Evaluation of Node Value of Military Transportation Network Based on Hyper-networks

doi:10.12382/bgxb.2022.0748

Abstract

Abstract:

A node value evaluation method based on hyper-networks is designed to select the high-value targets in military transportation networks. Considering the interaction mechanisms within and between multilayer networks, a military transportation hyper-network that consists of a communication subnetwork, a military subnetwork, and a logistic service subnetwork is constructed. An evaluation algorithm for computing the comprehensive efficiency of the hyper-network is proposed by integrating both topological and functional features. On this basis, the node deletion method is used to obtain the system values and striking orders of nodes in the hyper-network. The experimental result reveals that the functional property of the node plays a decisive role in its system value. Moreover, the better a node is located, the more important its neighbors are, and the higher its system value is. It is verified that similar rankings of nodes can be obtained after several rounds of strikes, which shows that the algorithm is of good robustness. Compared with the existing method, the proposed method can determine the importance of targets fully and objectively, improve the accuracy of decision-making effectively, and be applied to the battlefield universally.

Key words: military transportation, node value, dynamic evaluation, hyper-network, comprehensive efficiency

CLC Number:

XU Yilan, GUO Tangyi, TANG Kun, ZHANG Yingying, LI Linwei. Evaluation of Node Value of Military Transportation Network Based on Hyper-networks[J]. Acta Armamentarii, 2024, 45(2): 552-563.

Figures/Tables 13

Fig.1 Schematic diagram of military transportation hyper-network

Fig.2 Evaluation index system of node basic scores

Fig.3 Military transportation hyper-network model of a border area in southwest China

Table 1 Adjacency of hyper-network

边	权重	边	权重
22-23	21.73	06-14	75.60
18-19	24.06	14-15	26.42
01-04	25.69	15-21	48.27
20-22	25.94	14-21	56.82
06-11	29.53	07-14	58.19
04-05	35.90	07-15	74.79
05-10	44.72	17-21	57.72
11-18	44.72	09-17	82.61
19-20	50.00	11-12	17.58
11-19	50.05	04-08	19.01
13-20	56.80	02-05	21.47
05-13	61.59	16-20	21.50
10-20	66.37	13-16	38.67
06-13	76.24	03-06	41.93
06-18	76.94	01-03	42.87
18-23	85.21	10-16	49.16
17-22	24.17	03-04	54.09
09-10	25.06	03-11	67.12
19-21	25.83	16-17	34.92
14-19	31.69	07-08	42.46
13-14	32.63	02-07	85.45
09-13	33.24	03-14	99.89
05-09	34.93	08-17	114.41
20-21	35.00	08-12	63.89
07-13	40.31	12-16	74.49
04-07	41.87	08-16	74.82
21-22	42.38	02-08	49.12
06-07	44.41	03-12	69.84
04-09	57.32	03-08	73.29
18-21	60.73	02-03	98.00
10-15	67.96	02-16	112.94
15-23	72.37

Table 2 Example of modified weighting method for expert scoring

迭代次数	参数	专家				Σ	$X ¯$	\| $X ¯ n + 1$ - $X ¯ n$ \|
迭代次数	参数	1	2	3	4	Σ	$X ¯$	\| $X ¯ n + 1$ - $X ¯ n$ \|
	u	0	0	0	0
0	P	1.00	1.00	1.00	1.00	4.00	3.75	0
	X	3.00	6.00	2.00	4.00	15.00
	u	0.43	-0.03	0.10	0.70
1	P	1.43	0.97	1.10	1.70	5.21	3.67	0.08
	X	4.30	5.83	2.20	6.82	19.14
	u	0.48	-0.04	0.13	0.67
2	P	1.92	0.93	1.23	2.37	6.46	3.61	0.06
	X	5.75	5.61	2.47	9.48	23.30
	u	0.53	-0.04	0.16	0.64
3	P	2.44	0.89	1.40	3.01	7.75	3.55	0.06
	X	7.33	5.35	2.80	12.05	27.53
	u	0.57	5.30	2.80	12.05
4	P	0.58	-0.04	0.19	0.62	9.08	3.50	0.05
	X	9.03	5.07	3.18	14.55	31.82
	u	0.60	-0.05	0.21	0.60
5	P	3.61	0.79	1.80	4.25	10.46	3.46	0.04
	X	10.84	4.75	3.61	16.99	36.19
	u	0.64	-0.06	0.24	0.60
6	P	4.25	0.74	2.04	4.84	11.88	3.42	0.04
	X	12.76	4.42	4.08	19.38	40.64
	u	0.67	-0.06	0.26	0.59
7	P	4.93	0.68	2.30	5.43	13.33	3.39	0.03
	X	14.78	4.07	4.59	21.73	45.17

