Optimal index shooting policy for layered missile defense system

doi:10.21629/JSEE.2020.01.13

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (1): 118-129.doi: 10.21629/JSEE.2020.01.13

收稿日期:2019-01-02 出版日期:2020-02-20 发布日期:2020-02-25

Optimal index shooting policy for layered missile defense system

Longyue LI(), Chengli FAN*(), Qinghua XING(), Hailong XU(), Huizhen ZHAO()

Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China

Received:2019-01-02 Online:2020-02-20 Published:2020-02-25
Contact: Chengli FAN E-mail:lilong_yue@126.com;ffq516@163.com;qh_xing@126.com;xhl_81329@163.com;margeryzhao@outlook.com
About author:LI Longyue was born in 1988. He received his master and doctor degrees from Air Force Engineering University (AFEU) in 2012 and 2016, respectively. Now he is a lecturer in Air and Missile Defense College of AFEU. His research interests are modeling and simulation of missile defense operations, intelligent optimization algorithm, and operational research theory. He has published more than 40 papers, presided over a number of projects of the National Natural Science Foundation of China, Shaanxi Natural Science Foundation, China Post-doctoral Fund, etc. E-mail: lilong_yue@126.com|FAN Chengli was born in 1988. She received her master and doctor degrees from Air Force Engineering University (AFEU) in 2011 and 2015, respectively. Now she is a lecturer in Air and Missile Defense College of AFEU. Her research interests are intelligent decision-making, intelligent evolutionary algorithms, and deep machine learning. E-mail: ffq516@163.com|XING Qinghua was born in 1964. She received her master and doctor degrees from Air Force Engineering University (AFEU) in 1992 and 2003, respectively. Now she is a professor in Air and Missile Defense College of AFEU. Her research interests are intelligent decision-making, intelligent evolutionary algorithms, and decision optimization theory and method. E-mail: qh_xing@126.com|XU Hailong was born in 1981. He received his doctor's degree from Air Force Engineering University (AFEU) in 2010. Now he is a lecturer in Air And Missile Defense College of AFEU. His research interests include machine learning, information retrieval, datamining and image processing. E-mail: xhl_81329@163.com|ZHAO Huizhen was born in 1990. She received her doctor's degree from Air Force Engineering University (AFEU) in 2018. Now he is a lecturer in Air and Missile Defense College of AFEU. Her research interests include deep machine learning, decision optimization theory and method. E-mail: margeryzhao@outlook.com
Supported by:
the National Natural Science Foundation of China(71701209);the National Natural Science Foundation of China(71771216);Shaanxi Natural Science Foundation(2019JQ-250);China Post-doctoral Fund(2019M653962);This work was supported by the National Natural Science Foundation of China (71701209;71771216), Shaanxi Natural Science Foundation (2019JQ-250), and China Post-doctoral Fund (2019M653962)

摘要/Abstract

Abstract:

In order to cope with the increasing threat of the ballistic missile (BM) in a shorter reaction time, the shooting policy of the layered defense system needs to be optimized. The main decision-making problem of shooting optimization is how to choose the next BM which needs to be shot according to the previous engagements and results, thus maximizing the expected return of BMs killed or minimizing the cost of BMs penetration. Motivated by this, this study aims to determine an optimal shooting policy for a two-layer missile defense (TLMD) system. This paper considers a scenario in which the TLMD system wishes to shoot at a collection of BMs one at a time, and to maximize the return obtained from BMs killed before the system demise. To provide a policy analysis tool, this paper develops a general model for shooting decision-making, the shooting engagements can be described as a discounted reward Markov decision process. The index shooting policy is a strategy that can effectively balance the shooting returns and the risk that the defense mission fails, and the goal is to maximize the return obtained from BMs killed before the system demise. The numerical results show that the index policy is better than a range of competitors, especially the mean returns and the mean killing BM number.

Key words: Gittins index, shooting policy, layered missile defense, multi-armed bandits problem, Markov decision process

. [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 118-129.

