基于多元公共品演化博弈的无人作战集群策略占优条件

doi:10.12305/j.issn.1001-506X.2021.09.23

系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (9): 2553-2561.doi: 10.12305/j.issn.1001-506X.2021.09.23

基于多元公共品演化博弈的无人作战集群策略占优条件

禹明刚^1,², 何明^1,*, 张东戈¹, 马子玉¹, 康凯¹

1. 陆军工程大学指挥控制工程学院, 江苏南京 210007
2. 陆军工程大学通信工程学院, 江苏南京 210007

收稿日期:2020-07-20 出版日期:2021-08-20 发布日期:2021-08-26
通讯作者: 何明
作者简介:禹明刚(1986—), 男, 副教授, 博士后, 主要研究方向为军事需求工程、体系工程、集群智能|何明(1978—), 男, 教授, 博士研究生导师, 博士, 主要研究方向为军事信息学、智能化指挥控制|张东戈(1965—), 男, 教授, 博士, 主要研究方向为复杂军事系统分析、军事信息学、军事运筹学|马子玉(1995—), 男, 硕士研究生, 主要研究方向为无人化指挥控制|康凯(1986—), 男, 讲师, 硕士, 主要研究方向为军事需求工程、智能化指挥控制
基金资助:
国家自然科学基金(71901217);军委科技委基础加强计划重点基础研究项目(2020-JCJQ-ZD-007);国家重点研发计划(2018YFC0806900);陆军工程大学军事理论创新工程项目(KYZYJQZL2101)

Strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game

Minggang YU^1,², Ming HE^1,*, Dongge ZHANG¹, Ziyu MA¹, Kai KANG¹

1. Institute of Command and Control Engineering, Army Engineering University, NanJing 210007, China
2. Institute of Communication Engineering, Army Engineering University, NanJing 210007, China

Received:2020-07-20 Online:2021-08-20 Published:2021-08-26
Contact: Ming HE

摘要/Abstract

摘要：

如何提高集群中合作者占比, 是无人集群作战中自主协同的关键问题之一。基于多元公共品演化博弈框架, 对无人作战集群策略占优条件进行了理论推导和特性分析。首先，给出无人集群自主协同需求, 建立基于愿景驱动的多元演化博弈模型。然后，以平均丰度函数为出发点, 理论推导多元演化博弈的合作策略占优条件。在此基础上, 针对线性和带门限值的两类公共品博弈, 仿真分析收益系数、愿景水平、门限值等参数对策略占优的影响, 获取两类博弈模型的策略占优特性。最后, 依据特性分析结果, 给出实现无人集群合作策略占优的建议, 为无人集群作战的机制设计提供决策支持。

关键词: 无人集群作战, 自主协同, 多元公共品演化博弈, 策略占优

Abstract:

How to improve the proportion of cooperators is one of the key problems of autonomous cooperation in unmanned cluster operations. This research makes theoretical derivation and characteristic analysis on the strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game. It starts with the requirement analysis of autonomous collaboration in unmanned cluster firstly. And the evolutionary game model of multi-player public goods based on aspiration-driven dynamics is established.Then, the average abundance function and strategy dominance condition are constructed by theoretical derivation. Furthermore, the influence of multiplication factor, threshold and aspiration level on the strategy dominance of linear public goods game and threshold public goods game are simulated. Finally, the rationalization proposals to improve the proportion of cooperators and achieve strategy dominance are suggested according to the simulation results, and to provide decision-making support for the mechanism design of unmanned cluster operation.

Key words: unmanned combat cluster, autonomous collaboration, multi-player public goods evolutionary game, strategy dominance

中图分类号:

TP391

禹明刚, 何明, 张东戈, 马子玉, 康凯. 基于多元公共品演化博弈的无人作战集群策略占优条件[J]. 系统工程与电子技术, 2021, 43(9): 2553-2561.

Minggang YU, Ming HE, Dongge ZHANG, Ziyu MA, Kai KANG. Strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game[J]. Systems Engineering and Electronics, 2021, 43(9): 2553-2561.

