Classification processing method and device, computer storage medium and terminal

Abstract

A classification processing method and device, a computer storage medium and a terminal are applied to combinatorial mathematics optimization, and the method comprises the following steps: determining an incidence matrix according to added values of an objective function during independent inversion and simultaneous inversion of more than two variables in an independent variable matrix, the incidence matrix is used for describing the mutual relation between more than two variables and the change of the target function caused by the change of the variables; constructing a Laplacian matrix according to the determined incidence matrix; constructing a matrix for variable classification through the constructed Laplacian matrix; when the matrix used for variable classification is optimized to converge, a preset number of first feature vectors are obtained; and clustering the obtained first feature vector into a preset number of clusters to obtain a preset number of variable classification groups. According to the embodiment of the invention, after the incidence matrix is determined, variable classification processing is performed through the Laplacian matrix, so that the dependence of the variable classification process on a heuristic method is reduced, and the quality of variable classification is improved.

Description

Technical Field

[0001] The present invention relates to combinatorial optimization technology, and more particularly to a classification processing method, device, computer storage medium and terminal. Background Art

[0002] Combinatorial optimization problems refer to solving how to take values ​​of variables for an objective function composed of many variables so that the objective function can obtain the optimal value. At the same time, this type of problem may involve different constraints and common problems. Among them, the quadratic unconstrained binary optimization problem (QUBO) is the most basic problem in combinatorial optimization problems. It is also a non-deterministic polynomial (NP-hard) problem that is difficult for classical computers to solve in polynomial time. The algorithms for related problems are widely used in finance, economics, machine learning and other fields.

[0003] In recent years, quantum computing technology has been effectively improved, and quantum computing methods have been proven to be effective in solving some of them; the development of quantum computing provides a new way and method to solve such NP-hard problems; among them, the quantum approximate optimization algorithm (QAOA) is a powerful hybrid method for solving these complex optimization problems. By converting the QUBO objective function into a cost Hamiltonian, QAOA can solve the QUBO problem with the number of variables corresponding to the number of available bits on a universal quantum computer. However, due to the limited connectivity of bits on current quantum computers, the number of available quantum bits is much smaller than the scale of the problem to be solved. In order to overcome this limitation, researchers have developed a sub-QUBO algorithm framework; this method is based on problem decomposition and splitting, and takes advantage of the excellent ability of QAOA to solve optimization problems, enabling the algorithm to escape from local minima and solve the global minimum with a greater probability. In this way, the sub-QUBO algorithm can handle complex combinatorial optimization problems with many variables.

[0004] The core idea of ​​the sub-QUBO algorithm in related technologies is to solve the problem by divide-and-conquer and iterate. The iterative process is as follows: first, the QUBO objective function problem (a total of N variables) is divided into multiple sub-problems, each of which consists of a certain number of independent variables (N 1It is composed of <N); since the number of variables in each sub-problem is small, QAOA or some simple methods can be used to solve the small-scale sub-problems simply and accurately, and then the solutions of all sub-problems are combined into a new candidate solution; then use classical tabu search or other classical algorithms to refine and optimize the current candidate solution, and then form a current optimal solution for the global problem (it cannot be proved to be the global optimal solution in the strict mathematical sense). Therefore, various methods including random selection are proposed for variable grouping; sort according to the impact or certainty of each variable on the objective function, and extract the most uncertain variables from the pool (set) of previously obtained solution schemes; then solve the problems composed of these variables. Generally speaking, sub-QUBO is an idea of divide and conquer. However, the existing methods for solving QUBO problems with a large number of variables largely rely on heuristic methods and make strong assumptions about the interactions between variables that affect the objective function. How to reduce the dependence on heuristic methods and improve the quality of variable classification has become a problem to be solved. Summary of the Invention

[0005] An embodiment of the present application provides a classification processing method, which is applied to combinatorial mathematics optimization problems, including:

[0006] Determine the correlation matrix according to the increased values of the objective function when two or more variables in the independent variable matrix are independently reversed and simultaneously reversed, where the correlation matrix is used to describe the mutual relationship between two or more variables and the change of the objective function when the variables change;

[0007] Construct a Laplacian matrix according to the determined correlation matrix;

[0008] Construct a matrix for variable classification through the constructed Laplacian matrix;

[0009] When the matrix for variable classification is optimized to convergence, obtain a preset number of first eigenvectors;

[0010] Cluster the obtained first eigenvectors into a preset number of clusters to obtain a preset number of variable classification groups.

