Optimization solving system for large-scale mixed integer linear programming problem

Abstract

The invention discloses an optimization solution system for a large-scale mixed integer linear programming problem, and the system is characterized in that the system comprises a problem decomposition module which is used for modeling the large-scale mixed integer linear programming problem into a bipartite graph for representation, and dividing the bipartite graph into a plurality of sub-graphs through a graph decomposition algorithm; the problem reduction module is used for obtaining a feature code of each sub-graph node, inputting the feature code into a pre-training neural network to obtain a variable prediction value, reducing the scale of the large-scale mixed integer linear programming problem through a redundancy constraint removal and coefficient priority variable fixing strategy based on the variable prediction value, and then outputting the problem; and the efficient solving module is used for solving the large-scale mixed integer linear programming problem based on the result output by the problem reduction module and weighted subgraph division. According to the method, the high-quality solution of the large-scale mixed integer linear programming problem can be quickly given, so that the high-quality feasible solution can be obtained within the acceptable time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer optimization algorithm, and particularly relates to an optimization solution system for large-scale mixed integer linear programming problems. BACKGROUND

[0002] The mixed integer linear programming can maximize or minimize a linear objective function by constructing a linear optimization model containing continuous variables and integer variables under the premise of meeting various linear constraint conditions, so as to realize the optimal allocation of resources, the effective reduction of cost and the significant improvement of efficiency, and thus provide corresponding technical support for the decision of each industry, help it to make the best decision in the complex real scene, and enhance the competitiveness and economic benefits.

[0003] With the rapid development of the field of operational optimization, the end-to-end efficient solution paradigm has gradually transformed from the traditional small-scale mixed integer linear programming problem to the large-scale complex optimization problem, thereby promoting the deep integration of mathematical programming theory and modern algorithm technology, including the development of frontiers such as heuristic algorithm improvement, decomposition strategy innovation and machine learning driven intelligent optimization method.

[0004] However, in the process of optimizing and solving problems based on large-scale mixed integer linear programming technology at present, due to the exponential growth of the scale of corresponding variables and constraints, the calculation complexity of traditional precise algorithms increases dramatically, so that in actual application scenarios, it is impossible to effectively balance the solution accuracy and calculation efficiency, that is, it is impossible to obtain a high-quality feasible solution within an acceptable time.

[0005] In summary, the existing optimization solution system cannot quickly give a high-quality solution to the large-scale mixed integer linear programming problem. SUMMARY

[0006] The purpose of the present application is to provide an optimization solution system for large-scale mixed integer linear programming problems, which can quickly give a high-quality solution to the large-scale mixed integer linear programming problem and solve the problems existing in the prior art.

[0007] The purpose of the present application is achieved by the following technical solutions:

[0008] An optimization solution system for large-scale mixed integer linear programming problems, comprising:

[0009] A problem decomposition module is used to model the large-scale mixed integer linear programming problem as a bipartite graph representation, and divide the bipartite graph into a plurality of subgraphs by a graph decomposition algorithm to obtain a weighted subgraph partitioning;

[0010] a problem reduction module, configured to obtain the feature encoding of each subgraph node obtained by the problem decomposition module, input the pre-trained neural network to obtain a variable prediction value, and reduce the scale of the large-scale mixed integer linear programming problem based on the variable prediction value through a redundant constraint removal and a coefficient priority variable fixing strategy, and output the reduced large-scale mixed integer linear programming problem;

[0011] an efficient solving module, configured to solve the large-scale mixed integer linear programming problem based on the result output by the problem reduction module and a weighted subgraph partition.

[0012] the processing procedure of modeling the large-scale mixed integer linear programming problem as a bipartite graph in the problem decomposition module comprises:

[0013] the bipartite graph representation method is used to model the large-scale mixed integer linear programming problem as a graph structure comprising variable nodes and constraint nodes, wherein the edge connection relationship reflects the relevance between the variables and the constraints;

[0014] the processing procedure of partitioning the bipartite graph into a plurality of subgraphs in the problem decomposition module comprises:

[0015] after determining the number of subgraph partitions and the load balancing parameters, the bipartite graph is decomposed into a plurality of subgraphs through a graph partition algorithm, and each subgraph corresponds to a local optimization subproblem.

