A deep reinforcement learning method for multi-stage equipment development planning in uncertain environments

doi:10.23919/JSEE.2022.000140

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (6): 1159-1175.doi: 10.23919/JSEE.2022.000140

• • 上一篇

收稿日期:2021-01-11 出版日期:2022-12-18 发布日期:2022-12-24

A deep reinforcement learning method for multi-stage equipment development planning in uncertain environments

Peng LIU(), Boyuan XIA(), Zhiwei YANG(), Jichao LI(), Yuejin TAN()

¹ College of Systems Engineering, National University of Defense Technology, Changsha 410073, China

Received:2021-01-11 Online:2022-12-18 Published:2022-12-24
Contact: Jichao LI E-mail:liupeng81@nudt.edu.cn;xiaboyuan11@nudt.edu.cn;zhwyang88@126.com;ljcnudt@hotmail.com;yjtan@nudt.edu.cn
About author:
LIU Peng was born in 1981. He received his M.S. degree in higher education management from the National University and Defense Technology (NUDT), Changsha, China, in 2008. He received his Ph.D. degree in management science and engineering from the NUDT, in 2020. His research interests include system of systems engineering, complex systems, and systems evaluation and optimization. E-mail: liupeng81@nudt.edu.cn

XIA Boyuan was born in 1994. He received his B.S. and M.S. degrees in management science and engineering from the National University and Defense Technology (NUDT), Changsha, China, in 2015 and 2017, respectively. He is currently a Ph.D. candidate in the College of Systems Engineering, NUDT. His research interests include system of systems engineering, complex systems, and systems evaluation and optimization E-mail: xiaboyuan11@nudt.edu.cn

YANG Zhiwei was born in 1988. He received his B.E. degree in management science and M.E. degree in management science and engineering from the National University of Defense Technology, Changsha, Hunan, China, in 2010 and 2012, respectively. He received his Ph.D. degree in computer science from Leiden University, Leiden, the Netherlands, in 2016. His research interests include studying intelligence computing and the evaluation of complex systems. E-mail: zhwyang88@126.com

LI Jichao was born in 1990. He received his B.E. degree in management science, M.E. and Ph.D. degrees in management science and engineering from the National University of Defense Technology, Changsha, Hunan, China, in 2013, 2015, and 2019, respectively. His research interests include studying complex systems with a combination of theoretical tool and data analysis, including mathematical modeling of heterogeneous information networks, applying network methodologies to analyze the development of complex system-of-systems, and data-driven studying of the collective behavior of humans. E-mail: ljcnudt@hotmail.com

TAN Yuejin was born in 1958. He received his B.E. degree in mathematics from Hunan Normal University, and M.E. degree in systems engineering from the National University of Defense Technology, Changsha, Hunan, China, in 1981 and 1985 respectively. His research interests include system of systems (SoS) requirements modeling, SoS architecture design and optimization, complex network, and system modeling and simulation.E-mail: yjtan@nudt.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (71690233;72001209), and the Scientific Research Foundation of the National University of Defense Technology (ZK19-16)

摘要/Abstract

Abstract:

Equipment development planning (EDP) is usually a long-term process often performed in an environment with high uncertainty. The traditional multi-stage dynamic programming cannot cope with this kind of uncertainty with unpredictable situations. To deal with this problem, a multi-stage EDP model based on a deep reinforcement learning (DRL) algorithm is proposed to respond quickly to any environmental changes within a reasonable range. Firstly, the basic problem of multi-stage EDP is described, and a mathematical planning model is constructed. Then, for two kinds of uncertainties (future capability requirements and the amount of investment in each stage), a corresponding DRL framework is designed to define the environment, state, action, and reward function for multi-stage EDP. After that, the dueling deep Q-network (Dueling DQN) algorithm is used to solve the multi-stage EDP to generate an approximately optimal multi-stage equipment development scheme. Finally, a case of ten kinds of equipment in 100 possible environments, which are randomly generated, is used to test the feasibility and effectiveness of the proposed models. The results show that the algorithm can respond instantaneously in any state of the multi-stage EDP environment and unlike traditional algorithms, the algorithm does not need to re-optimize the problem for any change in the environment. In addition, the algorithm can flexibly adjust at subsequent planning stages in the event of a change to the equipment capability requirements to adapt to the new requirements.

