attributes of variables in constraints. This can fully characterize the coupling structure between the embedded auxiliary constraints and the original problem variables.

[0183] (33) Layered screening and reduction strategy:

[0184] Based on the risk score obtained above (32) All constraint groups are divided according to a preset first risk threshold τ1 and a second risk threshold τ2, where 0 ≤ τ1 < τ2 ≤ 1.

[0185] (331) Constraint groups that must be retained; when When ≥τ2, the k-th constraint group is classified as a constraint group that must be retained;

[0186] (332) Priority retention of constraint sets; when τ1≤ When <τ2, the k-th constraint group is assigned as the constraint group to be retained first;

[0187] (333) Candidate deletable constraint group: when When <τ1, the k-th constraint group is divided into candidate deletable constraint groups;

[0188] When performing constraint reduction, only candidate deletable constraint groups are deleted in ascending order of risk score, and the number of deleted constraint groups or constraints does not exceed the preset constraint reduction budget. This ensures that the constraint reduction budget is met. Under the premise of prioritizing the removal of low-risk constraint groups from the candidate deletable groups, a simplified constraint set is obtained. and the original hard constraint set Together they constitute the simplified MILP model.

[0189] To avoid excessive deletion, the present invention may also set the following protection rules:

[0190] (341) Minimum retention ratio for each network layer;

[0191] (342) Minimum retention ratio for each output channel;

[0192] (343) Constraint sets that are highly coupled with key objective variables are forcibly retained;

[0193] (344) Increase the retention priority of constraint groups that frequently trigger replenishment in the first few rounds.

[0194] (344) For any set of constraints Count the number of times a deletion triggered a replacement in the most recent L iterations. Where L is a preset positive integer; when ≥M, or When / L≥ρ, the constraint group is determined to be a constraint group that frequently triggers retracement, where M is a preset retracement count threshold, ρ is a preset retracement frequency threshold and 0<ρ≤1; for constraint groups that frequently trigger retracement, their risk scores are determined. Adjust to max( Alternatively, they can be directly classified as a constraint group that must be retained to increase their retention priority.

[0195] See Figure 3 The system corresponding to the method of the present invention is equipped with a constraint risk assessment and hierarchical reduction module, which can complete step 2 by outputting risk scores for each constraint group based on structural information and solution status, and performing hierarchical reduction under a given budget.

[0196] Step 4: Solve the simplified neural network embedded mixed integer linear programming industrial problem model after deletion, and determine whether the deleted constraint groups need to be reinstated. If yes, proceed to step 5; otherwise, proceed to step 6.

[0197] In step 4, the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion is solved in the following manner, and it is determined whether the deleted constraint groups need to be reinstated, as follows:

[0198] (41) Simplified model solution:

[0199] Will Combined with the filtered and reduced set of embedded auxiliary constraints, a simplified model is constructed. (That is, a simplified neural network embedded mixed-integer linear programming industrial problem model), calling the solver to obtain candidate solutions. The candidate solution can be an integer feasible solution, the optimal solution, the current best solution under time truncation, or an approximate solution that satisfies a given tolerance.

[0200] (42) Assessment of the degree of violation of deleted constraints:

[0201] For each constraint in the deleted constraint group, the candidate solution will be... Substitute back into the original embedded expression and calculate the violation metric. If the constraint is... Then the degree of violation can be defined as:

[0202] ;

[0203] For a certain set of constraints Group-level verification indicators can be calculated:

[0204] ;

[0205] (43) Evaluation of agent output deviation and target deviation:

[0206] In addition to the direct constraint violation rate, the present invention can further evaluate the following errors:

[0207] (431) Fix the original decision variable values ​​in the candidate solution, and perform forward computation using the unreduced complete neural network surrogate model or its complete embedding expression to obtain the complete surrogate output corresponding to the candidate solution; compare the complete surrogate output with the surrogate output obtained in the process of solving the simplified model, and calculate the surrogate output deviation. Here, this step is used to verify the output consistency of the candidate solution, and is not to resolve the original complete neural network embedded mixed integer linear programming industrial problem model.

[0208] (432) Fix the original decision variable values ​​in the candidate solution, substitute them into the complete evaluation expression containing the original physical hard constraints and the unreduced embedded auxiliary constraints, calculate the objective function value corresponding to the candidate solution under the complete model, and compare it with the objective function value obtained by solving the simplified model or the benchmark objective function value of the previous round to obtain the objective deviation; when the complete objective function value cannot be directly calculated, estimate the objective deviation based on the output of the complete neural network surrogate model and the original objective function expression. Here, this step is used to evaluate the consistency of the objective of the candidate solution, and is not to resolve the original complete neural network embedded mixed integer linear programming industrial problem model.

