三元相关性量子行为粒子群优化算法研究

doi:10.11959/j.issn.1000-436x.2015076

通信学报 ›› 2015, Vol. 36 ›› Issue (3): 208-215.doi: 10.11959/j.issn.1000-436x.2015076

三元相关性量子行为粒子群优化算法研究

吴涛¹,陈曦²,严余松³

¹ 成都信息工程学院计算机学院，四川成都 610225
² 西南民族大学计算机科学与技术学院，四川成都 610041
³ 西南交通大学计算机科学与技术学院，四川成都 610031

出版日期:2015-03-25 发布日期:2017-06-21
基金资助:
国家自然科学基金资助项目;四川省软科学研究计划基金资助项目;四川省科技支撑计划基金资助项目

Study of the ternary correlation quantum-behaved PSO algorithm

Tao WU¹,Xi CHEN²,Yu-song YAN³

¹ Department of Computer Science, Chengdu University of Information Technology, Chengdu 610225,China
² School of Computer Science ＆ Technology,Southwest University for Nationalities, Chengdu 610041,China
³ School of Computer Science ＆ Technology,Southwest Jiaotong University, Chengdu 610031,China

Online:2015-03-25 Published:2017-06-21
Supported by:
The National Natural Science Foundation of China;Sichuan Province Soft Science Research Project;Sichuan Province Science Support Project

摘要/Abstract

摘要：

为了提高QPSO算法的收敛性能，在对随机因子进行分析的基础上提出了三元相关性QPSO(TC-QPSO, ternary correlation QPSO)算法。该算法使用正态Copula函数建立了粒子对自身经验信息、群体共享信息以及粒子当前位置与群体平均最好位置的距离信息之间的内在认知和联系，并利用Cholesky平方根公式给出了三元相关因子的生成方法。对测试函数的仿真结果证明，当三元相关因子u与r1或r2之间存在负线性相关关系时，TC-QPSO算法可以获得比标准QPSO算法更好的优化性能。

关键词: 粒子群优化, 量子粒子群优化, 量子势阱, 正态Copula函数, 收敛

Abstract:

In order to more effectively utilize existing information and improve QPSO's (quantum-behaved particle swarm optimization) convergence performance, the ternary correlation QPSO (TC-QPSO) algorithm was proposed based on the analysis of the random factors in location formula. The novel algorithm changed the information independent ran-dom processing method of standard QPSO and established internal relations during particles' own experience information, group sharing information and the distance from the particles' current location to the population mean best position using normal copula functions.Then, the method of generating ternary correlation factors was given by using the Cholesky square root formula. The simulation results of the test functions showed that TC-QPSO algorithm outperforms the stan-dard QPSO algorithm in terms of optimization results, given that the negative linear correlation exists betweenu and r1 or u andr2.

Key words: particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), quantum poten-tial well, normal copula function; convergence

吴涛,陈曦,严余松. 三元相关性量子行为粒子群优化算法研究[J]. 通信学报, 2015, 36(3): 208-215.

Tao WU,Xi CHEN,Yu-song YAN. Study of the ternary correlation quantum-behaved PSO algorithm[J]. Journal on Communications, 2015, 36(3): 208-215.

图/表 4

表1

单峰函数"

名称	表达式	搜索范围	初始化范围	最优解和最优值
Sphere	$f_{1} (x) = \sum_{i = 1}^{D} x_{i}^{2}$	[-100,100]^D	[-100,50]^D	f ₁(0,0,…,0)=0
Rosenbrock	$f_{2} (x) = [100 {(x_{i + 1} - x_{i}^{2})}^{2} + {(x_{i} - 1)}^{2}]$	[-10,10]^D	[-10,10]^D	f ₂(1,1,…,1)=0

表1

表2

多峰函数"