[0011] On the other hand, an embodiment of the present application also provides a computer storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the above classification processing method is implemented.

[0012] On yet another aspect, an embodiment of the present application also provides a terminal, including: a memory and a processor, and a computer program is stored in the memory; wherein,

[0013] The processor is configured to execute the computer program in the memory;

[0014] When the computer program is executed by the processor, the above-mentioned classification processing method is implemented.

[0015] In another aspect, the embodiment of the present application further provides a classification processing device, which is applied to combinatorial mathematical optimization problems, comprising: a determination association unit, a first construction unit, a second construction unit, an optimization processing unit and a classification unit; wherein,

[0016] Determine the association unit setting as follows: determine the association matrix according to the increase in the objective function when two or more variables in the independent variable matrix are independently reversed and simultaneously reversed, wherein the association matrix is ​​used to describe the relationship between the two or more variables and the change of the objective function caused by the change of the variable;

[0017] The first construction unit is configured to: construct a Laplace matrix according to the determined incidence matrix;

[0018] The second construction unit is configured to: construct a matrix for variable classification through the constructed Laplace matrix;

[0019] The optimization processing unit is configured to: optimize the matrix for variable classification until convergence, and obtain a preset number of first eigenvectors;

[0020] The classification unit is set to: cluster the obtained first eigenvector into a preset number of clusters to obtain a preset number of variable classification groups.

[0021] After determining the association matrix, the embodiment of the present disclosure performs variable classification processing through the Laplace matrix, which reduces the dependence of the variable classification process on the heuristic method, improves the quality of variable classification, and further improves the ability to solve combinatorial mathematical optimization problems.

[0022] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or be understood by implementing the present application. Other advantages of the present application can be realized and obtained by the schemes described in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings are used to provide an understanding of the technical solution of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the technical solution of the present application and do not constitute a limitation on the technical solution of the present application.

[0024] Figure 1 A flowchart of a classification processing method according to an embodiment of the present disclosure;

[0025] FIG2( a ) is a comparison diagram of the solution quality of a mathematical combinatorial optimization problem in a first embodiment of the present disclosure;

[0026] FIG2( b ) is a comparison diagram of solution quality of another mathematical combinatorial optimization problem according to an embodiment of the present disclosure;

[0027] FIG2( c ) is a comparison diagram of solution quality of another mathematical combinatorial optimization problem according to an embodiment of the present disclosure;

[0028] FIG2( d ) is a comparison diagram of solution quality of another mathematical combinatorial optimization problem according to an embodiment of the present disclosure;

[0029] FIG3( a ) is a comparison diagram of solution quality after changing the number of quantum bits used in solving sub-problems in Example 1 of the present disclosure;

[0030] FIG3( b ) is a comparison diagram of solution quality after changing the number of quantum bits used in solving sub-problems in another embodiment of the present disclosure;

[0031] Figure 4 The present invention is a structural block diagram of a device for classification processing according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The present application describes multiple embodiments, but the description is exemplary rather than restrictive, and it is obvious to those skilled in the art that there may be more embodiments and implementations within the scope of the embodiments described in the present application. Although many possible feature combinations are shown in the drawings and discussed in the specific embodiments, many other combinations of the disclosed features are also possible. Unless specifically limited, any feature or element of any embodiment may be used in combination with any other feature or element in any other embodiment, or may replace any other feature or element in any other embodiment.

[0033] The present application includes and contemplates combinations of features and elements known to those of ordinary skill in the art. The embodiments, features and elements disclosed in the present application may also be combined with any conventional features or elements to form a unique invention scheme. Any features or elements of any embodiment may also be combined with features or elements from other invention schemes to form another unique invention scheme. Therefore, it should be understood that any feature shown and / or discussed in the present application may be implemented individually or in any appropriate combination. Therefore, except for the limitations made according to the attached claims and their equivalents, the embodiments are not subject to other restrictions. In addition, various modifications and changes may be made within the scope of protection of the attached claims.

