Method for accelerating solving of mixed integer linear programming engineering problem based on cutting plane

Abstract

The invention discloses a solving acceleration method for a mixed integer linear programming engineering problem based on a cut plane, which belongs to the field of solving and optimizing engineering problems by using mixed integer programming, and comprises the following steps of: 1, acquiring increment information by using a solver callback mechanism under the current node of a branch and bound tree; 2, extracting a lexical block of a current separation round from an incremental ternary graph constructed by incremental information by using a graph feature encoder; 3, arranging the lexical element blocks of the current separation round and the historical lexical element blocks according to a time sequence, inputting the lexical element blocks and the historical lexical element blocks into a dynamic configuration agent model, and outputting a maximum separation round and an activation state of a joint action configuration cut plane separator, so that the separator is configured and matched with a real-time structure of a sub-problem corresponding to a current node; step 4, executing multi-round separation of the current node according to the step 1 to the step 3 until the maximum separation round or solver termination condition is decided in the first round of separation in the step 3; and step 5, entering the next node, repeating the step 1 to the step 4 until a preset solving time limit, and completing solving acceleration.

Description

Technical Field

[0001] This invention relates to the field of solving optimization engineering problems using mixed-integer programming, and in particular to a method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting planes. Background Technology

[0002] Mixed integer programming (MIP) problems are widely used in critical scenarios such as industrial scheduling, energy dispatching, chip design, logistics, and finance. Mainstream solvers (such as SCIP) generally employ a branch-and-cut (B&C) framework: at each branch-bound node, a linear programming (LP) relaxation problem is first solved to obtain the dual bound, and the relaxation is continuously tightened through several rounds of cutting plane separation; if an acceptable integer solution is still not obtained, variable branching is performed to generate child nodes until the global upper and lower bounds meet to establish the optimal solution. With the diversification of intelligent industries and the increasing complexity of constraints, traditional heuristic configurations based on human experience are difficult to consistently match the diverse and heterogeneous large-scale instance structures. In recent years, intelligent solving (Learning to Optimization) emphasizes using machine learning to provide data-driven decision-making for key modules of the solver (such as branching, cutting plane selection, and heuristics) to improve efficiency, stability, and generalization ability, and has become an important development direction for next-generation mixed integer programming solvers.

[0003] The performance bottleneck of mixed-integer programming solvers is highly dependent on the synergistic performance of their core modules. Among these, the cuts module is one of the key modules for solving mixed-integer linear programming (MILP) problems. At each node of the branch and bound tree, the solver calls various cut plane separators to generate candidate cuts in batches, and selects a batch of high-quality and complementary cuts to add to the original integer programming model. This process is repeated round by round at each node (i.e., multiple rounds of separation) until the termination condition is triggered. The multiple rounds of cut plane generation and addition can tighten the relaxed feasible region of the integer programming model and improve the dual solution to accelerate the solution. Modern MILP solvers provide a variety of cut plane separators to generate cuts, allowing users to leverage the complementary advantages of different separators to handle problems with varying structures. Recent machine learning methods attempt to learn separator configurations based on instance features, selecting effective separators and disabling ineffective separators to save unnecessary computation time.

[0004] However, existing machine learning-based cutting plane separator configurations mostly focus on static global configurations. This means using a fixed list of separator activation or deactivation configurations for each MILP problem instance and reusing this configuration across nodes and rounds of separation. This static global configuration approach ignores the dynamic benefits of cutting plane separators at different stages and the interaction dependencies between separators, making it difficult to adapt to the evolving subproblem structure after multiple rounds of separation. On the one hand, the number of rounds of cutting plane separation exhibits diminishing marginal returns and a threshold effect; blindly increasing the number of rounds amplifies the cost of cutting plane generation and the risk of numerical instability. On the other hand, there are significant stage dependencies and interaction effects among separators; some separators are suitable for early activation, while others are more suitable for later activation, and there are both complementary and redundant combinations among separators. Therefore, how to dynamically adjust the configuration of cutting plane separators according to nodes and separation rounds to match the real-time structure of MILP subproblems, and thus improve the overall solution efficiency of mixed-integer linear programming engineering problems by enhancing the quality of candidate cuts, is a problem that needs to be solved.

[0005] In view of this, the present invention is hereby proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting planes. This method can dynamically adjust the configuration of the cutting plane separator according to the nodes and the separation rounds, so as to match the real-time structure of the MILP subproblem. In this way, by improving the quality of candidate cuts, the overall solution efficiency and convergence quality of mixed-integer linear programming engineering problems are accelerated, thereby solving the above-mentioned technical problems existing in the prior art.

[0007] The objective of this invention is achieved through the following technical solution: A method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting planes is proposed. This method dynamically adjusts the configuration of the cutting plane separator to accelerate the solution process when solving the subproblems corresponding to each node of the branch-bound tree of the mixed-integer linear programming engineering problem within a branch-cut plane framework. The method includes: Step 1: Under the current node of the branch and bound tree, use the solver callback mechanism to obtain the incremental information of the current separation round; Step 2: Based on the incremental information, construct an incremental triple graph containing three types of nodes: variables, new cuts, and separators. Encode the incremental triple graph into a full graph representation and a separator node representation using a trained graph feature encoder, and then concatenate them into a word block for the current separation round. Step 3: Arrange the word blocks of the current separation round and the historical word blocks in chronological order, input them into the trained dynamic configuration agent model, output the joint action, configure the maximum separation round and activation state of the cutting plane separator based on the joint action, so that the configuration of the cutting plane separator matches the real-time structure of the subproblem corresponding to the current node; Step 4: Perform multiple rounds of separation within the current node according to Steps 1 to 3 until the maximum number of separation rounds determined in the first round of separation in Step 3 or the solver termination condition is reached; Step 5: Proceed to the next node and repeat steps 1 to 4 until the preset solution time limit is reached, thus completing the solution acceleration.

[0008] Compared with existing technologies, the method for improving the efficiency of engineering problems using mixed-integer programming provided by this invention has the following beneficial effects: Within the solver's Branch-Cut Plane (B&C) framework, incremental state information is collected at trigger nodes based on the solver callback mechanism. This information is used to construct an incremental ternary graph of "variable node – newly added cut node – separator node," and the resulting word blocks are encoded using graph features as incremental state representations. The word blocks of the current separation round and the sequence of historical word blocks are input into a decoding-based temporal decision model, which outputs a joint action of "maximum separation round and separator activation state vector" and writes it back to the solver parameter interface. This allows for dynamic and adaptive configuration of the cut plane process during multiple separation rounds within a node. Simultaneously, incremental rewards are constructed based on the time cost penalty of each separation round, dual boundary improvement, and separator contribution, and updated using the deep reinforcement learning algorithm PPO. This enables the learned strategy to adaptively configure the maximum separation round and separator activation state as the MILP subproblem evolves, thereby improving overall solution efficiency and robustness.

[0009] Because incremental ternary graphs provide low-redundancy and structurally sufficient state representations on a round-by-round basis, the graph feature encoder explicitly models the performance dependencies between separators, while the decoding-based temporal decision model integrates each incremental transition to characterize the temporal correlation across rounds. This invention can clearly capture the phased patterns of multi-round separation and the interactions between separators, improve the quality of candidate cuts generated by the separators, thereby accelerating the convergence of dual boundaries, and reducing the average solution time and primordial-dual gap integral (PDintegral) within the same time limit. Simultaneously, the design of incremental ternary graphs avoids global graph-level inference in each round of separation and, in conjunction with the maximum separation rounds mechanism, controls inference and configuration overhead, achieving controllable deployment costs. This invention is compatible with the callback and parameter interfaces of the mainstream open-source solver SCIP, maintaining good robustness and generalization ability on heterogeneous instances and larger-scale problems. Attached Figure Description

[0010] 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.

[0011] Figure 1 A flowchart of a method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs, provided in an embodiment of the present invention.

[0012] Figure 2 This is a schematic diagram of a multi-round separation process within the current node, provided by an embodiment of the present invention.

[0013] Figure 3 A schematic diagram of the reinforcement learning framework used in the method provided in the embodiments of the present invention. Detailed Implementation

[0014] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the specific content of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments, which do not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0015] First, the following explanations are provided for the terms that may be used in this article: 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".

[0016] 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.

[0017] 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.

[0018] 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.

[0019] When concentration, temperature, pressure, size, or other parameters are expressed as numerical ranges, such ranges should be understood to specifically disclose all ranges formed by any pairing of upper limits, lower limits, or preferred values ​​within that range, regardless of whether the range is explicitly stated; for example, if the numerical range "2 to 8" is stated, then that range should be interpreted to include ranges such as "2 to 7", "2 to 6", "5 to 7", "3 to 4 and 6 to 7", "3 to 5 and 7", "2 and 5 to 7", etc. Unless otherwise stated, the numerical ranges described herein include both their endpoints and all integers and fractions within that range.

[0020] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “upper,” “lower,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience and simplification of description and do not imply 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.

[0021] The 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.

