Dynamic decision-making method based on Riemannian geometry geodesic optimization

Abstract

The invention discloses a dynamic decision-making method based on Riemannian geometry geodesic optimization. The dynamic decision-making method comprises the following steps: step 1, defining a Riemannian manifold and a measurement corresponding to the Riemannian manifold; step 2, calculating a geodesic line between two points on the manifold by using Riemannian metric; and step 3, implementing a Riemannian gradient descent algorithm, and dynamically adjusting the position of the decision node on the Riemannian manifold. Through a method based on Riemannian geometry and in combination with a global command and control system, variable battlefield environments can be effectively dealt with, the decision making speed and quality are improved, efficient collaboration of strategic and tactical levels is ensured, and the system not only optimizes the execution efficiency of a single task, but also improves the task execution efficiency. And dynamic optimization and adaptability of overall combat command are ensured through continuous algorithm iteration.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimization of information and decision-making processes, and relates to a dynamic decision-making method based on Riemannian geometry geodesic optimization, which is applied to a joint global command and control system to optimize information transmission and decision-making paths. The concept of geodesics in Riemannian geometry is introduced to minimize delays and improve decision-making efficiency. Background Art

[0002] In modern military command and control systems, the rapid and accurate transmission and processing of information is crucial. Traditional decision path optimization methods mostly rely on direct data processing technology, which is often inefficient when processing high-dimensional and complex geometric data and is difficult to meet the needs of real-time decision-making. The Joint Global Command and Control System places special emphasis on cross-domain combat command and control, among which the geographical and network dynamic path optimization of information is particularly critical. Summary of the invention

[0003] (I) Purpose of the invention

[0004] The purpose of the present invention is to provide a dynamic decision-making method based on Riemannian geometry geodesic optimization, which can effectively improve the dynamics and response speed of command and control in a multi-domain environment.

[0005] (II) Technical solution

[0006] In order to solve the above technical problems, the present invention provides a dynamic decision-making method based on Riemannian geometry geodesic optimization, comprising the following steps:

[0007] Step 1: Define the Riemann manifold and its corresponding metric:

[0008] Modeling the decision paths in the command and control system as Riemann manifolds Provides a powerful framework to process and optimize the data flow and instruction flow between different military services and combat domains (land, sea, air, space and network). The Riemann metric g not only reflects the geometric and topological properties of the data, but also optimizes the transmission path of information to make it more efficient and secure.

[0009] g(χ)(u,υ)=<u,υ> χ , u,υ are the tangent spaces of the point χ on the manifold The vector in .

[0010] Step 2: Use the Riemannian metric to calculate the geodesic between two points on the manifold:

[0011] The shortest path between decision nodes, i.e., geodesic, is calculated using defined metrics to determine the optimal communication and decision paths between various decision nodes on the battlefield (such as radar stations, submarines, aircraft carriers, drone control center stations, etc.). It is suitable for dynamic and rapidly changing battlefield environments, and can adjust the path in real time to respond to changes in tactical requirements.

[0012] The geodesic distance d(χ, y) is calculated by the formula:

[0013]

[0014] Where γ is the curve connecting χ and y, representing a possible communication or action path.

[0015] Step 3: Implement the Riemann gradient descent algorithm:

[0016] Dynamically adjusting the position of decision nodes on the manifold (command and control system) is the key to responding to battlefield dynamics and optimizing commands. By implementing the Riemann gradient descent algorithm, the system can quickly adapt to environmental changes and optimize tactical and strategic deployments between nodes, thereby improving overall combat efficiency and decision-making quality.

[0017] The node position is updated using the formula: new =Exp χ (-αgrad f(χ)), where α is the learning rate and grad f(χ) is the Riemann gradient of the objective function f at χ, indicating how to adjust the direction and steps on the manifold to maximize efficiency.

[0018] The above scheme based on Riemann geometry provides a powerful tool for enhancing the accuracy and response speed of decision-making. Through this revised method, the joint global command and control system can not only effectively cope with the complex and changing battlefield environment, but also ensure that the decision path is theoretically optimized.

[0019] The present invention also provides a dynamic decision-making system based on Riemannian geometry geodesic optimization, comprising:

[0020] (1) Data collection unit:

[0021] Responsible for collecting operational data from different military services and platforms, including but not limited to geographic location information, sensor data, communication records, etc. These data are the basis for decision path optimization and are pre-processed to adapt to subsequent geometric modeling.

[0022] (2) Geometric modeling unit:

[0023] Mapping the collected data onto a predefined Riemannian manifold. This unit uses complex mathematical models to define the manifold and the corresponding metrics, ensuring that the geometric properties of the data are correctly represented and utilized.

