Fast Force Capability Cognition and Combined Quantity Optimization Method Based on Deviation Clustering

Abstract

A fast force capability cognition and combination quantity optimization method based on deviation clustering, including Step 1: preset scenarios. For different combat units and different scenarios, preset different force combinations required under different scenarios, and form a combat power distribution histogram of each force combination; Step 2: obtain the current battlefield situation; Step 3: model the clustering problem to form a clustering problem model; Step 4: modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank; Step 5: use the alternating optimization method to solve the bipartite graph partitioning problem to obtain the optimal force combination, thus completing the fast force capability cognition and combination quantity optimization based on deviation clustering. The present invention can solve multiple clustering results simultaneously, can adjust the clustering center in real time, formalize the multi-mean clustering problem into an optimization problem, and use the alternating optimization method to solve this problem. This method has better performance than the existing multi-mean methods.

Description

Technical Field

[0001] The present invention specifically relates to a method for quickly recognizing the capabilities of military forces and optimizing the combination quantity based on deviation clustering, which can be used in combat scenarios with multiple units, multiple tasks, multiple combinations, and high real-time requirements. Background Art

[0002] In the field of military confrontation, the understanding of the capabilities of each military branch unit includes both the understanding of the capabilities of individual units and, more importantly, the understanding of the capabilities of combined military force units. This understanding of capabilities is the prerequisite for formulating combat strategies and allocating tasks, and is of great significance for enhancing combat effectiveness.

[0003] There are two traditional ideas for the design of military force combinations: one is to optimize the military force combination for specific tasks. The other is to adopt a method of system capability evaluation, draw on the evaluation methods of weapon equipment systems and combat systems to design the military force combination method, generate various military force combination plans for various tasks, and then use evaluation methods such as the ideal point method and grey correlation to evaluate the combination effectiveness.

[0004] However, for the situation where there are many unit elements, the tasks change rapidly, and the task objectives are not single, the number of combinations is large, and the required evaluation space explodes. Therefore, a method for quickly recognizing the capabilities of military forces and optimizing the combination quantity is needed. Currently, with the development of artificial intelligence technology, new ideas have been brought to solve this problem. However, there is no mature and reliable method for using artificial intelligence technology to solve the optimization of military force combinations, and it is still in the initial research stage. Currently, the commonly used method is clustering, but the commonly used K-means clustering only uses one center to model each class of data. And due to the assumption of the shape of the cluster, it cannot capture non-convex patterns. In addition, many classes consist of multiple subclasses, which obviously cannot meet the battlefield application scenarios. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art, and provide a method for quickly recognizing the capabilities of military forces and optimizing the combination quantity based on deviation clustering, which solves the problems of single battlefield situation and exponential growth of military force combinations in the prior art.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for quickly recognizing the capabilities of military forces and optimizing the combination quantity based on deviation clustering, the steps are as follows:

[0008] Step 1: Preset scenarios. For different combat units and different scenarios, assume that there are n units dispersed in total. The number of combatants of the i-th unit Ui is Pi, and the coordinates of its geographical location are (Xi, Yi), where i = 1, 2, 3, …, n. Through full permutation, preset different force combinations required in different scenarios, and form a combat power distribution histogram for each force combination.

[0009] Step 2: Obtain the current battlefield situation, store the data in X = {x1, x2,..., x i ,..., x n} ∈ R n×d where x i ∈ R 1×d , and calculate the similarity S with the preset scenario.

[0010] Step 3: Model the clustering problem to form a clustering problem model.

[0011] Step 4: Modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank.

[0012] Step 5: Use the alternating optimization method to solve the bipartite graph partitioning problem, obtain the optimal force combination, and complete the rapid force capacity cognition and combination quantity optimization based on deviation clustering.

[0013] Furthermore, in Step 1, store the preset scenarios in the matrix A = [a1, a2,... a i ,..., a m T ∈ R m×d ;

[0014] where a i represents the battlefield situation in the i-th preset scenario. A total of m scenarios are preset, and each scenario is represented by d parameters to indicate the current situation.