[0022] like Figures 1 to 3As shown, this invention provides a method for accelerating the solution of mixed-integer linear programming engineering problems based on a cutting plane. When solving subproblems corresponding to nodes of the branch-bound tree of a mixed-integer linear programming engineering problem using a solver within a branch-cut plane framework, the method dynamically adjusts the configuration of the cutting plane separator to accelerate the solution. The method includes: Step 1: Under the current node of the branch and bound tree, use the solver callback mechanism to obtain the incremental information of the current separation round; Step 2: Based on the incremental information, construct an incremental triple graph containing three types of nodes: variables, new cuts, and separators. Encode the incremental triple graph into a full graph representation and a separator node representation using a trained graph feature encoder, and then concatenate them into a word block for the current separation round. Step 3: Arrange the word blocks of the current separation round and the word blocks of the past round (i.e., word blocks of the past rounds) in chronological order, input them into the trained dynamic configuration agent model, output the joint action, configure the maximum separation round and activation state of the cutting plane separator based on the joint action, so that the configuration of the cutting plane separator matches the real-time structure of the subproblem corresponding to the current node. Step 4: Perform multiple rounds of separation within the current node according to Steps 1 to 3 until the maximum number of separation rounds determined in the first round of separation in Step 3 or the solver termination condition is reached; Step 5: Proceed to the next node and repeat steps 1 to 4 until the preset solution time limit is reached, thus completing the solution acceleration.

[0023] Preferably, in the above method, the mixed-integer linear programming engineering problem includes any of the following: Engineering problems including: facility site selection, resource allocation, social network analysis, communication network design, logistics and distribution, resource distribution, forest resource management, ecological protection, production scheduling, portfolio optimization, data center resource scheduling, cloud computing resource scheduling, ship scheduling between multiple ports, inventory management, multi-source constrained engineering problems, multi-source constrained logistics engineering problems, and engineering problems with sparse and dense intersecting industrial-grade constraint structures.

[0024] Among them, (1) the facility location engineering problem and the resource allocation engineering problem belong to the set covering problem: the problem aims to select as few subsets as possible from a given family of sets to ensure that all elements are covered. It is a typical representative of mixed integer linear programming problems of location and covering, and is widely used in optimization engineering fields such as facility location and resource allocation.

[0025] (2) Social network analysis engineering problems and communication network design engineering problems belong to the Maximum Independent Set (MIS) problem: In graph theory, the maximum independent set problem requires selecting the maximum number of non-adjacent vertices in a graph. It is a classic benchmark problem in combinatorial optimization and is often used in fields such as social network analysis and communication network design.

[0026] (3) Resource allocation engineering problems and forest resource management engineering problems belong to the Multiple Knapsack problem: This problem involves allocating items with value and volume into multiple knapsacks to maximize the total value under capacity constraints. It has important significance in practical applications such as logistics distribution and resource allocation.

[0027] (4) Forest resource management engineering problems and ecological protection engineering problems belong to the CORLAT dataset: The CORLAT dataset is derived from actual planning tasks in forestry and conservation, and typically includes constraint structures such as site selection and resource allocation. This dataset is used for MILP benchmarking in fields such as forest resource management and ecological protection.

[0028] (5) Production scheduling engineering problems and portfolio optimization engineering problems belong to the mixed-integer knapsack (MIK) problem: Under knapsack constraints, the mixed-integer knapsack problem involves mixed-integer optimization of integer and continuous variables, combining selection and matching characteristics. It has wide applications in production scheduling, portfolio optimization, and other fields.

[0029] (6) Data center resource scheduling engineering problems and cloud computing resource scheduling engineering problems belong to load balancing (LB) problems: This problem comes from the actual large-scale system scenarios of the ML4CO competition and aims to distribute tasks or traffic to multiple nodes to balance the load and reduce peak loads. It is widely used in data center, cloud computing resource scheduling and other fields.

[0030] (7) The ship scheduling engineering problem and inventory management engineering problem between multiple ports are classified as Anonymous Industrial Problems: This problem originates from the Maritime Inventory Management Problem (MIRP) in global bulk shipping. The goal is to optimize ship scheduling and inventory management across multiple ports to meet demand and reduce costs. The dataset is derived from a publicly available MIRP dataset, but was anonymized during the competition. This problem represents an optimization engineering problem within a real-world scheduling scenario.

[0031] (8) Multi-source constrained engineering problems and multi-source constrained logistics engineering problems belong to the MIPLIB mixed neos subset: This subset is part of the MIPLIB 2017 benchmark and covers mixed integer models with multi-source constraints such as engineering and logistics. It is used to test the performance of mixed integer programming solvers.

[0032] (9) Engineering problems with sparse and dense intersecting industrial-grade constraint structures belong to the MIPLIB mixed supportcase subset: This subset is another part of the MIPLIB 2017 benchmark and contains sparse and dense intersecting industrial-grade constraint structures. It is used to test the performance of mixed-integer programming solvers.

[0033] Among the aforementioned datasets, CORLAT, LB, Anonymous, MIPLIB mixed neos, and MIPLIB mixed supportcase all originate from real-world applications, representing optimization engineering problems across multiple domains. The CORLAT dataset covers practical planning tasks such as forest resource management and ecological protection; the LB dataset stems from large-scale load balancing problems; and the Anonymous dataset originates from maritime inventory management problems in global bulk shipping. MIPLIB mixedneos and MIPLIB mixed supportcase are real-world datasets from the MIPLIB 2017 benchmark, containing complex engineering and logistical constraints. These datasets not only reflect real-world optimization challenges but also provide valuable practical data for solving optimization engineering problems.

[0034] The optimization engineering problem is first modeled as a mixed-integer linear programming engineering problem using a unified mathematical programming modeling paradigm: business decisions are reduced to decision variables, business rules such as process, resources, timing, and logic are characterized as linear constraints, and the optimization objective is rewritten as a linear objective (using standard linearization or approximation when necessary); engineering data is used as model parameters to ensure a one-to-one correspondence between the model and the actual scenario. Then, using a solver within a branch-cut plane framework, the subproblems corresponding to each node of the branch and bound tree of the mixed-integer linear programming engineering problem are solved based on the cut plane. The present invention uses dynamic adjustment of the cut plane separator configuration to accelerate the solution.

[0035] Preferably, the incremental information in step 1 of the above method includes: new cut, variable bound tightening increment, and separator statistics; wherein, the separator statistics include: candidate cut application rate, domain shrinkage, and node pruning count.

[0036] Preferably, in step 2 of the above method, an incremental ternary graph containing three types of nodes—variables, newly added cuts, and separators—is constructed based on incremental information in the following manner: Construct variable nodes, add cut nodes, and separator nodes respectively; among them, The constructed variable node represents a variable in a mixed-integer linear programming problem. The features of the variable node, including the variable type, current value range, current solution value, whether the variable's upper and lower bounds are touched, and whether the variable is in the base state in the current relaxation problem, are combined into the feature vector of the variable node. The newly constructed cut node represents the cut newly generated in the current separation round. The features of the newly constructed cut node, including the source of the cut, the target parallelism of the cut, the efficiency of the cut, and the sparsity of the cut, are combined into the feature vector of the newly constructed cut node. The constructed separator node represents a separator used in the current separation round. The features of the separator node, including the number of cuts generated by the separator, the application rate of the cuts, the pruning contribution, the time consumed by the separator, and the domain shrinkage, are combined into the feature vector of the separator node. By transforming the relationships between the variable nodes, newly added cut nodes, and separator nodes constructed above into graph edges, the edge weight between the newly added cut node and the variable node is determined based on the coefficients of the variables involved in the cut. The edges between the separator node and the variable node and the newly added cut node adopt a lightweight fully connected connection method, and the edge weight is initialized to 1. This edge weight is subsequently adaptively adjusted by the dynamically configured agent model.

[0037] Preferably, in step 2 of the above method, the incremental triple graph is encoded into a full graph representation and a separator node representation using a trained graph feature encoder, and then concatenated into a word block for the current separation round, including: The incremental ternary graph is input into the graph feature encoder, which normalizes and performs two fully connected layers on the feature vectors of the three types of nodes, mapping the feature vectors uniformly into a 64-dimensional implicit embedding space. Then, bidirectional two-part message passing is performed on the incremental ternary graph: a layer of bidirectional convolution with edge features is performed between variable nodes and newly added cut nodes, between separator nodes and variable nodes, and between separator nodes and newly added cut nodes, aggregating the feature information from the other end before fusing it with the local feature. A self-attention mechanism is added between separator nodes to capture the dependencies between them and allow the dynamically configured agent model to focus on separator nodes with higher efficiency. Finally, the vectors obtained from the above operations on the three types of nodes are batch-added and pooled, then concatenated with the instance-level global features of the incremental ternary graph, and compressed into a 64-dimensional full-graph representation through two layers of multilayer perceptrons. Meanwhile, the node-level embedding vector of each separator node before pooling is retained as a 64-dimensional representation of each separator node. , The 64-dimensional full graph representation and the K separator node representations are vertically concatenated into a vector, which represents the word block for the current separation round. : ; Among them, subscript Refers to the first Round separation, For the first Incremental ternary graph of round separation, For graph feature encoders, Let K be the real number field, and K be the number of separators. The value is 22, and d is the representation dimension, with a value of 64.

