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Combat capability requirement generation of warship area air defense based on constrained optimization
XU Junfei , XING Changfeng , WU Ling
School of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China
Received: 2015-05-26; Accepted: 2015-06-26; Published online: 2016-05-25 12: 00
Corresponding author. Tel.: 027-65461236 E-mail:xingchf@sohu.com
Abstract: Capability requirement generation is performed under multiple constraints, so seeking the constraint set is its focus. In the background of area air defense of ship-to-air missile, by extracting the constraint set that has an effect on generation of capability index through the comprehensive analysis of combat requirement constraints, capability requirement constraints, technology development constraints and other constraints, the target function of warship air defense combat effectiveness was established, and we solved constrained optimization of capability index through particle swarm algorithm based on the penalty function method. The curves of the other combat capability indices before and after optimization were simulated and verified with the max distance of early warning as the variable. Finally the capability indices produced verify the feasibility of the model and algorithm and provide quantitative basis for combat capability requirement generation of warship area air defense.
Key words: warship air defense     capability requirement generation     index method     penalty function     particle swarm algorithm     constrained optimization

1 舰艇区域防空作战能力约束提取

 图 1 作战能力需求生成问题描述 Fig. 1 Combat capability requirement generation problem description
1.1 作战需求约束

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1.2 能力需求约束

 图 2 舰艇作战能力指标关系图 Fig. 2 Warship combat capability index relationship diagram

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1.3 技术发展约束

 参数 数值 作战距离/km 15~150 作战高度/m 10~29000 速度/ Ma 2.5 拦截概率/% 80 系统反应时间/s 1

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1.4 其他约束

2 基于APSO算法能力需求约束优化

2.1 适应度函数的建立

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2.2 约束处理的罚函数法

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x是不可行解时,p(x,r)>f(x);当x是可行解时,p(x,r)=f(x)。罚因子η越来越大时,不可行解的函数值也将越来越大,能够促使一系列无约束问题的极小值点靠近可行域,或者在可行域内移动,直到收敛到满足目标函数的最优值。因此,给原函数加了一个整数以示惩罚,当η足够大时,就可以保证原函数的最优解和增广目标函数的最优解一致[13]

2.3 APSO算法流程

2.4 实例求解

 参数 μ′ σ tzk( s) 10 2 ttx( s) 3 1 tfs( s) 20 3 twk( s) 3.5 0.05 tfy( s) 8 2 σt 3.1 0.1 P( t≤ tjs) 0.94 0.03 tz( s) 0.1 0.05 μ′-参数期望；σ-参数方差。

 能力指标 区间值 Dqc/km [88.69,95.10] hE/m [220.32,268.88] Rbyj/km [337.79,347.59] RE/km [304.89,311.30] Ssyj/km [149.12,149.12] Ssjj/km [4.72,6.17] Sfyj/km [323.02,323.02] Sfjj/km [10.23,13.37] Sfx/km [339.65,349.87] Swgz/km [323.38,323.45] n [1,4] p/% [31.23,90]

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 能力指标 指标值 Dqc/km 93.24 hE/m 256.14 Rbyj/km 384.82 RE/km 307.46 Ssyj/km 158.89 Ssjj/km 15.17 Sfyj/km 335.06 Sfjj/km 24.24 Sfx/km 372.82 Swgz/km 346.10 n 4 p/% 64.47

 图 3 APSO适应度曲线 Fig. 3 APSO fitness curve
 图 4 最优个体效能值曲线 Fig. 4 Optimal individual effectiveness value curve

 图 5 Dqc、Rbyj、RE、hE、Ssyj、Ssjj与Rdyj之间优化前后关系 Fig. 5 Relationship between Dqc、Rbyj、RE、hE、Ssyj、Ssjj and Rdyj before and after optimization

3 结 论

1) 较为全面地提取了能力需求生成所需满足的约束集,为约束优化模型提供了基础。

2) 采用指数法较好地表征了舰艇防空作战效能,使约束优化问题更具有目标性。

3) 建立的APSO算法模型可得到满足多维约束条件优化的能力需求生成方案,寻优速度快,优化效果较好。

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文章信息

XU Junfei, XING Changfeng, WU Ling

Combat capability requirement generation of warship area air defense based on constrained optimization

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(5): 1039-1045
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0337