Table 2 Example of modified weighting method for expert scoring

迭代次数	参数	专家				Σ	$X ¯$	\| $X ¯ n + 1$ - $X ¯ n$ \|
迭代次数	参数	1	2	3	4	Σ	$X ¯$	\| $X ¯ n + 1$ - $X ¯ n$ \|
	u	0	0	0	0
0	P	1.00	1.00	1.00	1.00	4.00	3.75	0
	X	3.00	6.00	2.00	4.00	15.00
	u	0.43	-0.03	0.10	0.70
1	P	1.43	0.97	1.10	1.70	5.21	3.67	0.08
	X	4.30	5.83	2.20	6.82	19.14
	u	0.48	-0.04	0.13	0.67
2	P	1.92	0.93	1.23	2.37	6.46	3.61	0.06
	X	5.75	5.61	2.47	9.48	23.30
	u	0.53	-0.04	0.16	0.64
3	P	2.44	0.89	1.40	3.01	7.75	3.55	0.06
	X	7.33	5.35	2.80	12.05	27.53
	u	0.57	5.30	2.80	12.05
4	P	0.58	-0.04	0.19	0.62	9.08	3.50	0.05
	X	9.03	5.07	3.18	14.55	31.82
	u	0.60	-0.05	0.21	0.60
5	P	3.61	0.79	1.80	4.25	10.46	3.46	0.04
	X	10.84	4.75	3.61	16.99	36.19
	u	0.64	-0.06	0.24	0.60
6	P	4.25	0.74	2.04	4.84	11.88	3.42	0.04
	X	12.76	4.42	4.08	19.38	40.64
	u	0.67	-0.06	0.26	0.59
7	P	4.93	0.68	2.30	5.43	13.33	3.39	0.03
	X	14.78	4.07	4.59	21.73	45.17

Table 3 The index values of each node in the hyper-network

超网标号	子网标号	度	介数	紧密度/10^-2	通行能力	火力水平	脆弱程度	物资储备量	物资运输量
01	C01	2	0	1.79	50	1×10^-6	1×10^-6	1×10^-6	1×10^-6
04	C02	6	12.97	2.27	100	1×10^-6	1×10^-6	1×10^-6	1×10^-6
05	C03	5	4.80	2.17	150	1×10^-6	1×10^-6	1×10^-6	1×10^-6
06	C04	6	12.15	2.44	150	1×10^-6	1×10^-6	1×10^-6	1×10^-6
11	C05	5	9.13	2.22	150	1×10^-6	1×10^-6	1×10^-6	1×10^-6
13	C06	7	18.47	2.56	150	1×10^-6	1×10^-6	1×10^-6	1×10^-6
10	C07	5	9.44	2.27	100	1×10^-6	1×10^-6	1×10^-6	1×10^-6
18	C08	5	8.90	2.13	200	1×10^-6	1×10^-6	1×10^-6	1×10^-6
19	C09	5	5.50	2.22	150	1×10^-6	1×10^-6	1×10^-6	1×10^-6
20	C10	6	13.75	2.38	200	1×10^-6	1×10^-6	1×10^-6	1×10^-6
22	C11	4	4.58	2.00	100	1×10^-6	1×10^-6	1×10^-6	1×10^-6
23	C12	3	2.59	1.92	100	1×10^-6	1×10^-6	1×10^-6	1×10^-6
03	M01	8	26.95	2.50	1×10^-6	6.26	7.58	1×10^-6	1×10^-6
02	M02	5	4.03	2.27	1×10^-6	4.05	7.94	1×10^-6	1×10^-6
08	M03	7	13.78	2.50	1×10^-6	7.46	6.03	1×10^-6	1×10^-6
12	M04	4	3.89	2.17	1×10^-6	3.53	3.50	1×10^-6	1×10^-6
16	M05	7	16.22	2.50	1×10^-6	8.00	4.07	1×10^-6	1×10^-6
07	S01	7	15.51	2.63	1×10^-6	1×10^-6	1×10^-6	86.52	74.93
09	S02	5	7.05	2.27	1×10^-6	1×10^-6	1×10^-6	67.79	56.54
14	S03	7	17.28	2.70	1×10^-6	1×10^-6	1×10^-6	69.26	59.29
15	S04	5	13.94	2.38	1×10^-6	1×10^-6	1×10^-6	28.50	15.76
21	S05	7	14.88	2.38	1×10^-6	1×10^-6	1×10^-6	41.01	24.42
17	S06	5	14.20	2.38	1×10^-6	1×10^-6	1×10^-6	45.58	37.43