[0038] Preferably, in the above method, the graph feature encoder used in step 2 and the dynamic configuration agent model used in step 3 are pre-trained in the following manner, including: Step 21, Callback Acquisition and Sample Generation: When solving the subproblems corresponding to each node of the branch and bound tree of the mixed integer linear programming engineering problem in the branch-cut plane framework using the solver, incremental information is collected when separation is triggered within the node based on the solver callback mechanism. Step 22, Incremental ternary graph construction: The ternary graph obtained in step 21 is... The incremental information of the round separation is organized as an incremental ternary graph of variable nodes - newly added cut nodes - separator nodes; Step 23: Construct incremental state representations in the form of word blocks using a graph feature encoder: Input the incremental ternary graph obtained in step 22 into the graph feature encoder to extract word blocks representing the incremental state representation of the current separation round. ; Step 24, Lexical Block Temporalization and Block-Level Position Encoding: This involves encoding the lexical blocks of the current separated round. The historical word blocks separated from the historical rounds in chronological order are concatenated into a word block sequence. Before being fed into the overall decoding time-series decision model of the dynamically configured intelligent agent model, block-level positional encoding is applied to the word block sequence to obtain the word block sequence with added block-level positional encoding. Step 25, Dynamically configure the policy network and value network of the agent model: Input the word block sequence with block-level position encoding into the policy network and value network of the dynamically configured agent model respectively. The policy network outputs a temporal embedding vector that is the same as the input, i.e., joint action. The value network outputs the temporal embedding vector of the value side. Step 26, Action Writeback and Reward Collection: Write the joint actions back to the solver's parameter callback interface, configure the separation parameter settings for this round of this node, and construct incremental rewards based on the solution feedback after completing this round of separation. After collecting the incremental reward for this round, the solver generates the incremental information for the next round, constructs the incremental ternary graph for the next round, and obtains the incremental state representation of the next separation round through the graph feature encoder. The data consisting of the current separation round incremental ternary graph, joint action, incremental reward, and next round incremental ternary graph is stored in the experience replay pool for training and updating in subsequent step 28. Step 27, Instance Data Collection: Repeat steps 21 to 26 until the current instance is solved; Step 28, Training and Update: Divide each dataset into 80% training set and 20% test set. Randomly select 16 instances from the training set and repeat steps 21 to 27. Take out a number of data consisting of the current separation round incremental ternary graph, joint action, incremental reward, and next round incremental ternary graph from the experience replay pool according to the set batch sampling to update the policy network and value network. Step 29, Training Stop Condition: Repeat steps 21 to 28 above until the upper limit of training rounds is reached, then stop training, and you will get the trained graph feature encoder and dynamically configured agent model.

[0039] Preferably, in the above method, the incremental reward in step 26 includes: time cost penalty for each separation round, dual boundary improvement, and separator contribution.

[0040] Preferably, in step 21 of the above method, the solver's callback mechanism refers to: a custom separator in the SCIP solver, specifically used for configuring parameters, triggering a callback during each separation round; The incremental information collected in step 21 when separation is triggered within a node includes: (211) Add new cut information: Read the cuts newly added in the previous separation stage and record the source category of the cut (which type of separator generated it), target parallelism (the similarity between the cut and the direction of the objective function), cut efficiency (the cutting depth of the cut on the current relaxed feasible region) and sparsity (the proportion of variables with non-zero parameters in the cut). If it is the initial separation round, then read the original constraint information of the mixed integer linear programming engineering problem; (212) Current round variable information: Read the variable information (i.e. column structure information), variable type (whether it is binary, integer, continuous, etc.), upper and lower bounds of the variable and whether the current value is in bounds, base state (whether the variable is on the basis of the LP relaxation problem), the current solution value of the variable and its fractional part, and marginal value (the unit benefit that changing the variable can bring to the current model); (213) Statistics of the current separator: record the number of cuts generated by each separator, the utilization rate of the generated cuts (the proportion of cuts generated by the separator that are selected), the pruning contribution (the cumulative number of unnecessary branches pruned by the cuts generated by the separator), the separator time (the cumulative time consumed by the separator being called up to the current subproblem), and the domain shrinkage (the cumulative number of times the domain of variable values ​​found by the cuts generated by the separator shrinks). (214) Instance-level global features: Lebesgue space (LP) dual degeneration degree (the degree of constraint redundancy of LP relaxation in the dual solution space, reflecting whether the model is sensitive to small cuts).

[0041] Preferably, in the above method, the incremental ternary graph in step 22 The node features and edge features of the three types of nodes are as follows: (221) Node characteristics: variable nodes Features The feature vectors of the variable information obtained in step 21 are used to represent the current round; new cut nodes are added. Features The feature vector representation of the newly added cut information obtained in step 21 is used; the separator node. Features The feature vector representation of the current round separator statistics obtained in step 21 is used, where, K represents the number of separators; (222) Edge features: (A) Sparse edge connections are established between the newly added cut nodes and the variable nodes. The edge features consist of two weights: one is the original coefficient of the variable in the newly added cut, and the other is the normalized coefficient obtained by normalizing the entire coefficient vector of the newly added cut. (B) Lightweight full connections are used between the separator nodes and the variable nodes, and between the separator nodes and the newly added cut nodes. The initial weight of the edges is uniformly set to 1 to represent the potential relationship between the separator and the variable and the newly added cut. The specific aggregate weights are adaptively adjusted by the dynamically configured agent model during training. (C) A complete graph without self-loops is constructed between the separator nodes. The initial weight of the edges is set to 1 to represent the cooperative or competitive relationship between different separator families. The aggregate weights are learned by the dynamically configured agent model and reweighted. In step 23, the graph feature encoder extracts incremental state representations in the form of word blocks from the input incremental ternary graph in the following manner: The feature vectors of the three types of nodes are normalized and mapped using two fully connected layers, uniformly mapping the feature vectors to a 64-dimensional implicit embedding space; then, bidirectional two-part message passing is performed on the incremental ternary graph: a layer of bidirectional convolution with edge features is performed between the variable and the new cut, between the separator and the variable, and between the separator and the new cut, aggregating the feature information of the other end and then fusing it with the feature of the local end; a self-attention mechanism is added between the separator nodes to capture the dependencies between separators and allow the dynamically configured agent model to focus on the separator with higher efficiency; finally, the vectors obtained from the above operations of the three types of nodes are batch-added and pooled, then concatenated with the instance-level global features in step 21, and compressed into a 64-dimensional full graph representation through two layers of multilayer perceptrons. Meanwhile, the node-level embedding vector of each separator node before pooling is retained as a 64-dimensional representation of each separator node. , The 64-dimensional full graph representation and the representations of the K separator nodes are vertically concatenated into a vector. This vector is the word block of the current separation round used to represent the incremental state representation of the current separation round. : ; Among them, subscript Refers to the first Round separation, For the first Incremental ternary graph of round separation, For graph feature encoders, Let K be the real number field, and K be the number of separators. The default value is 22, and d is the representation dimension, with a default value of 64.

[0042] Preferably, in step 24 of the above method, block-level positional encoding is applied to the word block sequence to obtain the word block sequence with added block-level positional encoding in the following manner: All word block sequences within the same separation round share the same position index, while the position indices of all word block sequences in different separation rounds increment over time. Meanwhile, the attention mask uses a causal mask with a lower triangle that only allows the current split round to use information from all previous split round blocks; In step 25, the policy network of the agent model is dynamically configured. From the first decoding time series decision model and its linear decision-making layer The policy network is structured such that it outputs a temporal embedding vector that is identical to the input, i.e., a joint action. ,for: The intra-block embedding vector of the word block sequence with K+1 words in the current separation round is input into the linear decision layer of the policy network. Output the classification distribution vector of the joint action, and obtain the current action based on the classification distribution vector. Combined actions of the round separation : ; in, This represents the maximum number of separation rounds. The i-th separator is in an active state. , Indicates the number of separators. Indicates activation later. Indicates that it is deactivated. Indicates initial activation; In step 25, the value network of the agent model is dynamically configured. The second decoding time series decision model and its linear value head The value network is constructed such that it outputs temporal embedding vectors on the value side in the following manner: The word block of the current separation round A sequence of lexical blocks formed by concatenating historical lexical blocks in chronological order is denoted as [lexical block sequence]. , the sequence of word blocks Input to the second decoding time series decision model Processing, i.e. After the second decoding time series decision model The processed output is the temporal embedding vector on the value side; from Extract the first word of the word block in the current separation round. The output at the corresponding position is used as the first word embedding vector. The first word embedding vector is then processed by a linear value head. Output scalar This value estimate of the state in the separation round is used to calculate the objective function for training in the subsequent reinforcement learning PPO algorithm.

[0043] In step 26, the incremental reward is constructed based on the solution feedback. for: ; The meanings of each item are as follows: First item The time-consuming penalty item is, among which, , Let be the solution time of the solver up to round t. This represents the increment of the cumulative solution time up to round t; N represents the estimated solution time for this instance based on the default separator parameter configuration; N is the total number of planned separation rounds in the full branch-cut plane process. Second item For duality improvement terms, where, , Let be the optimal value for LP relaxation before the t-th separation round. This represents the increase in the current LP relaxation duality. Third item Contributions to the separator, among which, , To summarize the immediate benefits brought by all activated separators in this round, the following metrics are included: cut application rate (adopted cuts / generated cuts), domain shrinkage count (cumulative number or magnitude of tightening of variable upper and lower bounds), and node pruning count (number of search nodes pruned due to bounds lifting or changes in feasibility). After collecting the rewards for this round, the solver generates incremental information for the next round, constructing the incremental ternary graph for the next round. The incremental state representation for the next separation round is obtained through a graph feature encoder. ,Will The resulting data is stored in the experience replay pool for training and updating the model network in subsequent step 29. In step 27, the overhead is controlled by the frequency based on node depth. =10 Trigger separator parameter configuration, global maximum number of separation rounds limit. That is, the maximum number of separation rounds generated in each separation round. ; In step 28, a network update is performed by the policy network. Generates joint action distribution, value network The state value is evaluated by joint optimization using the policy loss function and value loss function of the reinforcement learning PPO algorithm; graph feature encoder. Updated in conjunction with the value network; In step 29, the maximum number of training rounds is 100.