[0024] (3) Path optimization processor:

[0025] It mainly performs geodesic calculations and Riemannian gradient descent algorithms. This processor uses metrics defined on Riemann manifolds to calculate the shortest paths between nodes and dynamically adjusts these paths in response to task requirements and environmental changes.

[0026] (4) Decision support system:

[0027] The system receives information output by the optimization processor and converts it into specific command and control decisions. The system provides a user interface that allows commanders to intuitively see changes in the decision path and manually adjust decision parameters.

[0028] (5) Communication interface unit:

[0029] Ensure efficient and secure transmission of information between various units within the system and between the system and external entities. This unit supports multiple communication standards and protocols to ensure real-time and reliable data transmission.

[0030] (III) Beneficial effects

[0031] The above technical solution provides a dynamic decision-making method based on Riemannian geometry geodesic optimization. Through the Riemannian geometry-based method, the joint global command and control system can effectively cope with the changing battlefield environment, improve the speed and quality of decision-making, and ensure efficient coordination at the strategic and tactical levels. This system not only optimizes the execution efficiency of a single task, but also ensures the dynamic optimization and adaptability of the overall combat command through continuous algorithm iteration. Rapid response, flexible adjustment and efficient coordination are achieved in a multi-domain battlefield environment, providing strong decision-making support for commanders. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the decision path for the spherical model.

[0033] Figure 2 Optimize the process flow chart for dynamic decision paths.

[0034] Figure 3 Schematic diagram of the application of Riemann gradient descent. DETAILED DESCRIPTION

[0035] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the drawings and examples.

[0036] This embodiment is based on the dynamic decision-making system of Riemannian geometry geodesic optimization, including:

[0037] (1) Data collection unit:

[0038] Responsible for collecting operational data from different military services and platforms, including but not limited to geographic location information, sensor data, communication records, etc. These data are the basis for decision path optimization and are pre-processed to adapt to subsequent geometric modeling.

[0039] (2) Geometric modeling unit:

[0040] Mapping the collected data onto a predefined Riemannian manifold. This unit uses complex mathematical models to define the manifold and the corresponding metrics, ensuring that the geometric properties of the data are correctly represented and utilized.

[0041] (3) Path optimization processor:

[0042] It mainly performs geodesic calculations and Riemannian gradient descent algorithms. This processor uses metrics defined on Riemann manifolds to calculate the shortest paths between nodes and dynamically adjusts these paths in response to task requirements and environmental changes.

[0043] (4) Decision support system:

[0044] The system receives information output by the optimization processor and converts it into specific command and control decisions. The system provides a user interface that allows commanders to intuitively see changes in the decision path and manually adjust decision parameters.

[0045] (5) Communication interface unit:

[0046] Ensure efficient and secure transmission of information between various units within the system and between the system and external entities. This unit supports multiple communication standards and protocols to ensure real-time and reliable data transmission.

[0047] like Figure 1 As shown in the figure, in the joint global command and control system, nodes in the three domains of land, air and network are selected. A three-dimensional sphere (S 3 ) was chosen as the Riemann manifold because the three-dimensional sphere provides a geometric structure on which clear distances and paths can be defined.

[0048] Three-dimensional sphere (usually denoted as S 3 ) is the set of all points with a fixed radius and center at the origin. The characteristic of this sphere is that the shortest path between any two points on it can be defined by a great circle arc on the sphere, which is particularly important in optimization and decision path calculation. The Riemann metric g is used to calculate such great circle arc distances and paths. In this context, the Riemann metric not only helps calculate distances, but also ensures the optimization of paths, thereby effectively improving the speed and security of information transmission and decision-making.

[0049] The following are the detailed solution steps:

[0050] 1. Node definition and geodesic calculation

[0051] Figure 1 A schematic diagram of the decision path for the spherical model, defined on a three-dimensional sphere, and the geodesics (shortest paths) between these nodes are calculated using the Riemann metric.

[0052] Node definition:

[0053] Land-based node: such as a land command center or a ground radar station, located at a certain position on the sphere, marked as node A.

[0054] Air-based node: such as an air command center or an airborne early warning aircraft, located at another position on the sphere, marked as node B.

[0055] Network command center: such as the joint command center or communication hub, located in the third position of the sphere, marked as node C.

[0056] Geodesic calculation:

[0057] After receiving an emergency mission order, the flight path from the air base to the target point needs to be replanned to ensure a quick response. To this end, the Riemann metric on the sphere is used to calculate the geodesic from node B to the target point (node ​​D) to determine the shortest flight path.

[0058]

[0059] Where γ is the curve connecting node B and node D, is the tangent vector of the curve at time t, and g is the Riemann metric on the sphere.