[0016] the redundant constraint removal strategy comprises:

[0017] the K-nearest neighbor (KNN) strategy is used to screen the active constraint set according to the subgraph correlation density and the subgraph allocation probability, the initial stage of the screening process retains a first predetermined number of constraints, and the number of constraints is gradually reduced to a second predetermined number of constraints with the iteration, so as to reduce the constraint conditions; the correlation density is used to reflect the relevance of the subgraphs in the neighborhood block, and the greater the correlation density, the higher the relevance; the subgraph allocation probability refers to the possibility of the entire subgraph being allocated to a certain neighborhood block.

[0018] the calculation formulae of the subgraph correlation density and the subgraph allocation probability comprise:

[0019] the calculation formula of the subgraph correlation density is:

[0020] the neighborhood block correlation density is between a pure random partition ( ) and a perturbed round robin partition ( );

[0021] wherein, is the number of subgraphs, is the number of partitions, , is the number of adjacent subgraph pairs in a neighborhood block, max value of adjacent subgraph pairs in the neighborhood block, denotes the expected value, is the correlation density;

[0022] The calculation formula of the subgraph allocation probability is:

[0023] ;

[0024] ;

[0025] ;

[0026] wherein, is the total number of subgraphs in all blocks; is the total number of blocks; is the number of subgraphs in the block ; is the weight of the block ; is the balance parameter; is the capacity of the block ; is the subgraph allocation probability of the block .

[0027] The coefficient priority variable fixing strategy comprises:

[0028] Based on the predicted variable edge probability and the coefficient sensitive priority rule, the variables are sorted according to the absolute value of the objective function coefficient, the high coefficient variable is fixed preferentially, and the variable fixing proportion is controlled through a dynamic threshold adjustment mechanism;

[0029] The calculation method of the dynamic threshold applied in the dynamic threshold adjustment mechanism comprises:

[0030] ;

[0031] wherein, denotes an initial threshold, is the updated dynamic threshold at the th iteration, is a decay rate, is a scaling factor.

[0032] The coefficient priority variable fixing strategy further comprises a boundary for controlling variable fixing by using a sensitivity function, and the calculation formula of the sensitivity function is: ; wherein, controls the steepness of the sensitivity function ; And the variable fixing rule in the variable fixing process comprises: ; wherein, a decision rule based on variable probability is defined, is a set of variable indices.

[0033] The process of solving large-scale mixed integer linear programming problems based on weighted subgraph partitioning comprises:

[0034] Given a set of decision variable collection , decision variable quantity , variable size limit coefficient , and four neighborhood blocks , , , The corresponding neighborhood search solution , , , , according to the single-layer cross-optimization strategy, the corresponding solution elements are selected according to the neighborhood block to which the variable belongs, and the cross-solution , the expression is:

[0035] If the th variable is in , then ; if in , then ; if in , then ; otherwise ;

[0036] The repair and search operation is performed on the cross-solution to obtain the first solving result, and the first solving result is locally optimized to obtain the final solution.

[0037] The process of locally optimizing the first solving result comprises:

[0038] When the preset time ratio threshold is reached, the sequential block optimization is started, and each neighborhood block is optimized in turn according to the subgraph distribution order, and only the current block variable is adjusted, and the remaining block variables remain fixed.

[0039] The processing performed by the efficient solving module comprises:

[0040] First stage: receiving the output of the problem reduction module, implementing distributed optimization on multiple neighborhood blocks under the guidance of weighted subgraph partitioning, and generating a complete feasible solution by aggregating global optimization information through multi-solution crossover;

[0041] The second stage: removing the dynamic constraint set update and the multi-solution intersection part, adjusting the multi-solution parallel optimization to a serial optimization strategy, and realizing the mode conversion from global exploration to local refinement.

[0042] The processing performed by the high-efficiency solving module further includes: automatically switching to the second stage when the first-stage iterative operation reaches a preset time ratio threshold; and outputting a current optimal solution when the second stage reaches a preset solving time limit.

[0043] Compared with the prior art, the optimization solving system for large-scale mixed integer linear programming problems provided by the application can quickly give a high-quality solution to a large-scale mixed integer linear programming problem as a high-efficiency solving system, so that a high-quality feasible solution can be obtained within an acceptable time. The technical scheme provided by the application can empower industry users to efficiently solve large-scale mixed integer linear programming problems in practical application scenarios, thereby significantly reducing operating costs and improving decision-making efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of these drawings.