[0034] In addition, when describing representative embodiments, the specification may have presented the method and / or process as a specific sequence of steps. However, to the extent that the method or process does not rely on the specific order of the steps described herein, the method or process should not be limited to the steps of the specific order described. As will be understood by those of ordinary skill in the art, other sequences of steps are also possible. Therefore, the specific sequence of the steps set forth in the specification should not be interpreted as a limitation to the claims. In addition, the claims for the method and / or process should not be limited to the steps of performing them in the order written, and those skilled in the art can easily understand that these sequences can be changed and still remain within the spirit and scope of the embodiments of the present application.

[0035] To facilitate understanding of the embodiments of the present disclosure, the following briefly describes the relevant technologies: Combinatorial mathematical optimization problem is to solve the value of N variables contained in a set of independent variable matrix X, so that the objective function takes the minimum value, and the expression is minX T QX; where matrix Q is the objective function matrix; generally speaking, the value in X can be any real number. If it is necessary to be compatible with quantum computing and quantum bit characteristics, it needs to be mapped to a binary variable, b i,t ∈{0,1}, the mapping method is not limited, the method in the related art is In this way, we can set an upper limit of A xi A real variable is converted into a variable group consisting of K {0, 1} binary variables. In order to solve the problem that there are many variables in the problem to be solved and quantum computing or some classical algorithms cannot be used to effectively solve the combinatorial optimization problem, the relevant technology adopts the idea of ​​sub-QUBO to solve it. The processing flow includes: initializing a current solution, updating the current optimal solution to the initialized solution, and then entering the iterative loop; in each iteration, the variables are grouped, and the sub-problems composed of each group of variables will form a small-scale QUBO problem, and quantum computing or some classical algorithms are used to solve the sub-problems. During the iterative loop, if the function value of the solution given at a certain time is the historical optimal solution, the historical optimal solution can be updated. After the iteration is completed, the final solution output is the optimal solution given by the algorithm. The variables are grouped based on their influence. For a given QUBO matrix Q and the current solution, the influence (impact) of the i-th independent variable in the independent variable matrix is ​​defined as the inversion of the variable (x iIf it was originally 1, it is reversed to 0). This increase is always positive if the current solution is a strict local minimum. After calculating the impact of the variables on the objective function, sort the variables in the independent variable matrix according to their impact; then, classify the N variables into R groups, that is, the variables in each group have roughly equal impact; ensure that the number of variables in each group is approximately [N / R], and ensure that the number of variables in a single subproblem is within the range allowed by quantum computers, or within the range of the number of variables that can be efficiently solved by classical solvers.

[0036] Figure 1 Flow chart of the classification processing method of the embodiment of the present disclosure, such as Figure 1 As shown, it is applied to combinatorial optimization problems, including:

[0037] Step 101, determining a correlation matrix according to the increase in the objective function when two or more variables in the independent variable matrix are inverted independently and simultaneously, wherein the correlation matrix is ​​used to describe the relationship between the two or more variables and the change of the objective function caused by the change of the variables;

[0038] Step 102: construct a Laplace matrix according to the determined incidence matrix;

[0039] Step 103, constructing a matrix for variable classification through the constructed Laplace matrix;

[0040] Step 104, optimizing the matrix for variable classification until convergence, and obtaining a preset number of first eigenvectors;

[0041] Step 105: cluster the obtained first eigenvector into a preset number of clusters to obtain a preset number of variable classification groups.

[0042] After determining the association matrix, the embodiment of the present disclosure performs variable classification processing through the Laplace matrix, which reduces the dependence of the variable classification process on the heuristic method, improves the quality of variable classification, and further improves the ability to solve combinatorial mathematical optimization problems.