[0209] (433) In a multi-output scenario, the proxy output deviation obtained in step 431 is further decomposed according to the output channel; for the q-th output channel, the channel output deviation Δy is calculated. q =|yq ^full-y q ^red|, where y q ^full represents the output of the q-th channel obtained using the undone full neural network surrogate model or the full embedding expression, where y q ^red represents the output of the q-th channel in the simplified model; step 433 is used to identify the output channels that have a significant impact on the feasibility of the objective function or constraints, and its result, together with the proxy output deviation in step 431 and the target deviation in step 432, serves as the input for constructing the group-level verification index in step 44; a sensitivity coefficient s is preset for each output channel. q And 0 ≤ s_q ≤ 1; s q It can be determined by normalizing the channel's weight in the objective function, its participation in the original physical hard constraints, and its historical backfill contribution. When s q When ≥σ, the q-th output channel is defined as a high-sensitivity channel, where σ is a preset sensitivity threshold and 0 < σ ≤ 1; a more stringent output deviation threshold ε is set for the high-sensitivity channel. y ,q=β·ε y , where ε y β is the normal output deviation threshold, and β is the tightening coefficient with 0 < β < 1;

[0210] (44) Group-level risk recovery judgment:

[0211] Based on the group-level violation degree obtained in step 42 and the proxy output deviation obtained in step 43 and target deviation Construct the group-level verification index for the k-th constraint group. ,for:

[0212] ;

[0213] in, Represents a constraint group Historical risk information; Preset weights;

[0214] If group-level verification indicators If the risk exceeds the preset risk threshold, the constraint group is determined to need to be replenished.

[0215] Step 5: By selectively restoring the deleted necessary constraint sets, the updated neural network embedded mixed integer linear programming industrial problem model is obtained. The updated neural network embedded mixed integer linear programming industrial problem model is incrementally re-optimized using the solution results of the previous round. Then, the solution is iteratively solved by returning to step 3.

[0216] In step 5, the updated neural network embedded mixed-integer linear programming industrial problem model is obtained by selectively restoring the deleted necessary constraint groups in the following manner. The updated neural network embedded mixed-integer linear programming industrial problem model is then incrementally re-optimized using the solution results from the previous round, as detailed below:

[0217] Step 5 is the key part of this invention that distinguishes it from existing one-time deletion schemes, as it is responsible for restoring necessary constraints while ensuring efficiency.

[0218] (51) Selective replenishment:

[0219] The constraint groups that trigger risk thresholds constitute a backfill set. Only the embedded auxiliary constraints corresponding to these constraint groups are restored to the model to obtain the updated model. This invention emphasizes "group-level backfilling" rather than "full backfilling" or "random backfilling line by line" in order to balance structural integrity and computational efficiency.

[0220] (52) Incremental re-optimization:

[0221] In the model from Updated to In this case, incremental re-optimization is performed using the results from the previous round of solutions. Reused content includes, but is not limited to:

[0222] (521) The candidate solutions from the previous round are used as the initial feasible solutions;

[0223] (522) Initial values ​​of variables, basic variables, or slack variables;

[0224] (523) Historical nodes, boundary changes, or re-optimization tree information in the branch and bounding tree;

[0225] (524) Historically feasible solution pool;

[0226] (525) Local search and heuristically generated candidate solutions.

[0227] In a preferred embodiment, a solver interface that supports reoptimization or warm start can be used to reuse existing search information rather than solving from scratch when only local constraint recovery occurs in the problem.

[0228] (53) Dynamic reduction ratio adjustment:

[0229] Let α be the candidate elimination ratio in round t. t And preset the minimum reduction ratio as α min The maximum deletion ratio is α. max Decrease step size δ down Increase step size δ up , Replenishment ratio threshold ρrestore and the threshold R for the number of consecutive rounds passed, where 0 ≤ α min ≤α t ≤α max ≤1; After the t-th round of verification, calculate the replenishment ratio p. t =|G restore ^t| / |G del ^t|, where G restore ^t represents the set of constraint groups that trigger backfilling in round t, G del ^t represents the set of constraint groups that are deleted and participate in the validation in round t;

[0230] When p t ≥ρ restore If the current round of replenishment is deemed to have triggered too frequently, the candidate reduction ratio for the next round will be adjusted to α. {t+1} =max(α min ,α t -δ down When all deleted constraint groups pass the verification in R consecutive rounds and p t When =0, the candidate elimination ratio for the next round will be adjusted to α. {t+1} =min(α max ,α t +δ up ); otherwise, keep α {t+1} =α t .