图/表 9

图1

图2

表1

图3

表2

图4

图5

表3

图6

参考文献 50

1	XU P , DHERBOMEZ G , HERY E , et al. System architecture of a driverless electric car in the grand cooperative driving challenge[J]. IEEE Intelligent Transportation Systems Magazine, 2018, 10 (1): 47- 59. doi: 10.1109/MITS.2017.2776135
2	LIANG H, QIANG H, FENG Z. Research on capability characteristics modeling and cooperative fire strike planning for unmanned ground vehicles[C]//Proc. of the 2nd International Conference on Artificial Intelligence and Big Data, 2019: 136-141.
3	ZOTO J, MUSCI M A, KHALIQ A, et al. Automatic path planning for unmanned ground vehicle using UAV imagery[C]//Proc. of the International Conference on Robotics in Alpe-Adria Danube Region, 2019: 223-230.
4	MA Y , HU M , YAN X . Multi-objective path planning for unmanned surface vehicle with currents effects[J]. ISA transactions, 2018, 75, 137- 156. doi: 10.1016/j.isatra.2018.02.003
5	SONG R , LIU Y U , BUCKNALL R . Smoothed A^* algorithm for practical unmanned surface vehicle path planning[J]. Applied Ocean Research, 2019, 83, 9- 20. doi: 10.1016/j.apor.2018.12.001
6	ZHOU Q, LI B F, ZHAN Z J. Research on the key technologies of unmanned cluster to sea combat[C]//Proc. of the Global Intelligence Industry Conference, 2018.
7	GILES K , GIAMMARCO K . A mission-based architecture for swarm unmanned systems[J]. Systems Engineering, 2019, 22 (3): 271- 281. doi: 10.1002/sys.21477
8	KHAWAJA W , GUVENC I , MATOLAK D W , et al. A survey of air-to-ground propagation channel modeling for unmanned aerial vehicles[J]. IEEE Communications Surveys & Tutorials, 2019, 21 (3): 2361- 2391.
9	SHAKERI R , Al-GARADI M A , BADAWY A , et al. Design challenges of multi-UAV systems in cyber-physical applications: a comprehensive survey, and future directions[J]. IEEE Communications Surveys & Tutorials, 2019, 21 (4): 3340- 3385.
10	DOLICANIN E , FETAHOVIC I , TUBA E , et al. Unmanned combat aerial vehicle path planning by brain storm optimization algorithm[J]. Studies in Informatics and Control, 2018, 27 (1): 15- 24.
11	FAN J R , LI D G , LI R P , et al. Analysis on MAV/UAV cooperative combat based on complex network[J]. Defense Technology, 2020, 16 (1): 154- 161.
12	全吉, 储育青, 王先甲. 具有惩罚策略的公共物品博弈与合作演化[J]. 系统工程理论与实践, 2019, 39 (1): 141- 149.
	QUAN J , CHU Y Q , WANG X J . Public goods with punishment and the evolution of cooperation[J]. Systems Engineering-Theory & Practice, 2019, 39 (1): 141- 149.
13	SMITH J M , PRICE G R . The logic of animal conflict[J]. Nature, 1973, 246 (5427): 15- 18. doi: 10.1038/246015a0
14	NOWAK M A , SIGMUND K . Evolution of indirect reciprocity[J]. Nature, 2005, 437 (6685): 1291- 1298.
15	WOLFF I . What are the equilibria in public-good experiments?[J]. Economics Letters, 2017, 150, 83- 85. doi: 10.1016/j.econlet.2016.11.015
16	NOWAK M A , SASAKI A , TAYLOR C , et al. Emergence of cooperation and evolutionary stability in finite populations[J]. Nature, 2004, 428 (6983): 646- 650. doi: 10.1038/nature02414
17	SU Q, MCAVOY A, WANG L, et al. Evolutionary dynamics with stochastic game transitions[EB/OL]. [2020-07-15]. http://arxiv.org/abs/1905.10269.
18	ANTAL T , NOWAK M A , TRAULSEN A . Strategy abundance in 2×2 games for arbitrary mutation rates[J]. Journal of Theoretical Biology, 2009, 257 (2): 340- 344. doi: 10.1016/j.jtbi.2008.11.023
19	GOKHALE C S , TRAULSEN A . Evolutionary games in the multiverse[J]. Proceedings of the National Academy of Sciences, 2010, 107 (12): 5500- 5504. doi: 10.1073/pnas.0912214107
20	HINDERSIN L , WU B , TRAULSEN A , et al. Computation and simulation of evolutionary game dynamics in finite populations[J]. Scientific Reports, 2019, 9 (1): 6946. doi: 10.1038/s41598-019-43102-z
21	WANG X J , GU C L , LV S J , et al. Evolutionary game dynamics of combining the Moran and imitation processes[J]. Chinese Physics B, 2019, 28 (2): 94- 105.
22	ROCA C P , HELBING D . Emergence of social cohesion in a model society of greedy, mobile individuals[J]. Proceedings of the National Academy of Sciences, 2011, 108 (28): 11370- 11374. doi: 10.1073/pnas.1101044108
23	TARNITA C E , OHTSUKI H , ANTAL T , et al. Strategy selection in structured populations[J]. Journal of Theoretical Biology, 2009, 259 (3): 570- 581. doi: 10.1016/j.jtbi.2009.03.035
24	DU J M , WU B , WANG L . Aspiration dynamics in structured population acts as if in a well-mixed one[J]. Scientific Reports, 2015, 5 (1): 8014. doi: 10.1038/srep08014
25	DU J M , WU B , ALTROCK P M , et al. Aspiration dynamics of multi-player games in finite populations[J]. Journal of the Royal Society Interface, 2014, 11 (94): 20140077. doi: 10.1098/rsif.2014.0077