Key words: equipment development planning (EDP), multi-stage, reinforcement learning, uncertainty, dueling deep Q-network (Dueling DQN)

. [J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1159-1175.

Peng LIU, Boyuan XIA, Zhiwei YANG, Jichao LI, Yuejin TAN. A deep reinforcement learning method for multi-stage equipment development planning in uncertain environments[J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1159-1175.

图/表 19

Number	Variable	Symbol definition
1	Number of equipment to be developed	$m \in { { {\bf{N}}}^ + }$
2	Equipment set to be developed	$ W = \left\{ {{w_i}} \right\},i = 1,2, \cdots ,m $
3	Cost of equipment to be developed	${\boldsymbol{E}} = {\left[ { {e_i} } \right]_{1 \times m} },{e_i} \in { {\bf{R} }^ + }$
4	Expected number of years for equipment development	${\bf{L} }{ {α } } = {\left[ { {\rm{l} }{\text{α} _i} } \right]_{1 \times m} }, \; {\rm{l} }{\text{α} _i} \in { { {\bf{N} } }^ + },{\rm{l} }{\text{α} _i} \gt 1$
5	Number of years the equipment has been developed	${\bf{L} }{ {β } } = {\left[ { {\rm{l} }{\text{β} _i} } \right]_{1 \times m} }, \; {\rm{l} }{\text{β} _i} \in { { {\bf{N} } }^ + },{\rm{l} }{\text{β} _i} \gt 1$
6	Whether the equipment has been successfully developed	${\boldsymbol{S}} = {\left[ { {s_i} } \right]_{1 \times m} },{s_i} \in \left\{ {0,1} \right\}$
7	Number of capabilities of concern	$n \in { {\bf N}^ + }$
8	Set of capabilities of concern	$ A = \left\{ {{a_j}} \right\},j = 1,2, \cdots ,n $
9	Expected capabilities of the equipment to be developed	${\boldsymbol{C}} = {\left[ { {c_{ij} } } \right]_{m \times n} }, \; {c_{ij} } \in { {\bf N}^ + },{c_{ij} } \in [1,9]$
10	Capabilities after multi-stage development	${\bf{R} }{ {α } } = {\left[ { {\rm{r} }{\text{α} _i} } \right]_{1 \times n} }, \; {\rm{r} }{\text{α} _i} \in {\bf N},{\rm{r} }{\text{α} _i} \in [0,9]$
11	Final capability requirement	${\bf{R} }{ {β } } = {\left[ { {\rm{r} }{\text{β} _i} } \right]_{1 \times n} }, \; {\rm{r} }{\text{β}_i} \in { {\bf N}^ + },{\rm{r}}{\text{β} _i} \in [1,9]$
12	Number of stages	$t \in { {\bf N}^ + },t \gt 1$
13	Current stage	${\rm{stage} }{_i},i = 1,2,\cdots,t$
14	Coefficient to transform year to stage	$\psi \in { {\bf N}^ + }$
14	The investment budget for each stage	${\boldsymbol{B}} = {\left[ { {b_i} } \right]_{1 \times t} },{b_i} \in { {\bf{R} }^ + }$
15	Development scheme	${\boldsymbol{X}} = {\left[ { {x_{ij} } } \right]_{m \times t} },{x_{ij} } \in \left\{ {0,1} \right\}$
16	Overall capability index	$ Q $

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Element	Data type	Normalization method	Normalized vector dimension
Current state of equipment development	Category	One-hot	$ 3m $
Number of years taken to develop the equipment	Scale	Divided by the maximum value	$ m $
Current stage	Category	One-hot	1
Investment amount at the current stage	Scale	Divided by the maximum value	1
Capability requirement	Scale	Divided by the maximum value	$ n $

