Scenario-based modeling and solving research on robust weapon project planning problems

doi:10.21629/JSEE.2019.01.09

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (1): 85-99.doi: 10.21629/JSEE.2019.01.09

• Systems Engineering • Previous Articles Next Articles

Scenario-based modeling and solving research on robust weapon project planning problems

Boyuan XIA(), Qingsong ZHAO*(), Kewei YANG(), Yajie DOU(), Zhiwei YANG()

College of Systems Engineering, National University of Defense Technology, Changsha 410073, China

Received:2018-01-30 Online:2019-02-27 Published:2019-02-27
Contact: Qingsong ZHAO E-mail:xiaboyuan@nudt.edu.cn;zhaoqingsong@nudt.edu.cn;kayyang27@nudt.edu.cn;yajiedou_nudt@163.com;zhwyang88@126.com
About author:XIA Boyuan was born in 1994. He is a Ph.D. in National University of Defense Technology. His research interests are defense acquisition, complex systems and system portfolio selection and optimization. E-mail:xiaboyuan@nudt.edu.cn|ZHAO Qingsong was born in 1975. He is a Ph.D. and an associate professor in National University of Defense Technology. His research interests are system integration, defense acquisition and system-ofsystems requirement modeling, and complex system analysis. E-mail:zhaoqingsong@nudt.edu.cn|YANG Kewei was born in 1977. He is a Ph.D. and a professor in National University of Defense Technology. His research interests are system of systems (SoS) requirements modeling, SoS architecture design and optimization, and system Modeling and Simulation. E-mail:kayyang27@nudt.edu.cn|DOU Yajie was born in 1987. He is a Ph.D. and a lecturer in National University of Defense Technology. His research interests are weapon alternative decision and effectiveness evaluation, systemof-systems architecting and engineering management, and portfolio decision analysis. E-mail:yajiedou_nudt@163.com|YANG Zhiwei was born in 1988. He is a Ph.D. and a lecturer in National University of Defense Technology. His research interests are system optimization, and supply chain optimization. E-mail:zhwyang88@126.com
Supported by:
the National Social Science Foundation of China(15GJ003-278);the National Natural Science Foundation of China(71501182);This work was supported by the National Social Science Foundation of China (15GJ003-278) and the National Natural Science Foundation of China (71501182)

Abstract

Abstract:

Weapon project planning (WPP) plays a critical role in the process of national defense development and establishment of the future national defense force. WPP faces the backgrounds of various uncertainties, intense inter-influence of weapon systems and involves modelling, assessment, and optimization procedures. The contents of this paper are mainly divided into three parts: first, the WPP processes are analyzed, and related elements are formulated to transform the qualitative problem to mathematics form; second, the value evaluation model of WPP solutions is proposed based on two criteria of total capability gap and total capability dispersion; third, two robustness optimization models are constructed based on the absolute robustness criterion and the robustness deviation criterion to support the robustness optimization process under multi-scenario. Finally, a case is studied to examine the feasibility and effectiveness of the proposed models and approaches.

Key words: weapon project planning (WPP), uncertainty, robustness, multi-stage, scenario

Boyuan XIA, Qingsong ZHAO, Kewei YANG, Yajie DOU, Zhiwei YANG. Scenario-based modeling and solving research on robust weapon project planning problems[J]. Journal of Systems Engineering and Electronics, 2019, 30(1): 85-99.