26	DU J M, WU B, WANG L. Evolutionary game dynamics of multi-agent cooperation driven by self-learning[C]//Proc. of the 9th Asian Control Conference, 2013.
27	王先甲, 夏可. 愿景驱动、演化博弈与环境污染治理进路[J]. 江汉论坛, 2018, (7): 38- 44.
	WANG X J , XIA K . Aspiration driven, evolutionary game and environmental pollution control[J]. Jianghan Tribune, 2018, (7): 38- 44.
28	DU J M , WU B , WANG L . Aspiration dynamics and the sustainability of resources in the public goods dilemma[J]. Physica A: Statistical Mechanics & its Application, 2016, 380 (16): 1432- 1436.
29	SMITH E A . Communication and collective action: language and the evolution of human cooperation[J]. Evolution & Human Behavior, 2010, 31 (4): 231- 245.
30	禹明刚, 张东戈, 康凯, 等. 基于多元公共品演化博弈的无人集群合作演化机制[J]. 系统工程与电子技术, 2020, 42 (12): 2787- 2794. doi: 10.3969/j.issn.1001-506X.2020.12.15
	YU M G , ZHANG D G , KANG K , et al. Cooperative evolution mechanism of unmanned swarm within the framework of public good game[J]. Systems Engineering and Electronics, 2020, 42 (12): 2787- 2794. doi: 10.3969/j.issn.1001-506X.2020.12.15
31	Department of Defence. Unmanned systems integrated Roadmap FY2017-2042[R]. Office of the Secretary of Defense, 2013.
32	胡晓峰, 荣明. 智能化作战研究值得关注的几个问题[J]. 指挥与控制学报, 2018, 4 (3): 195- 200.
	HU X F , RONG M . Several important questions of intelligent warfare research[J]. Journal of Command and Control, 2018, 4 (3): 195- 200.
33	李林林, 张承龙, 卓志敏. 智能无人作战系统发展及关键技术[J]. 现代防御技术, 2020, 48 (3): 37- 44.
	LI L L , ZHANG C L , ZHUO Z M . Development and key technology of intelligent unmanned combat system[J]. Modern Defence Technology, 2020, 48 (3): 37- 43.
34	杨进, 沈文科. 对陆军智能化建设的深层思考[J]. 国防科技, 2019, 40 (4): 41- 44.
	YANG J , SHEN W K . Deep thinking on army intelligence construction[J]. National Defense Science and technology, 2019, 40 (4): 41- 44.
35	GARRO A , MAX M , TUNDIS A , et al. Intelligent agents: multi-agent systems[J]. Encyclopedia of Bioinformatics and Computational Biology, 2019, doi: 10.1016/B978-0-12-809633-8.20328-2
36	约翰·霍兰. 隐秩序—适应性造就复杂性[D]. 周晓牧译. 上海: 上海科技教育出版社, 2000.
	HOLLAND J. Hidden order—adaptability makes complexity[D]. ZHOU X M. Shanghai: Shanghai Science and technology education press, 2000.
37	YANG Z S , WANG W , KIM D . On multi-path routing for reliable communications in failure interdependent complex networks[J]. Journal of Combinatorial Optimization, 2021, 41 (1): 170- 196. doi: 10.1007/s10878-020-00665-2
38	CHONG Y Z , YANG H , LIU Z X , et al. Stability of replicator dynamics with bounded continuously distributed time delay[J]. Mathematics, 2020, 8 (431): 1- 11.
39	GAO S P , WU T , WANG L . Evolution of global cooperation and ethnocentrism in group-structured populations[J]. Physics Letters A, 2018, 382 (31): 2027- 2043. doi: 10.1016/j.physleta.2018.05.020
40	GRAHAM R L , KNUTH D E , PATASHNIK O . Concrete mathematics[M]. 2nd ed.Massachusetts: Addison-Wesley Publishing Company, 1994.
41	CHEN Y S , YANG H X , GUO W Z . Aspiration-induced dormancy promotes cooperation in the spatial Prisoner's Dilemma games[J]. Physica A: Statistical Mechanics and its Applications, 2017, 469, 625- 630. doi: 10.1016/j.physa.2016.11.082
42	PLATKOWSKI T . Aspiration-based full cooperation in finite systems of players[J]. Applied Mathematics and Computation, 2015, 251, 46- 54. doi: 10.1016/j.amc.2014.11.054
43	王先甲, 刘佳. 具有外部性的合作博弈问题中的稳定的联盟结构[J]. 系统工程理论与实践, 2018, 38 (5): 1173- 1183.
	WANG X J , LIU J . Stable coalition structures in cooperative game with externalities[J]. Systems Engineering-Theory & Practice, 2018, 38 (5): 1173- 1183.
44	LIU X S , HE M F , KANG Y B , et al. Fixation of strategies with the Moran and Fermi processes in evolutionary games[J]. Physica A: Statistical Mechanics and its Applications, 2017, 484, 336- 344.
45	LIU X S , HE M F , KANG Y B , et al. Aspiration promotes cooperation in the prisoner's dilemma game with the imitation rule[J]. Physical Review E, 2016, 94, 012124.
46	VAN K N G . Stochastic process in physics and chemistry[M]. Netherlands: Elsevier, 1992.
47	GARDINER C W . Handbook of stochastic methods[M]. Berlin: springer, 1985.
48	KIMURA M . The neutral theory of molecular evolution[M]. Cambridge: Cambridge University Press, 1983.
49	TRAULSEN A, SEMMANN D, SOMMERFELD R D, et al. Human strategy updating in evolutionary games[J]//Proceedings of the National Academy of Science of the USA, 2010, 107(7): 2962-2966.
50	WU B , ALTROCK P M , WANG L , et al. Universality of weak selection[J]. Physical Review E, 2010, 82, 046106.

