基于超网络的军事交通运输网络节点价值评估方法

doi:10.12382/bgxb.2022.0748

摘要/Abstract

摘要：

针对军事交通运输网络中的高价值目标选择问题,提出一种基于超网络的节点价值评估方法。考虑多层网络内部和网络之间的交互机制,构建由通行枢纽子网、军事力量子网和后勤保障子网组成的军事交通运输超网络模型;提出综合拓扑维度和功能维度的超网络综合效能评价算法,在此基础上运用节点删除法,获得超网络中节点的体系价值和优先打击顺序。实验结果表明:节点的功能属性对其体系价值起决定性作用,且所处位置越优、邻近节点越重要,其体系价值越高;经过多轮打击后,通过该方法获得的节点打击排序相近,表明了该方法的鲁棒性;与现有方法相比,该方法能够全面客观地判断目标的重要度,有效提高决策的准确率,具有较高的战场普适性。

关键词: 军事交通运输, 节点价值, 动态评估, 超网络, 综合效能

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

中图分类号:

许怡岚, 郭唐仪, 唐坤, 张滢颖, 李林蔚. 基于超网络的军事交通运输网络节点价值评估方法[J]. 兵工学报, 2024, 45(2): 552-563.

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.

图/表 13

图1 军事交通运输超网络示意图

Fig.1 Schematic diagram of military transportation hyper-network

图2 节点基础得分评价指标体系

Fig.2 Evaluation index system of node basic scores

图3 西南边境某地区军事交通运输超网络模型

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

表1 超网络的邻接关系

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

表2 专家打分的修正加权法示例表

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

表2 专家打分的修正加权法示例表

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

表3 超网络中各节点的指标数值

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

图4 各项评价指标的权重

Fig.4 Weights of evaluation indexes

图5 初始超网络中节点的基础得分

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

表4 各节点的超度和功能得分

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

表5 超网络中节点的体系价值和打击排序

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

表6 第2轮节点价值评估结果

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

图6 前两轮的节点打击排序对比

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

图7 本文方法与现有方法的结果对比

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

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