多粒度协同演化的病毒传播控制资源分配方法

doi:10.16182/j.issn1004731x.joss.24-0315

摘要/Abstract

摘要：

基于分而治之的思想，提出了多粒度协同演化的病毒传播控制资源分配方法(multi-granularity cooperative coevolution，MGCC)。根据人类社交网络结构特征，将网络按照不同分解粒度分解为不同规模的子网络；设计了一种基于贡献度的分解粒度选择策略，用历史档案记录不同分解粒度对问题优化的贡献度，并根据优化状态选择合适分解粒度；设计了基于投影的约束修复策略，保证解的可行性。结果表明：MGCC算法可以将复杂的社交网络结构分解，并结合不同演化算子协同解决资源分配问题，可以提高演化算子对解决病毒传播控制资源分配问题的有效性。

关键词: 病毒传播控制, 网络传播, 协同演化, 演化计算, 资源分配

Abstract:

According to the principle of simplifying a complex problem into sub-problems for solution, a resource allocation method for virus spreading control based on multi-granularity cooperative coevolution (MGCC) was proposed. According to the characteristics of human's social network structures, MGCC decomposed the network into sub-networks with different scales according to different decomposition granularities. A contribution-based decomposition granularity selection strategy was proposed. Historical archives were used to record the contribution of different decomposition granularities to optimization, and the appropriate decomposition granularity was selected according to the optimization status. A projection-based constraint repairing strategy was designed to ensure the feasibility of solutions. The results show that MGCC can decompose complex social network structures and ensure resource allocation by combining different evolutionary operators, improving the effectiveness of evolutionary operators in solving the resource allocation problem for virus spreading control.

Key words: virus spreading control, network spreading, cooperative coevolution, evolutionary computation, resource allocation

中图分类号:

TP391.9

史宣莉,陈伟能,宋安等 . 多粒度协同演化的病毒传播控制资源分配方法[J]. 系统仿真学报, 2025, 37(8): 2043-2060.

Shi Xuanli,Chen Weineng,Song An,et al . Resource Allocation Method for Virus Spreading Control Based on Multi-granularity Cooperative Coevolution[J]. Journal of System Simulation, 2025, 37(8): 2043-2060.