[0015] Furthermore, in Step 2, denote the similarity between the j-th preset scenario a j and the current scenario x i as s ij , and the distance i between x j and a is the similarity.

[0016] Furthermore, Step 3 models the clustering problem specifically as:

[0017]

[0018] s.t. S ≥ 0, S1 = 1, A ∈ R m×d

[0019] In the formula, x​i is the current scenario, a j is the preset scenario, s ij is the (i, j) - th element of matrix S, representing the j - th preset scenario a j and the current scenario x i the similarity between them. γ is the regularization parameter, and I is the identity matrix, which is used to control the sparsity of the connection of multi - preset scenario data points.

[0020] Furthermore, step four modifies the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank, specifically:

[0021] Introduce matrix and the normalized Laplacian matrix Modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank, where D ∈ R (n+m)×(n+m) is a diagonal matrix, and its i - th diagonal element is d ii = ∑ j p ij ;

[0022]

[0023] s.t. S ≥ 0, S1 = 1, A ∈ R m×d , F ∈ R (n+m ) ×k , F Τ F = I

[0024] where Tr() represents taking the trace.

[0025] Furthermore, step five uses the alternating optimization method to solve the bipartite graph partitioning problem and obtain the optimal force combination, specifically:

[0026] (5.1) Fix A and update S, F;

[0027] Specifically:

[0028] When A is fixed, select k exact connected components of S, and the bipartite graph partitioning problem with a constrained Laplacian rank is transformed into:

[0029]

[0030] When S is fixed, solve for F:

[0031] Since the bipartite graph partitioning problem with a constrained Laplacian rank becomes:

[0032]

[0033] Express F and D as block matrices where U ∈ R n×k , V ∈ R m×k ,

[0034] D V ∈ R m×m , Equation (14) is further described as:

[0035]

[0036] Furthermore, Equation (15) is solved by the following lemma:

[0037] Assume The optimal solution of is where respectively are the first k left singular value vectors of A, are the first k right singular value vectors.

[0038] When F is fixed, solve for S:

[0039] Express Equation (13) as:

[0040]

[0041] Because And D S depends on S, there is the following relationship:

[0042]

[0043] According to the structure of F, Equation (17) is rewritten as:

[0044]

[0045] Denote Equation (16) is reformulated as:

[0046]

[0047] Each different i in Equation (19) is independent of each other, so it is solved for each i:

[0048]

[0049] Introduce the vector whose elements are where Then the vector form in Equation (20) is expressed as:

[0050]

[0051] And there is a closed-form solution.

[0052] (5.2) Fix S and F, and update A.

[0053] Specifically:

[0054] When S and F are fixed, the re - representation of each sub - cluster is the weighted average of all data points assigned to it. Then the j - th sample is updated as follows

[0055]

[0056] The algorithm converges when the assignment no longer changes.

[0057] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0058] The present invention can solve multiple clustering results simultaneously, can adjust the clustering centers in real - time, formalize the multi - mean clustering problem as an optimization problem, and use the method of alternating optimization to solve this problem. In summary, this method has better performance than the existing multi - mean methods. Brief Description of the Drawings

[0059] Figure 1 It is a schematic flowchart of an embodiment of the method of the present invention. Detailed Embodiment

[0060] The present invention will be further described below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and cannot be used to limit the protection scope of the present invention.

[0061] Considering that the order of magnitude of the arms combinations grows exponentially, in order to control the number of combinations within an operable range for the next - step specific combat effectiveness assessment, it is necessary to select an appropriate clustering method. The present invention transforms the arms combat power distribution into a histogram and transforms the clustering problem into an optimization problem, which is of great significance for the research on rapid military force capacity cognition and combination number optimization.

[0062] The innovative idea of the present invention is: realizing the cognition of combat force distribution through the distribution - perception abstraction method, and modeling the clustering problem as a bipartite graph partitioning problem with a constrained Laplacian rank, thereby formalizing the problem as an optimization problem and using an effective alternating optimization strategy to solve the required force combinations under the current battlefield situation.