[0043] In an exemplary embodiment, the embodiment of the present disclosure constructs a Laplacian matrix according to the determined incidence matrix, including:

[0044] Calculate the unnormalized Laplacian matrix from the incidence matrix;

[0045] Wherein, the Laplace matrix is ​​L, L = DW, and W represents the correlation matrix Σ(Σ ij ), D is the diagonal matrix D calculated by W ii =Σ j W ij, each diagonal element of the matrix D is an element on the diagonal of the matrix, which is the element of the i-th row and i-th column of Dii. It is calculated by taking W i1 , W i2 ,…W in Add together.

[0046] The Laplacian matrix L of the disclosed embodiment is a semi-positive definite matrix, and its smaller eigenvalues ​​correspond to some important features; for example, the eigenvalue 0 corresponds to the feature space spanned by the indicator vectors of the connected components of the graph. Therefore, the characteristics between variables can be obtained through the L matrix; using the characteristics between variables, the first preset number k eigenvectors of the Laplacian matrix L can be determined, which are u 1 ,u 2 ,…,u k These eigenvectors are used to form a matrix for variable classification; when the preset number is k, the dimension of the matrix for variable classification is N*k; deriving the matrix for variable classification corresponds to solving the optimization problem of the Laplace matrix L. Solving the above optimization problem is equivalent to connecting some eigenvectors and reflecting it to the original QUBO matrix problem (min x (x T Qx)) is equivalent to sorting out the correlation between the changes in the independent variables and analyzing which variables are also beneficial to the problem optimization. In addition to solving the Laplace matrix, there is also a normalized Laplace matrix It can play the same role as the Laplace matrix.

[0047] After obtaining the Laplace matrix, we need to optimize mintr(U T LU), until an optimal U is given.

[0048] In an exemplary embodiment, the method of the present disclosure further includes:

[0049] The correlation matrix is ​​weighted by a pre-set weighting matrix W = Σ, which is the direct use of the correlation matrix; weighting can specifically amplify the correlation between some independent variables, such as amplifying the correlation between two independent variables 2 and 3, W ij =Σ ij (i,j≠2,3or 3,2),W 23 =c·Σ 23 ,W 32 =c·Σ 32 , used to assume that the correlation between variables 2 and 3 is extremely high, then c is set to a very large coefficient; or more concerned with optimizing the correlation in the correlation matrix, that is, more concerned with Σ ij <0, W ij =Σ ij (Σij ≥0); W ij =c·Σ ij (Σ ij <0), set c to a very large coefficient. In this way, the weights are adjusted according to the pre-defined rules, and the correlation matrix is ​​processed to convert Σ into W.

[0050] In an exemplary embodiment, the embodiment of the present disclosure clusters the obtained first feature vector into a preset number of clusters, including:

[0051] The first eigenvector is clustered into a preset number of clusters using a k-means clustering method to obtain a preset number of groups.

[0052] The k-means clustering in the embodiment of the present disclosure is only an example, and clustering methods including K-Medoids clustering, hierarchical clustering, density-based clustering method, grid-based clustering method, etc. may also be used, and the embodiment of the present disclosure does not limit this.

[0053] The constructed Laplacian matrix is ​​used to construct a matrix for variable classification, including:

[0054] Obtaining a preset number of second eigenvectors of characteristics between variables through the Laplacian matrix;

[0055] Based on the obtained second eigenvector, a matrix for variable classification is constructed.

[0056] In an exemplary embodiment, when the two or more variables in the embodiment of the present disclosure are variable i and variable j, the expression of the association matrix is: Σ ij (x,Q)=Δf ij (x;Q)-Δf i (x;Q)-Δf j (x; Q);

[0057] Where Δf ij (X;Q) is the inversion variable x i and variable x j When the objective function is increased, the expression of Δf ij (X;Q) = f(x 1 ,x 2 ,…,x i ⊕1,…,x j ⊕1,…,x N ;Q)-f(X;Q);Δf i (X;Q) means inverting variable x i When the objective function is increased, the expression of Δf i (X;Q) = f(x 1 ,x 2 ,…,xi ⊕1,…,x N ;Q)-f(X;Q);Δf j (X;Q) means inverting variable x j When the objective function is increased, the expression of Δf j (X;Q) = f(x 1 ,x 2 ,…,x j ⊕1,…,x N ; Q)-f(X; Q), f(X; Q) is the optimization objective function x when the independent variable takes the value x T Function value of Qx.