[0231] See Figure 3 The system corresponding to the method of the present invention is equipped with a simplified model solving and fast verification module, which can solve the simplified model after deletion in step 5 and quickly determine whether the deleted constraints need to be replenished.

[0232] Step 6: Determine whether the solution termination condition is met. If the solution termination condition is met, end the solution and output the solution result. If the solution termination condition is not met, update the iteration status based on the current candidate solution, verification result and historical risk information, and return to step 3 to re-perform risk scoring and stratified screening to continue iterative solution.

[0233] In step 6, the solution termination condition is met when any of the following conditions are satisfied, at which point the iteration terminates and the result is output:

[0234] (61) All deleted constraint groups passed the validation, i.e. ;

[0235] (62) The feasibility of the current candidate solution with respect to the complete model and the deviation from the objective satisfy the error budget;

[0236] (63) Reach the maximum number of iterations;

[0237] (64) The maximum allowable solution time is reached;

[0238] (65) The profit from solving the problem for several consecutive rounds is lower than the preset threshold.

[0239] In step 6, the final output includes:

[0240] (66) The results of the optimal or near-optimal decision variables that have passed the verification;

[0241] (67) The final set of constraint groups to be retained and replenished;

[0242] (68) Solving time, deletion ratio, replenishment ratio and verification log;

[0243] (69) Historical risk information and screening strategy records that can be reused in subsequent similar instances.

[0244] See Figure 3 The system corresponding to the method of the present invention is provided with a stop determination and result output module, which can complete step 6. When any of the following conditions are met, the solution termination condition is confirmed, the iteration is terminated and the result is output.

[0245] Compared with existing methods for automatic embedding or one-time pruning of neural networks, this invention has at least the following positive effects.

[0246] First, this invention is not limited to a certain form of neural network linearization, but rather plays a role in the solution enhancement stage "after embedding is completed". It is compatible with different embedding techniques such as Big-M, SOS1, and indicator variables, and therefore has good versatility and engineering transferability.

[0247] Second, by dividing constraints into original hard constraints and embedded auxiliary constraints, this invention performs sieving and replenishment only on the embedded auxiliary constraints, thereby avoiding the accidental deletion of the original problem's physical rules and improving the security and reliability of the results.

[0248] Third, the closed-loop process of "risk scoring - hierarchical reduction - rapid verification - selective replenishment" proposed in this invention solves the problem that errors cannot be evaluated and repaired after a one-time reduction in existing technologies. Especially in complex heterogeneous problems, it can significantly reduce the feasibility loss and target value fluctuation caused by excessive reduction.

[0249] Fourth, this invention adopts a group-level recovery mechanism instead of a full recovery mechanism, only recovering the high-risk constraint groups that actually cause deviations, thereby retaining most of the constraint compression benefits while maintaining the solution quality, and achieving a better time-accuracy trade-off.

[0250] Fifth, this invention introduces an incremental re-optimization mechanism, which can reuse the previous round of solution state, feasible solution and search tree information, significantly reducing the redundant calculation overhead in multi-round backfilling scenarios, and making the closed-loop verification scheme feasible in practical engineering.

[0251] Sixth, the present invention can adaptively adjust the reduction intensity and termination conditions according to the error budget and time budget, making it suitable for various industrial scenarios with different speed and accuracy requirements, and has better robustness and configurability.

[0252] Seventh, this invention is not only applicable to single static optimization, but also to rolling optimization, batch similar instance solving, and online decision-making systems that require long-term accumulation of screening and reduction experience, and has good prospects for expansion.

[0253] Example 2:

[0254] The neural network-embedded mixed-integer linear programming industrial problem-solving method provided in this embodiment is an application of the method to urban infrastructure layout optimization scenarios, including:

[0255] The industrial problem of mixed-integer linear programming embedded in neural networks is the urban infrastructure layout optimization problem. In this problem, decision-makers need to determine the layout of facilities such as schools, hospitals, and public service points to maximize residents' overall satisfaction while meeting constraints such as budget, coverage, number of buildings, and service radius. Since there is a complex nonlinear relationship between infrastructure layout and residents' satisfaction, a pre-trained multilayer perceptron is used as a surrogate model to predict residents' quality of life under a given infrastructure location plan.