[0063] A method for rapid military force capacity cognition and combination number optimization based on deviation clustering of the present invention is applicable to the cognition of the capabilities of rapid combat unit elements and the assessment of optimization combination capabilities. Refer to Figure 1 as shown, and includes the following steps:

[0064] Step 1, preset the scenario.

[0065] An abstract method based on distribution aware of combat power. For different combat units and different combat scenarios, different required troop combinations in different scenarios are preset, and a combat power distribution histogram of this military branch is formed.

[0066] For different combat units and different scenarios, assume that there are n units dispersed. The number of combatants of the i-th unit Ui is Pi, and the coordinates of its location are (Xi, Yi), where i = 1, 2, 3,..., n. Different required troop combinations in different scenarios are preset through full permutation, and a combat power distribution histogram of each troop combination is formed.

[0067] Store the preset scenarios into the matrix A = [a1, a2,... a i ,..., a m T ∈R m×d .

[0068] Where a i represents the battlefield situation in the i-th preset scenario. A total of m scenarios are preset, and each scenario is represented by d parameters to indicate the current situation.

[0069] The essence of the problem of rapid troop ability cognition and combination quantity optimization is how to find the scenario most similar to the current scenario from multiple preset scenarios, that is, to find the clustering result of the current scenario among the preset scenarios.

[0070] Step 2, obtain the current battlefield situation, store the data into X = {x1, x2,..., x i ,..., x n} ∈ R n×d , where x i ∈R 1×d , and calculate its similarity S with the preset scenarios in A;

[0071] Denote the similarity between the j-th preset scenario a j and the current scenario x i as s ij , and the distance i between x j and a is the similarity.

[0072] Step 3, model the clustering problem to form a clustering problem model;

[0073] Model the similarity problem of n current scenarios and m preset scenarios based on the weighted square error criterion as:

[0074]

[0075] In the formula, x​i is the current scenario, a j is the preset scenario, s ij is the (i, j) - th element of the matrix S, representing the j - th preset scenario a j and the current scenario x i The similarity between them, γ is the regularization parameter, and 1 is the identity matrix, which is used to control the sparsity of the connection of multi - preset scenario data points.

[0076] The second term in Equation (5) is the regularization term. The regularization parameter γ is used to control the sparsity of the connection of multi - preset scenario data points. When γ = 0, Equation (5) has a trivial solution, and only the nearest preset scenario can be connected to x ij with a probability of s i = 1, and no other scenarios can be connected to x i , and this situation is hard partitioning. When γ is large enough, all m scenarios can be connected to x with the same probability i .

[0077] Each scenario x i is independent of each other. Therefore, we can calculate the similarity between each scenario and the preset scenarios separately.

[0078] Let Express as a vector, where the j - th element is denoted as (the same as s i ). x i The assignment of the nearest - neighbor scenarios can be written in vector form as:

[0079]

[0080] When S is updated, each preset scenario can be re - positioned to the average of all the data points assigned to it. For the j - th scenario, a j can be updated by Equation (7):

[0081]

[0082] This process can be iteratively executed by the following Equation (8) to obtain the optimal multi - nearest - neighbor assignment until the assignment is not updated.

[0083]

[0084] Step 4, modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank;

[0085] The above formula can only find a clustering result of the current scenario. In order to find multiple clustering results of the current scenario simultaneously, the present invention introduces a matrix and the normalized Laplacian matrix Modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank, where D ∈ R (n+m)×(n+m) is a diagonal matrix, and its i-th diagonal element is d ii = ∑ j p ij . If the similarity matrix is non-negative, the normalized Laplacian matrix has the following important properties:

[0086] The number of eigenvalues 0 in the normalized Laplacian matrix is equal to the number of connected components in the bipartite graph associated with S. That is, if then the bipartite graph associated with S has k connected components, that is, n data points and m scenarios are divided into k clusters, and the clustering results of k current scenarios can be found simultaneously.