[0058] After obtaining the first feature vector group in the embodiment of the present disclosure, assuming that the first feature vector group is {yi} (1*k, k is a preset number of values, there are N in total, and N is the number of variables), the first feature vector is clustered into R clusters (classes) using the k-means clustering method, and the generated cluster C 1 ,C 2 ,…,C R The final output clustering is that there are R clusters, namely A 1 ,A 2 ,…,A R , where A i ={j|y j ∈C i}, at this time, the N variables in the independent variable matrix are classified into R clusters, achieving grouping.

[0059] When solving the sub-problem in the embodiment of the present disclosure, N independent variables x 1 ~x N Classified as A 1 ~A R This R group. For example: Assume A 1 The cluster contains {1, 3, 4}, then the vector x {134} ={x 1 ,x 3 ,x 4 The sub-optimization problem of From the original question (minX T QX); then we can use quantum QAOA or quantum annealing or other classical methods to solve it. Get the current best {x 1 ,x 3 ,x 4}; Next, solve the subproblems in the other R-1 clusters, and finally piece together the current solutions to form an overall solution with N independent variables; where, It is a sub-problem defined in the sub-QUBO framework, and is also a sub-problem that is usually better handled by quantum computing algorithms such as QAOA and quantum annealing.

[0060] In the disclosed embodiment, when flipping variables i and j at the same time will lead to worse results, the correlation matrix element is positive; therefore, it is not recommended to flip variables i and j at the same time, as they are like mutually repelling forces. On the contrary, the correlation matrix element is negative, and the negative correlation is like the attraction between the two variables, and reversing them at the same time will be more optimized; therefore, this indicator can better describe the role of many variables in the overall objective function optimization problem, and the effect is improved compared to the single reversal in related technologies to calculate the impact or other solutions.

[0061] The disclosed embodiment calculates the increased value of the objective function value of each variable of the inverted independent variable matrix for each set of solutions to the combinatorial mathematical optimization problem (including the initial solution or any set of solutions in the iteration) based on the current solution and the objective function matrix, and uses the increased value of the objective function when each of the N variables contained in the independent variable matrix is ​​inverted as the matrix element to obtain an N*1 vector matrix.

[0062] In an exemplary embodiment, when the variables that are simultaneously inverted in the embodiment of the present disclosure include variable i, variable j, and variable k, the expression of the increase value of the objective function is:

[0063] Δf ijk (X;Q) = f(x 1 ,x 2 ,…,x i ⊕1,…,x j ⊕1,…,x k ⊕1,…,x N ;Q)-f(X;Q).

[0064] The association matrix can be obtained by subtracting the increase in the objective function of each variable from the increase in the objective function of the variables that are inverted simultaneously.

[0065] In an exemplary embodiment, when the embodiment of the present disclosure simultaneously inverts the variable i, the variable j, and the variable k, the expression of the association matrix is:

[0066] Σ ijk (x,Q)=Δf ijk (x;Q)-Δf i (x;Q)-Δf j (x;Q)-Δf k (x;Q).

[0067] The embodiment of the present disclosure can determine the relationship between variables through the association matrix. The association matrix is ​​used to measure the influence and association of variables in combinatorial mathematical optimization problems, providing better classification indicators for subsequent classification solutions.

[0068] In an exemplary embodiment, after clustering the obtained first feature vector into a preset number of clusters and obtaining a preset number of variable classification groups, the method of the embodiment of the present disclosure further includes:

[0069] The obtained variable classification grouping is used to group the independent variables in the combinatorial optimization problem, and the combinatorial optimization problem is broken down into multiple sub-problems, thereby executing the solution of the combinatorial mathematical optimization problem.

[0070] The independent variable matrix of the disclosed embodiment has a total of N variables, which are too many to be solved at one time, so it is divided into a preset number (R) of groups, and the subproblem solver needs to solve the subproblems consisting of [N / R] variables at one time, that is, the group with the largest number of variables must be less than ([N / R]+1); therefore, R usually needs to be at least a positive integer greater than or equal to [N / allowed number of subproblems].