名称	表达式	搜索范围	初始化范围	最优解和最优值
Rastrigin	$f_{3} (x) = \sum_{i = 1}^{D} (x_{i}^{2} - 10 \cos (2 π x_{i}) + 10)$	[-5.12,5.12]^D	[-5.12,2]^D	f ₃(0,0,…,0)=0
Griewank	$f_{4} (x) = \sum_{i = 1}^{D} \frac{x_{i}^{2}}{4000} - \prod_{i = 1}^{D} \cos (\frac{x_{i}}{\sqrt{i}}) + 1$	[-600,600]^D	[-600,200] ^D	f ₄(0,0,…,0)=0
Ackley	$f_{5} (x) = - 20 \exp (- 0.2 \sqrt{\frac{1}{D} \sum_{i = 1}^{D} x_{i}^{2}}) - \exp (\frac{1}{D} \sum_{i = 1}^{D} \cos (2 π x_{i})) + 20 + e$	[-32.786,32.786]^D	[-32.786,16]^D	f ₅(0,0,…,0)=0
Expanded Shaffer	f ₆(X)=g(x₁,x₂)+g(x₂,x₃)+…+g(x_D-1,x_D)+g(x_D,x₁)	[-100,100]^D	[-100,50] ^D	f ₆(0,0,…,0)=0
	$g (x, y) = 0.5 + \frac{{(\sin \sqrt{x^{2} + y^{2}})}^{2} - 0.5}{{(1.0 + 0.001 (\sqrt{x^{2} + y^{2}}))}^{2}}$

表2

表3

图1

参考文献 16

[1]	KENNEDY J , EBERHART R . Particle swarm optimization[A]. Proceedings of the IEEE International Conference on Neural Networks[C]. Perth, 1995.1942-1948.
[2]	BERGH F V D . An Analysis of Particle Swarm Optimizers[D]. South Africa: University of Pretoria, 2002.
[3]	孙俊，方伟，吴小俊等．量子行为粒子群优化：原理及其应用[M]. 北京：清华大学出版社， 2011. SUN J , FANG W , WU X J , et al. Quantum-behaved Particle Swarm Optimization Principle and its Application[M]. Beijing: Tsinghua University Press, 2011.
[4]	MIKKI S , KISHK A . Investigation of the quantum particle swarm optimization technique for electromagnetic applications[A]. IEEE International Symposium on Antennas and Propagation Society[C]. 2005.45-48.
[5]	MIKKI S , KISHK A . Quantum particle swarm optimization for electromagnetics[J]. IEEE Transactions on Antennas and Propagation, 2006,54(10):2764-2775.
[6]	李盼池，王海英，宋考平等．量子势阱粒子群优化算法的改进研究[J]．物理学报， 2012,61(06):19-28. LI P C , WANG H Y , SONG K P , et al. Research on the improvement of quantum potential well-based particle swarm optimization algorithm[J]. Acta Physica Sinica, 2012,61(06):19-28.
[7]	孙俊．量子行为粒子群优化算法[D]．江苏：江南大学， 2009. SUN J . Particle Swarm Optimization With Particles Having Quantum Behavior[D]. Jiangsu: Jiangnan University, 2009.
[8]	CLERC M , KENNEDY J . The particle swarm-explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Computation, 2002,6(1):58-73.
[9]	郭文忠，陈国龙．离散粒子群优化算法及其应用[M]. 北京：清华大学出版社， 2012. GUO W Z , CHEN G L . Discrete Particle Swarm Optimization Algorithm and its Application[M]. Beijing: Tsinghua University Press, 2012.
[10]	ARUMUGAM M S , RAO M V C , TAN A W C . A novel and effective particle swarm optimization like algorithm with extrapolation technique[J]. Applied Soft Computing, 2009,9(1):308-320.
[11]	申元霞．相关性粒子群优化模型及其应用研究[D]．成都：西南交通大学， 2010. SHEN Y X . Reaearch on Corrlative Particle Swarm Optimization Model and its Application[D]. Chengdu: Southwest Jiaotong University, 2010.
[12]	韦艳华，张世英． Copula 理论及其在金融分析上的应用[M]. 北京：清华大学出版社， 2008. WEI Y H , ZHANG S Y . Copula Theory and Its Applications in Financial Analysis[M]. Beijing: Tsinghua University Press, 2008.
[13]	CHERUBINI U , LUCIANO E , VECCHIATO W . Copula Methods in Finance[M]. England: John Wiley＆Sons Ltd, 2004.
[14]	SKLAR A . Fonctions de Répartition à N Dimensions et Leurs Marges[D]. Paris: Université Paris, 1959.
[15]	SKLAR A . Random variables, distribution functions, and copulas: A personal look backward and forward[J]. Lecture Notes-Monograph Series, 1996,28:1-14.
[16]	NELSEN R B . An Introduction to Copulas[M]. New York: Springer, 2006.

