共建共享双层策略驱动的复杂装备组合优化求解

doi:10.12305/j.issn.1001-506X.2023.02.14

Abstract

Abstract:

Combinatorial optimization of complex equipment considering constribution and sharing is a new equipment development concept that meets the needs of joint operations and equipment development. It needs to consider not only the integration of resources from different institutions in the construction step, but also different constraints under the expected application scenarios in the sharing step. To efficiently obtain a high-quality portfolio planning plan, the problem of complex equipment combinatorial optimization driven by contribution and sharing two-tier strategy is analyzed and modeled, and then a deep neural network assisted branch and bound heuristic method is designed, with a learnable model used to give reasonable results in the process of branch selection and pruning. Finally, the effectiveness of the proposed model and algorithm is demonstrated by a case of intelligence, surveillance and reconnaissance armament system of systems.

Key words: contribution and sharing, equipment combinatorial optimization, branch and bound method, modeling and optimization of system of systems

CLC Number:

N945

Ziyi CHEN, Yajie DOU, Xiangqian XU, Yuejin TAN, Kewei YANG, Jiang JIANG. Combinatorial optimization solution of complex equipment driven by contribution and sharing two-tier strategy[J]. Systems Engineering and Electronics, 2023, 45(2): 431-443.

Figures/Tables 15

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References 30

1	杜智远, 廖学军, 黄昊. 美军武器装备联合试验的发展与启示[J]. 军事运筹与系统工程, 2018, 32 (1): 73- 80. doi: 10.3969/j.issn.1672-8211.2018.01.013
	DU Z Y , LIAO X J , HUANG H . The development and enlightenment of the joint test of U.S. arms and equipment[J]. Military Ope-rations Research and Systems Engineering, 2018, 32 (1): 73- 80. doi: 10.3969/j.issn.1672-8211.2018.01.013
2	新华社. 新时代的中国国防[EB/OL]. [2021-03-18]. http://www.gov.cn/zhengce/2019-07/24/content_5414325.htm.
	Xinhua News Agency. China's national defense in the new era[EB/OL]. [2021-03-18]. http://www.gov.cn/zhengce/2019-07/24/content_5414325.htm.
3	向南, 豆亚杰, 姜江, 等. 马赛克战概念下作战模块应急重构自主决策[J]. 指挥与控制学报, 2020, 6 (3): 223- 228. doi: 10.3969/j.issn.2096-0204.2020.03.0223
	XIANG N , DOU Y J , JIANG J , et al. Autonomous emergency decision-making of combat module under mosaic warfare[J]. Journal of Command an Control, 2020, 6 (3): 223- 228. doi: 10.3969/j.issn.2096-0204.2020.03.0223
4	The Military Operations Research Society Workshop. Capabilities based planning: the road ahead[R]. Virginia: Institute for Defense Analysis Arlington, 2004.
5	Joint Chiefs of Staff. Chairman of the joint chiefs of staff instruction 3170.01G: Joint capabilities integration and development system[EB/OL]. [2021-02-07]. http://www.dtic.mil/cjcsdirectives/cdata/unlimit/317001.pdf.
6	Department of Defense. Department of Defense DIRECTIVE 8115.01: IT portfolio management[EB/OL]. [2021-02-07]. http://www.dtic.mil/whs/directives/corres/pdf/811501p.pdf.
7	NEAGA E I, HENSHAW M, YUE Y. The influence of the concept of capability-based management on the development of the systems engineering discipline[C]//Proc. of the 7th Annual Conference on Systems Engineering Researc, 2009: 34-41.
8	程贲, 鲁延京, 葛冰峰, 等. 武器装备体系能力多视图模型研究[J]. 国防科技大学学报, 2011, 33 (6): 163- 168. doi: 10.3969/j.issn.1001-2486.2011.06.030
	CHENG B , LU Y J , GE B F , et al. Capability view model for weapon system of systems[J]. Journal of National University of Defense Technology, 2011, 33 (6): 163- 168. doi: 10.3969/j.issn.1001-2486.2011.06.030
9	张西林, 谭跃进, 杨志伟. 多重不确定因素影响下的高端装备研制任务流程优化[J]. 系统工程理论与实践, 2019, 39 (3): 725- 734.
	ZHANG X L , TAN Y J , YANG Z W . Optimization of high-end equipment development task process influenced by multiple uncertainty factors[J]. Systems Engineering-Theory & Practice, 2019, 39 (3): 725- 734.
10	周宇, 姜江, 赵青松, 等. 武器装备体系组合规划的高维多目标优化决策[J]. 系统工程理论与实践, 2014, 34 (11): 2944- 2954.