Fig.4 Weights of evaluation indexes

Fig.5 Basic scores of nodes in the initial hyper-network

Table 4 Hyperdegree and functional score of each node

超网标号	子网标号	超度	功能得分
01	C01	1	0.05
04	C02	4	0.46
05	C03	2	0.37
06	C04	3	0.56
11	C05	2	0.29
13	C06	4	0.64
10	C07	3	0.32
18	C08	1	0.19
19	C09	2	0.29
20	C10	2	0.38
22	C11	2	0.20
23	C12	1	0.10
03	M01	5	2.30
02	M02	2	0.83
08	M03	3	1.34
12	M04	1	0.27
16	M05	4	1.69
07	S01	5	2.43
09	S02	4	1.65
14	S03	4	1.71
15	S04	2	0.37
21	S05	4	1.02
17	S06	3	0.93

Table 5 System value and striking order of each node in the hyper-network

超网标号	子网标号	体系价值/%	打击排序
14	S03	29.61	1
07	S01	28.62	2
09	S02	27.28	3
16	M05	26.62	4
03	M01	25.96	5
13	C06	25.82	6
21	S05	24.46	7
08	M03	23.41	8
04	C02	21.61	9
02	M02	18.42	10
17	S06	17.61	11
06	C04	15.88	12
05	C03	15.23	13
10	C07	13.93	14
20	C10	13.82	15
19	C09	11.03	16
22	C11	10.78	17
12	M04	9.32	18
11	C05	8.59	19
01	C01	6.26	20
15	S04	5.79	21
18	C08	2.60	22
23	C12	1.02	23

Table 6 Results of the second round of node value evaluation

子网标号	删后综合效能	体系价值/%	打击排序	子网标号	删后综合效能	体系价值/%	打击排序
S02	3.88	33.72	1	C07	4.89	16.51	12
S01	3.94	32.81	2	C10	4.94	15.67	13
M05	4.12	29.69	3	C04	5.07	13.53	14
C02	4.35	25.81	4	C11	5.13	12.48	15
S05	4.35	25.71	5	M04	5.28	9.97	16
M03	4.37	25.43	6	C05	5.30	9.61	17
M01	4.54	22.49	7	C01	5.41	7.66	18
S06	4.56	22.18	8	S04	5.51	5.91	19
C06	4.57	22.07	9	C09	5.57	4.92	20
M02	4.80	18.02	10	C08	5.72	2.46	21
C03	4.83	17.58	11	C12	5.78	1.35	22

Fig.6 Comparison of nodes’ striking orders in the first two rounds

Fig.7 Comparison of striking order results obtained by the proposed eveluation method and the existing eveluation methods