图/表 12

图1

图2

图3

表1

表2

图4

表3

MGCC不同粒度对比实验

网络	指标	MGCC_CSO	CSO_g2	CSO_g3	CSO_g4	MGCC_DE	DE_g2	DE_g3	DE_g4
Net_01	mean	0.487 0	0.499 8	0.504 2	0.496 8	0.462 3	0.518 9	0.485 2	0.463 1
	std	1.73×10^-2	2.28×10^-2	2.33×10^-2	2.26×10^-2	2.47×10^-2	2.50×10^-2	3.40×10^-2	2.52×10^-2
	p-value	—	4.68×10^-2(+)	3.67×10^-3(+)	1.26×10^-1(≈)	—	2.67×10^-9(+)	7.96×10^-3(+)	9.00×10^-1(≈)
Net_02	mean	0.449 8	0.473 6	0.466 7	0.477 5	0.416 4	0.481 7	0.464 7	0.438 1
	std	2.27×10^-2	2.86×10^-2	2.48×10^-2	2.61×10^-2	2.46×10^-2	3.26×10^-2	3.48×10^-2	2.51×10^-2
	p-value	—	9.52×10^-4(+)	1.17×10^-2(+)	1.25×10^-4(+)	—	3.82×10^-9(+)	8.20×10^-7(+)	7.70×10^-4(+)
Net_03	mean	0.474 8	0.489 7	0.496 1	0.491 5	0.453 9	0.511 6	0.473 2	0.463 7
	std	2.63×10^-2	1.97×10^-2	2.19×10^-2	2.72×10^-2	3.33×10^-2	2.74×10^-2	2.83×10^-2	3.06×10^-2
	p-value	—	1.76×10^-2(+)	2.16×10^-3(+)	2.51×10^-2(+)	—	4.69×10^-8(+)	3.39×10^-2(+)	3.11×10^-1(+)
Net_04	mean	0.473 1	0.500 3	0.493 3	0.500 6	0.439 9	0.504 3	0.483 8	0.458 3
	std	2.11×10^-2	2.64×10^-2	2.63×10^-2	2.58×10^-2	3.16×10^-2	2.81×10^-2	3.18×10^-2	2.77×10^-2
	p-value	—	1.17×10^-4(+)	3.50×10^-3(+)	9.79×10^-5(+)	—	7.77×10^-9(+)	6.28×10^-6(+)	1.99×10^-2(+)
Net_05	mean	0.466 8	0.492 7	0.492 1	0.493 8	0.452 0	0.507 1	0.490 2	0.466 1
	std	1.97×10^-2	2.58×10^-2	1.96×10^-2	2.81×10^-2	2.50×10^-2	3.31×10^-2	1.91×10^-2	2.23×10^-2
	p-value	—	1.41×10^-4(+)	2.77×10^-5(+)	2.68×10^-4(+)	—	1.60×10^-7(+)	1.16×10^-7(+)	1.38×10^-2(+)
Net_06	mean	0.472 5	0.479 9	0.477 4	0.477 3	0.428 5	0.483 5	0.463 0	0.440 1
	std	2.54×10^-2	3.06×10^-2	2.19×10^-2	2.28×10^-2	2.45×10^-2	2.70×10^-2	2.78×10^-2	2.93×10^-2
	p-value	—	2.46×10^-1(≈)	6.31×10^-1(≈)	6.10×10^-1(≈)	—	8.48×10^-9(+)	1.53×10^-5(+)	1.54×10^-1(≈)
Net_07	mean	0.518 3	0.530 4	0.542 9	0.526 7	0.491 0	0.543 1	0.532 5	0.497 3
	std	2.23×10^-2	2.34×10^-2	2.54×10^-2	2.45×10^-2	2.65×10^-2	3.28×10^-2	2.50×10^-2	2.95×10^-2
	p-value	—	1.54×10^-1(≈)	5.56×10^-4(+)	3.71×10^-1(≈)	—	2.38×10^-7(+)	1.39×10^-6(+)	2.84×10^-1(≈)
Net_08	mean	0.480 5	0.497 3	0.506 8	0.503 8	0.447 6	0.508 0	0.501 3	0.463 1
	std	2.42×10^-2	2.69×10^-2	2.75×10^-2	2.71×10^-2	2.88×10^-2	3.29×10^-2	2.52×10^-2	2.80×10^-2
	p-value	—	3.39×10^-2(+)	1.06×10^-3(+)	1.52×10^-3(+)	—	5.09×10^-8(+)	1.70×10^-8(+)	9.05×10^-2(≈)
Net_09	mean	0.535 6	0.553 8	0.553 8	0.548 8	0.489 3	0.558 3	0.543 9	0.517 3
	std	2.14×10^-2	3.02×10^-2	2.59×10^-2	2.70×10^-2	2.92×10^-2	3.90×10^-2	3.27×10^-2	3.10×10^-2
	p-value	—	1.17×10^-2(+)	1.50×10^-2(+)	7.98×10^-2(≈)	—	1.31×10^-8(+)	2.38×10^-7(+)	1.17×10^-3(+)
Net_10	mean	0.479 5	0.500 1	0.515 0	0.505 4	0.450 5	0.513 9	0.503 3	0.476 0
	std	2.77×10^-2	2.48×10^-2	2.74×10^-2	2.28×10^-2	2.31×10^-2	2.83×10^-2	3.36×10^-2	2.67×10^-2
	p-value	—	4.03×10^-3(+)	2.13×10^-5(+)	7.66×10^-5(+)	—	8.89×10^-10(+)	7.09×10^-8(+)	3.99×10^-4(+)
w/l/d		—	8/0/2	9/0/1	6/0/4	—	10/0/0	10/0/0	6/0/4