	ZHOU Y , JIANG J , ZHAO Q S , et al. Many-objective optimization and decision-making for portfolio planning of armament system of systems[J]. Systems Engineering-Theory & Practice, 2014, 34 (11): 2944- 2954.
11	向南, 豆亚杰, 姜江, 等. 基于专家信任网络的不完全信息武器选择决策[J]. 系统工程理论与实践, 2021, 41 (3): 759- 770.
	XIANG N , DOU Y J , JIANG J , et al. Hesitant fuzzy group decision-making method for weapon selection based on expert trust network under incomplete information[J]. Systems Engineering-Theory & Practice, 2021, 41 (3): 759- 770.
12	豆亚杰, 徐向前, 周哲轩, 等. 系统组合选择方法及典型军事应用[J]. 系统工程与电子技术, 2019, 41 (12): 2754- 2762.
	DOU Y J , XU X Q , ZHOU Z X , et al. Analysis of system portfolio selection and typical military application[J]. Systems Engineering and Electronics, 2019, 41 (12): 2754- 2762.
13	徐泽水, 任珮嘉. 犹豫模糊偏好决策研究进展与前景[J]. 系统工程理论与实践, 2020, 40 (8): 2193- 2202.
	XU Z S , REN P J . A survey of decision making with hesitant fuzzy preference relations: progress and prospect[J]. Systems Engineering-Theory & Practice, 2020, 40 (8): 2193- 2202.
14	MENG F Y , AN Q X . A new approach for group decision making method with hesitant fuzzy preference relations[J]. Know-ledge-Based Systems, 2017, 127, 1- 15.
15	XU Y J , LI C Y , WEN X W . Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency[J]. International Journal of Computational Intelligence Systems, 2018, 11, 101- 119.
16	MOU Q , XU Z S , LIAO H C , et al. Two regression methods for hesitant multiplicative preference relations with different consistencies[J]. Soft Computing, 2019, 23, 7029- 7044.
17	GEORGE T, AMUDHA T. Genetic algorithm based multi-objective optimization framework to solve traveling salesman problem[M]. Singapore: Springer, 2020: 141-151.
18	MIRJALILI S , DONG J S , LEWIS A . Ant colony optimizer: theory, literature review, and application in AUV path planning[J]. Nature-Inspired Optimizers, 2020, 811, 7- 21.
19	HOJJATI A , MONADI M , FARIDHOSSEINI A , et al. Application and comparison of NSGA-Ⅱ and MOPSO in multi-objective optimization of water resources systems[J]. Journal of Hydrology and Hydromechanics, 2018, 66 (3): 323- 329.
20	KHAN B, HANOUN S, JOHNSTONE M, et al. Multi-objective job shop scheduling using i-NSGA-Ⅲ[C]//Proc. of the Annual IEEE International Systems Conference, 2018.
21	HOTTUNG A , TANAKA S , TIERNEY K . Deep learning assisted heuristic tree search for the container pre-marshalling problem[J]. Computers & Operations Research, 2020, 113, 104781.
22	CHEN Z Y, DE CAUSMAECKER P, DOU Y J. Neural networked assisted tree search for the personnel rostering problem[EB/OL]. [2021-09-06]. https://arxiv.org/abs/2010.14252.
23	VACLAVIK R , NOVAK A , SUCHA P , et al. Accelerating the branch-and-price algorithm using machine learning[J]. European Journal of Operational Research, 2018, 271 (3): 1055- 1069.
24	DENG Y , LIU Y , ZHOU D Y . An improved genetic algorithm with initial population strategy for symmetric TSP[J]. Mathematical Problems in Engineering, 2015, 2015, 212794.
25	KATIYAR S, IBRAHEEM N, ANSARI A Q. Ant colony optimization: a tutorial review[C]//Proc. of the National Confe-rence on Advances in Power and Control, 2015: 99-110.
26	CHEN Z Y , DOU Y J , XU X Q , et al. Service-oriented wea-pon systems of system portfolio selection method[J]. Journal of Systems Engineering and Electronics, 2020, 31 (3): 551- 566.
27	张骁雄, 葛冰峰, 姜江, 等. 面向能力需求的武器装备体系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. Capability requirements oriented weapon system of systems portfolio planning model and algorithm[J]. Journal of National University of Defense Technology, 2017, 39 (1): 102- 108.
28	BURKE E K , CURTOIS T . New approaches to nurse rostering benchmark instances[J]. European Journal of Operational Research, 2014, 237 (1): 71- 81.
29	苏宙行, 王卓, 吕志鹏. 求解多阶段护士排班问题的带权禁忌搜索算法[J]. 中国科学: 信息科学, 2016, 7 (7): 834- 854.
	SU Z X , WANG Z , LYU Z P . Weighted tabu search for multi-stage nurse rostering problem[J]. Scientia Sinica Informationis, 2016, 7 (7): 834- 854.
30	KINGMA D P, BA J. Adam: a method for stochastic optimization[EB/OL]. [2021-09-06]. https://arxiv.org/abs/1412.6980.