[0256] First, the multilayer perceptron is embedded into the original MILP model (i.e., the mixed-integer linear programming industrial problem corresponding to the urban infrastructure layout optimization problem), forming a complete optimization neural network embedded in the mixed-integer linear programming industrial problem model, which includes the original hard constraints and embedded auxiliary constraints. Then, the embedded auxiliary constraints are divided into multiple constraint groups according to network layers and output channels, and the static structural features and current linear relaxation state features of each constraint group are extracted and input into the risk scoring model. Based on the risk score, the system preferentially removes a portion of low-risk constraint groups, obtaining a simplified model and solving it quickly to obtain candidate layout schemes.

[0257] Next, the candidate layout scheme is substituted back into the deleted constraints, and its violation rate and satisfaction prediction deviation are verified. If it is found that the constraint group corresponding to a certain output channel causes the satisfaction deviation to exceed the threshold, only the constraint group highly correlated with that output channel is restored, and the remaining low-risk deletion results are retained. The previous round of candidate solutions is then used as a warm start to perform incremental re-optimization on the updated model. The above process is repeated until the candidate scheme meets the satisfaction deviation constraint and the original physical constraint requirements, and the final facility layout decision is output.

[0258] In this embodiment, the method of the present invention not only reduces the constraint scale brought about by the embedded model, but also avoids service quality prediction distortion caused by excessive deletion at one time through the replenishment mechanism. It is suitable for scenarios with high requirements for solution quality stability, such as urban management and public resource allocation.

[0259] Example 3:

[0260] The neural network-embedded mixed-integer linear programming industrial problem-solving method provided in this embodiment is an application method for solving neural network-embedded mixed-integer linear programming industrial problems in workload scheduling and resource allocation scenarios, including:

[0261] The industrial problem of embedding neural networks into mixed-integer linear programming (MILP) is a workload scheduling scenario. In this scenario, tasks need to be allocated and scheduled based on server status, historical task characteristics, resource usage, and predicted performance indicators to minimize total completion time, energy consumption, or default costs. Since there is a complex nonlinear coupling between task allocation and system performance, a neural network model is pre-trained to predict performance indicators under different scheduling strategies. This neural network is then embedded into MILP to form the solution model.

[0262] In practice, the embedded auxiliary constraints are first grouped by neuron groups and local paths, a variable-constraint bipartite graph is constructed, and the coupling strength between each constraint group and key scheduling variables is extracted. Based on risk scores, the system removes some low-risk embedded constraint groups and solves the simplified model to obtain candidate task allocation schemes. Subsequently, the full embedded network is used to re-evaluate the performance predictions under the candidate schemes, and selective backfilling is performed on constraint groups exceeding the deviation threshold. Considering that this scenario typically requires multiple rounds of continuous solving, the system reuses the task allocation scheme, initial variable values, and historical search states obtained in the previous round, and performs incremental re-solving based on the solver re-optimization interface.

[0263] Through the above process, historical risk information can be continuously accumulated during rolling scheduling or batch processing of similar instances, enabling subsequent instances to identify high-risk constraint groups more quickly, further reducing overall solution time and system response latency. This embodiment demonstrates that the present invention is applicable not only to single offline optimization but also to online scheduling systems with continuously similar problem inputs.

[0264] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make various equivalent changes or substitutions to the constraint grouping method, risk scoring model, threshold setting, incremental re-optimization interface, and application scenarios without departing from the concept of the present invention, and all such changes should fall within the scope of protection of the present invention.

[0265] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0266] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for solving mixed-integer linear programming industrial problems using neural network embeddings, characterized in that, include: Step 1: Obtain the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution; Step 2: Transform the trained neural network surrogate model into an embedded auxiliary constraint that can be recognized by the mixed integer linear programming industrial problem model to be solved. Retain the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved. Divide the embedded auxiliary constraints into several constraint groups that can be subsequently filtered and supplemented to obtain the neural network embedded mixed integer linear programming industrial problem model. Step 3: Based on the structural information and solution status of the neural network embedded mixed-integer linear programming industrial problem model, output risk scores for each constraint group, and perform hierarchical reduction of several constraint groups under a given budget, in combination with the risk scores, to obtain the reduced simplified neural network embedded mixed-integer linear programming industrial problem model. Step 4: Solve the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion, and determine whether the deleted constraint groups need to be reinstated. If yes, proceed to step 5; otherwise, proceed to step 6. Step 5: By selectively restoring the deleted necessary constraint groups, an updated neural network embedded mixed-integer linear programming industrial problem model is obtained. The model is then incrementally re-optimized using the previous solution results to obtain new candidate solutions. These new candidate solutions are returned to Step 4 for rapid verification. When the constraint reduction strategy needs to be readjusted, the historical verification information is updated based on the verification results obtained in Step 4 and the restoring records obtained in Step 5. The process then returns to Step 3 for risk scoring and stratified screening. The historical verification information includes one or more of the following: constraint violation rate of the deleted constraint groups, proxy output deviation, target deviation, whether restoring was triggered, number of restoring attempts, and verification results after restoring. Step 6: Determine whether the solution termination condition is met. If it is met, end the solution and output the solution result. If it is not met, update the iteration state based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and return to step 3 to re-perform risk scoring and stratified screening to continue iterative solution.

