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

Abstract

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

CLC Number:

TP202

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.

Figures/Tables 8

Fig.1

Fig.2

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

References 42

1	MARKOWITZ H . Portfolio selection[J]. The Journal of Finance, 1952, 7 (1): 77- 91.
2	BAKER S F , GREEN S G , LOWE J K , et al. A value-focused approach for laboratory equipment purchases[J]. Military Ope-rations Research, 2000, 5 (4): 43- 56. doi: 10.5711/morj.5.4.43
3	WALMSLEY N S , HEARN P . An application of linear programming in the defence environment[J]. International Transactions in Operational Research, 2003, 10 (2): 155- 167. doi: 10.1111/1475-3995.00401
4	TSAGANEA D . Appropriation of funds for anti-ballistic missile defense: a dynamic model[J]. Kybernetes, 2005, 34 (6): 824- 833. doi: 10.1108/03684920510595517
5	WHITACRE J M, ABBASS H A, SARKER R, et al. Strategic positioning in tactical scenario planning[C]//Proc. of the 10th Annual Conference on Genetic and Evolutionary Computation, 2008: 1081-1088.
6	HURLEY W J , SCHOBEL K B . Selecting low expenditure defence projects: an estimate of the value of optimization relative to AD HOC procedures[J]. Military Operations Research, 2009, 14 (4): 41- 46. doi: 10.3969/j.issn.1672-8211.2009.04.008
7	LEE J , KANG S H , ROSENBERGER J , et al. A hybrid approach of goal programming for weapon systems selection[J]. Computers & Industrial Engineering, 2010, 58 (3): 521- 527.
8	GOLANY B , KRESS M , PENN M , et al. Network optimization models for resource allocation in developing military countermeasures[J]. Operations Research, 2012, 60 (1): 48- 63. doi: 10.1287/opre.1110.1002
9	DAVENDRALINGAM N , DELAURENTIS D A . A robust portfolio optimization approach to system of system architectures[J]. Systems Engineering, 2015, 18 (3): 269- 283. doi: 10.1002/sys.21302
10	MOALLEMI E A, ELSAWAH S, TURAN H H, et al. Multi-objective decision making in multi-period acquisition planning under deep uncertainty[C]//Proc. of the Winter Simulation Conference, 2018: 1334-1345.
11	JONES D W , BJORNSTAD D J , REDUS K S . Prioritizing R&D for the US department of energy's weapons complex clean-up[J]. Environmental Modeling & Assessment, 2001, 6, 209- 215.
12	BUCKSHAW D L , PARNELL G S , UNKENHOLZ W L , et al. Mission oriented risk and design analysis of critical information systems[J]. Military Operations Research, 2005, 10 (2): 19- 38. doi: 10.5711/morj.10.2.19
13	BJORKMAN E A , SARKANI S , MAZZUCHI T A . Test and evaluation resource allocation using uncertainty reduction[J]. IEEE Trans.on Engineering Management, 2012, 60 (3): 541- 551.
14	HURLEY W J , BRIMBERG J , FISHER B . Risk-analytic appro-aches to the allocation of defence operating funds[J]. The Journal of Defense Modeling and Simulation, 2013, 10 (3): 275- 282. doi: 10.1177/1548512912466195
15	DAVENDRALINGAM N , DELAURENTIS D . An analytic portfolio approach to system of systems evolutions[J]. Procedia Computer Science, 2014, 28, 711- 719. doi: 10.1016/j.procs.2014.03.085
16	CHAN Y , DISALVO J P , GARRAMBONE M W . A goal-seeking approach to capital budgeting[J]. Socio-Economic Planning Sciences, 2005, 39 (2): 165- 182. doi: 10.1016/j.seps.2004.04.002
17	PREISS B, GREENE L, KRIEBEL J, et al. Air force research laboratory space technology strategic investment model: analysis and outcomes for warfighter capabilities[C]//Proc. of the Modeling and Simulation for Military Applications, 2006: 14-21.
18	BAKIRLI B B , GENCER C , AYDOGAN E K . A combined approach for fuzzy multi-objective multiple knapsack problems for defence project selection[J]. Journal of the Operational Research Society, 2014, 65, 1001- 1016. doi: 10.1057/jors.2013.36
19	FISHER B , BRIMBERG J , HURLEY W J . An approximate dynamic programming heuristic to support non-strategic project selection for the Royal Canadian Navy[J]. The Journal of Defense Modeling and Simulation, 2015, 12 (2): 83- 90. doi: 10.1177/1548512913509031
20	XIN B , CHEN J , PENG Z H , et al. An efficient rule-based constructive heuristic to solve dynamic weapon-target assignment problem[J]. IEEE Trans.on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2010, 41 (3): 598- 606.
21	ZHOU Y, TAN Y, YANG K W, et al. Research on evolving capability requirements oriented weapon system of systems portfolio planning[C]//Proc. of the 7th International Conference on System of Systems Engineering, 2012: 275-280.
22	DOU Y J , ZHANG P , GE B F , et al. An integrated technology pushing and requirement pulling model for weapon system portfolio selection in defence acquisition and manufacturing[J]. Proc.of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2015, 229 (6): 1046- 1067. doi: 10.1177/0954405414534640