[0045] Figure 1 The system architecture diagram of the optimization solving system provided by the embodiments of the application. DETAILED DESCRIPTION

[0046] The technical solutions in the embodiments of the application will be described clearly and completely in combination with the specific contents of the application. Obviously, the described embodiments are only some of the embodiments of the application, but not all the embodiments, which do not constitute a limitation to the application. Based on the embodiments of the application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the application.

[0047] Firstly, the terms possibly used in the present text are explained as follows:

[0048] The term "and / or" means either one or both, for example, X and / or Y means three cases including "X", "Y" or "X and Y".

[0049] The terms "comprise", "comprising", "include", "including", "contain", "containing", "have", "having", or any other similar semantic descriptions, are to be construed as open-ended rather than limiting. For example, the inclusion of an element, such as a raw material, component, ingredient, carrier, dosage form, material, dimension, part, component, mechanism, device, step, process, method, reaction condition, processing condition, parameter, algorithm, signal, data, product, or article, is to be interpreted as including not only the explicitly recited element, but also any element known to one of ordinary skill in the art to be associated with or useful in conjunction with the explicitly recited element.

[0050] The term "consisting of" means excluding any element not specifically recited. If the term is used in the context of a claim, the term shall make the claim closed, meaning that the claim does not include any element not specifically recited. If the term is used in the context of a clause in a claim, the term shall limit the clause to only the elements specifically recited in that clause, but other clauses in the claim are not excluded from the overall claim.

[0051] Unless specifically stated otherwise, the terms "mount", "connected", "connected", "fixed", and the like, are to be construed broadly, for example, as either a fixed connection, or as a detachable connection, or as an integral connection; as either a mechanical connection, or as an electrical connection; as either a direct connection, or as an indirect connection via an intermediate medium; as a communication between the internal elements of two components. The specific meaning of the above terms in the context of the present disclosure can be understood by one of ordinary skill in the art according to the specific circumstances.

[0052] When a concentration, temperature, pressure, dimension, or other parameter is expressed as a numerical range, the numerical range should be understood to specifically disclose all ranges formed from any upper limit value, lower limit value, or preferred value within the numerical range, regardless of whether the range is explicitly recited; for example, if a numerical range "2-8" is recited, the numerical range should be interpreted to include ranges "2-7", "2-6", "5-7", "3-4 and 6-7", "3-5 and 7", "2 and 5-7", etc. Unless otherwise specified, numerical ranges recited herein include all integers and fractions within the range.

[0053] 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.

[0054] This invention provides an efficient optimization solution system for large-scale mixed-integer linear programming problems. Its core objective is to help users quickly and accurately solve various mixed-integer linear programming problems in complex real-world scenarios, thereby achieving efficient and high-quality rapid decision-making.

[0055] In terms of system architecture, this embodiment of the invention establishes the solver as the basic platform. Based on this platform, it focuses deeply on key elements of the problem, such as variables, constraints, and subgraph partitioning, and designs optimization strategies that are highly compatible with these key elements. This optimization strategy can precisely control variables by cleverly employing innovative algorithms, making the search of the solution space more directional; it utilizes efficient constraint filtering and simplification techniques to eliminate redundant constraints and reduce the solution burden; simultaneously, after reasonably decomposing the large-scale problem into multiple subproblems that can be processed in parallel, it uses advanced subgraph partitioning methods to divide the corresponding subgraphs into different neighborhood blocks for independent solving.

[0056] In the implementation of this invention, to efficiently solve large-scale mixed-integer linear programming problems and meet the rapid decision-making needs in real-time decision-making scenarios such as supply chain optimization and production scheduling, the specific implementation is as follows: Figure 1 As shown, Figure 1 This paper presents an intuitive system architecture for weighted subgraph partitioning optimization of large-scale mixed-integer linear programming problems. This architecture comprises three core components: a problem decomposition module, a problem reduction module, and an efficient solution module. These components work together to achieve rapid problem processing and efficient solution. The implementation of each module will be explained in detail below.