[0044] This invention also provides a control device, comprising: At least one memory for storing one or more programs; At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the methods described above.

[0045] The present invention further provides a readable storage medium storing a computer program that, when executed by a processor, can implement the above-described method.

[0046] The purpose of this invention is to provide a method, device, and storage medium for dynamic configuration of cutting plane separators based on reinforcement learning (RL). This method can be implemented as an embedded module in a mathematical programming solver (SCIP compatible) to enhance its adaptive decision-making regarding the number of separation rounds and separator configuration, thereby improving solution efficiency and convergence quality, and thus solving the aforementioned technical problems in the prior art. In summary, the method of this invention provides a low-redundancy and structurally sufficient state representation through incremental ternary graphs and word blocks. Combined with block-level positional encoding and decoding-based temporal decision models, it achieves sequential joint decision-making on the maximum separation round and the separator activation state. This clearly characterizes the phased patterns of multi-round separation and the interactive dependencies between separators, thereby reducing redundant separation and numerical instability risks, improving candidate cut quality, accelerating dual boundary convergence, and reducing the average solution time and the original dual gap integral within the same time limit. Meanwhile, relying on incremental graph representation and the maximum separation round mechanism, the inference and configuration overhead can be jointly controlled, and it is compatible with the callback and parameter interface of the mainstream open-source solver SCIP. It has robustness and generalization ability on heterogeneous instances and larger-scale problems, and greatly improves the solution efficiency of mixed-integer linear programming engineering problems. This method is based on reinforcement learning (RL) to dynamically adjust the configuration of the cutting plane separator, and can be implemented as an embedded module in mathematical programming solvers (compatible with SCIP) to enhance its adaptive decision separation round and separator configuration, so as to improve the solution efficiency and convergence quality.

[0047] To more clearly demonstrate the technical solution and its effects provided by the present invention, the vision-based robot control method provided by the present invention will be described in detail below with reference to specific embodiments.

[0048] Example 1 like Figure 1 As shown, this invention provides a method for accelerating the solution of mixed-integer linear programming engineering problems based on the branch-cut plane. This method improves the efficiency of solving mixed-integer linear programming problems within the branch-cut plane (B&C) framework of the solver. It can dynamically and adaptively configure the multi-round separation process without changing other default module configurations, thereby improving the efficiency of solving engineering problems. The method includes the following steps: Step 1, Solver Interaction and Input Data Acquisition: Under the solver's branch-cut plane (B&C) framework, the status and control are connected based on the solver callback mechanism: When the search branch-bound tree (which is the branch-bound tree corresponding to the mixed integer linear programming engineering problem) reaches the trigger node, the incremental information obtained by that node in the current round of separation is collected, including the new cut, variable bound tightening increment, and separator statistics, etc., to obtain the original input data for subsequent decision-making.

[0049] Step 2, Incremental Triple Graph Construction and Transition Feature Encoding: Based on the incremental information from Step 1, an incremental triple graph containing variable nodes, newly added cut nodes, separator nodes, and their connecting edges is constructed. The trained graph feature encoder is used to encode the incremental triple graph into a full graph representation and the representations of each separator node. The full graph representation and the representations of each separator node are then concatenated into a word block representing the current separation round, which serves as the incremental state representation data.

[0050] Step 3, Timing Decision and Configuration Adjustment: Arrange the word blocks obtained in Step 2 and the word blocks generated in the historical separation rounds in chronological order, input them into the trained dynamic configuration agent model, output joint actions, configure the maximum separation round and activation state of the cutting plane separator based on the joint actions, so that the configuration of the cutting plane separator matches the real-time structure of the subproblem corresponding to the current node.

[0051] Step 4, Multi-round execution and node evolution: In the current node, perform multiple rounds of separation and decision-making according to steps 1 to 3 until the maximum number of separation rounds decided in the first separation round of step 3 is reached or the solver triggers the termination condition; then move to the next node and repeat steps 1 to 4 until the preset solution time limit is reached.

[0052] Step 5: Proceed to the next node and repeat steps 1 to 4 until the preset solution time limit is reached, thus completing the solution acceleration.

[0053] Furthermore, in step 1 of the above method, the separator statistics include candidate cut application rate, domain shrinkage, node pruning count, and other statistics; the hyperparameters such as the lexical block dimension, separator set size K, maximum separation round limit T, and trigger frequency can be set and optimized according to different dataset sizes. Specifically, the separator set size is determined by the separator set provided internally by the SCIP solver; the lexical block dimension, maximum separation round limit, and trigger frequency hyperparameters are set and optimized according to different dataset sizes, specifically through the following principles: Lexical block dimension: The lexical block dimension is adjusted according to the complexity of the dataset. For smaller datasets, the lexical block dimension can be smaller to reduce computational resource consumption; while for large-scale datasets, the lexical block dimension can be appropriately increased to capture more feature information and complex cutting plane patterns. Maximum number of separation rounds: The maximum number of separation rounds should be adjusted based on the size of the dataset and the required solution accuracy. For smaller datasets, a lower maximum number of separation rounds can be set to avoid overcomputation; for large datasets, appropriately increasing the maximum number of separation rounds can help improve solution accuracy. Trigger Frequency: The trigger frequency should be adjusted based on the difficulty of solving the dataset. Setting the trigger frequency too high may waste computational resources, while setting it too low may fail to capture changes in the problem in a timely manner. For simpler problems, a lower trigger frequency is sufficient; however, for complex datasets, frequent triggering of the separator can help better capture changes in the problem and improve solution efficiency.

[0054] See Figure 2 , Figure 3 Furthermore, in the above method, the graph feature encoder is processed in the following manner. The agent model is pre-trained by dynamically configuring the agent model, where the policy network of the dynamically configured agent model is... From the first decoding time series decision model and its linear decision-making layer The value network that constitutes and dynamically configures intelligent agent models The second decoding time series decision model and its linear value head The final result is a well-trained graph feature encoder and a policy-value network for dynamically configured agent models. The training process includes the following steps: Step 21, Callback Acquisition and Sample Generation: Within the solver's Branch-Cut Plane (B&C) framework, based on the solver callback mechanism (a custom separator for configuring parameters is defined in the SCIP solver, triggering a callback during each separation round), incremental information is collected when separation is triggered within a node, including: (211) New cut information: Read the cuts newly added in the previous separation stage (if it is the initial separation round, read the original constraint information of the MILP subproblem. Since the cut is a newly added constraint, the feature reading method is consistent), and record its: source category (which type of separator generated it), target parallelism (the similarity between this cut and the direction of the objective function), cut efficiency (the cutting depth of the cut on the current relaxed feasible region), sparsity (the proportion of variables with non-zero parameters in this cut to all variables); (212) Current round variable information: Read the column structure information (i.e. variable information) of the current MILP problem from the solver. Variable type (whether it is binary, integer, continuous, etc.), upper and lower bounds of the variable and whether the current value is in bounds, base state (whether the variable is on the basis of the LP relaxation problem), the current solution value of the variable and its fractional part, marginal value (the unit benefit that changing the variable can bring to the current model); (213) Statistics of the current separator: For each separator, record the number of cuts generated, the utilization rate of the generated cuts (the proportion of cuts generated by the separator that are selected), the pruning contribution (the cumulative number of unnecessary branches pruned by the cuts generated by the separator), the separator time (the cumulative time consumed by the separator being called up to the current subproblem), and the domain shrinkage (the cumulative number of times the domain of variable values ​​found by the cuts generated by the separator shrinks). (214) Instance-level global features: LP dual degeneration degree (the degree of constraint redundancy of LP relaxation in the dual solution space, reflecting whether the model is sensitive to small cuts). Step 22, Incremental ternary graph feature construction: The features obtained in step 21 are... The incremental information of the round separation is organized as an incremental ternary graph of "variable node - newly added cut node - separator node". The features of the three types of nodes and edge features in the incremental ternary graph include: (221) Node characteristics: variable nodes Features The feature vectors of the variable information obtained in step 21 are used to represent the current round; new cut nodes are added. Features The feature vector representation of the newly obtained cut information from step 21; the separator. Node features The feature vector representation of the current round separator statistics obtained in step 21 is used, where, , representing K separators, actually configured in SCIP A separator.

[0055] (222) Edge features: (1) Sparse edge connections are established between the newly added cut node and the variable node. The edge features consist of two weights: one is the original coefficient of the variable in the newly added cut, and the other is the normalized coefficient obtained by normalizing the entire coefficient vector of the newly added cut. The former provides the numerical scale information of the edge, and the latter provides the geometric direction information of the edge, which weakens the impact of the coefficient scale difference on training. (2) Lightweight full connections are used between the separator node and the variable node, and between the separator node and the newly added cut node. The initial weight of the edge is uniformly set to 1 to represent the potential relationship between the separator and the variable and the cut. The specific aggregate weight can be adaptively adjusted by the model during training. (3) A complete graph without self-loops is constructed between the separator nodes. The initial weight of the edge is also set to 1 to express the cooperative or competitive relationship between different separator families. The subsequent aggregate weight is also learned by the model and reweighted.