[0071] The disclosed embodiment constructs an association matrix that captures the impact of variables on the objective function; this association matrix represents the degree of association derived from the QUBO matrix and the current solution, and is used to describe the relationship between two or more variables and the change in the objective function caused by the change in the variable. By mapping the association matrix to the Laplace matrix, the variables are grouped by clustering, and each group constitutes a sub-problem; after determining the classification of the variables according to the clustering results, the sub-problems are solved, thereby improving the ability to solve the global optimal solution; the disclosed embodiment refers to the relevant technology, and QAOA (or other effective methods for solving sub-problems) can be applied to each sub-problem to obtain a better solution, and finally iterate to form the optimal solution to the problem.

[0072] The disclosed embodiment is based on the regular graph and Numerical simulations are performed on the Max-Cut problem of the -Rényi graph using the method of the embodiment of the present disclosure, which proves that the method of the embodiment of the present disclosure is superior to the related technologies in terms of solution quality. Figure 2(a) to Figure 2(d): This is a comparison diagram of the solution quality of the mathematical combinatorial optimization problem of the embodiment of the present disclosure. In the figure, curve 2-1-1 and data bar 2-1-2 correspond to the results obtained by sorting and grouping the independent variables and then applying sub-QUBO when the calculation of the indicator in the sub-QUBO problem in the related technology is the impact; curve 2-2-1 and data bar 2-2-2 correspond to the results obtained by sorting and grouping the independent variables and then applying sub-QUBO when the calculation of the indicator in the sub-QUBO problem in the related technology is the certainty; curve 2-3-1 and data bar 2-3-2 correspond to the results obtained by classifying the independent variables using the Laplace matrix clustering method of the embodiment of the present disclosure and then applying them to sub-QUBO; the sub-problems of the above methods are solved using the QAOA algorithm; the problem to be solved here is a MAXCUT problem with 100 random independent variables and the number of N=100, wherein the side lengths in the MAXCUT problem are randomly generated, and then the problem to be solved is solved by the above three methods respectively to obtain the final result. The horizontal axis in Figure 2(a) is the final solution (x end ) corresponds to the objective function value Then the vertical axis is the frequency of occurrence (how many times in 100 problems). It can be seen from the figure that the cluster method we proposed can give a better solution, because the overall solved objective function value is lower (better); the horizontal axis of Figure 2 (b) is the average number of times the quantum computer is used to solve the sub-problems in one iteration; the horizontal axis of Figure 2 (c) is the number of sub-problems called by the quantum computer in the whole problem; the horizontal axis of Figure 2 (d) is the computing time used to solve the whole problem. Through analysis, it can be determined that the algorithm of the disclosed embodiment can achieve better results. With the improvement of quantum computer performance in the future, the speed of the algorithm of the disclosed embodiment will be further improved.

[0073] Figure 3(a) to Figure 3(b)3(a) shows the objective function value. By comparison, it can be found that no matter how the quantum computing capability is enhanced, the method of the embodiment of the present invention can maintain a constant advantage. The y-axis of FIG3(b) shows the number of quantum subproblem process calls, which can also be equivalently understood as the running time. It can be found that as the performance of quantum computers improves and the subproblems are allowed to expand in scale, the time spent on the algorithm of the embodiment of the present invention will be close to that of the traditional algorithm.

[0074] The embodiment of the present disclosure further provides a computer storage medium, in which a computer program is stored. When the computer program is executed by a processor, the above-mentioned classification processing method is implemented.

[0075] The embodiment of the present disclosure also provides a terminal, including: a memory and a processor, wherein a computer program is stored in the memory;

[0076] in,

[0077] The processor is configured to execute the computer program in the memory;

[0078] When the computer program is executed by a processor, the above-mentioned classification processing method is implemented.

