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基于障礙函數內點法的防御武器配系部署建模與智能優化

Modeling and intelligent optimization of the deployment system of defensive weapons based on the interior point method with barrier functions

  • 摘要: 針對防空任務中我方多平臺、多武器、多區域部署帶來的防御武器配系難以建模和實時優化難的問題,在考慮敵我雙方攻防武器對抗博弈的條件下,提出了一種基于障礙函數內點法的我方防御武器部署優化模型,并綜合武器防御效能、防御成本、保衛目標的資產價值等指標對模型進行智能優化解算與分析. 首先,建立我方部陣地、防御武器與保衛目標的參數化模型,并建立我方武器對于敵方武器攔截的概率函數與約束條件;然后,將防御武器優化部署問題轉化為性能指標函數為凸函數的無約束優化問題;最后,引入障礙函數內點法對其進行快速求解,給出了防御陣地武器部署的最優配置方案. 所提方法充分考慮了來襲目標的不同類型、異構特性以及大氣層內外防御的多元化火力運用方式;能夠在具有混合整數非線性、約束強耦合、變量規模大等特征的防御武器配系場景下快速給出最優配置結果. 并且,通過數值仿真驗證了在對抗博弈條件下所提部署建模與智能優化方法的有效性與優越性.

     

    Abstract: Under modern war conditions, it is difficult for a single air defense weapon to complete the combat task. Establishing an effective ground–air defense system can form a tight defense and control system network. The rapid development of attack and defense weapons and equipment has caused varied situation changes, complexities, and uncertainties in the effective defense and interception areas of weapons, which makes the modeling of the deployment of our defense weapons challenging. In addition to effective deployment models, the efficient deployment of defense weapons is crucial for completing the configuration of weapon systems in real time, which requires quick optimization of the deployment model of defense weapon systems. In this study, we established a defensive weapon deployment model using the interior point method with barrier functions under the conflict situation between hostile assault weapons and our defensive weapons to address the challenges in modeling the configuration and real-time optimization of defensive weapon systems for deploying multiple platforms and weapons in multiple areas. Furthermore, we performed an intelligent optimization analysis by integrating defense efficiency, defense cost, and asset value of defense objects. The proposed method is established with the following three steps: First, a parametric model of our defensive positions, weapons, and objects is established, and the probability functions and constraints for intercepting hostile weapons are formulated. Thereafter, the concerned optimization deployment problem of defensive weapons is transformed into an unconstrained optimization problem with convex performance index functions. Finally, the obstacle function interior point method is employed to solve the problem, and the optimal deployment scheme of defense position weapons is obtained. The following are the main contributions of the proposed method: (1) A dynamic deployment model of defense weapon systems is established by considering the different types and heterogeneous characteristics of incoming targets and the diversified fire application modes of the defense system inside and outside the atmosphere. (2) An optimal deployment algorithm for defense weapons is proposed based on the interior point method of the obstacle function by focusing on the deployment model of defense weapons with mixed-integer nonlinearity, strong coupling of constraints, and large-scale variables. Further, the effectiveness and superiority of the proposed intelligent optimization modeling and calculating method are verified through numerical simulation under a complicated conflict situation.

     

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