[0056] Step 23, the graph feature encoder constructs the incremental state representation of the word block: the incremental ternary graph obtained in step 22 is used to construct the incremental state representation of the word block. Input graph feature encoder Representation extraction is performed. The graph feature encoder normalizes and maps the three types of nodes with two fully connected layers, unifying the original features into a 64-dimensional implicit embedding space. Then, bidirectional two-part message passing is performed on the graph: a layer of bidirectional convolution with edge features is performed between variables and new cuts, between separators and variables, and between separators and new cuts, aggregating the feature information from the other end before fusing it with the local feature. Furthermore, a self-attention mechanism is added between separator nodes to capture the dependencies between separators and make the model focus more on the more efficient separators. Finally, the vectors obtained from the above operations on the three types of nodes are batch-added and pooled, then concatenated with the instance-level global features from step 21, and compressed into a 64-dimensional full-graph representation through two layers of multilayer perceptrons. Meanwhile, the node-level embedding vector of each separator node before pooling is retained as the 64-dimensional node representation of each separator. By vertically concatenating a full-graph representation and the representations of K separator nodes, this set of vectors forms the word block for the current separation round. ; Among them, subscript Refers to the first Round separation, For the first Incremental ternary graph of round separation, For graph feature encoders, Let K be the real number field, and K be the number of separators. The value is 22, and d is the representation dimension, with a value of 64. Meta-block Used to represent the incremental state representation of the current separation round.

[0057] Step 24, Lexical Block Temporalization and Block-Level Position Encoding: This involves encoding the lexical blocks of the current separated round. Word blocks are strung together in chronological order and according to historical rounds to form a sequence. Before being fed into the decision model, block-level positional encoding is applied: all tokens within the same round share the same position index, and the position indices of different rounds increase sequentially over time. This design allows the model to focus on the temporal relationships between separate rounds without distinguishing the order of tokens within the same round. Simultaneously, the attention mask uses a block-based lower triangle causal mask, allowing the current separate round to use information from all past rounds (not future rounds), ensuring autoregressive decision-making.

[0058] Step 25, Dynamically configure the policy network and value network of the agent model: Input the word block sequence with block-level positional encoding into the policy network and value network: Policy network Decoding time series decision model and its linear decision-making layer Composition, value network Decoding time series decision model and its linear value head Composition. For policy networks, The output is a temporal embedding vector that is identical to the input; for the lexical block (K+1 lexical units) of the current separation round, the in-block embedding is input into... Output the classification distribution vector of the joint action, and obtain the current action based on the classification distribution vector. Combined actions of the round separation : ; Among them, the maximum number of separation rounds is capped. (Deciding "when to stop the separation"); the first Separator activation status ( (where K represents K separators), Indicates "post-activation". Indicates "disabled". This indicates "early activation".

[0059] The design satisfies permutation equivariance within the block, namely the upper limit of the first element block and the maximum separation round. Correspondingly, the arrangement of the separator terms is aligned one-to-one with the corresponding activation state components. During inference, the last term block is processed only once through the policy network, and the joint action is output. During training, the distribution of each block in the entire historical word block sequence can be solved to calculate the target and loss. For the value network, the word block of the current separation round is used. A sequence of lexical blocks concatenated chronologically with historical lexical blocks is denoted as... ,Will go through The processed output is the temporal embedding vector on the value side; from Extract the first word of the word block in the current separation round. The output at the corresponding position is used as the first word embedding vector. The first word embedding vector is then processed by a linear value head. Output scalar This value estimate of the state in the separation round is used to calculate the objective function for training in the subsequent reinforcement learning PPO algorithm.

[0060] Step 26, Action Rewriting and Reward Collection: Combine Actions Write back to the solver's parameter callback interface to configure the current node's separation parameter settings for this round, including the maximum upper limit of separation rounds. With each separator in activation status After completing this round of separation, an incremental reward is constructed based on the solution feedback. : ; The meanings of each item are as follows: First item The time-consuming penalty item is, among which, , Let be the solution time of the solver up to round t. This represents the increment of the cumulative solution time up to round t; This represents the solver's estimated solution time for this instance based on the default separator parameter configuration; N is the total number of planned separation rounds in the complete B&C process. Therefore, the first term means: time exceeding the amortized budget in each round is a negative score, while time saved is a positive score, and this can be adjusted in the implementation. Standardization or cropping can be performed to avoid extreme samples causing unstable training.

[0061] Second item For dual boundary improvement terms, among which , Let be the optimal value for LP relaxation before the t-th separation round. This represents the increase in the current LP relaxation duality; expressed as a relative ratio. Scoring can align different units and scales across instances, avoiding the impact of excessively large / small absolute boundaries of individual instances on learning stability.

[0062] Third item Contributions to the separator, among which, , To summarize the immediate benefits brought by all activated separators in this round, the following three types of statistics are weighted and implemented: (1) Cut application rate (cuts adopted / cuts generated); (2) Domain shrinkage count (the cumulative number or magnitude of tightening of the upper and lower bounds of variables).

[0063] (3) Number of node prunings (the number of search nodes pruned due to boundary improvement or changes in feasibility). These three types of indicators directly reflect whether the cuts are truly reducing the search space or improving the dual boundary.

[0064] After collecting the incremental rewards for this round, the solver generates the incremental information for the next round and constructs the incremental ternary graph for the next round. The incremental state representation for the next separation round is obtained through a graph feature encoder. ,Will The data is stored in the experience replay pool for training and updating the model network in subsequent step 29.

[0065] Step 27 (Instance Data Collection): Repeat steps 21-26 until the current instance is solved. In practice, data is collected based on node depth frequency. Trigger separator parameter configuration (in practice, take...) (That is, it triggers once every 10 layers) to control overhead, with a global maximum limit on the number of separation rounds. That is, the maximum number of separation rounds generated in each separation round. ; Step 28, Training and Update: Randomly select 16 instances from the training set and repeat steps 21-27. Mini-sample and extract a number of instances from the experience replay pool. Perform a network update. (By policy network) Generates joint action distribution, value network Evaluate state value and perform joint optimization using the policy loss function and value loss function according to PPO; encoder Updated in conjunction with the value network; Step 29, Training Stop Condition: Training will stop when the maximum number of training rounds (100) is reached.

[0066] Figure 2 The diagram illustrates a multi-round separation process within the current node. In each tree node, the dual boundary is obtained by solving the current LP relaxation first. Then, candidate cuts are generated only for the activated separators and selected for inclusion in the model. The LP relaxation is iteratively tightened until the preset maximum number of separation rounds is reached. Figure 3 The diagram illustrates the reinforcement learning framework used; in this framework, the environment provides incremental ternary graphs on a per-separation basis. ;Graphic feature encoder Map it to a full graph representation and Each separator node is characterized And stacked into word blocks subscript Refers to the first In each round of separation, block-level positional encoding is applied to the word block sequence and then input into the policy network and value network of the dynamically configured agent model. The policy network outputs joint actions through autoregression, and the value network provides state values. The incremental rewards obtained after each round of separation are collected for training.

[0067] This invention proposes a dynamic configuration method for separators based on incremental ternary graphs. Combining block-level positional encoding and a decoder-based temporal decision model, it provides low-redundancy and structurally sufficient state representations at the separation round granularity. Based on this, a policy network outputs the joint action of the maximum separation round and the separator activation state, and a value network evaluates the state value, achieving serialized, joint, and adaptive configuration of the cut plane process. By directly integrating three types of structural information—"new cuts, variables, and separators"—in each round, these representations explicitly include the phased regularities of cut generation and the interaction dependencies between separators, significantly enhancing the learnability and interpretability of "when to stop, which should be early / late / stop," thereby improving the efficiency and stability of solving mixed-integer linear programming problems.

[0068] Compared with existing methods based on static configuration or single-round optimization, this invention has at least the following advantages: (1) Stronger structural prior: The incremental ternary graph explicitly graphs the relationship between "variable-new cut-splitter". The word block produced by the graph feature encoder retains the MILP sub-problem graph structure and context of each separation round. Combined with block-level positional encoding and decoding-type temporal decision model, it can directly capture the stage-wise rules of multiple separation rounds and the dependencies between separators.

[0069] (2) The learning objectives are closer to the actual effectiveness of the solver: the policy network outputs the joint decision of "maximum separation round and separator activation state", avoiding only static start and stop; the value network and incremental reward are aligned with "time cost, dual boundary improvement and separator contribution", making training more stable and convergence more reliable.

[0070] (3) Controllable computation and deployment costs: Incremental representation avoids global recoding in each round; the incremental graph reasoning and the decoder-only structure of "intra-block permutation and equivariance + block-level causal mask" make reasoning lightweight, and the reasoning and configuration overhead can be jointly controlled by the "maximum separation rounds" mechanism, which is seamlessly coupled with the existing solution process.

[0071] (4) Better engineering compatibility and generalization: The method is natively adapted to SCIP callbacks and parameter interfaces (and can also be extended to other solvers), maintaining good robustness and generalization ability on heterogeneous instances and larger-scale problems, which facilitates engineering implementation and continuous iteration.

