引用本文: 宋晓程, 李陟, 陈鹏飞, 张坤, 邹尧, 贺威. 基于障碍函数内点法的防御武器配系部署建模与智能优化[J]. 工程科学学报, 2024, 46(1): 157-165.
SONG Xiaocheng, LI Zhi, CHEN Pengfei, ZHANG Kun, ZOU Yao, HE Wei. Modeling and intelligent optimization of the deployment system of defensive weapons based on the interior point method with barrier functions[J]. Chinese Journal of Engineering, 2024, 46(1): 157-165.
 Citation: SONG Xiaocheng, LI Zhi, CHEN Pengfei, ZHANG Kun, ZOU Yao, HE Wei. Modeling and intelligent optimization of the deployment system of defensive weapons based on the interior point method with barrier functions[J]. Chinese Journal of Engineering, 2024, 46(1): 157-165.

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

• 摘要: 针对防空任务中我方多平台、多武器、多区域部署带来的防御武器配系难以建模和实时优化难的问题，在考虑敌我双方攻防武器对抗博弈的条件下，提出了一种基于障碍函数内点法的我方防御武器部署优化模型，并综合武器防御效能、防御成本、保卫目标的资产价值等指标对模型进行智能优化解算与分析. 首先，建立我方部阵地、防御武器与保卫目标的参数化模型，并建立我方武器对于敌方武器拦截的概率函数与约束条件；然后，将防御武器优化部署问题转化为性能指标函数为凸函数的无约束优化问题；最后，引入障碍函数内点法对其进行快速求解，给出了防御阵地武器部署的最优配置方案. 所提方法充分考虑了来袭目标的不同类型、异构特性以及大气层内外防御的多元化火力运用方式；能够在具有混合整数非线性、约束强耦合、变量规模大等特征的防御武器配系场景下快速给出最优配置结果. 并且，通过数值仿真验证了在对抗博弈条件下所提部署建模与智能优化方法的有效性与优越性.

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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