23	YANG S L , YANG M , WANG S , et al. Adaptive immune genetic algorithm for weapon system portfolio optimization in mi-litary big data environment[J]. Cluster Computing, 2016, 19, 1359- 1372. doi: 10.1007/s10586-016-0596-3
24	夏博远, 赵青松, 张骁雄, 等. 基于动态能力需求的鲁棒性武器系统组合决策[J]. 系统工程与电子技术, 2017, 39 (6): 1280- 1286. doi: 10.3969/j.issn.1001-506X.2017.06.15
	XIA B Y , ZHAO Q S , ZHANG X X , et al. Robust weapon system combination decision based on dynamic capability requirements[J]. Systems Engineering and Electronics, 2017, 39 (6): 1280- 1286. doi: 10.3969/j.issn.1001-506X.2017.06.15
25	张骁雄, 葛冰峰, 姜江, 等. 面向能力需求的武器装备组合规划模型与算法[J]. 国防科技大学学报, 2017, 39 (1): 102- 108.
	ZHANG X X , GE B F , JIANG J , et al. A weapon equipment combination planning model and algorithm for capability requirements[J]. Journal of National University of Defense Technology, 2017, 39 (1): 102- 108.
26	CHENG C, LI J C, ZHAO Q S, et al. Research on weapon system portfolio selection based on combat network modeling[C]//Proc. of the 2017 Annual IEEE International Systems Conference, 2017.
27	XIONG J , ZHOU Z B , TIAN K , et al. A multi-objective approach for weapon selection and planning problems in dynamic environments[J]. Journal of Industrial & Management Optimization, 2017, 13 (3): 1189- 1211.
28	WANG M, ZHANG H Q, ZHANG K. A model and solving algorithm of combination planning for weapon equipment based on epoch-era analysis method[C]//Proc. of the International Conference on Materials, Sciences, Resource and Environment Engineering, 2017.
29	李清韦. 基于能力组合的体系能力水平评估方法研究[D]. 长沙: 国防科技大学, 2021.
	LI Q W. Research on system capability level evaluation method based on capability combination[D]. Changsha: National University of Defense Technology, 2021.
30	YANG S C , LIN T L , CHANG T J , et al. A semi-variance portfolio selection model for military investment assets[J]. Expert Systems with Applications, 2011, 38 (3): 2292- 2301. doi: 10.1016/j.eswa.2010.08.017
31	XIONG J , YANG K W , LIU J , et al. A two-stage preference-based evolutionary multi-objective approach for capability planning problems[J]. Knowledge-Based Systems, 2012, 31, 128- 139. doi: 10.1016/j.knosys.2012.02.003
32	XIONG J , LIU J , CHEN Y W , et al. A knowledge-based evolutionary multi-objective approach for stochastic extended resource investment project scheduling problems[J]. IEEE Trans.on Evolutionary Computation, 2013, 18 (5): 742- 763.
33	ZHOU Y , LI Y B , SHI Z Z , et al. A variables clustering based differential evolution algorithm to solve multistage goal programming model in defense projects portfolio[J]. Advanced Materials Research, 2014, 1046, 367- 370. doi: 10.4028/www.scientific.net/AMR.1046.367
34	ZHANG P L , YANG K W , DOU Y J , et al. Scenario-based approach for project portfolio selection in army engineering and manufacturing development[J]. Journal of Systems Engineering and Electronics, 2016, 27 (1): 166- 176.
35	LI M H , LI M J , YANG K W , et al. A network-based portfolio optimization approach for military system of systems architecting[J]. IEEE Access, 2018, 6, 53452- 53472. doi: 10.1109/ACCESS.2018.2870654
36	XIA B Y , ZHAD Q S , YANG K W , et al. Scenario-based modeling and solving research on robust weapon project planning problems[J]. Journal of Systems Engineering and Electronics, 2019, 30 (1): 85- 99. doi: 10.21629/JSEE.2019.01.09
37	王涛, 李小波, 张杰, 等. 基于"项目-能力"关联的战略规划项目体系贡献率评估方法[J]. 系统工程与电子技术, 2023, 45 (8): 2295- 2304. doi: 10.12305/j.issn.1001-506X.2023.08.01
	WANG T , LI X B , ZHANG J , et al. A method for evaluating the contribution rate of strategic planning project systems based on the "project capability" correlation[J]. Systems Engineering and Electronics, 2023, 45 (8): 2295- 2304. doi: 10.12305/j.issn.1001-506X.2023.08.01
38	BOWEN H R . The interpretation of voting in the allocation of economic resources[J]. The Quarterly Journal of Economics, 1943, 58 (1): 27- 48. doi: 10.2307/1885754
39	CIRIACY-WANTRUP S V . Capital returns from soil-conservation practices[J]. Journal of Farm Economics, 1947, 29 (4): 1181- 1196. doi: 10.2307/1232747
40	HANEMANN M W . Welfare evaluations in contingent valuation experiments with discrete responses[J]. American Journal of Agricultural Economics, 1987, 69 (1): 182- 184. doi: 10.2307/1241322
41	CAMERON T A . A new paradigm for valuing non-market goods using referendum data: maximum likelihood estimation by censored logistic regression[J]. Journal of Environmental Economics and Management, 1988, 15 (3): 355- 379. doi: 10.1016/0095-0696(88)90008-3
42	SOKRI A, TEAM D E. Valuation of military training benefit: a contingent valuation method approach[R]. Ottaua: DRDC CORA Technical Memorandum, 2012.