2. The method for solving mixed-integer linear programming industrial problems using neural network embeddings according to claim 1, characterized in that, In step 1, the mixed-integer linear programming industrial problem model to be solved is a mixed-integer linear programming model that includes an objective function, continuous decision variables, integer decision variables, original physical hard constraints, and upper and lower bound information; wherein, the original physical hard constraints are derived from the business rules of the industrial problem corresponding to the mixed-integer linear programming industrial problem model to be solved, and the business rules include at least one of the following: production scheduling rules, capacity limits, supply and demand balance, equipment logic, and service radius.

3. The method for solving industrial problems involving mixed-integer linear programming with neural network embeddings according to claim 1 or 2, characterized in that, The acquired trained neural network proxy model is a multilayer perceptron or a feedforward neural network with ReLU activation function; The control parameters required for the closed-loop solution include one or more of the following: embedding method selection parameters, pruning threshold, constraint grouping granularity, risk scoring model parameters, upper limit of constraint reduction ratio, constraint violation threshold, proxy output deviation threshold, target deviation threshold, maximum number of iterations, maximum solution time, and re-optimization switch parameters; The industrial problems corresponding to the mixed-integer linear programming industrial problem model to be solved include any one of the following: production scheduling problem, vehicle routing problem, energy dispatching problem, resource allocation problem, supply chain management problem, urban facility layout optimization problem, public service facility site selection problem, workload scheduling problem, computing resource allocation problem, and industrial park energy management optimization problem.

4. The method for solving industrial problems involving mixed-integer linear programming embedded in neural networks according to claim 1 or 2, characterized in that, In step 2, the trained neural network surrogate model is converted into embedded auxiliary constraints that can be recognized by the mixed-integer linear programming industrial problem model to be solved, in the following manner: When transforming the forward propagation process of the trained neural network surrogate model into the constraints of the mixed-integer linear programming industrial problem model to be solved, the trained neural network surrogate model is subjected to equivalent linear processing to obtain a set of auxiliary variables and linear constraints describing the neuron states of the neural network surrogate model, which serve as embedded auxiliary constraints that the mixed-integer linear programming industrial problem model to be solved can recognize.

5. The method for solving mixed-integer linear programming industrial problems using neural network embeddings according to claim 4, characterized in that, In step 2, the embedded auxiliary constraints are divided into several constraint groups that can be subsequently filtered and replenished, as follows: The embedded auxiliary constraints are grouped in at least one of the following ways to form a constraint group set. ,include: (231) Grouping by network layer with embedded auxiliary constraints; (232) Grouping neurons according to embedded auxiliary constraints; (233) Grouping according to the linearized constraint clusters corresponding to the individual neurons with embedded auxiliary constraints; (234) Group the output channels according to embedded auxiliary constraints; (235) Group by local subnetworks or paths with embedded auxiliary constraints; (236) Grouped by the sparse pattern of the constraint coefficients of the embedded auxiliary constraints or the similarity of the activation intervals.