[0060] You can also directly call the special spherical geodesic formula to calculate:

[0061] d(p,q)=cos -1 (sinθ p sinθ q cos(φ p -φ q )+cosθ p cosθ q ) γ

[0062] θ is the polar angle, φ is the azimuth angle

[0063] 2. Application of Riemannian Gradient Descent

[0064] Dynamic path adjustment:

[0065] like Figure 2 As shown in the figure, in a rapidly changing battlefield environment, the path planning of the air force base needs to be adjusted in real time. Through the Riemann gradient descent method, the system can quickly adjust the strategic position of the base to optimize the arrival time and energy consumption. The specific steps are as follows:

[0066] Initial path settings:

[0067] According to the inter-node distances and paths obtained in step S1, an initial flight path is set, and the positions of each node (A, B, C) on the initial path are calculated.

[0068] Compute the Riemann gradient:

[0069] Figure 3 This is the application of Riemannian gradient descent, which reflects the description in the "Application of Riemannian gradient descent" step. It explains how to adjust the position of each node through Riemannian gradient descent to optimize the action path and decision efficiency, including the process of calculating Riemannian gradients, updating node positions, and continuously iterating the optimization path.

[0070] Calculate the Riemannian gradient grad f(χ) of the objective function f at the current node position χ. This gradient is defined on the Riemann manifold. It not only reflects the direction of the steepest descent of the objective function at that point, but is also a key indicator of the decision path optimization process. By calculating grad f(χ), the system can clearly determine how each node should adjust its position in a multi-domain battlefield environment to optimize information flow and decision paths. The calculation results of this gradient will directly indicate how decision nodes should be dynamically adjusted in a complex combat environment to respond to changes in tactical requirements and optimize their tactical deployment and operational efficiency.

[0071] Update node location:

[0072] Using exponential mapping Exp χ , update the node position along the Riemann gradient direction.

[0073] χ new =Exp χ (-αgradf(χ))

[0074] Here, α is the learning rate.

[0075] Repeat the iteration:

[0076] The process of calculating gradients and updating node positions is repeated until the optimal configuration is reached to maximize battlefield response and fully optimize the command and control system. After each iteration, the system checks the effectiveness of the path and resource consumption to ensure that the path is continuously optimized.

[0077] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A dynamic decision-making method based on Riemannian geometry geodesic optimization, characterized in that: The following steps are involved: Step 1: Define the Riemannian manifold and its corresponding metric; Step 2: Use the Riemannian metric to calculate the geodesic between two points on the manifold; Step 3: Implement the Riemannian gradient descent algorithm to dynamically adjust the position of the decision node on the Riemann manifold.

2. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 1, characterized in that: In step 1, the decision path in the command and control system is modeled as a Riemann manifold The Riemann metric is: g(χ)(u,υ)=<u,υ> χ , u,υ is the tangent space of point χ on the manifold The vector in .

3. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 2, characterized in that: In step 2, the shortest path between decision nodes, i.e., geodesic, is calculated using the defined metric to determine the optimal communication and decision paths between various decision nodes on the battlefield.

4. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 3, characterized in that: In step 2, the geodesic distance d(x, y) is calculated by the formula: Where γ is the curve connecting χ and y, representing a possible communication or action path.

5. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 4, characterized in that: Step 3 includes the following sub-steps: Step 31, initial path setting; Step 32, calculate the Riemann gradient; Step 33: Update node position; Step 34, repeat the iteration.

6. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 5, characterized in that: In step 31, the initial path setting process is: according to the distance between nodes and the path, the initial flight path is set, and the position of each node on the initial path is calculated.

7. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 6, characterized in that: In step 32, the process of calculating the Riemann gradient is: calculating the Riemann gradient grad f((χ)) of the objective function f at the current node position χ, where the Riemann gradient reflects the steepest descent direction of the objective function at that point.

8. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 7, characterized in that: In step 33, the process of updating the node position is: Using exponential mapping Exp χ , update the node position along the Riemann gradient direction: x new =Exp χ (-agrad f(x)) Here, α is the learning rate.

9. The dynamic decision-making method based on Riemannian geometry geodesic optimization according to claim 8, characterized in that: In step 34, the iterative process is: repeatedly calculating the gradient and updating the node position until the optimal configuration is reached to maximize the battlefield response and fully optimize the command and control system.

10. A dynamic decision-making system based on Riemannian geometry geodesic optimization, characterized in that: include: (1) Data collection unit Collect operational data from different services and platforms, including geolocation information, sensor data, and communications records; (2) Geometric modeling unit Mapping the collected data onto a predefined Riemannian manifold; (3) Path optimization processor: Perform geodesic calculations and Riemannian gradient descent algorithms; compute shortest paths between nodes using metrics defined on Riemannian manifolds; (4) Decision support system: Receive information output from the optimization processor and convert it into command and control decisions; (5) Communication interface unit: Realize information transmission between each unit within the system and between the system and external entities.

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