符号	定义
x_ij	研发单位j是否承担装备i的研发任务
t_ij	研发单位j研发装备i的时间
n_ij	研发单位j研发装备i的数量
q_ik	待接收单位k接受装备i的数量
r_ik	待接收单位k现有装备i的数量
I	待发展装备集合
J	可选择研发单位集合
K	待接受装备的单位集合
N1_i	无法承担装备i研发任务的研发单位集合
N2_i	无法接受装备i的待接受单位集合
C	能力需求集合
H	装备发展数量对能力提升的指数幂多项式的项数集合
p_c	能力c的能力需求数值
lt_j	研发单位j可承担的最大工程量
m_j	研发单位j每单位年工程量所需经费
lm_i	装备i的最大支持经费
ubt_i	装备i的发展时间上限
lbt_i	装备i的发展时间下限
ubn_i	装备i的发展数量上限
lbn_i	装备i的发展数量下限
α_ic	装备i发展数量对能力c提升的指数幂多项式常量
β_ich	装备i发展数量对能力c提升的指数幂多项式的第h项指数
γ_ic	装备i发展数量对能力c提升的指数幂多项式的最大值系数
δ_ich	装备i发展数量对能力c提升的指数幂多项式的第h项系数
μ_ij	第j家研发单位研发装备i的研发时间与研发数量关系系数
ε	能力满足度阈值
t_norm	装备发展与组合规划方案所需时间的归一化表示
m_norm	装备发展与组合规划方案所需经费的归一化表示
c_norm	装备发展与组合规划方案对能力满足度的归一化表示
w_m	经费权重
w_t	时间权重

装备	支撑经费/亿元	研发时间/年	研发数量	所属类型	可满足能力
装备	支撑经费/亿元	研发时间/年	研发数量	所属类型	目标识别	定位跟踪	持续监视	传输分发	互操作	自适应	指挥控制
侦察卫星	60	[5, 10]	[5, 20]	航天类	√	√	√	√	-	-	-
预警机	48	[5, 9]	[20, 50]	航空类	√	√	-	√	-	-	√
无人机	60	[6, 10]	[20, 200]	航空类	√	√	-	-	√	√	-
预警雷达	46	[5, 9]	[8, 25]	配属类	√	√	√	-	-	-	√
侦察船	50	[4, 8]	[5, 15]	船舶类	√	√	√	-	-	-	-
装甲侦察车	30	[4, 8]	[5, 15]	装甲类	√	√	√	-	-	-	-
数据链	25	[5, 10]	[5, 10]	系统类	-	-	-	√	√	√	-
指控系统	28	[5, 10]	[5, 10]	系统类	-	-	-	-	√	√	√

单位	每单位年工程量所需经费/亿元	最大可承担工程量/年	可承研武器装备类型
单位	每单位年工程量所需经费/亿元	最大可承担工程量/年	航天类	航空类	配属类	船舶类	装甲类	系统类
1	1.8	30	√	-	√	-	-	√
2	2	40	-	√	√	-	-	√
3	3.5	60	-	√	√	-	-	-
4	3.2	50	-	√	-	-	-	√
5	3.8	50	√	-	√	-	-	√
6	4.2	60	√	-	√	-	-	√
7	3.5	60	-	-	√	√	-	-
8	3	50	-	-	-	√	-	√
9	3.2	70	-	-	√	-	√	-
10	2.8	60	-	-	-	-	√	√

能力	需求数值
目标识别	0.9
定位跟踪	0.9
持续监视	0.87
传输分发	0.95
互操作	0.95
自适应	0.95
指挥控制	0.95

装备	研发单位
装备	1	2	3	4	5	6	7	8	9	10
侦察卫星	10, 11	-	-	-	8, 8	-	-	-	-	-
预警机	-	9, 26	-	8, 23	-	-	-	-	-	-
无人机	-	10, 110	-	8, 88	-	-	-	-	-	-
预警雷达	8, 11	9, 14	-	-	-	-	-	-	-	-
侦察船	-	-	-	-	-	-	7, 7	8, 8	-	-
装甲侦察车	-	-	-	-	-	-	-	-	-	8, 8
数据链	7, 6	5, 4	-	-	-	-	-	-	-	-
指控系统	5, 4	7, 6	-	-	-	-	-	-	-	-

Combinatorial optimization solution of complex equipment driven by contribution and sharing two-tier strategy

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References 30

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装备	待接收单位
装备	A	B	C	D	E
侦察卫星	19	18	17	16	10
预警机	48	43	47	44	18
无人机	158	170	166	46	171
预警雷达	22	24	7	23	24
侦察船	14	14	15	2	15
装甲侦察车	10	10	1	10	9
数据链	9	9	9	9	4
指控系统	9	5	9	9	8

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