6. The method for solving industrial problems involving mixed-integer linear programming embedded in neural networks according to claim 1 or 2, characterized in that, In step 3, risk scores are output for each constraint group based on the structural information and solution status of the neural network-embedded mixed-integer linear programming industrial problem model, and hierarchical reduction is performed on several constraint groups under a given budget, in conjunction with the risk scores, to obtain a simplified neural network-embedded mixed-integer linear programming industrial problem model, including: Step 31: Extract features from each constraint group based on the model structure information and solution status: For each constraint group, extract at least one of the following types of features: (311) Static structural characteristics: network layer, number of neurons, number of constraints, number of non-zero coefficients, proportion of variable types, input-output connectivity, intra-group coefficient norm, and theoretical activation boundary; (312) Dynamic solution state characteristics: variable values, constraint relaxation, dual value, pseudo cost, branch depth, constraint activity frequency and historical node statistics in the current linear relaxation solution; (313) Historical verification characteristics: the degree of violation, proxy output deviation, number of times the constraint group was deleted in past rounds, and the effect after the replacement; Step 32: Construct a risk scoring model based on the features extracted in Step 31, and use the risk scoring model to score the risk of each constraint group. The risk scoring model is as follows: ； in, This represents the risk score for the k-th constraint group. After normalization, it satisfies 0 ≤ ≤1; The scoring function is implemented using any of the following: graph neural network, reinforcement learning policy network, supervised learning model, or heuristic rule. This represents the static structural feature of the k-th constraint group; Indicates the characteristics of the current solution state. This represents historical verification features; a first risk threshold τ1 and a second risk threshold τ2 are preset, and 0 ≤ τ1 < τ2 ≤ 1. When τ1 ≥ τ2, the k-th constraint group is confirmed as unsuitable for deletion; when τ1 ≤ r_k < τ2, the k-th constraint group is confirmed as a priority retention constraint group; when When < τ1, the k-th constraint group is confirmed as a candidate deletable constraint group; Step 33: Based on the risk scores of each constraint group obtained in Step 32 All constraint groups are divided according to a preset first risk threshold τ1 and a second risk threshold τ2, where 0 ≤ τ1 < τ2 ≤ 1: when When τ1 ≥ τ2, the k-th constraint group is designated as a mandatory constraint group; when τ1 ≤ τ2, the k-th constraint group is designated as a mandatory constraint group. When <τ2, the k-th constraint group is assigned as the priority retention constraint group; when When <τ1, the kth constraint group is divided into candidate deletable constraint groups; when performing constraint reduction, only constraint groups are deleted from the candidate deletable constraint groups in order of risk score from low to high, and the number of constraint groups or constraints deleted does not exceed the preset constraint reduction budget. Under the premise of satisfying the constraint reduction budget, low-risk constraint groups are removed first from the candidate deletable constraint groups to obtain a simplified embedded auxiliary constraint set. The simplified embedded auxiliary constraint set is combined with the original physical hard constraint set to form a simplified neural network embedded mixed integer linear programming industrial problem model. In step 3, the following protection rules are set to avoid excessive reduction of constraint groups, including: (341) Set the minimum retention ratio for each network layer; (342) Set the minimum retention ratio for each output channel; (343) Force the retention of constraint groups that are highly coupled with key objective variables; (344) Statistical analysis of any constraint group The number of times a deletion was triggered in the most recent L iterations. , where L is a preset positive integer; when ≥M or When / L≥ρ, determine the constraint group. For constraint groups that frequently trigger retracement, M is a preset retracement count threshold, and ρ is a preset retracement frequency threshold where 0 < ρ ≤ 1; the risk score for the frequently triggered retracement constraint group is then calculated. Adjust to max( Alternatively, they can be directly classified into constraint groups that must be retained to increase the retention priority of frequently triggered constraint replenishment groups.