[0079] Figure 4 The structural block diagram of the device for classification processing in the embodiment of the present disclosure is as follows: Figure 4 As shown, it is applied to combinatorial mathematical optimization problems, including: determining an association unit, a first construction unit, a second construction unit, an optimization processing unit and a classification unit; wherein,

[0080] Determine the association unit setting as follows: determine the association matrix according to the increase in the objective function when two or more variables in the independent variable matrix are independently reversed and simultaneously reversed, wherein the association matrix is ​​used to describe the relationship between the two or more variables and the change of the objective function caused by the change of the variable;

[0081] The first construction unit is configured to: construct a Laplace matrix according to the determined incidence matrix;

[0082] The second construction unit is configured to: construct a matrix for variable classification through the constructed Laplace matrix;

[0083] The optimization processing unit is configured to: optimize the matrix for variable classification until convergence, and obtain a preset number of first eigenvectors;

[0084] The classification unit is set to: cluster the obtained first eigenvector into a preset number of clusters to obtain a preset number of variable classification groups.

[0085] In an exemplary embodiment, the first construction unit of the embodiment of the present disclosure is configured as follows:

[0086] Calculate the unnormalized Laplacian matrix from the incidence matrix;

[0087] Among them, the Laplace matrix is ​​L, L = DW, W represents the correlation matrix, and D is the diagonal matrix D ii =Σ j W ij .

[0088] In an exemplary embodiment, the embodiment of the present disclosure determines that the association unit is further configured to:

[0089] The correlation matrix is ​​weighted by a preset weighting matrix.

[0090] In an exemplary embodiment, the classification unit of the embodiment of the present disclosure is configured as follows:

[0091] The first eigenvector is clustered into a preset number of clusters using a k-means clustering method to obtain a preset number of groups.

[0092] In an exemplary embodiment, the second construction unit of the embodiment of the present disclosure is configured as follows:

[0093] Obtaining a preset number of second eigenvectors of characteristics between variables through the Laplacian matrix;

[0094] Based on the obtained second eigenvector, a matrix for variable classification is constructed.

[0095] In an exemplary embodiment, when the two or more variables in the embodiment of the present disclosure are variable i and variable j, the expression of the association matrix is:

[0096] Σ ij (x,Q)=Δf ij (x;Q)-Δf i (x;Q)-Δf j (x; Q);

[0097] Where Δf ij (X;Q) is the inversion variable x i and variable x j When the objective function is increased, the expression of Δf ij (X;Q) = f(x1 ,x 2 ,…,x i ⊕1,…,x j ⊕1,…,x N ;Q)-f(X;Q);Δf i (X;Q) means inverting variable x i When the objective function is increased, the expression of Δf i (X;Q) = f(x 1 ,x 2 ,…,x i ⊕1,…,x N ;Q)-f(X;Q);Δf j (X;Q) means inverting variable x j When the objective function is increased, the expression of Δf j (X;Q) = f(x 1 ,x 2 ,…,x j ⊕1,…,x N ; Q)-f(X; Q), f(X; Q) is the optimization objective function x when the independent variable takes the value x T Function value of Qx.

[0098] In an exemplary instance, the device of the embodiment of the present disclosure also includes a solving unit, which is configured to: group the independent variables in the combinatorial optimization problem according to the obtained variable classification, decompose the combinatorial optimization problem into multiple sub-problems, and then perform the solution of the combinatorial mathematical optimization problem.

[0099] It will be appreciated by those skilled in the art that all or some of the steps, systems, and functional modules / units in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. In hardware implementations, the division between the functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed by several physical components in cooperation. Some or all components may be implemented as software executed by a processor, such as a digital signal processor or a microprocessor, or implemented as hardware, or implemented as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable medium, which may include a computer storage medium (or non-transitory medium) and a communication medium (or temporary medium). As known to those skilled in the art, the term "computer storage medium" includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. In addition, it is well known to those of ordinary skill in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

Claims

1. A classification processing method, applied to combinatorial optimization problems, characterized in that: include: According to the increase in the objective function when two or more variables in the independent variable matrix are inverted independently and simultaneously, the correlation matrix is ​​determined, wherein the correlation matrix is ​​used to describe the relationship between two or more variables and the change of the objective function caused by the change of the variables; Construct a Laplacian matrix based on the determined incidence matrix; The matrix for variable classification is constructed through the constructed Laplacian matrix; Optimizing the matrix for variable classification until convergence, obtaining a preset number of first eigenvectors; The obtained first eigenvector is clustered into a preset number of clusters to obtain a preset number of variable classification groups.