Figures/Tables 14

Fig 1

Table 1

Table 2

Fig 2

Fig 3

Table 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Fig 10

Fig 11

References 30

1	Defense acquisitions: many analyses of alternatives have not provided a robust assessment of weapon system options. https://www.gao.gov/products/GAO-09-665.
2	FLIEGE J, WERNER R. Robust multi-objective optimization & applications in portfolio optimization. European Journal of Operational Research, 2013, 234 (2): 422- 433.
3	GREGORY C, DARBY-DOWMAN K, MITRA G. Robust optimization and portfolio selection:the cost of robustness. European Journal of Operational Research, 2011, 212 (2): 417- 428.
4	SHAFI K, ELSAYED S, SARKER R, et al. Scenario-based multi-period program optimization for capability-based planning using evolutionary algorithms. Applied Soft Computing, 2017, 56, 717- 729. doi: 10.1016/j.asoc.2016.07.009
5	BRYANT B P. sdtoolkit. Scenario discovery tools to support robust decision making. http://cran.r.project.org/web/packages/sdtoolkit/index.html.
6	GUPTA S K, ROSENHEAD J. Robustness in sequential investment decision. Management Science, 1968, 15 (2): 18- 29. doi: 10.1287/mnsc.15.2.B18
7	CHIM L, NUNES-VAZ R, PRANDOLINI R. Capabilitybased planning for Australia's national security. Security Challenges, 2010, 6 (3): 79- 96.
8	BRYANT B P, LEMPERT R J. Thinking inside the box:a participatory, computer-assisted approach to scenario discovery. Technological Forecasting & Social Change, 2010, 77 (1): 34- 49.
9	CHEN Z L. A scenario-based stochastic programming approach for technology and capacity planning. Computers & Operations Research, 2002, 29 (7): 781- 806.
10	AHMED S, SAHINIDIS N V. An approximation scheme for stochastic integer programs arising in capacity expansion. Operations Research, 2003, 51, 461- 471. doi: 10.1287/opre.51.3.461.14960
11	LIESIO J, SALO A. Scenario-based portfolio selection of investment projects with incomplete probability and utility information. European Journal of Operational Research, 2012, 217 (1): 162- 172.
12	RAFIEE M, KIANFAR F. A scenario tree approach to multiperiod project selection problem using real-option valuation method. International Journal of Advanced Manufacturing Technology, 2011, 56 (4): 411- 420.
13	LI Y P, HUANG G H, CHEN X. Multistage scenario-based interval-stochastic programming for planning water resources allocation. Stochastic Environmental Research and Risk Assessment, 2009, 23 (6): 781- 792. doi: 10.1007/s00477-008-0258-y
14	P MAGHOULI, HOSSEINI S H, BUYGI M O, et al. A scenario-based multi-objective model for multi-stage transmission expansion planning. IEEE Trans. on Power Systems, 2011, 26 (1): 270- 278.
15	JOHNSON K A, CAIN W. Adaptation and application of federal capabilities-based planning models to individual states:State of Colorado case study. Journal of Homeland Security and Emergency Management, 2010, 7 (1): 1271- 1283.
16	Maritime Operational Research Team. Determining extreme capability requirements using orthogonal arrays: an empirical study. https://pubs.drdc.gc.ca/PDFS/unc92/p532775.pdf.
17	DHS/SLGCP/OPIA/Policy and Planning Branch. Capabilitiesbased planning overview. https://www.scd.hawaii.gov.
18	D ZAMALIEVA, A YILMAZ, T ALDEMIR. Online scenario labeling using a hidden Markov model for assessment of nuclear plant state. Reliability Engineering and System Safety, 2013, 110 (2): 1- 13.
19	BRYANT B P, LEMPERT R J. Thinking inside the box:a participatory, computer-assisted approach to scenario discovery. Technological Forecasting & Social Change, 2010, 77 (1): 34- 49.
20	BRYANT B P. Scenario discovery tools to support robust decision making. http://cran.r.project.org/web/packages/sdtoolkit/index.html.
21	STEWART T J. Scenario analysis and multicriteria decision making. CLIMACO J, ed. Multicriteria Analysis. Berlin: Springer, 1997.
22	BROOKS A, BENNETT B, BANKS S. An application of exploratory analysis:the weapon mix problem. Military Operations Research, 1999, 4 (1): 67- 80.
23	ALI S, MACIEJEWSKI A A, SIEGEL H J, et al. Measuring the robustness of a resource allocation. IEEE Trans. on Parallel & Distributed System, 2014, 15 (7): 630- 641.
24	BRANKE J, LU K. Finding the trade-off between robustness and worst-case quality. Proc. of the Genetic and Evolutionary Computation Conference, 2015: 623-630.
25	GUPTA S K, ROSENHEAD J. Robustness in sequential investment decisions. Management Science, 1972, 15 (2): 18- 29.
26	DIAZ J E, HANDL J, XU D L. Evolutionary robust optimization in production planning interactions between number of objectives, sample size and choice of robustness measure, computers and operation research. http://dx.doi.org/10.1016/j.cor.2016.06.020.
27	PAENKE I, BRANKE J, JIN Y. Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation. IEEE Trans. on Evolutionary Computation, 2006, 10 (4): 405- 420.
28	BEN-TAL A, CHUNG B D, MANDALA S R, et al. Robust optimization for emergency logistics planning:risk mitigation in humanitarian relief supply chains. Transportation Research Part B-Methodological, 2011, 45 (8): 1177- 1189. doi: 10.1016/j.trb.2010.09.002
29	HU J, MEHROTRA S. Robust and stochastically weighted multi-objective optimization models and reformulations. Operations Research, 2012, 60 (4): 939- 953.
30	LEMPERT R J, POPPER S W, BANKES S C. Shaping the next one hundred years: new methods for quantitative, longterm policy analysis. California: RAND Corporation, 2015.