7. The method for solving mixed-integer linear programming industrial problems using neural network embeddings according to claim 6, characterized in that, In step 4, the simplified neural network embedded mixed-integer linear programming industrial problem model after deletion is solved in the following manner, and it is determined whether the deleted constraint groups need to be reinstated, including: Step 41: Call the solver to solve the simplified neural network embedded mixed integer linear programming industrial problem model to obtain candidate solutions. The candidate solutions are any one of the following: integer feasible solution, optimal solution, current best solution under time truncation, and approximate solution that meets the given tolerance. Step 42, evaluate the violation of the deleted constraint in the following ways, including: For each constraint in the deleted constraint group, select candidate solutions. Substitute back into the original embedded expression to calculate the violation index, if the constraint is This violates the degree index. Defined as: ； For a certain set of constraints Calculate group-level verification indicators for: ； in, To find the function with the maximum value; Step 43, after evaluating the violation of the deleted constraints, also evaluates the deviation of the proxy output from the target, including: Step 431: Fix the original decision variable values ​​in the candidate solution, perform forward computation using the unreduced complete neural network surrogate model or its complete embedding expression to obtain the complete surrogate output corresponding to the candidate solution; compare the complete surrogate output with the surrogate output obtained in the process of solving the simplified neural network embedded mixed integer linear programming industrial problem model, and calculate the surrogate output deviation; wherein, this step 431 is used to verify the output consistency of the candidate solution, and is not to re-solve the original complete neural network embedded mixed integer linear programming industrial problem model; Step 432: Fix the original decision variable values ​​in the candidate solution, substitute the original decision variables into the complete evaluation expression containing the original physical hard constraints and the unreduced embedded auxiliary constraints, calculate the objective function value corresponding to the candidate solution under the complete model, and compare it with the objective function value obtained by solving the simplified neural network embedded mixed integer linear programming industrial problem model or the previous round's benchmark objective function value to obtain the objective deviation; when the complete objective function value cannot be directly calculated, estimate the objective deviation based on the output of the complete neural network surrogate model and the original objective function expression; here, this step 432 is used to evaluate the objective consistency of the candidate solution, and is not to re-solve the original complete neural network embedded mixed integer linear programming industrial problem model; Step 433: In a multi-output scenario, the proxy output deviation obtained in step 431 is further decomposed by output channel; for the q-th output channel, the channel output deviation Δy is calculated. q =|y q ^full-y q ^red|, where y q ^full represents the output of the q-th channel obtained using the undone full neural network surrogate model or the full embedding expression, where y q ^red represents the output of the q-th channel in the simplified model; step 433 is used to identify the output channels that have a significant impact on the feasibility of the objective function or constraints, and its result, together with the proxy output deviation in step 431 and the target deviation in step 432, serves as the input for constructing the group-level verification index in step 44; a sensitivity coefficient s is preset for each output channel. q And 0 ≤ s_q ≤ 1; s q It can be determined by normalizing the channel's weight in the objective function, its participation in the original physical hard constraints, and its historical backfill contribution. When s q When ≥σ, the q-th output channel is defined as a high-sensitivity channel, where σ is a preset sensitivity threshold and 0 < σ ≤ 1; a more stringent output deviation threshold ε is set for the high-sensitivity channel. y ,q=β·ε y , where ε y β is the normal output deviation threshold, and β is the tightening coefficient with 0 < β < 1; Step 44, based on the group-level violation degree obtained in step 42 and the proxy output deviation obtained in step 43 and target deviation Construct the group-level verification index for the k-th constraint group. ,for: ； in, Represents a constraint group Historical risk information; Preset weights; If group-level verification indicators If the risk exceeds the preset risk threshold, the constraint group is determined to need to be replenished.

8. The method for solving mixed-integer linear programming industrial problems using neural network embeddings according to claim 7, characterized in that, In step 5, the updated neural network embedded mixed-integer linear programming industrial problem model is obtained by selectively restoring the deleted necessary constraint sets in the following manner: The updated neural network embedded mixed-integer linear programming industrial problem model is then incrementally re-optimized using the solution results from the previous round, including: Step 51, selective replenishment: The set of constraint groups that trigger the risk threshold is used to construct a set of back constraint groups. The embedded auxiliary constraints corresponding to all constraint groups in the set of back constraint groups are restored to the neural network embedded mixed integer linear programming industrial problem model to obtain the updated neural network embedded mixed integer linear programming industrial problem model. Step 52, Incremental Re-optimization: After obtaining the updated neural network embedded mixed-integer linear programming industrial problem model, the updated neural network embedded mixed-integer linear programming industrial problem model is solved using incremental re-optimization based on the solution results of the previous round. The incremental re-optimization method includes at least one of the following methods: (521) Use the candidate solutions from the previous round as the initial feasible solutions; (522) Use initial values ​​for variables, basic variables, or slack variables; (523) Use historical nodes, boundary changes, or re-optimization tree information in the branch and bounding tree; (524) Adopt the historically feasible solution pool; (525) Candidate solutions are generated using local search and heuristics; Step 53, Adjust the dynamic deletion ratio: Let α be the candidate elimination ratio in round t. t And preset the minimum reduction ratio as α min The maximum deletion ratio is α. max Decrease step size δ down Increase step size δ up , Replenishment ratio threshold ρ restore and the threshold R for the number of consecutive rounds passed, where 0 ≤ α min ≤α t ≤α max ≤1; After the t-th round of verification, calculate the replenishment ratio p. t =|G restore ^t| / |G del ^t|, where G restore ^t represents the set of constraint groups that trigger backfilling in round t, G del ^t represents the set of constraint groups that are deleted and participate in the validation in round t; When p t ≥ρ restore If the current round of replenishment is deemed to have triggered too frequently, the candidate reduction ratio for the next round will be adjusted to α. {t+1} =max(α min ,α t -δ down When all deleted constraint groups pass the verification in R consecutive rounds and p t When =0, the candidate elimination ratio for the next round will be adjusted to α. {t+1} =min(α max ,α t +δ up ); otherwise, keep α {t+1} =α t .