References 28

[1]	高寒冰, 刘洪娟. 战时战区军事交通网络建模与分析[J]. 物流技术, 2018, 37(10):113-118.
	GAO H B, LIU H J. Modeling and analysis of wartime theater military transportation network[J]. Logistics Technology, 2018, 37(10):113-118. (in Chinese)
[2]	刘成刚, 王永刚, 刚建勋, 等. 联合作战指挥控制体系网络建模与分析[J]. 指挥控制与仿真, 2018, 40(2):8-14, 21. doi: 10.3969/j.issn.1673-3819.2018.02.002
	LIU C G, WANG Y G, GANG J X, et al. Network modeling and analysis of the joint operations command and control system based on networks[J]. Command Control & Simulation, 2018, 40(2):8-14, 21. (in Chinese)
[3]	CHEN B, YU H Y, WANG Y M, et al. Multilevel command and control supernetwork modeling based on attribute synergy prioritization[J]. IEEE Access, 2019, 7: 32693-32702. doi: 10.1109/ACCESS.2019.2903520 URL
[4]	YE L B, PAN L F, LI C. Supernetwork-based invulnerability evaluation of topology for wireless communication network[C]//Proceedings of the 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference. Chongqing, China: IEEE, 2018: 2487-2490.
[5]	肖兵, 刘凤增, 秦一帅. 基于复杂网络的预警情报体系结构适应性研究[J]. 现代防御技术, 2022, 50(2):1-10. doi: 10.3969/j.issn.1009-086x.2022.02.001
	XIAO B, LIU F Z, QIN Y S. Research on the structure adaptability of early warning intelligence system-of-systems based on complex network[J]. Modern Defence Technology, 2022, 50(2):1-10. (in Chinese)
[6]	高龙, 曹军海, 宋太亮, 等. 基于复杂网络理论的装备保障体系演化模型[J]. 兵工学报, 2017, 38(10):2019-2030. doi: 10.3969/j.issn.1000-1093.2017.10.019
	GAO L, CAO J H, SONG T L, et al. Evolution model of equipment support system of systems based on complex network theory[J]. Acta Armamentarii, 2017, 38(10):2019-2030. (in Chinese) doi: 10.3969/j.issn.1000-1093.2017.10.019
[7]	陈春良, 昝翔, 张仕新, 等. 基于多维关系复杂网络的装备重要度评估方法[J]. 兵工学报, 2017, 38(6):1168-1177. doi: 10.3969/j.issn.1000-1093.2017.06.017
	CHEN C L, ZAN X, ZHANG S X, et al. Evaluation method for equipment important degree based on multidimensional relationship complex networks[J]. Acta Armamentarii, 2017, 38(6):1168-1177. (in Chinese)
[8]	LUO J, YU X H, JIANG W, et al. Research on the application of super network model in anti-missile system operation[C]//Proceedings of 2020 IEEE 9th Joint International Information Technology and Artificial Intelligence Conference. Chongqing, China: IEEE, 2020, 9: 550-557.
[9]	XING Q H, GAO J L. A super-network equilibrium optimization method for operation architecture with fuzzy demands[J]. Journal of Systems Engineering and Electronics, 2020, 31(5): 969-982. doi: 10.23919/JSEE.2020.000072
[10]	段威. 基于超网络理论的联合作战目标价值评估问题研究[D]. 长沙: 国防科技大学, 2018.
	DUAN W. Research on target value evaluation in joint operations based on hyper-network theory[D]. Changsha: School of National University of Defense Technology, 2018. (in Chinese)
[11]	WEN X X, TU C L, WU M G. Node importance evaluation in aviation network based on “No Return” node deletion method[J]. Physica A: Statistical Mechanics and its Applications, 2018, 503: 546-559. doi: 10.1016/j.physa.2018.02.109 URL
[12]	LU M K. Node importance evaluation based on neighborhood structure hole and improved TOPSIS[J]. Computer Networks, 2020, 178: 107336. doi: 10.1016/j.comnet.2020.107336 URL
[13]	YANG Y Z, WANG X, CHEN Y, et al. A novel centrality of influential nodes identification in complex networks[J]. IEEE Access, 2020, 8: 58742-58751. doi: 10.1109/Access.6287639 URL