[0057] (1) Problem decomposition module

[0058] The original mixed-integer linear programming problem bipartite graph model is processed by a graph partitioning algorithm, which decomposes the original problem into multiple independent and smaller subproblems.

[0059] Through this splitting mode, not only the scale of the sub-problems can be dynamically adjusted, but also the computational load among the sub-problems can be effectively balanced, thereby greatly reducing the consumption of the subsequent problem reduction module in terms of computing and storage resources, and further accelerating the decision response speed of the entire system.

[0060] In Figure 1 , the problem decomposition module is composed of two parts of bipartite graph modeling and problem decomposition; the problem decomposition module first models the large-scale mixed integer linear programming problem as a bipartite graph representation, and then divides the large-size bipartite graph into multiple sub-graphs through a graph decomposition algorithm, each sub-graph corresponding to an independent sub-problem; the segmented sub-graphs constitute the system running basis, providing data support for neural network training and sub-graph problem solving; the problem decomposition module embodies the data hub role through the connection arrows with other modules, both providing data input for problem reduction and receiving and processing the original mixed integer linear programming problem.

[0061] (2) Problem reduction module

[0062] The problem reduction module plays a key role in the system architecture, which can input the feature encoding of the decomposed sub-problems into the pre-trained neural network to predict the variable values, and simultaneously implement constraint reduction and variable dimension compression;

[0063] Specifically, the problem reduction module can filter and simplify the constraints and variables in the corresponding sub-problems according to the prediction results of the neural network, reduce the scale of the problem while preserving key information;

[0064] In the specific implementation process, the module is started immediately after obtaining the decomposed sub-graphs, reads the feature encoding of each sub-graph node and inputs it into the pre-trained neural network to obtain the variable prediction value; based on the prediction results, and through the two strategies of redundant constraint removal and coefficient priority variable fixing, the large-scale optimization problem is converted into a computable small-scale problem; in the system architecture diagram, the module can obtain sub-graph data through the connection arrow with the problem decomposition module, and generate partial solutions as the input basis of the efficient solving stage, providing initial support for the generation of high-quality solutions;

[0065] Through the module, the large-scale problem can be converted into a small-scale optimization model, which can significantly reduce the computational scale and greatly improve the solving speed in real-time decision-making scenarios.

[0066] (3) Efficient solving module

[0067] Based on the weighted sub-graph partitioning results, the sub-problems are processed in a distributed manner, which drives the initial solution search, parallel computation and multi-solution cross optimization operations in the iterative solving process;

[0068] In the solving process, the coupling relationship between the sub-problems can be dynamically adjusted, the resources and information of each sub-problem can be fully utilized, and the sub-problems can be mutually cooperative and optimized together.

[0069] Specifically, the high-efficiency solving module can adopt a two-stage architecture design, in which:

[0070] The first stage receives the small-scale optimization problem and partial solution output by the problem reduction module, generates a complete feasible solution through initial solution search, implements distributed optimization on multiple neighborhood blocks under the guidance of weighted subgraph division, and aggregates global optimization information through multi-solution crossover to improve solution quality; the iteration process continues to run until a preset time ratio threshold is reached, and then automatically switches to the second stage;

[0071] The second stage executes strategy optimization, that is, removes the dynamic constraint set update and multi-solution crossover part to reduce the computational load, adjusts the multi-solution parallel optimization to serial optimization strategy, and realizes the mode conversion from global exploration to local refinement; Figure 1 The arrows in the system architecture diagram indicate the information flow path and processing time sequence within the module. When the preset solving time limit is reached, the system outputs the current optimal solution to provide intelligent decision support for enterprises.

[0072] It can be seen that the module can significantly improve the computational efficiency under the premise of ensuring the solution quality, and is suitable for scenarios such as supply chain planning and production scheduling that require real-time decision-making; the partitioned processing strategy based on weighted subgraph division can effectively balance the load of each computing node, while reducing the cross-node communication overhead, further improving the overall performance and solving efficiency of the system.

[0073] For the convenience of understanding the embodiments of the present application, the specific implementation method of the optimization solving system for large-scale mixed integer linear programming problems based on the solver will be described in detail below.