9. The method for solving mixed-integer linear programming industrial problems using neural network embeddings according to claim 8, characterized in that, In step 6, if any of the following conditions are met, the solution termination condition is determined to be met, the iteration is terminated, and the result is output, including: (61) All deleted constraint groups passed the validation, that is, for any deleted constraint group ∈ All satisfy ≤ ;in, This represents the set of constraint groups that have been deleted and require validation in the current round. This indicates the k-th deleted constraint group. This represents the group-level verification index calculated based on the group-level violation rate, proxy output deviation, target deviation, and historical risk information of the constraint group. This represents the preset risk threshold corresponding to the k-th constraint group, where k represents the constraint group number; if all deleted constraint groups satisfy... ≤ If so, then all deleted constraint groups are deemed to have passed the validation. (62) The feasibility and objective deviation of the current candidate solution to the mixed-integer linear programming industrial problem model embedded in the complete neural network meet the error budget; (63) The maximum number of iterations is reached; (64) The maximum allowable solution time is reached; (65) The solution yield is lower than the preset threshold for several consecutive rounds; In step 6, the output of the solution results after the solution is completed includes: (66) The results of the optimal or near-optimal decision variables after verification; (67) The final set of constraint groups to be retained and replenished; (68) Solving time, deletion ratio, replenishment ratio and verification log; (69) Historical risk information and screening strategy records that can be reused for subsequent similar instances.

10. A system for implementing the neural network embedded mixed-integer linear programming industrial problem solving method according to any one of claims 1-9, characterized in that, include: The system comprises the following modules: data and model input module, embedded constraint generation and grouping module, constraint risk assessment and hierarchical screening module, simplified model solution and fast verification module, selective backfilling and incremental re-optimization module, and stopping decision and result output module. The data and model input module is connected to the embedded constraint generation and grouping module, and can respectively obtain the mixed integer linear programming industrial problem model to be solved, the trained neural network surrogate model, and the control parameters required for closed-loop solution; The embedded constraint generation and grouping module, connected to the constraint risk assessment and hierarchical screening module, can transform the trained neural network surrogate model obtained by the data and model input module into embedded auxiliary constraints that can be recognized by the mixed integer linear programming industrial problem model to be solved. It retains the original physical hard constraints of the mixed integer linear programming industrial problem model to be solved, and divides the embedded auxiliary constraints into several constraint groups that can be subsequently screened and supplemented, thus obtaining the neural network embedded mixed integer linear programming industrial problem model. The constraint risk assessment and hierarchical reduction module is connected to the simplified model solution and fast verification module. It can output risk scores for each constraint group based on the structural information and solution status of the neural network embedded mixed integer linear programming industrial problem model output by the embedded constraint generation and grouping module. Under a given budget, it performs hierarchical reduction on several constraint groups in combination with the risk scores to obtain the reduced simplified neural network embedded mixed integer linear programming industrial problem model. The simplified model solving and fast verification module is connected to the selective backfilling and incremental re-optimization module and the stop determination and result output module, respectively. It can solve the simplified neural network embedded mixed integer linear programming industrial problem model after the constraint risk assessment and hierarchical screening module has been reduced, and determine whether the deleted constraint group needs to be backfilled. If so, it is handed over to the selective backfilling and incremental re-optimization module for execution; otherwise, it is handed over to the stop determination and result output module for execution. The selective backfilling and incremental re-optimization module is connected to the stopping judgment and result output module and the constraint risk assessment and hierarchical screening module, respectively. It can recover the deleted necessary constraint groups determined by the simplified model solving and fast verification module through selective backfilling, obtain an updated neural network embedded mixed-integer linear programming industrial problem model, and use the previous solution results to perform incremental re-optimization on the updated neural network embedded mixed-integer linear programming industrial problem model to obtain new candidate solutions. The new candidate solutions are then returned to the simplified model solving and fast verification module for fast verification. When it is necessary to readjust the constraint reduction strategy, the historical verification information updated by the backfilling record obtained by the selective backfilling and incremental re-optimization module, based on the verification results obtained by the simplified model solving and fast verification module and the backfilling record obtained by the selective backfilling and incremental re-optimization module, is returned to the constraint risk assessment and hierarchical screening module. The historical verification information includes one or more of the following: constraint violation degree of the deleted constraint group, proxy output deviation, target deviation, whether backfilling was triggered, number of backfilling attempts, and verification results after backfilling. The stop determination and result output module is connected to the constraint risk assessment and hierarchical screening module. It can determine whether the solution termination condition is met. If it is met, the solution is terminated and the solution result is output. If it is not met, the iteration state is updated based on the current candidate solution, the verification result and the historical risk information obtained by updating the historical verification information, and the module returns to the constraint risk assessment and hierarchical screening module to re-perform risk scoring and hierarchical screening in order to continue iterative solution.

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