无人集群自主协同	多元公共品演化博弈
无人集群	混合均匀种群
自主协同所需公共资源(如弹药、通信等)	公共品
参与自主协同的多个无人平台	多元
单个无人平台	个体
作为研究对象的单个无人平台	焦点个体
平台愿意向集群贡献资源的合作行为	策略A
平台不愿向集群贡献资源，而选择“搭便车”的非合作行为	策略B
不同策略下，集群回馈给平台的公共资源	收益
无人平台间基于收益的策略转换	博弈
多轮博弈中，采用不同策略的平台在集群中占比动态变化	演化
多轮博弈后，占比稳定，博弈终止	演化稳定
演化稳定后，合作者(非合作者)在集群中占比的期望值	平均丰度
合作者在集群中平均丰度大于0.5	合作策略占优

策略	d-1	⋯	k	⋯	1	0
A	rc-c	⋯	r(kc+c)/d-c	⋯	2rc/d-c	rc/d-c
B	r(d-1)c/2	⋯	rkc/d	⋯	rc/d	0

策略	d-1	⋯	k	⋯	m-1	⋯
A	rc	⋯	r(kc+c)/d	⋯	mrc/d	⋯
B	r(d-1)c/d+c	⋯	rkc/d+c	⋯	0	⋯

基于多元公共品演化博弈的无人作战集群策略占优条件

Strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 9

参考文献 50

相关文章 1

编辑推荐

Metrics

本文评价