表3

图5

表4

表5

图6

图7

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网络	指标	MGCC_ CSO	MGCC_ CSO_2	MGCC_ DE	MGCC_ DE_2	网络	指标	MGCC_ CSO	MGCC_ CSO_2	MGCC_ DE	MGCC_ DE_2
Net_01	mean	0.487 5	0.510 8	0.462 4	0.543 2	Net_06	mean	0.472 9	0.491 9	0.428 7	0.518 2
	std	1.71×10^-2	3.06×10^-2	2.47×10^-2	3.21×10^-2		std	2.56×10^-2	2.03×10^-2	2.45×10^-2	3.24×10^-2
	p-value	2.24×10^-7(+)		8.57×10^-72(+)			p-value	8.80×10^-6(+)		1.70×10^-76(+)
Net_02	mean	0.450 0	0.487 6	0.416 5	0.511 2	Net_07	mean	0.518 7	0.540 4	0.491 1	0.560 6
	std	2.28×10^-2	2.61×10^-2	2.46×10^-2	2.97×10^-2		std	2.23×10^-2	2.88×10^-2	2.65×10^-2	3.12×10^-2
	p-value	1.58×10^-14(+)		1.25×10^-82(+)			p-value	5.93×10^-7(+)		8.37×10^-67(+)
Net_03	mean	0.474 9	0.512 3	0.454 1	0.536 3	Net_08	mean	0.480 8	0.499 7	0.447 7	0.514 0
	std	2.64×10^-2	2.50×10^-2	3.33×10^-2	2.98×10^-2		std	2.41×10^-2	2.17×10^-2	2.87×10^-2	3.10×10^-2
	p-value	5.16×10^-12(+)		5.86×10^-71(+)			p-value	9.89×10^-6(+)		9.51×10^-62(+)
Net_04	mean	0.473 4	0.503 8	0.440 0	0.530 5	Net_09	mean	0.536 0	0.573 0	0.489 4	0.591 7
	std	2.12×10^-2	2.77×10^-2	3.15×10^-2	2.19×10^-2		std	2.12×10^-2	3.36×10^-2	2.92×10^-2	3.54×10^-2
	p-value	7.89×10^-11(+)		8.07×10^-78(+)			p-value	3.84×10^-11(+)		6.29×10^-77(+)
Net_05	mean	0.467 2	0.506 1	0.452 1	0.537 0	Net_10	mean	0.479 9	0.515 1	0.450 6	0.539 7
	std	1.97×10^-2	2.76×10^-2	2.50×10^-2	2.75×10^-2		std	2.78×10^-2	2.66×10^-2	2.31×10^-2	3.42×10^-2
	p-value	4.18×10^-16(+)		3.29×10^-76(+)			p-value	1.17×10^-10(+)		2.69×10^-75(+)

算法	congress-Twitter			US_Airport_top500
算法	mean	std	p-value	mean	std	p-value
MGCC_CSO	3.812 8	0.094 1	—	1.624 3	0.149 6	—
CSO	3.872 6	0.139 3	1.54×10^-16(+)	1.695 6	0.079 3	5.61×10^-33(+)
CSO_g2	3.846 9	0.102 7	4.07×10^-5(+)	1.641 8	0.188 2	6.48×10^-9(+)
CSO_g3	3.892 5	0.175 8	1.02×10^-18(+)	1.690 9	0.220 0	1.88×10^-28(+)
CSO_g4	3.834 7	0.158 2	1.23×10^-2(+)	1.666 5	0.174 1	4.51×10^-16(+)
CSO_g5	3.908 8	0.132 4	7.55×10^-21(+)	1.723 5	0.108 1	3.38×10^-42(+)
CSO_g10	3.907 6	0.151 6	3.15×10^-20(+)	1.716 2	0.214 8	9.01×10^-44(+)
CSO_g15	3.889 9	0.134 5	2.65×10^-17(+)	1.660 7	0.151 7	2.47×10^-17(+)
CSO_g20	3.888 2	0.157 3	3.81×10^-14(+)	1.657 0	0.170 7	4.07×10^-11(+)
w/l/d	8/0/0			8/0/0
MGCC_DE	3.448 2	0.112 1	—	1.582 7	0.084 8	—
DE	3.493 6	0.110 3	1.03×10^-4(+)	1.678 9	0.100 5	4.12×10^-27(+)
DE_g2	3.396 5	0.111 9	1.81×10^-6(-)	1.608 5	0.161 5	1.41×10^-5(+)
DE_g3	3.525 8	0.093 2	4.51×10^-5(+)	1.600 1	0.146 5	0.000 462(+)
DE_g4	3.517 3	0.159 0	3.45×10^-4(+)	1.588 4	0.115 2	0.647 967(≈)
DE_g5	3.401 0	0.126 2	5.13×10^-3(+)	1.618 3	0.138 1	1.32×10^-8(+)
DE_g10	3.477 5	0.230 0	2.32×10^-1(+)	1.647 1	0.109 2	5.71×10^-14(+)
DE_g15	3.420 4	0.130 9	3.67×10^-3(-)	1.535 7	0.133 2	1.39×10^-8(-)
DE_g20	3.535 1	0.219 1	2.16×10^-8(+)	1.660 8	0.142 4	1.19×10^-23(+)
w/l/d	6/2/0			6/1/1