[0087] Therefore, add an additional constraint in Equation (8) to obtain the ideal scenario allocation with specified k clusters:

[0088]

[0089] However, due to the rank constraint it is difficult to solve. Therefore, relax the rank constraint and express as the i-th smallest eigenvalue of. Because is a positive semi-definite matrix, so the optimal solution of S with a rank constraint can be obtained by solving the following problem:

[0090]

[0091] When λ is large enough, the optimal solution of S in Equation (10) will make be 0, thus satisfying the rank constraint. According to the KyFan theorem, we have:

[0092]

[0093] Therefore, Equation (10) can be further written as:

[0094]

[0095] where

[0096] Step 5. Next, use the alternating optimization method to solve problem (12);

[0097] The objective model is solved using an alternating optimization framework. When updating a certain variable each time, other variables are fixed, thus transforming the objective problem into a series of sub-problems for solution.

[0098] Step 5.1: Fix A and update S, F.

[0099] When A is fixed, the algorithm can select k exact connected components of S. Thus, Equation (12) is transformed into:

[0100]

[0101] Similarly, Equation (13) can also be solved by the method of alternating optimization.

[0102] When S is fixed, solve for F:

[0103] Since (12) can be changed to:

[0104]

[0105] We represent F and D as block matrices where U ∈ R n×k , V ∈ R m×k , D V ∈ R m×m . Equation (14) can be further described as:

[0106]

[0107] Equation (15) can be solved by the following lemma.

[0108] Lemma: Assume that The optimal solution of is where respectively are the first k left singular value vectors of A, are the first k right singular value vectors.

[0109] When F is fixed, solve for S:

[0110] Equation (13) can be expressed as:

[0111]

[0112] Because And D S depends on S, so it seems unsolvable, but there is the following relationship:

[0113]

[0114] According to the structure of F, formula (17) can be rewritten as:

[0115]

[0116] Record Equation (16) can be reformulated as:

[0117]

[0118] Each different \(i\) in Equation (19) is independent of each other. Therefore, the problem is divided into solving for each \(i\):

[0119]

[0120] Introduce the vector whose elements are where Then the vector form in Equation (20) is expressed as follows:

[0121]

[0122] and has a closed-form solution. When the rank constraint is satisfied, the iterative sub-step will stop. For example: and

[0123] Step 5.2 Fix \(S\), \(F\) and update \(A\)

[0124] When \(S\) and \(F\) are fixed, each sub-cluster can be re-expressed as the weighted average of all the data points assigned to it. Then the \(j\)-th sample can be updated as follows

[0125]

[0126] The algorithm converges when the assignment no longer changes.

[0127] The present invention can solve multiple clustering results simultaneously, can adjust the clustering centers in real time, and formalizes the multi-mean clustering problem as an optimization problem, and uses the method of alternating optimization to solve this problem. In summary, this method has better performance than the existing multi-mean methods.

[0128] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0129] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, such that the instructions executed by the processors of the computer or other programmable data processing devices produce means for implementing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or means for implementing the functions specified in one or more of the blocks.

[0130] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means for implementing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or means for implementing the functions specified in one or more of the blocks.

[0131] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or means for implementing the functions specified in one or more of the blocks.