[14]	RUAN Y R, TANG J, HU Y L, et al. Efficient algorithm for the identification of node significance in complex network[J]. IEEE Access, 2020, 8: 28947-28955. doi: 10.1109/Access.6287639 URL
[15]	刘菁, 陈威. 国防交通网络关键节点识别模型研究[J]. 军事运筹与系统工程, 2019, 33(1): 58-62.
	LIU J, CHEN W. Research on key node identification model of national defense transportation network[J]. Military Operations Research and Systems Engineering, 2019, 33(1):58-62. (in Chinese)
[16]	ZENG Y. Evaluation of node importance and invulnerability simulation analysis in complex load-network[J]. Neurocomputing, 2020, 416: 158-164. doi: 10.1016/j.neucom.2019.05.092 URL
[17]	王海燕, 赵宗可. 基于复杂网络理论的加权供应链网络节点重要度评价[J]. 物流技术, 2019, 38(1):104-110.
	WANG H Y, ZHAO Z K. Evaluation of node importance of weighted supply chain network based on complex network theory[J]. Logistics Technology, 2019, 38(1):104-110. (in Chinese)
[18]	马丹. 基于复杂网络的轨道交通网络节点重要度评价[J]. 交通科技与经济, 2017, 19(2):44-49.
	MA D. Evaluation method of importance for nodes in rail transit network based on complex network[J]. Technology & Economy in Areas of Communications, 2017, 19(2):44-49. (in Chinese)
[19]	于会, 刘尊, 李勇军. 基于多属性决策的复杂网络节点重要性综合评价方法[J]. 物理学报, 2013, 62(2):54-62.
	YU H, LIU Z, LI Y J. Key nodes in complex networks identified by multi-attribute decision-making method[J]. Acta Physica Sinica, 2013, 62(2):54-62. (in Chinese)
[20]	李尔玉, 龚建兴, 黄健, 等. 基于功能链的作战体系复杂网络节点重要性评价方法[J]. 指挥与控制学报, 2018, 4(1):42-49.
	LI E Y, GONG J X, HUANG J, et al. Node importance analysis of complex networks for combat systems based on function chain[J]. Journal of Command and Control, 2018, 4(1):42-49 (in Chinese)
[21]	张鑫伟, 李亚雄, 赵久奋, 等. 基于复杂网络理论的熵值法军事目标价值评估[J]. 指挥控制与仿真, 2021, 43(6):53-57. doi: 10.3969/j.issn.1673-3819.2021.06.009
	ZHANG X W, LI Y X, ZHAO J F, et al. Evaluation method of military target based on complex network theory and entropy method[J]. Command Control & Simulation, 2021, 43(6):53-57. (in Chinese)
[22]	段婷, 李小波, 周鑫, 等. 超网络研究进展综述: 理论, 应用和工具[C]//第二十届中国系统仿真技术及其应用学术年会论文集. 合肥:中国自动化学会/中国系统仿真学会, 2019.
	DUAN T, LI X B, ZHOU X, et al. Review on the research progress of supernetworks : theory, application and tools[C]. Command Control & Simulation, 2021, 43(6):53-57. (in Chinese)
[23]	BERGE C. Graphs and hypergraphs[M]. Amsterdam, the Netherlands: North Holland Publishing Co., 1973.
[24]	ESTRADA E, RODRIGUEZ-VELAZQUEZ J A. Subgraph centrality in complex networks[J]. Physical Review E, 2005, 71(5): 056103. doi: 10.1103/PhysRevE.71.056103 URL
[25]	任晓龙, 吕琳媛. 网络重要节点排序方法综述[J]. 科学通报, 2014, 59(13):1175-1197.
	REN X L, LÜ L Y. A review of network important node ranking methods[J]. Chinese Science Bulletin, 2014, 59(13):1175-1197. (in Chinese)
[26]	COSTENBADER E, VALENTE T W. The stability of centrality measures when networks are sampled[J]. Social Networks, 2003, 25(4): 283-307. doi: 10.1016/S0378-8733(03)00012-1 URL
[27]	刘昊, 谢鹏, 李玥. 联合火力打击中的多目标组合排序算法[J]. 兵工学报, 2020, 41(12):2570-2578. doi: 10.3969/j.issn.1000-1093.2020.12.023
	LIU H, XIE P, LI Y. Combined sorting algorithm for multi-target sorting in joint firepower strike[J]. Acta Armamentarii, 2020, 41(12):2570-2578. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.12.023
[28]	史本山, 文忠平. 专家评分评判的修正加权法[J]. 技术经济, 1996(9):57-58.
	SHI B S, WEN Z P. Revised weighting method of expert evaluation[J]. Journal of Technology Economics, 1996(9):57-58. (in Chinese)