模型	f₁	f₂	f₃	f₄	f₅	f₆
PTC-QPSO	2.87×10^-206	17.01	19.48	0.48	1.48×10^-13	6.51×10^-8
QPSO	4.24×10^-302	16.55	23.41	0.40	2.66×10^-15	1.91×10^-9
TC-QPSO1	0	16.54	12.80	1.56	2.66×10^-15	0
TC-QPSO2	3.81×10^-205	13.99	15.01	0	6.22×10^-15	4.52×10^-7
TC-QPSO3	0	14.69	11.95	0	1.33×10^-14	2.78×10^-8

三元相关性量子行为粒子群优化算法研究

Study of the ternary correlation quantum-behaved PSO algorithm

在线阅读

PDF下载

可视化

被引次数

摘要/Abstract

引用本文

使用本文

图/表 4

参考文献 16

相关文章 15

Metrics

推荐阅读 0

[1]	赵庶旭, 韦萍, 王小龙. 多任务并发边缘计算环境中最优联盟结构生成策略[J]. 通信学报, 2023, 44(2): 172-184.
[2]	宋鑫, 倪淑燕, 张喆, 廖育荣, 雷拓峰. 面向不等差错保护的低误码平台LT编码算法[J]. 通信学报, 2022, 43(6): 85-97.
[3]	李翠然, 王雪洁, 谢健骊, 吕安琪. 基于改进PSO的铁路监测线性无线传感器网络路由算法[J]. 通信学报, 2022, 43(5): 155-165.
[4]	曹阳, 钟烨, 彭醇陵, 彭小峰. 基于混合供能和能量协作的异构网络能量效率优化算法[J]. 通信学报, 2022, 43(3): 135-147.
[5]	毛伊敏, 甘德瑾, 廖列法, 陈志刚. 基于Spark框架和ASPSO的并行划分聚类算法[J]. 通信学报, 2022, 43(3): 148-163.
[6]	李传煌, 陈泱婷, 唐晶晶, 楼佳丽, 谢仁华, 方春涛, 王伟明, 陈超. QL-STCT：一种SDN链路故障智能路由收敛方法[J]. 通信学报, 2022, 43(2): 131-142.
[7]	田有亮, 袁延森, 高鸿峰, 杨旸, 熊金波. 基于激励相容的权益分散共识算法[J]. 通信学报, 2022, 43(12): 101-112.
[8]	宋鑫, 程乃平, 倪淑燕, 廖育荣, 雷拓峰. 采用定长节点分类窗口的低误码平台LT编码算法[J]. 通信学报, 2021, 42(9): 31-42.
[9]	陶梅霞, 王栋, 孙瑞, 张乃夫. 联邦学习中基于时分多址接入的用户调度策略[J]. 通信学报, 2021, 42(6): 1-29.
[10]	蔡剑平, 刘西蒙, 熊金波, 应作斌, 吴英杰. 差分隐私下多重一致性约束问题的逼近方法[J]. 通信学报, 2021, 42(6): 107-117.
[11]	苏新, 薛淏阳, 周一青, 朱金秀. 面向海洋观监测传感网的计算卸载方法研究[J]. 通信学报, 2021, 42(5): 149-163.
[12]	孙爱晶, 李世昌, 张艺才. 基于PSO优化模糊C均值的WSN分簇路由算法[J]. 通信学报, 2021, 42(3): 91-99.
[13]	陈迪, 邱菡, 张万里, 朱会虎, 朱俊虎, 王清贤. 基于路由状态因果链的域间路由不稳定溯源检测方法[J]. 通信学报, 2021, 42(12): 76-87.
[14]	杨国伟, 黄兆标, 樊冰, 周雪芳, 毕美华. 基于可见光通信的室内定位与定向系统[J]. 通信学报, 2020, 41(12): 162-170.
[15]	裴家正,黄勇,董云龙,陈小龙. 改进的SMC-CBMeMBer前向后向平滑检测前跟踪算法[J]. 通信学报, 2019, 40(8): 102-113.