[0074] The processing process adopted by the optimization solving system for large-scale mixed integer linear programming problems based on the solver provided by the embodiments of the present application can include:

[0075] (1) obtaining the information of the large-scale mixed integer linear programming problem to be optimized;

[0076] defining the decision variable set in the problem , the target function coefficient vector , the constraint matrix and the right end item ;

[0077] A mixed integer linear programming problem is modeled as a graph structure containing variable nodes and constraint nodes by a bipartite graph (i.e. a bipartite graph) representation method, wherein the edge connection relationship reflects the association between variables and constraints; the corresponding information is used to construct the basic topology of the subsequent optimization model.

[0078] (2) Obtain problem decomposition parameters and perform problem decomposition;

[0079] Determine the number k of subgraph partitioning and the load balancing parameter a, and decompose the original bipartite graph (i.e. a bipartite graph) into multiple subgraphs by a FENNEL (Fast, Efficient, Neighborhood and Edge Feature Consistent) graph partitioning algorithm, each subgraph corresponding to a local optimization subproblem.

[0080] (3) Perform variable dimension compression and constraint condition reduction on the decomposed subproblems;

[0081] The core of this processing process is to further reduce the size of the problem while preserving key information, which specifically includes:

[0082] (31) Key information can be achieved by variable fixing, which can be implemented based on an initialization variable fixing strategy and a variable fixing rule;

[0083] The corresponding initialization variable fixing strategy includes:

[0084] Based on the predicted variable edge probability , combined with the coefficient sensitivity priority rule to determine the variable set to be fixed; specifically, according to the absolute value of the objective function coefficient, the variables are sorted, and the high coefficient variables are fixed first, and the fixed proportion is controlled through a dynamic threshold adjustment mechanism to improve the quality of the initial solution;

[0085] The corresponding dynamic threshold update formula and variable fixing rule are as follows:

[0086] The dynamic threshold update formula is as follows:

[0087]

[0088] Wherein, represents the initial threshold, is the dynamic update threshold at the th iteration, is the decay rate, is the scaling factor;

[0089] Further, a sensitivity function is used to improve the boundary precision of variable fixing, wherein:

[0090] The sensitivity function is:

[0091]

[0092] in, Control sensitivity function The steepness.

[0093] The rules for fixing the variables are as follows:

[0094]

[0095] in, Defined based on variables probability Decision-making rules It is a collection of variable indices.

[0096] Using the above method, the threshold can be dynamically adjusted and the variable fixed according to the probability of the variable, thereby optimizing the data processing process.

[0097] (32) Construct a constraint set reduction mechanism to reduce constraint conditions.

[0098] The active constraint set is selected using the KNN (K Nearest Neighbor) strategy, initially retaining 80% of the constraints. ), gradually decreasing to 20% as iterations progress ( Furthermore, the REPAIR algorithm can be used to dynamically repair infeasible solutions caused by constraint updates, ensuring the feasibility of the solution.

[0099] Specifically, the KNN strategy achieves constraint reduction in the weighted subgraph partitioning optimization model based on the following first and second indicators, and its indicator quantification model includes:

[0100] Subgraph association density optimization (first metric):

[0101] The neighbor block association density is between that of a purely random partition through a load balancing weight selection algorithm. ) and perturbation polling partition ( Improve iteration efficiency between ) )

[0102] in, The number of subgraphs Number of partitions , This represents the number of adjacent subgraph pairs within a neighborhood block. This represents the maximum value of adjacent subgraph pairs within the neighborhood block. Indicates the expected value. The correlation density reflects the correlation of subgraphs within a neighborhood block; the higher the correlation density, the higher the correlation.

[0103] The subgraph distribution probability (second index) is calculated, and the calculation formula is as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] Wherein, is the total number of subgraphs in all blocks; is the total number of blocks; is the number of subgraphs in the block ; is the weight of the block ; is the balance parameter; is the capacity of the block ; is the subgraph distribution probability of the block ; in the above formula, by introducing the weight mechanism, the balance of the subgraph division of the neighborhood block is improved, and the problem of waste of solving resources and calculation bottleneck caused by uneven division is avoided.