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

[1]	Feiran GUO, Jianqiao YU, Bao SONG. Optimal design of missile types in missile equipment system based on assignment model [J]. Systems Engineering and Electronics, 2022, 44(3): 850-862.
[2]	SONG Xiaoxue, WEI Lu, LIN Shuisheng. Adaptive synchronization technology of mobile Ad Hoc network [J]. Systems Engineering and Electronics, 2018, 40(9): 2113-2118.
[3]	WANG Xing, GUO Pengcheng, WANG Yubing, CHENG Yue. Fast searching clustering centers algorithm based on linear regression analysis [J]. Systems Engineering and Electronics, 2017, 39(11): 2614-2622.
[4]	ZHAO Jian-zhong， LI Hai-jun， YE Wen, DONG Qi. Fault prediction based on information fusion and improved UGM(1,1) model [J]. Systems Engineering and Electronics, 2013, 35(10): 2135-2140.
[5]	XING Li-ning, YAO Feng. Learnable genetic algorithm to double-layer CARP optimization problems [J]. Journal of Systems Engineering and Electronics, 2012, 34(6): 1187-1192.

A cost-capability combination optimization model for military system construction based on XGboost and linear regression

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 8

References 42

Related Articles 5

Recommended Articles

Metrics

Comments

序号	能力						成本	预算	决策值	Logistic
序号	1	2	3	4	5	6	成本	预算	决策值	Logistic
1	83	82	91	94	95	85	9.469 5	9.00	0	0.07
2	85	82	94	81	95	85	9.314 0	9.00	0	0.07
3	85	82	94	93	95	85	9.782 9	9.00	0	0.07
4	85	82	91	81	89	85	9.006 1	9.00	1	0.64
5	85	82	91	94	95	85	9.522 8	9.00	0	0.07
6	85	82	91	94	89	85	9.487 9	9.00	0	0.21
7	69	82	91	81	95	85	8.779 5	9.00	0	0.26
8	69	82	91	81	95	77	8.733 6	9.00	1	0.92
9	69	82	91	81	95	74	8.542 0	9.00	1	0.92
10	69	82	91	81	95	75	8.508 4	9.00	1	0.92
11	69	82	91	81	89	85	8.744 6	9.00	0	0.57
12	69	82	91	81	89	74	8.507 1	9.00	1	0.95
13	69	82	91	81	89	75	8.473 5	9.00	1	0.95
14	69	82	91	93	95	85	9.248 4	9.00	0	0.07
15	69	82	91	93	89	85	9.213 5	9.00	0	0.36
16	69	82	91	94	95	85	9.261 3	9.00	0	0.07
17	69	82	91	94	89	85	9.226 4	9.00	1	0.36
18	69	70	91	81	95	74	8.378 6	9.00	1	0.92
19	69	70	91	81	82	74	8.210 7	9.00	1	0.95
20	69	74	91	81	95	74	8.314 4	9.00	1	0.92