[0072] Example 2 To verify the effectiveness of the method of this invention, the proposed acceleration method for solving mixed-integer linear programming (MILP) engineering problems based on cutting plane pairs was applied to the open-source solver SCIP, and tested on public mixed-integer linear programming (MILP) engineering problem datasets, mainly using nine dataset benchmarks: (1) Set Covering Problem: This problem aims to select as few subsets as possible from a given family of sets to ensure that all elements are covered. It is a typical example of mixed integer linear programming problems involving location selection and covering, and is widely used in optimization engineering fields such as facility location and resource allocation.

[0073] (2) Maximum Independent Set (MIS) Problem: In graph theory, the maximum independent set problem requires selecting the maximum number of non-adjacent vertices in a graph. It is a classic benchmark problem in combinatorial optimization and is often used in social network analysis, communication network design and other fields.

[0074] (3) Multiple Knapsack Problem: This problem involves distributing items with value and volume into multiple knapsacks to maximize the total value under capacity constraints. It is of great significance in practical applications such as logistics distribution and resource allocation.

[0075] (4) CORLAT Dataset: The CORLAT dataset originates from actual planning tasks in forestry and conservation, and typically includes constraint structures such as site selection and resource allocation. This dataset is used for MILP benchmarking in fields such as forest resource management and ecological protection.

[0076] (5) Mixed Integer Knapsack (MIK): Under knapsack constraints, the mixed integer knapsack problem involves mixed integer optimization with both integer and continuous variables, combining selection and allocation characteristics. It has wide applications in production scheduling, portfolio optimization, and other fields.

[0077] (6) Load Balancing (LB): This problem comes from the actual large-scale system scenario of the ML4CO competition. It aims to distribute tasks or traffic to multiple nodes to balance the load and reduce peak loads. It is widely used in data centers, cloud computing resource scheduling and other fields.

[0078] (7) Anonymous Industrial Problem: This problem originates from the Maritime Inventory Management Problem (MIRP) in global bulk shipping. The goal is to optimize vessel scheduling and inventory management across multiple ports to meet demand and reduce costs. The dataset is derived from a publicly available MIRP dataset, but has been anonymized for the competition. This problem falls under the category of optimization engineering problems in real-world scheduling scenarios.

[0079] (8) MIPLIB Mixed NEOS Subset: This subset is part of the MIPLIB 2017 benchmark and covers mixed integer models with multi-source constraints, such as engineering and logistics. It is used to test the performance of mixed integer programming solvers.

[0080] (9) MIPLIB Mixed Support Case Subset: This subset is another part of the MIPLIB 2017 benchmark and contains industrial-grade constraint structures with sparse and dense intersections. It is used to test the performance of mixed integer programming solvers.

[0081] Among the aforementioned datasets, CORLAT, LB, Anonymous, MIPLIB mixed neos, and MIPLIB mixed supportcase all originate from real-world applications, representing optimization engineering problems across multiple domains. The CORLAT dataset covers practical planning tasks such as forest resource management and ecological protection; the LB dataset stems from large-scale load balancing problems; and the Anonymous dataset originates from maritime inventory management problems in global bulk shipping. MIPLIB mixedneos and MIPLIB mixed supportcase are real-world datasets from the MIPLIB 2017 benchmark, containing complex engineering and logistical constraints. These datasets not only reflect real-world optimization challenges but also provide valuable practical data for solving optimization engineering problems.

[0082] Table 1 shows the comparison results between the proposed method and the baseline method on easy, medium, and difficult datasets. It reports the average solution time (lower is better) and the primal-dual gap integral (lower is better), and provides the improvement rate relative to NoCuts. Table 1 also lists the average size (number of variables, number of constraints) of each benchmark. The main methods compared are: (1) NoCuts: No cuts are added, only the pure B&B baseline is used.

[0083] (2) Default: The default splitter configuration for SCIP 8.0.0.

[0084] (3) Search(k): Randomly sample k groups of configurations and select the best performing group on the validation set for testing. In this invention, k is 50 or 30.

[0085] (4) Prune: During the validation phase, deactivate separators that do not contribute.

[0086] (5) L2Sep(R1): A learning method that learns the configuration only during the first round of separation.

[0087] (6) L2Sep(R2): A learning method that learns the configuration only during the first and second rounds of separation.

[0088] (7) LLM4Sep: A learning method based on the large language model (LLM) to generate / select the splitter configuration.

[0089] Table 1 consists of Tables 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, and 1-9, among which... Table 1-1 shows the comparison results of various methods with the present invention on a set-coverage problem dataset, which is considered an easy dataset. Here, n represents the average number of variables in all samples of the set-coverage problem dataset, with a value of 1000, and m represents the average number of constraints in all samples of the set-coverage problem dataset, with a value of 500. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral. .

[0090] Table 1-2 shows the comparison results of various methods with the present invention on the maximally independent set problem dataset, which is an easy dataset. Here, n represents the average number of variables in all samples of the maximally independent set problem dataset, with a value of 500, and m represents the average number of constraints in all samples of the maximally independent set problem dataset, with a value of 1953. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral.

[0091] .

[0092] Table 1-3 shows the comparison results of various methods with the present invention on the multiple knapsack problem dataset, which is an easy dataset. Here, n represents the average number of variables in all samples of the multiple knapsack problem dataset, with a value of 720, and m represents the average number of constraints in all samples of the multiple knapsack problem dataset, with a value of 72. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral.

[0093] .

[0094] Table 1-4 shows the comparison results of various methods with the present invention on the CORLAT dataset, which is a medium-sized dataset. Here, n represents the average number of variables in all samples of the CORLAT dataset, with a value of 466, and m represents the average number of constraints in all samples of the CORLAT dataset, with a value of 486. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PDintegral is the primal-dual gap integral.

[0095] .

[0096] Table 1-5 compares the methods of this invention on a mixed integer knapsack problem dataset of medium size. Here, n represents the average number of variables in all samples of the mixed integer knapsack problem dataset, with a value of 413, and m represents the average number of constraints in all samples of the mixed integer knapsack problem dataset, with a value of 346. In the second row header, Time indicates the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral.

[0097] .

[0098] Table 1-6 shows the comparison results of various methods with the present invention on the anonymous industrial problem dataset, which is a difficult dataset. Here, n represents the average number of variables in all samples of the anonymous industrial problem dataset, which is 37881, and m represents the average number of constraints in all samples of the anonymous industrial problem dataset, which is 49603. In the second row of the table header, Time refers to the solution time in seconds (s), PD integral is the primal-dual gap integral, and Improve.(PD Int., %) indicates the improvement of the primal-dual gap integral solved by the current method relative to the NoCuts baseline method.

[0099] .

[0100] Table 1-7 shows the comparison results of various methods with the present invention on a load balancing problem dataset, which is a difficult dataset. Here, n represents the average number of variables in all samples of the load balancing problem dataset, with a value of 61000, and m represents the average number of constraints in all samples of the load balancing problem dataset, with a value of 64304. In the second row header, Time refers to the solution time in seconds (s), PD integral is the primal-dual gap integral, and Improve.(PD Int., %) indicates the improvement of the primal-dual gap integral solved by the current method compared to the NoCuts baseline method.

[0101] .

[0102] Table 1-8 shows the comparison results of various methods with the present invention on the MIPLIB mixed NEOS subset dataset, which is a difficult dataset. Here, n represents the average number of variables in all samples of the MIPLIB mixed NEOS subset dataset, with a value of 6958, and m represents the average number of constraints in all samples of the MIPLIB mixed NEOS subset dataset, with a value of 5660. In the second row header, Time refers to the solution time in seconds (s), PD integral is the primal-dual gap integral, and Improve.(PDInt., %) indicates the improvement of the primal-dual gap integral solved by the current method compared to the NoCuts baseline method.

[0103] .

[0104] Tables 1-9 show the comparison results of various methods with the present invention on the MIPLIB hybrid supportcase subset dataset, which is a difficult dataset. Here, n represents the average number of variables in all samples of the MIPLIB hybrid supportcase subset dataset, with a value of 19766, and m represents the average number of constraints in all samples of the MIPLIB hybrid supportcase subset dataset, with a value of 19910. In the second row header, Time refers to the solution time in seconds (s), PD integral is the primal-dual gap integral, and Improve.(PD Int., %) indicates the improvement of the primal-dual gap integral solved by the current method compared to the NoCuts baseline method.

[0105] .

[0106] Table 2 shows the comparison results of the proposed method with its four reduced versions on datasets of different difficulties: easy, medium, and hard datasets: (1) removing the maximum separation round decision (w / o MaxR); (2) replacing the decoding-based temporal decision model with LSTM (Long Short-Term Memory Network) (w / o TF); (3) removing the incremental state representation of the incremental ternary graph (w / o DynG); (4) and simultaneously removing the two modules mentioned in (2) and (3) above (w / o DynG&TF). From the two indicators—average solution time and primal-dual gap integral—the proposed method consistently performs best. The removal of any key component will worsen the average solution time and primal-dual gap integral, indicating that learning when to stop, using the incremental ternary graph as the state, and adopting the decoding-based temporal decision model for separation round-level temporal decision-making are all indispensable for performance.