Weapon project type	Decision variable
Weapon projects not yet developed	Whether to develop the weapon projects and when
	The acquisition number of the weapons after being developed
	When to retire
Weapons already developed	The acquisition number of the weapons having been developed
Weapons already developed	When to retire

Serial	Condition description
1	When a candidate project is still in the development period, the project cannot be manufactured, meaning that the variables of acquisition amount in stages later than current time should be set as 0.
2	The variable of retirement time of a weapon project must be later than that of the service starting time.
3	The variable of the acquisition amount of a retired weapon must be set as 0 in stages after retirement.
4	The cost of each phase cannot exceed the budget.

Rule	Assembled capability value of $c_t$
Additive rule	$\sum c^{w_i}_t, i = 1, 2, \ldots, n$
Maximal rule	$\max\{c^{w_i}_i\}, i = 1, 2, \ldots, n$
Minimal rule	$\min\{c^{w_i}_t\}, i = 1, 2, \ldots, n$
Average rule	$\sum c^{w_i}_t/n, i = 1, 2, \ldots, n$

[1]	Xu LYU, Baiqing HU, Yongbin DAI, Mingfang SUN, Yi LIU, Duanyang GAO. Gaussian process regression-based quaternion unscented Kalman robust filter for integrated SINS/GNSS [J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1079-1088.
[2]	Bing WANG, Pengfei ZHANG, Yufeng HE, Xiaozhi WANG, Xianxia ZHANG. Scenario-oriented hybrid particle swarm optimization algorithm for robust economic dispatch of power system with wind power [J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1143-1150.
[3]	Shang SHI, Guosheng ZHANG, Huifang MIN, Yinlong HU, Yonghui SUN. Exact uncertainty compensation of linear systems by continuous fixed-time output-feedback controller [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 706-715.
[4]	Xiaomei LIU, Naiming XIE. Grey-based approach for estimating software reliability under nonhomogeneous Poisson process [J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 360-369.
[5]	Sader MALIKA, Fuyong WANG, Zhongxin LIU, Zengqiang CHEN. Distributed fuzzy fault-tolerant consensus of leader-follower multi-agent systems with mismatched uncertainties [J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 1031-1040.
[6]	Yun LI, Kaige JIANG, Ting ZENG, Wenbin CHEN, Xiaoyang LI, Deyong LI, Zhiqiang ZHANG. Belief reliability modeling and analysis for planetary reducer considering multi-source uncertainties and wear [J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 1246-1262.
[7]	Jianjiang WANG, Xuejun HU, Chuan HE. Reactive scheduling of multiple EOSs under cloud uncertainties: model and algorithms [J]. Journal of Systems Engineering and Electronics, 2021, 32(1): 163-177.
[8]	Jiuyao JIANG, Jichao LI, Kewei YANG. Weapon system portfolio selection based on structural robustness [J]. Journal of Systems Engineering and Electronics, 2020, 31(6): 1216-1229.
[9]	Qingsong ZHAO, Junyi DING, Yu GUO, Peng LIU, Kewei YANG. A scenario construction and similarity measurement method for navy combat search and rescue [J]. Journal of Systems Engineering and Electronics, 2020, 31(5): 957-968.
[10]	Tianpei ZU, Rui KANG, Meilin WEN. Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty [J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 626-633.
[11]	Yandong LI, Ling ZHU, Yuan GUO. Observer-based multivariable fixed-time formation control of mobile robots [J]. Journal of Systems Engineering and Electronics, 2020, 31(2): 403-414.
[12]	Chao CHEN, Zhengjun DU, Xingxing LIANG, Jianmai SHI, Hao ZHANG. Modeling and solution based on stochastic games for development of COA under uncertainty [J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 288-296.
[13]	Liangqi WAN, Hongzhuan CHEN, Linhan OUYANG. Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties [J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 308-318.
[14]	Xiangfei MENG, Ying WANG, Chao LI, Xiaoyang WANG, Maolong LYU. Approach for uncertain multi-objective programming problems with correlated objective functions under C_EV criterion [J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1197-1208.
[15]	Yang WANG, Shanshan FU, Bing WU, Jinhui HUANG, Xiaoyang WEI. Towards optimal recovery scheduling for dynamic resilience of networked infrastructure [J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 995-1008.

Scenario-based modeling and solving research on robust weapon project planning problems

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 14

References 30

Related Articles 15

Recommended Articles

Metrics

Comments