[0132] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principles of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A rapid force capability cognition and combination quantity optimization method based on deviation clustering, characterized in that The steps are as follows: Step 1, preset scenarios. For different combat units and different scenarios, assume that there are n units scattered in total. The number of combatants of the i-th unit Ui is Pi, and the coordinates of its location are (Xi, Yi), where i = 1, 2, 3, …, n. Through full permutation, preset different force combinations required in different scenarios, and form a combat power distribution histogram of each force combination; Step 2: Obtain the current battlefield situation, store the data in \(X = \{x_1, x_2,..., x i ,..., x n \} \in R n×d , where \(x i \in R 1×d , and calculate the similarity \(S\) with the preset scenario; Step 3, model the clustering problem to form a clustering problem model; Step 4: Modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank; Step 5: Use the alternating optimization method to solve the bipartite graph partitioning problem to obtain the optimal force combination, and complete the rapid force capability perception and combination quantity optimization based on deviation clustering; The specific method for Step 3 to model the clustering problem is as follows: s.t. S ≥ 0, S1 = 1, A ∈ R m×d where x i is the current scenario, a j is the preset scenario, s ij is the (i, j) - th element of the matrix S, representing the similarity between the j - th preset scenario a j and the current scenario x i ; γ is the regularization parameter, and 1 is the identity matrix, which is used to control the sparsity of the connection of multi - preset scenario data points; The specific method for Step 4 to modify the clustering problem model into a bipartite graph partitioning problem with a constrained Laplacian rank is as follows: Introduction matrix and the normalized Laplacian matrix Modify the clustering problem model into a bipartite graph partitioning problem with constrained Laplacian rank, where D ∈ R (n+m)×(n+m) is a diagonal matrix, and its i-th diagonal element is d ii = ∑ j p ij ; s.t. S≥0, S1=1, A∈R m×d , F∈R (n+m ) ×k , F Τ F=I Among them Tr() represents taking the trace.

2. The rapid force capacity cognition and combination quantity optimization method based on deviation clustering according to claim 1, wherein: In step one, store the preset scenario into matrix A = [a1, a2,... a i ,..., a m T ∈R m×d ;​ where a i represents the battlefield situation in the preset i-th scenario. There are m preset scenarios in total, and each scenario uses d parameters to represent the current situation.

3. The method for rapid military force capability cognition and combination quantity optimization based on deviation clustering according to claim 2, wherein: In Step 2, the similarity between the j-th preset scenario a j and the current scenario x i is denoted as s ij , where the distance i between x j and a is the similarity.

4. The method for rapid military force capability cognition and combination quantity optimization based on deviation clustering according to claim 1, wherein: The specific method for Step 5 to use the alternating optimization method to solve the bipartite graph partitioning problem to obtain the optimal force combination is as follows: (5.1) Fix A and update S, F; (5.2) Fix S, F and update A.

5. The method for rapid military force capability cognition and combination quantity optimization based on deviation clustering according to claim 4, characterized in that: The specific method for the above step (5.1) to fix A and update S, F is as follows: When A is fixed, select k exact connected components of S, and the bipartite graph partitioning problem with a constrained Laplacian rank is transformed into: s.t. S ≥ 0, S1 = 1, F ∈ R (n+m)×k , F Τ F = I (13) When S is fixed, solve for F: Since The bipartite graph partitioning problem with constrained Laplacian rank becomes: Express F and D as block matrices where U ∈ R n×k , V ∈ R m×k , D V ∈ R m×m , Equation (14) is further described as: When F is fixed, solve for S: Express equation (13) as: s.t. S≥0, S1 = 1 (16) Because and D S depends on S, the following relationship exists: According to the structure of F, equation (17) is rewritten as: Record Equation (16) is reformulated as follows: s.t. S≥0, S1 = 1 (19) In equation (19), each different i is independent of each other, so it is solved for each i: Introduce a vector whose elements are where Then the vector form in Equation (20) is expressed as follows: And there is a closed-form solution.

6. The rapid force capability cognition and combination quantity optimization method based on deviation clustering according to claim 5, characterized in that: Equation (15) is solved by the following lemma: Assume The optimal solution of wherein respectively are the first k left singular value vectors of A, are the first k right singular value vectors.

7. The method for rapid military force capability cognition and combination quantity optimization based on deviation clustering according to claim 4, characterized in that: The specific method for the above step (5.2) to fix S, F and update A is as follows: When S and F are fixed, the re-representation of each sub-cluster is the weighted average of all data points assigned to it, then the j-th sample is updated in the following way The algorithm converges when the assignment no longer changes.

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