基于XGboost和线性回归的军队体系建设“成本-能力”组合优化模型

doi:10.12305/j.issn.1001-506X.2025.02.15

摘要/Abstract

摘要：

不确定性条件下的体系能力评估和优化是提升军事体系建设效能的重要方式和手段。着眼军队体系建设中多种“成本-能力”方案优选问题, 借鉴投资组合优化理论, 采用极端梯度提升(eXtreme gradient boosting, XGboost)二分类模型、线性回归、三点估计等方法, 构建“成本-能力”组合优化模型, 汇总多个评估标准, 得出备选方案的经济价值和对备选方案不确定性的敏感程度, 综合分析, 得到最优备选方案, 并将模型应用于体系建设案例中进行验证, 研究成果为“成本-能力”组合备选方案评估优选提供理论依据及实践方法。

关键词: 组合优化, XGboost二分类, 线性回归, 三点估计, 体系能力

Abstract:

Evaluating and optimizing system of system (SoS) capabilities under uncertain conditions is an important way and means to enhance the efficiency of military system construction. This paper focuses on the optimization problem of multiple "cost-capability" options in the construction of the military system. Drawing on the theory of portfolio optimization, eXtreme gradient boosting (XGboost) binary classification model, linear regression, three-point estimation and other methods are used to construct a "cost-capability" combination optimization model. Multiple evaluation criteria are summarized to determine the economic value and sensitivity to the uncertainty of the alternative options. The optimal alternative solution is comprehensively analyzed and applied to a system construction cases for verification. The research results provide theoretical basis and practical methods for the evaluation and optimization of "cost-capability" combination alternative options.

Key words: combination optimization, eXtreme gradient boosting (XGboost) binary classification, linear regression, three-point estimation, system of system (SoS) capability

中图分类号:

TP202

张玉婷, 杨镜宇. 基于XGboost和线性回归的军队体系建设“成本-能力”组合优化模型[J]. 系统工程与电子技术, 2025, 47(2): 486-495.

Yuting ZHANG, Jingyu YANG. A cost-capability combination optimization model for military system construction based on XGboost and linear regression[J]. Systems Engineering and Electronics, 2025, 47(2): 486-495.

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参数	系数		系数置信区间
参数	w	p-value	下界	上界
常数项	10.74	0	4.80	16.68
能力1	-0.04	0.32	-0.14	0.05
能力2	0	0.97	-0.14	0.14
能力3	-0.61	0.04	-1.21	-0.02
能力4	-0.19	0.05	-0.38	0
能力5	-0.13	0.01	-0.21	-0.04
能力6	-0.35	0	-0.50	-0.20
成本	2.14	0.37	-2.77	7.06

参数	系数		系数置信区间
参数	w	p-value	下界	上界
常数项	-5.47	0.60	-26.65	15.71
能力1	0.12	0.62	-0.36	0.60
能力2	0.16	0.54	-0.37	0.69
能力3	1.19	0.30	-1.13	3.51
能力4	0.23	0.63	-0.76	1.23
能力5	0.17	0.42	-0.26	0.60
能力6	0.12	0.81	-0.89	1.14
成本	-13.80	0.40	-47.00	19.37

参数	备选方案S₁	备选方案S₂	S₂/S₁
概率	0.64	0.52	0.81
赔率	1.79	1.1	0.61
经济价值	7 633	7 420	0.97

备选方案S₁		概率	ln(E(r))	备选方案S₂		概率	ln(E(r))
边际效应	能力1	0.02	0.02	边际效应	能力1	0	0.02
	能力2	0.03	0.04		能力2	0	0.01
	能力3	0.01	0.16		能力3	0.01	0.04
	能力4	0.04	0.06		能力4	0.01	0.02
	能力5	0.03	0.02		能力5	0	0.02
	能力6	0.01	0.05		能力6	0.03	0.01
	预算	0.06	0.42		预算	0.04	0.13
三点估计	最小值	0.01	8.85	三点估计	最小值	0.23	8.62
	最可能值	0.64	8.94		最可能值	0.6	9.26
	最大值	1	9.29		最大值	0.87	9.9
标准差		0.389	0.149	标准差		0.331	0.112

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