[0107] Table 2 consists of the following sub-tables, namely Table 2-1, Table 2-2, and Table 2-3, among which... Table 2-1 shows the comparison results of various methods with the present invention on the multiple knapsack problem dataset, which is an easy dataset. Here, n represents the average number of variables in all samples of the multiple knapsack problem dataset, with a value of 720, and m represents the average number of constraints in all samples of the multiple knapsack problem dataset, with a value of 72. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral. .

[0108] Table 2-2 shows the comparison results of various methods with the present invention on the CORLAT dataset, which is a medium-sized dataset. Here, n represents the average number of variables in all samples of the CORLAT dataset, with a value of 466, and m represents the average number of constraints in all samples of the CORLAT dataset, with a value of 486. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PDintegral is the primal-dual gap integral.

[0109] .

[0110] Table 2-3 shows the comparison results of various methods with the present invention on the MIPLIB mixed NEOS subset dataset, which is a difficult dataset. Here, n represents the average number of variables in all samples of the MIPLIB mixed NEOS subset dataset, with a value of 6958, and m represents the average number of constraints in all samples of the MIPLIB mixed NEOS subset dataset, with a value of 5660. In the second row header, Time refers to the solution time in seconds (s), PD integral is the primal-dual gap integral, and Improve.(PDInt., %) indicates the improvement of the primal-dual gap integral solved by the current method compared to the NoCuts baseline method.

[0111] .

[0112] Table 3 is an evaluation table of the generalization ability of the method of the present invention on the larger-scale Maximum Independent Set (MIS) problem: the average solution time and primal dual gap integral of each method are compared on MIS scaled up by 4 times and 9 times, showing that the present invention is not only effective within the training scale, but also can robustly generalize to larger and more difficult instances.

[0113] Table 3 consists of Table 3-1 and Table 3-2, among which, Table 3-1 shows the comparison results of various methods with the present invention on the maximum independent set problem dataset. Here, n represents the average number of variables in all samples of the maximum independent set problem dataset after a 4-fold expansion, with a value of 1000; m represents the average number of constraints in all samples of the maximum independent set problem dataset after a 4-fold expansion, with a value of 3946; the 4× indicates that the overall dataset size has been expanded by 4 times, where size refers to the number of variables multiplied by the number of constraints. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PD integral is the primal-dual gap integral. .

[0114] Table 3-2 shows the comparison results of various methods with the present invention on the maximum independent set problem dataset. Here, n represents the average number of variables in all samples of the maximum independent set problem dataset after a 9-fold expansion, with a value of 1500; m represents the average number of constraints in all samples of the maximum independent set problem dataset after a 9-fold expansion, with a value of 5940; the 9× indicates that the overall dataset size has been expanded by 9 times, where size refers to the number of variables multiplied by the number of constraints. In the second row header, Time refers to the solution time in seconds (s), Improve.(time, %) indicates the improvement in solution time of the current method relative to the NoCuts baseline method, and PDintegral is the primal-dual gap integral.

[0115]

[0116] Example 3

[0117] Preparation phase: The MILP dataset and the B&C Solver Environment (SCIP) were selected for the experiment. The problem was split into two parts: a "solver (environment)" and a "policy controller (agent)". The solver executes the LP relaxation and separation process within each node and provides incremental information on separation rounds (new cuts, variable states, separator statistics, global metrics, etc.) through callbacks. The policy controller receives this information and decides on the "maximum number of separation rounds and separator activation state". The action space and round-level rewards defined in the paper are abstracted (time cost penalty, relative duality improvement, and weighted sum of separator contributions). The optimization objective is to maximize the cumulative reward, thereby reducing the average solution time and the original duality gap integral.

[0118] Training phase: The steps and flow given in Embodiment 1 of this invention are implemented using deep learning methods and deployed in the open-source solver SCIP for cutting plane algorithm configuration. The configuration strategy follows the corresponding flow in the steps to interact with the SCIP solver, and the interaction information is used for strategy training. The training is repeated for a period of time.

[0119] Verification phase: The trained policy is fixed in inference mode, performing only forward decision-making and dynamic configuration without updating network parameters. Evaluation is conducted on independent validation / test instances with the same SCIP configuration, time limit, and callback frequency as during training. The average solution time and primal-dual gap integral on each benchmark are statistically analyzed and compared with the baseline. Lower average solution time and primal-dual gap integral indicate that the policy can more quickly tighten the dual boundary, reduce redundant separation, and improve overall search efficiency in actual solutions, thus verifying the practical performance and generalization ability of the invention.

[0120] 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.

[0121] 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 accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs, characterized in that, This tool is used to dynamically adjust the configuration of the cutting plane separator to accelerate the solution process when solving subproblems corresponding to nodes of the branch and bound tree for mixed integer linear programming engineering problems within a branch-cut plane framework. The algorithm includes: Step 1: Under the current node of the branch and bound tree, use the solver callback mechanism to obtain the incremental information of the current separation round; Step 2: Based on the incremental information, construct an incremental triple graph containing three types of nodes: variables, new cuts, and separators. Encode the incremental triple graph into a full graph representation and a separator node representation using a trained graph feature encoder, and then concatenate them into a word block for the current separation round. Step 3: Arrange the word blocks of the current separation round and the historical word blocks in chronological order, input them into the trained dynamic configuration agent model, output the joint action, configure the maximum separation round and activation state of the cutting plane separator based on the joint action, so that the configuration of the cutting plane separator matches the real-time structure of the subproblem corresponding to the current node; Step 4: Perform multiple rounds of separation within the current node according to Steps 1 to 3 until the maximum number of separation rounds determined in the first round of separation in Step 3 or the solver termination condition is reached; Step 5: Proceed to the next node and repeat steps 1 to 4 until the preset solution time limit is reached, thus completing the solution acceleration.

2. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting planes according to claim 1, characterized in that, The mixed-integer linear programming engineering problem includes any of the following: Engineering problems including: facility site selection, resource allocation, social network analysis, communication network design, logistics and distribution, resource distribution, forest resource management, ecological protection, production scheduling, portfolio optimization, data center resource scheduling, cloud computing resource scheduling, ship scheduling between multiple ports, inventory management, multi-source constrained engineering problems, multi-source constrained logistics engineering problems, and engineering problems with sparse and dense intersecting industrial-grade constraint structures.

3. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 1, characterized in that, The incremental information in step 1 includes: new cut, variable bound tightening increment, and separator statistics; wherein, the separator statistics include: candidate cut application rate, domain shrinkage, and node pruning count.

4. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 3, characterized in that, In step 2, an incremental ternary graph containing three types of nodes—variables, newly added cuts, and separators—is constructed based on incremental information in the following manner: Construct variable nodes, add cut nodes, and separator nodes respectively; among them, The constructed variable node represents a variable in a mixed-integer linear programming problem. The features of the variable node, including the variable type, current value range, current solution value, whether the variable's upper and lower bounds are touched, and whether the variable is in the base state in the current relaxation problem, are combined into the feature vector of the variable node. The newly constructed cut node represents the cut newly generated in the current separation round. The features of the newly constructed cut node, including the source of the cut, the target parallelism of the cut, the efficiency of the cut, and the sparsity of the cut, are combined into the feature vector of the newly constructed cut node. The constructed separator node represents a separator used in the current separation round. The features of the separator node, including the number of cuts generated by the separator, the application rate of the cuts, the pruning contribution, the time consumed by the separator, and the domain shrinkage, are combined into the feature vector of the separator node. By transforming the relationships between the variable nodes, newly added cut nodes, and separator nodes constructed above into graph edges, the edge weight between the newly added cut node and the variable node is determined based on the coefficients of the variables involved in the cut. The edges between the separator node and the variable node and the newly added cut node adopt a lightweight fully connected connection method, and the edge weight is initialized to 1. This edge weight is subsequently adaptively adjusted by the dynamically configured agent model.

5. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to any one of claims 1-4, characterized in that, In step 2, the incremental triple graph is encoded into a full graph representation and a separator node representation using the trained graph feature encoder, and then concatenated into a word block for the current separation round, including: The incremental ternary graph is input into the graph feature encoder, which normalizes and performs two fully connected layers on the feature vectors of the three types of nodes, mapping the feature vectors uniformly into a 64-dimensional implicit embedding space. Then, bidirectional two-part message passing is performed on the incremental ternary graph: a layer of bidirectional convolution with edge features is performed between variable nodes and newly added cut nodes, between separator nodes and variable nodes, and between separator nodes and newly added cut nodes, aggregating the feature information from the other end before fusing it with the local feature. A self-attention mechanism is added between separator nodes to capture the dependencies between them and allow the dynamically configured agent model to focus on separator nodes with higher efficiency. Finally, the vectors obtained from the above operations on the three types of nodes are batch-added and pooled, then concatenated with the instance-level global features of the incremental ternary graph, and compressed into a 64-dimensional full-graph representation through two layers of multilayer perceptrons. Meanwhile, the node-level embedding vector of each separator node before pooling is retained as a 64-dimensional representation of each separator node. , The 64-dimensional full graph representation and the K separator node representations are vertically concatenated into a vector, which represents the word block for the current separation round. : ； Among them, subscript Refers to the first Round separation, For the first Incremental ternary graph of round separation, For graph feature encoders, Let K be the real number field, and K be the number of separators. The value is 22, and d is the representation dimension, with a value of 64.

6. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to any one of claims 1-4, characterized in that, The graph feature encoder used in step 2 and the dynamically configured agent model used in step 3 are pre-trained in the following manner, including: Step 21, Callback Acquisition and Sample Generation: When solving the subproblems corresponding to each node of the branch and bound tree of the mixed integer linear programming engineering problem in the branch-cut plane framework using the solver, incremental information is collected when separation is triggered within the node based on the solver callback mechanism. Step 22, Incremental ternary graph construction: The ternary graph obtained in step 21 is... The incremental information of the round separation is organized as an incremental ternary graph of variable nodes - newly added cut nodes - separator nodes; Step 23: Construct incremental state representations in the form of word blocks using a graph feature encoder: Input the incremental ternary graph obtained in step 22 into the graph feature encoder to extract word blocks representing the incremental state representation of the current separation round. ; Step 24, Lexical Block Temporalization and Block-Level Position Encoding: This involves encoding the lexical blocks of the current separated round. The historical word blocks separated from the historical rounds in chronological order are concatenated into a word block sequence. Before being fed into the overall decoding time-series decision model of the dynamically configured intelligent agent model, block-level positional encoding is applied to the word block sequence to obtain the word block sequence with added block-level positional encoding. Step 25, Dynamically configure the policy network and value network of the agent model: Input the word block sequence with block-level position encoding into the policy network and value network of the dynamically configured agent model respectively. The policy network outputs a temporal embedding vector that is the same as the input, i.e., joint action. The value network outputs the temporal embedding vector of the value side. Step 26, Action Writeback and Reward Collection: Write the joint actions back to the solver's parameter callback interface, configure the separation parameter settings for this round of this node, and construct incremental rewards based on the solution feedback after completing this round of separation. After collecting the incremental reward for this round, the solver generates the incremental information for the next round, constructs the incremental ternary graph for the next round, and obtains the incremental state representation of the next separation round through the graph feature encoder. The data consisting of the current separation round incremental ternary graph, joint action, incremental reward, and next round incremental ternary graph is stored in the experience replay pool for training and updating in subsequent step 28. Step 27, Instance Data Collection: Repeat steps 21 to 26 until the current instance is solved; Step 28, Training and Update: Divide each dataset into 80% training set and 20% test set. Randomly select 16 instances from the training set and repeat steps 21 to 27. Take out a number of data consisting of the current separation round incremental ternary graph, joint action, incremental reward, and next round incremental ternary graph from the experience replay pool according to the set batch sampling to update the policy network and value network. Step 29, Training Stop Condition: Repeat steps 21 to 28 above until the upper limit of training rounds is reached, then stop training, and you will get the trained graph feature encoder and dynamically configured agent model.

7. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 6, characterized in that, The incremental rewards in step 26 include: time cost penalty for each round of separation, dual boundary improvement, and separator contribution.

8. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 6, characterized in that, In step 21, the solver's callback mechanism refers to the following: a custom separator in the SCIP solver, specifically designed for configuring parameters, triggers a callback during each separation round. The incremental information collected in step 21 when separation is triggered within a node includes: (211) New cut information: Read the cuts newly added in the previous separation phase and record the source category, target parallelism, cut efficiency and sparsity of the cut; If it is the initial separation round, then read the original constraint information of the mixed integer linear programming engineering problem; (212) Current round variable information: Read the variable information of the current mixed integer linear programming engineering problem from the solver, including variable type, upper and lower bounds of the variable and whether the current value is in bounds, base state, current solution value of the variable and its decimal part value, and marginal value; (213) Statistical information of the separator in this round: record the number of generated cuts, utilization rate of generated cuts, pruning contribution, separator time and domain shrinkage of each separator; (214) Instance-level global features: Lebesgue space duality degeneracy.

9. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 8, characterized in that, The incremental ternary graph in step 22 The node features and edge features of the three types of nodes are as follows: (221) Node characteristics: variable nodes Features The feature vectors of the variable information obtained in step 21 are used to represent the current round; new cut nodes are added. Features The feature vector representation of the newly added cut information obtained in step 21 is used; the separator node. Features The feature vector representation of the current round separator statistics obtained in step 21 is used, where, , representing K separators; (222) Edge features: (A) Sparse edge connections are established between the newly added cut nodes and the variable nodes. The edge features consist of two weights: one is the original coefficient of the variable in the newly added cut, and the other is the normalized coefficient obtained by normalizing the entire coefficient vector of the newly added cut. (B) Lightweight full connections are used between the separator nodes and the variable nodes, and between the separator nodes and the newly added cut nodes. The initial weight of the edges is uniformly set to 1 to represent the potential relationship between the separator and the variable and the newly added cut. The specific aggregate weights are adaptively adjusted by the dynamically configured agent model during training. (C) A complete graph without self-loops is constructed between the separator nodes. The initial weight of the edges is set to 1 to represent the cooperative or competitive relationship between different separator families. The aggregate weights are learned by the dynamically configured agent model and reweighted. In step 23, the graph feature encoder extracts incremental state representations in the form of word blocks from the input incremental ternary graph in the following manner: The feature vectors of the three types of nodes are normalized and mapped using two fully connected layers, uniformly mapping the feature vectors to a 64-dimensional implicit embedding space; then, bidirectional two-part message passing is performed on the incremental ternary graph: a layer of bidirectional convolution with edge features is performed between the variable and the new cut, between the separator and the variable, and between the separator and the new cut, aggregating the feature information of the other end and then fusing it with the feature of the local end; a self-attention mechanism is added between the separator nodes to capture the dependencies between separators and allow the dynamically configured agent model to focus on the separator with higher efficiency; finally, the vectors obtained from the above operations of the three types of nodes are batch-added and pooled, then concatenated with the instance-level global features in step 21, and compressed into a 64-dimensional full graph representation through two layers of multilayer perceptrons. Meanwhile, the node-level embedding vector of each separator node before pooling is retained as a 64-dimensional representation of each separator node. , The 64-dimensional full graph representation and the representations of the K separator nodes are vertically concatenated into a vector. This vector is the word block of the current separation round used to represent the incremental state representation of the current separation round. : ； Among them, subscript Refers to the first Round separation, For the first Incremental ternary graph of round separation, For graph feature encoders, Let K be the real number field, and K be the number of separators. The value is 22, and d is the representation dimension, with a value of 64.

10. The method for accelerating the solution of mixed-integer linear programming engineering problems based on cutting plane pairs according to claim 9, characterized in that, In step 24, block-level positional encoding is applied to the word block sequence to obtain the word block sequence with added block-level positional encoding in the following manner: All word block sequences within the same separation round share the same position index, while the position indices of all word block sequences in different separation rounds increment over time. Meanwhile, the attention mask uses a causal mask with a lower triangle that only allows the current split round to use information from all previous split round blocks; In step 25, the policy network of the agent model is dynamically configured. From the first decoding time series decision model and its linear decision-making layer The policy network is structured such that it outputs a temporal embedding vector that is identical to the input, i.e., a joint action. ,for: The intra-block embedding vector of the word block sequence with K+1 words in the current separation round is input into the linear decision layer of the policy network. Output the classification distribution vector of the joint action, and obtain the current action based on the classification distribution vector. Combined actions of the round separation : ； in, This represents the maximum number of separation rounds. The i-th separator is in an active state. ; Indicates activation later. Indicates that it is deactivated. Indicates initial activation; In step 25, the value network of the agent model is dynamically configured. The second decoding time series decision model and its linear value head The value network is constructed such that it outputs temporal embedding vectors on the value side in the following manner: The word block of the current separation round A sequence of lexical blocks formed by concatenating historical lexical blocks in chronological order is denoted as [lexical block sequence]. , the sequence of word blocks Input to the second decoding time series decision model Processing, i.e. After processing by the second decoding-based temporal decision model, the output is the temporal embedding vector of the value side; from Extract the first word of the word block in the current separation round. The output at the corresponding position is used as the first word embedding vector. The first word embedding vector is then processed by a linear value head. Output scalar This serves as a value estimate of the state in the separation round, which is used by the subsequent reinforcement learning algorithm to calculate the objective function for training. In step 26, the incremental reward is constructed based on the solution feedback. for: ； The meanings of each item are as follows: First item The time-consuming penalty item is, among which, , Let be the solution time of the solver up to round t. This represents the increment of the cumulative solution time up to round t; N represents the estimated solution time for this instance based on the default separator parameter configuration; N is the total number of planned separation rounds in the full branch-cut plane process. Second item For duality improvement terms, where, , Let be the optimal value for LP relaxation before the t-th separation round. This represents the increase in the current LP relaxation duality. Third item Contributions to the separator, among which, , To summarize the immediate benefits brought by all activated separators in this round, including: generation cut application rate, number of domain shrinkages, and number of node prunings; After collecting the rewards for this round, the solver generates incremental information for the next round, constructing the incremental ternary graph for the next round. The incremental state representation for the next separation round is obtained through a graph feature encoder. ,Will The resulting data is stored in the experience replay pool for training and updating the model network in subsequent step 29. In step 27, the overhead is controlled by the frequency based on node depth. =10 Trigger separator parameter configuration, global maximum number of separation rounds limit. That is, the maximum number of separation rounds generated in each separation round. ; In step 28, a network update is performed by the policy network. Generates joint action distribution, value network The state value is evaluated and jointly optimized using the policy loss function and value loss function of the reinforcement learning algorithm; the graph feature encoder and value network are updated together. In step 29, the maximum number of training rounds is 100.

Images