基于不完全信息博弈的云制造群智能优化方法

doi:10.16182/j.issn1004731x.joss.22-1500

摘要/Abstract

摘要：

为解决云制造过程中云平台经营方与需求方之间的不完全信息以及相互竞争制约的关系导致制造服务难以抉择的问题，提出了一种基于不完全信息博弈模型的云制造群智能优化方法。以各自理性追求自身收益函数最大化为目标，针对需求方与云平台之间的利益竞争关系建立了基于不完全信息的静态博弈模型，并提出了需求方与云平台之间的竞争规则，通过海萨尼转换引入自然，将其转换为完全信息下的动态博弈得到贝叶斯扩展式，并证明了贝叶斯纳什均衡的存在性和唯一性。提出了一种基于高斯函数与扰动策略更新的粒子群算法对上述模型进行求解。仿真结果表明：改进算法相对其他算法有较快的收敛速度与较高的云制造系统总收益，不完全信息博弈模型能够兼顾不同类型的需求方提高云制造系统的总收益。

关键词: 云制造, 博弈, 不完全信息, 贝叶斯纳什均衡, 收益函数, 粒子群算法

Abstract:

In the process of cloud manufacturing, the incomplete information status and the mutual competition and restriction relationship between cloud platform operator and demander lead to the difficult choice of manufacturing services. A cloud manufacturing swarm intelligent optimization method based on incomplete information game model is proposed. A static game model based on incomplete information is established for the interest competition between demand-side and cloud platform, with the goal of rationally pursuing the maximization of their own revenue function. The competition rules between demand-side and cloud platform are proposed, which are introduced into nature through Harsanyi transformation and converted into a dynamic game under complete information to obtain Bayesian extended formula, and the existence and uniqueness of Bayesian Nash equilibrium are proved. A particle swarm optimization algorithm based on the update of Gaussian function and perturbation strategy is proposed to solve the above model. The simulation shows that the improved algorithm has faster convergence rate and higher total revenue of cloud manufacturing system compared with the other algorithms, and the incomplete information game model can take into account different types of demand side to improve the total revenue of cloud manufacturing system.

Key words: cloud manufacturing, the game, incomplete information, Bayesian Nash equilibrium, income function, PSO

中图分类号:

TP391.9

张坤鹏,王艳,纪志成 . 基于不完全信息博弈的云制造群智能优化方法[J]. 系统仿真学报, 2024, 36(4): 915-928.

Zhang Kunpeng,Wang Yan,Ji Zhicheng . Intelligent Optimization Method of Cloud Manufacturing Swarm Based on Incomplete Information Game[J]. Journal of System Simulation, 2024, 36(4): 915-928.

图/表 23

图1

图2

表1

表2

图3

图4

图5

图6

图7

表3

任务信息加工

候选资源	$O 1$	$O 2$	$O 3$	$O 4$	$O 5$	$O 6$
$R 1$	20/125/0.75	—	30/100/0.70	—	25/115/0.85	—
$R 2$	—	35/100/0.70	25/100/0.60	20/110/0.50	—	30/130/0.80
$R 3$	30/110/0.60	—	30/120/0.85	—	30/110/0.80	40/120/0.85
$R 4$	—	20/130/0.70	—	60/120/0.90	—	—
$R 5$	20/120/0.70	—	—	50/100/0.70	—	40/110/0.90
$R 6$	—	30/130/0.80	40/120/0.85	—	40/110/0.90	—
$R 7$	—	25/110/0.60	—	—	—	35/100/0.70
$R 8$	—	—	25/100/0.60	—	50/120/0.95	—
$R 9$	—	30/110/0.60	—	40/130/0.80	—	—
$R 10$	35/100/0.80	—	20/130/0.80	—	40/120/0.95	35/120/0.90
$R 11$	30/100/0.60	35/120/0.80	—	45/130/0.85	—	—
$R 12$	—	—	35/120/0.80	—	30/100/0.75	40/130/0.95
$R 13$	40/90/0.70	—	—	35/110/0.65	—	—
$R 14$	20/120/0.70	—	30/110/0.60	—	20/120/0.60	—
$R 15$	—	—	—	35/120/0.70	—	30/120/0.85
$R 16$	—	25/110/0.65	—	50/110/0.80	—	25/100/0.60

表3

图8

表4

表5

表6

最优解方案

算法	最优解方案
文献[7]	$R 5 → R 4 → R 10 → R 2 → R 1 → R 16$
文献[10]	$R 5 → R 3 → R 6 → R 2 → R 8 → R 16$
本文	$R 5 → R 4 → R 10 → R 2 → R 1 → R 16$

表6

表7

表8

图9

图10

表9

分布式候选资源集

任务	候选资源集
$O 1$	${R 1, R 3, R 5, R 10, R 11, R 13, R 14}$
$O 2$	${R 6, R 7, R 9, R 11, R 16}$
$O 3$	${R 1, R 3, R 6, R 8, R 10, R 12, R 13}$
$O 4$	${R 5, R 9, R 11, R 13, R 15, R 16}$
$O 5$	${R 1, R 3, R 6, R 8, R 10, R 12, R 14}$
$O 6$	${R 3, R 5, R 7, R 10, R 12, R 15, R 16}$

表9

表10

最优解方案

算法	资源选择方案
文献[7]	$R 5 → R 7 → R 10 → R 13 → R 1 → R 16$
文献[10]	$R 5 → R 3 → R 6 → R 2 → R 15 → R 16$
本文	$R 5 → R 7 → R 10 → R 13 → R 1 → R 16$

表10

图11

表11

表12

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关系	拒绝	接受
竞争	(a, b)	(c, d)
不竞争	(0, 0)	(0, 0.1v₂)

关系	拒绝	接受
竞争	(e, f )	(g, h)
不竞争	(0, 0)	(0, 0.1v₂)

算法	收益	C/元	t/min	Q	CPU/s
文献[7]	0.156	4 005	700	20.5	42.8
文献[10]	0.162	3 980	725	20.1	31.4
本文	0.177	3 935	675	20.5	30.6

算法	收益	C/元	S	CPU/s
文献[7]	0.116	852.5	0.8	42.8
文献[10]	0.115	877.5	0.8	31.4
本文	0.128	812.5	0.8	30.6

算法	总收益	C/元	t/min	Q	CPU/s
文献[7]	0.276	4 015	720	20.4	44.5
文献[10]	0.279	3 995	715	20.5	32.1
本文	0.314	3 945	680	20.4	31.5