Longyue LI, Chengli FAN, Qinghua XING, Hailong XU, Huizhen ZHAO. Optimal index shooting policy for layered missile defense system[J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 118-129.

图/表 6

参考文献 46

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Constant	Variable	Variables declaration	Variation tendency	$H_j (n)$
$\xi _{Hb} ,r_{Hb} ,r_{Lb} ,$$\theta _{Hb} ,\theta _{Lb} ,\phi_b $	$R_b $	BM threat values	$ \nearrow $	$ \nearrow $
$R_b ,\xi _{Hb} ,\phi _b $	$r_{Hb} ,r_{Lb} $	Kill probabilities	$ \nearrow $	$ \nearrow $
$R_b ,\xi _{Hb} ,\phi _b $	$\theta _{Hb} ,\theta _{Lb} $	Demise probabilities	$ \nearrow $	$ \searrow $

Example	$b$	$\phi _b$	$R_b$	$r_{Hb}$	$r_{Lb}$	$\theta _{Hb}$	$\theta _{Lb}$	$\xi _{Hb}$	$\xi _{Lb}$
	1	0	50	0.95	0.80	0.25	0.10
	2	0	60	0.90	0.60	0.10	0.10
1	3	0	70	0.85	0.60	0.20	0.05	2/3	1/3
	4	0	100	0.90	0.90	0.12	0.06
	5	0	125	0.80	0.80	0.05	0.05
	1	0	100	0.95	0.75	0.09	0.13
	2	0	150	0.60	0.20	0.40	0.40
2	3	0	200	0.45	0.20	0.45	0.25	1/4	3/4
	4	0	750	0.65	0.45	0.25	0.05
	5	0	1 000	0.45	0.25	0.45	0.25

Example 1
Policy	System	Minimum	Mean	Maximum
Index	EXOHI	0.00	199.25	2~077.31
Index	ENOLI	0.00	99.62	1~038.65
Myopic	EXOHI	0.00	133.00	2~196.55
Myopic	ENOLI	0.00	66.50	1~098.27
Exhaustive	EXOHI	0.00	164.84	2~202.44
Exhaustive	ENOLI	0.00	82.42	1~101.22
Round-robin	EXOHI	0.00	155.27	2~238.81
Round-robin	ENOLI	0.00	77.63	1~119.40

Example 2
Policy	System	Minimum	Mean	Maximum
Index	EXOHI	0.00	844.88	9~678.44
Index	ENOLI	0.00	281.63	3~226.15
Myopic	EXOHI	0.00	710.64	11~132.63
Myopic	ENOLI	0.00	236.88	3~710.88
Exhaustive	EXOHI	0.00	734.69	9~625.36
Exhaustive	ENOLI	0.00	244.90	3~208.45
Round-robin	EXOHI	0.00	734.12	9~863.72
Round-robin	ENOLI	0.00	244.71	3~287.91

Example 1
Policy	System	Minimum	Mean	Maximum
Index	EXOHI	0.00	199.25	2~077.31
Index	ENOLI	0.00	99.62	1~038.65
Myopic	EXOHI	0.00	133.00	2~196.55
Myopic	ENOLI	0.00	66.50	1~098.27
Exhaustive	EXOHI	0.00	164.84	2~202.44
Exhaustive	ENOLI	0.00	82.42	1~101.22
Round-robin	EXOHI	0.00	155.27	2~238.81
Round-robin	ENOLI	0.00	77.63	1~119.40

Example 2
Policy	System	Minimum	Mean	Maximum
Index	EXOHI	0.00	3.74	7.50
Index	ENOLI	0.00	1.25	2.50
Myopic	EXOHI	0.00	1.69	7.50
Myopic	ENOLI	0.00	1.06	2.50
Exhaustive	EXOHI	0.00	3.02	7.50
Exhaustive	ENOLI	0.00	1.01	2.50
Round-robin	EXOHI	0.00	2.63	7.50
Round-robin	ENOLI	0.00	1.08	2.50

Optimal index shooting policy for layered missile defense system

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