2. The method according to claim 1, characterized in that The step of constructing a Laplace matrix according to the determined incidence matrix comprises: Calculating the non-normalized Laplacian matrix according to the incidence matrix; Wherein, the Laplace matrix is ​​L, L=DW, W represents the correlation matrix, and D is the diagonal matrix D ii =Σ j W ij .

3. The method according to claim 1, characterized in that The method further comprises: The association matrix is ​​weighted by a preset weighting matrix.

4. The method according to claim 1, characterized in that: The clustering of the obtained first feature vector into a preset number of clusters includes: clustering the first feature vector into a preset number of clusters using a k-means clustering method to obtain a preset number of groups.

5. The method according to any one of claims 1 to 4, characterized in that: The constructed Laplace matrix is ​​used to construct a matrix for variable classification, including: Obtaining a preset number of second eigenvectors of characteristics between variables through the Laplacian matrix; The matrix for variable classification is constructed according to the obtained second eigenvector.

6. The method according to any one of claims 1 to 4, characterized in that: When the two or more variables are variable i and variable j, the expression of the association matrix is: Σ ij (x,Q)=Δf ij (x;Q)-Δf i (x;Q)-Δf j (x;Q); Where Δf ij (X;Q) is the inversion variable x i and variable x j When the expression of the increase in the objective function is ij (X;Q) = f(x1,x2,…,x i ⊕1,…,x j ⊕1,…,x N ; Q)-f(X; Q); Δf i (X;Q) means inverting variable x i When the expression of the increase in the objective function is i (X;Q) = f(x1,x2,…,x i ⊕1,…,x N ; Q)-f(X; Q); Δf j (X;Q) means inverting variable x j When the expression of the increase in the objective function is j (X;Q) = f(x1,x2,…,x j ⊕1,…,x N ; Q)-f(X; Q), f(X; Q) is the optimization objective function x when the independent variable takes the value x T Function value of Qx.

7. The method according to any one of claims 1 to 4, characterized in that: The first eigenvectors include N, where N is the number of variables in the independent variable matrix, the preset number is R, and the clusters generated by clustering the first eigenvectors are C1, C2, ..., C R The preset number of variable classification groups are obtained as A1, A2, ..., A R ; Among them, A i ={j|y j ∈C i }.

8. The method according to any one of claims 1 to 4, characterized in that: After clustering the obtained first feature vector into a preset number of clusters to obtain a preset number of variable classification groups, the method further includes: According to the obtained grouping of the variable classifications, solving the combinatorial mathematical optimization problem is performed.

9. A computer storage medium, wherein a computer program is stored in the computer storage medium, and when the computer program is executed by a processor, the classification processing method according to any one of claims 1 to 8 is implemented.

10. A terminal, comprising: A memory and a processor, wherein the memory stores a computer program; wherein, The processor is configured to execute the computer program in the memory; When the computer program is executed by the processor, the classification processing method according to any one of claims 1 to 8 is implemented.

11. A classification processing device, applied to combinatorial mathematical optimization problems, comprising: Determine an association unit, a first construction unit, a second construction unit, an optimization processing unit and a classification unit; wherein, Determine the association unit setting as follows: determine the association matrix according to the increase value of the objective function when two or more variables in the independent variable matrix are independently reversed and simultaneously reversed, wherein the association matrix is ​​used to describe the relationship between the two or more variables and the change of the objective function caused by the change of the variable; The first construction unit is configured to: construct a Laplace matrix according to the determined incidence matrix; The second construction unit is configured to: construct a matrix for variable classification through the constructed Laplace matrix; The optimization processing unit is configured to: optimize the matrix for variable classification until convergence, and obtain a preset number of first eigenvectors; The classification unit is set to: cluster the obtained first eigenvector into a preset number of clusters to obtain a preset number of variable classification groups.

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