Equipment to be developed	Cost (×1000 $)	Expected years of development
w1: Digital signal processor	31	4
w2: Digital image processor	40	1
w3: Speech synthesizer	66	3
w4: Low-voltage computer chip	59	4
w5: High-efficiency solar cell	51	1
w6: Digital-to-analog converter	42	4
w7: Analog-to-digital converter	50	4
w8: Frequency converter module	60	1
w9: Conformal phased-array antenna	65	2
w10: Radiofrequency mixer	75	3

Capability	w1	w2	w3	w4	w5	w6	w7	w8	w9	w10
C1	1	9	0	0	0	0	0	0	0	0
C2	0	1	8	0	0	0	0	0	0	0
C3	0	3	2	7	0	0	0	0	0	0
C4	0	0	0	4	7	0	0	0	0	0
C5	0	0	0	0	8	1	1	0	0	0
C6	0	0	0	0	2	7	5	0	0	0
C7	0	0	0	0	0	0	3	8	0	0
C8	0	0	0	0	0	0	0	2	8	0
C9	0	0	0	0	0	0	0	8	3	9
C10	9	0	0	0	0	0	0	0	0	3

Equipment	s1	a1	s2	a2	s3	a3	s4	a4	s5	a5	s6	a6	s7		a7	s8		a8	s9		a9	S10
Equipment 1	0	●	1	○	1	●	1	●	1	●	2	○	2		●	2		○	2		●	2
Equipment 2	0	○	0	○	0	○	0	●	2	○	2	○	2		○	2		○	2		○	2
Equipment 3	0	●	1	○	1	●	1	○	1	○	1	○	1		●	2		○	2		●	2
Equipment 4	0	●	1	●	1	●	1	○	1	○	1	○	1		●	2			2		●	2
Equipment 5	0	○	0	○	0	○	0	○	0	○	0	●	2		○	2		○	2		○	2
Equipment 6	0	●	1	○	1	●	1	○	1	●	1	○	2		○	2		○	2		○	2
Equipment 7	0	○	0	○	0	○	0	○	0	○	0	○	0		○	0		○	0		○	0
Equipment 8	0	○	0	○	0	○	0	○	0	○	0	○	0		○	0		●	2		○	2
Equipment 9	0	○	0	●	1	○	1	○	1	●	2	○	2		○	2		○	2		○	2
Equipment 10	0	○	0	○	0	○	0	○	0	○	0	○	0		○	0		○	0		○	0
Development cost	55.00		47.25		55.00		47.75		50.75		51.00			44.50			30.00			44.50		End

Equipment	s1	a1	s2	a2	s3	a3	s4	a4	s5	a5	s6	a6	s7	a7	s8	a8	s9	a9	S10
Equipment 1	0	●	1	○	1	●	1	●	1	●	2	○	2	●	2	○	2	●	2
Equipment 2	0	○	0	○	0	○	0	●	2	○	2	○	2	○	2	○	2	○	2
Equipment 3	0	●	1	○	1	●	1	○	1	○	1	○	1	●	2	○	2	●	2
Equipment 4	0	●	1	●	1	●	1	○	1	○	1	○	1	●	2		2	●	2
Equipment 5	0	○	0	○	0	○	0	○	0	○	0	●	2	○	2	○	2	○	2
Equipment 6	0	●	1	○	1	●	1	○	1	●	1	○	1	○	1	○	1	○	1
Equipment 7	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0
Equipment 8	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0	●	2	○	2
Equipment 9	0	○	0	●	1	○	1	○	1	●	2	○	2	○	2	○	2	○	2
Equipment 10	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0	○	0
Development cost	55.00		47.25		55.00		47.75		50.75		51.00		44.50		60.00		44.50		End

A deep reinforcement learning method for multi-stage equipment development planning in uncertain environments

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Parameter	Stage
Parameter	1	2	3	4	5	6	7	8	9	10
Investment amount	71	59	60	63	68	73	63	79	70	−
Required capacity	4	3	4	3	4	5	4	3	6	3

Stage	Capability requirement
Stages 1−5	4	3	4	3	4	5	4	3	6	3
Stages 6−10	4	7	3	6	5	7	6	3	4	6