[0108] (4) Establish a single-layer cross optimization strategy and perform corresponding solving

[0109] Single-layer cross operation is used instead of traditional hierarchical cross to reduce computational consumption; specifically, given a set of decision variable collection , the number of decision variables , the variable size limit coefficient , and the four neighborhood blocks , , , corresponding to the neighborhood search solution , , , , the operation of single-layer cross optimization strategy selects the corresponding solution element according to the neighborhood to which the variable belongs, and generates a new cross solution , the expression is:

[0110] If the first variable is in , then ; if in , then ; if in , then ; otherwise ;

[0111] After that , the final solution is obtained through repair and search operations.

[0112] (5) Implementing local optimization processing to optimize the corresponding final solution

[0113] When the preset time ratio threshold is reached, the dynamic constraint updating module is removed and the sequential block optimization is started; each neighborhood block is optimized in turn according to the subgraph distribution order, and only the current block variable is adjusted each time, and the remaining block variables remain fixed;

[0114] Specifically, when the solving time reaches the preset time ratio threshold, it means that the global exploration such as "subgraph division, constraint reduction, variable fixing, cross search" has been completed in the early stage, and the values of most variables are close to the optimal range. At this time, there is no need to perform dynamic adjustment at the global level, and instead, it is switched to the local deep cultivation stage. For example, if the total solving time is set to 100 seconds and the preset time ratio threshold is set to 80%, when the solving proceeds to 80 seconds, the subsequent processing flow is automatically triggered;

[0115] Removing the dynamic constraint updating module means that the constraint set has been reduced to the core range, and at this time, the sequential block optimization needs to be started for processing, that is, the blocks are optimized in turn according to the preset order of the neighborhood blocks, that is: the first neighborhood block is selected, the variables of the block are set as adjustable variables, and the variables of the remaining blocks are fixed as the optimization values in the early stage. The current block variable is locally optimized within the fixed constraint range to improve the solution quality. After completion, the block variable is fixed, and the next neighborhood block is repeated according to the order of the above-mentioned "only adjust the current block, fix the other blocks" operation, until all neighborhood blocks complete a round of optimization.

[0116] The large-scale mixed integer linear programming problem optimization solving system provided by the embodiments of the present application has significant advantages in practical applications. For example, in the field of logistics distribution, the system can efficiently solve large-scale transportation path optimization problems to plan more optimal distribution routes for enterprises, saving transportation costs and time; in terms of resource allocation, such as human and material resource allocation of enterprises, it reasonably allocates resources according to specific needs to improve resource utilization; in the field of path planning, such as unmanned aerial vehicle inspection path design, urban traffic flow optimization and the like, the system can quickly generate high-quality path schemes to improve work efficiency.

[0117] ​Further, the coefficient-sensitive variable fixing strategy and the weighted subgraph partitioning local optimization strategy adopted by the system can avoid falling into local optimization and provide a better solution for decision-making. Its machine learning capability makes it adaptable and robust, and it can cope with complex and changing scenarios and data fluctuations. At the same time, the embodiment of the present application can also reduce the consumption of computing resources, reduce redundant calculations, improve resource utilization, and reduce enterprise operating costs. In general, the implementation of the embodiment of the present application provides an efficient, high-quality, adaptable and low-resource consumption solution for large-scale mixed integer linear programming problems, which has effectively promoted the research progress and application development in related fields and helped enterprises to realize intelligent decision-making and operation optimization.

[0118] In summary, the synergistic effect of the various optimization strategies adopted by the embodiment of the present application significantly improves the computational efficiency in the iterative optimization solution process, greatly shortening the solution time. Even in the face of complex large-scale mixed integer linear programming problems, it can still provide users with better or even near-optimal high-quality solutions in a very short time window, greatly meeting the urgent need for rapid decision-making in practical applications, and effectively promoting the efficient solution and wide application of mixed integer linear programming problems in various real-world scenarios.

[0119] The actual application of the embodiment of the present application will be described in detail below in conjunction with specific application scenarios.

[0120] The embodiment specifically discloses a large-scale mixed integer linear programming problem optimization solution system based on weighted subgraph partitioning, which can include a problem decomposition module, a problem reduction module and an efficient solution module, wherein:

[0121] The problem decomposition module includes:

[0122] The power system unit commitment problem is converted into a mixed integer linear programming model, the objective function is to minimize the generation cost (including fuel cost, start-stop cost, etc.), and the constraint conditions cover unit ramp rate, load balance, network security constraints (such as transmission line capacity limit) and renewable energy volatility constraints.

[0123] The mixed integer linear programming model is abstracted into a graph structure containing unit variable nodes (such as power generation power, start-stop state) and constraint nodes (such as load demand, ramp limit) by bipartite graph representation method, providing a basis for subsequent subgraph partitioning.

[0124] The FENNEL algorithm is used to perform subgraph decomposition on the power system bipartite graph, and the large-scale unit commitment problem is decomposed into multiple subproblems. For example, the subgraph is decomposed according to the regional power grid or unit type (such as thermal power, wind power, photovoltaic), so that each subgraph corresponds to a subproblem.

[0125] The problem reduction module includes:

[0126] Variable priority ranking: predict the unit on-off probability based on edge aggregation graph attention network (EGAT), determine the variable priority combined with the objective function coefficient (such as generation cost), and preferentially fix the on-off state of high-cost units (such as preferentially shutting down high-fuel-cost thermal power units).

[0127] Dynamic threshold adjustment: dynamically adjust the variable fixing threshold according to the solving progress, reserve more variables at the initial stage to explore the solution space, and gradually tighten the threshold to focus on key decisions (such as renewable energy consumption priority adjustment) at the later stage.

[0128] Redundancy constraint screening: use KNN strategy to screen active constraints (such as key transmission line capacity constraints near the current solution), and eliminate low conflict constraints (such as relaxed standby capacity limits) to reduce model complexity.

[0129] The high-efficiency solving module comprises:

[0130] Weighted subgraph partitioning: independently solve local optimal solutions for each partitioned neighborhood block (such as unit combination schemes within regional power grids), integrate the results of each neighborhood block through single-layer cross operation, and avoid redundant calculations of traditional hierarchical cross (such as conflict resolution of cross-regional power transactions). The subgraph partitioning weight is dynamically adjusted by unit capacity and load demand to balance the computational load of each subgraph and ensure moderate correlation density between subgraphs (neither too high to cause global optimization difficulties, nor too low to affect local optimization efficiency).

[0131] After reaching the preset time ratio threshold (such as 80% of the total solving time), switch to the local optimization phase, remove the dynamic constraint update module and the single-layer cross module, and use the sequential block optimization strategy:

[0132] Hierarchical optimization: first optimize high-cost units (such as thermal power), then optimize low-cost units (such as wind power and photovoltaic power), and gradually refine key variables (such as marginal unit output allocation).

[0133] Fast fine-tuning: fine-tune for weak links in the power grid (such as heavily loaded transmission lines) to improve the feasibility and economy of the solution.

[0134] Through the description of the above embodiments, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by means of software plus necessary general hardware platforms. Based on such understanding, the technical solutions of the above embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a U disk, a mobile hard disk, etc.), and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments of the present application.

[0135] The above description is only the preferred embodiment of the present application, but the protection scope of the present application is not limited to this. Any change or replacement within the technical range disclosed by the present application can be easily thought by those skilled in the art, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims. The information disclosed in the background section of the present application is only intended to deepen the understanding of the general background of the present application, and should not be regarded as acknowledging or implying in any form that the information constitutes the prior art known by those skilled in the art.

Claims

1. An optimization solution system for large scale mixed integer linear programming problems, characterized in that, include: The problem decomposition module is used to model large-scale mixed-integer linear programming problems as bipartite graph representations, and to divide the bipartite graph into multiple subgraphs using a graph decomposition algorithm to obtain a weighted subgraph partition. The problem reduction module is used to obtain the feature encoding of each subgraph node obtained by the problem decomposition module and input it into a pre-trained neural network to obtain the variable prediction value. Then, based on the variable prediction value, the size of the large-scale mixed integer linear programming problem is reduced by a strategy of removing redundant constraints and fixing coefficient priority variables, and then the output is given. An efficient solution module is used to solve large-scale mixed-integer linear programming problems based on the results output by the problem reduction module and the weighted subgraph partitioning.

2. The system of claim 1, wherein, The process of modeling the problem decomposition module as a bipartite graph includes: The large-scale mixed-integer linear programming problem is modeled as a graph structure containing variable nodes and constraint nodes using a bipartite graph representation, where the edge connections reflect the relationship between variables and constraints. The process of dividing the bipartite graph into multiple subgraphs in the problem decomposition module includes: After determining the number of subgraphs and the load balancing parameters, the bipartite graph is decomposed into multiple subgraphs using a graph partitioning algorithm, and each subgraph corresponds to a local optimization subproblem.

3. The system of claim 1 or 2, wherein, The redundant constraint removal strategy includes: The K-Nearest Neighbors (KNN) strategy filters the active constraint set based on subgraph association density and subgraph assignment probability. In the initial stage of the filtering process, a first predetermined amount of constraints is retained, and the constraints are gradually reduced to a second predetermined amount as the iteration progresses, thereby reducing the constraints. The association density is used to reflect the correlation of subgraphs within a neighborhood block. The higher the association density, the higher the correlation. The subgraph assignment probability refers to the probability that the entire subgraph will be assigned to a certain neighborhood block.

4. The system of claim 3, wherein, The formulas for calculating the subgraph association density and subgraph assignment probability include: The formula for calculating the subgraph association density is: , the neighborhood block correlation density is between pure random partition ( ) and perturbed round robin partition ( ). in, The number of subgraphs Number of partitions , This represents the number of adjacent subgraph pairs within a neighborhood block. This represents the maximum value of adjacent subgraph pairs within the neighborhood block. Indicates the expected value. For correlation density; The formula for calculating the subgraph assignment probability is: ； ； ； in, It is the total number of subgraphs in all blocks; It is the total number of blocks; It is a piece Number of subgraphs in; It is a piece The weights; It is a balance parameter; It is a piece The capacity; It is a piece The probability of subgraph assignment.

5. The system according to claim 3, characterized in that, The coefficient priority variable fixing strategy includes: Based on the predicted marginal probabilities of variables and coefficient sensitivity priority rules, variables are sorted according to the absolute value of the objective function coefficients, high-coefficient variables are fixed first, and the fixed proportion of variables is controlled by a dynamic threshold adjustment mechanism. The dynamic threshold calculation method used in the dynamic threshold adjustment mechanism includes: ； in, Indicates the initial threshold. For the first The dynamic threshold is updated in the next iteration. It is the attenuation rate. It is the scaling factor.

6. The system according to claim 5, characterized in that, The coefficient priority variable fixing strategy also includes using a sensitivity function to control the boundary of variable fixing, and the formula for calculating the sensitivity function is as follows: ； in, Control sensitivity function The steepness; Furthermore, the variable fixing rules in the variable fixing process include: ； in, Defined based on variables probability Decision-making rules It is a collection of variable indices.

7. The system according to claim 3, characterized in that, The process of solving large-scale mixed-integer linear programming problems based on weighted subgraph partitioning includes: Given a set of decision variables Number of decision variables Variable size restriction coefficient and four neighboring blocks , , , Corresponding neighborhood search solution , , , Based on a single-layer crossover optimization strategy, the corresponding solution elements are selected according to the neighborhood block to which the variable belongs, and crossover solutions are generated. Its expression is: If the first Variables in ,but If in ,but If in ,but ;otherwise ; Repair and search operations are performed on the cross solutions to obtain a first solution result. Local optimization processing is then performed on the first solution result to obtain the final solution.

8. The system according to claim 7, characterized in that, The process of performing local optimization on the first solution result includes: When the preset time ratio threshold is reached, sequential block optimization is initiated. The first solution result is optimized sequentially according to the subgraph allocation order, and only the current block variable is adjusted each time, while the variables of the other blocks remain fixed.

9. The system according to claim 3, characterized in that, The processes performed by the efficient solution module include: Phase 1: Receive the output of the problem reduction module, perform distributed optimization on multiple neighborhood blocks under the guidance of weighted subgraph partitioning, and generate a complete feasible solution by cross-aggregating global optimization information through multiple solutions; The second stage involves removing the dynamic constraint set update and the intersection of multiple solutions, adjusting the parallel optimization of multiple solutions to a serial optimization strategy, and realizing the mode transformation from global exploration to local refinement.

10. The system according to claim 9, characterized in that, The efficient solution module also includes the following processing steps: when the first stage of iterative operation reaches a preset time ratio threshold, it automatically switches to the second stage; when the second stage reaches a preset solution time limit, the system outputs the current optimal solution.

Images