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Proceedings of the 7th
    World Congress on Intelligent Control and Automation
           June 25 - 27, 2008, Chongqing, China



                         Particle Swarm Optimization based RBF Neural
                                Networks Learning Algorithm
                                           Qi Kang1, Jing An2, Dongsheng Yang1,3, Lei Wang1, Qidi Wu1
                    1)
                         College of Electronics and Information Engineering, Tongji University, Shanghai 200092, China
                                                         (E-mail: kangqi_kz@hotmail.com)
                           2)
                              Shanghai Institute of Technology, Shanghai 200235, China (E-mail: anjing_tj@163.com)
                                   3)
                                        Shanghai Municipal Informatization Commission, Shanghai 200040, China

     Abstract—Swarm intelligence optimization is introduced into RBF neural networks training in this paper, a novel RBF
neural networks learning algorithm based on particle swarm optimization is presented, and validated through numerical
simulation. Finally, the unite framework of this RBF algorithm based on natural-inspired computation is proposed.
     Keywords— Particle Swarm Optimization, RBF Neural Networks, Natural-inspired Computation



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978-1-4244-2114-5/08/$25.00 © 2008 IEEE.                                                   605


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                                                                                          610


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Ieee Xplore 4

  • 1. Proceedings of the 7th World Congress on Intelligent Control and Automation June 25 - 27, 2008, Chongqing, China Particle Swarm Optimization based RBF Neural Networks Learning Algorithm Qi Kang1, Jing An2, Dongsheng Yang1,3, Lei Wang1, Qidi Wu1 1) College of Electronics and Information Engineering, Tongji University, Shanghai 200092, China (E-mail: kangqi_kz@hotmail.com) 2) Shanghai Institute of Technology, Shanghai 200235, China (E-mail: anjing_tj@163.com) 3) Shanghai Municipal Informatization Commission, Shanghai 200040, China Abstract—Swarm intelligence optimization is introduced into RBF neural networks training in this paper, a novel RBF neural networks learning algorithm based on particle swarm optimization is presented, and validated through numerical simulation. Finally, the unite framework of this RBF algorithm based on natural-inspired computation is proposed. Keywords— Particle Swarm Optimization, RBF Neural Networks, Natural-inspired Computation RBF * 1 2 1,3 1 1 1) 200092 2) 200235 3) 200040 RBF RBF RBF 1 [3] RBF RBF [1-2] RBF RBF , 2 RBF RBF RBF [4] RBF L RBF L - * (70531020), RBF -(G0525002), - (A0401) -(CNGI-04-15-5A-2) CNGI 978-1-4244-2114-5/08/$25.00 © 2008 IEEE. 605 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.
  • 2. 2 / 2σ i2 ) Ri ( x ) = exp( − x − ci i = 1,2, quot; , m ( ) : [7] i x n ci σi RBF x i RBF x − ci x − ci x ci ’ RBF RBF RBF 1 RBF L Ri (x) ci RBF x − ci Ri (x ) 8 x ∈ Rn 1 m RBF Hardy 8 Multi-Quadric Multi-Quadric Duchon RBF RBF c ¦ wi Ri ( x) y = F ( x) = i = 1,2, quot;quot; , m 8 i =1 1 RBF 2 N RBF RBF RBF K x 1 RBF OLS [5] RBF RBF K RBF 2 x Kennedy Eberhart 1995 RBF [6] 3 ’ N C ¦ ¦ ( y dj ,i − y j ,i ) 2 J= i =1 j =1 606 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.
  • 3. y d,i y = 1.1* (1 − x + 2 * x 2 ) * e ( − x 2
  • 4. + 0.1* rand () / 2) j N i j rand () y j ,i j i @ C ε J ε = 1 5%) Tmax = 2000 K 5%) x max neur = 30 m = 20 3625%) 362 vmax = 2 ω C1 = 2, C 2 = 2 5%) ω m vmax ω C2 ω max neur Tmax C1 5%) ε 5%) J p = 0.9736 ε 5%) 5%) t =0 x v Jp =∞ J g = ( ∞, ! , ∞) ∞ p g while (t T max J p ε ) 5%) J for i = 1 : 1 : m J i J p (i ) J p (i ) = J i pi = xi end if if J i J g J g = J i p g = xi end if if end for 5%) for i = 1 : 1 : m 5%) 362 end for ω1,i (1) b1,i ω t = t +1 endwhile ω i,1 (2) b2 Jp ε t = Tmax ε 5%) G 5%) x best b1,1 w1,1 (1) -0.0675 -5.1148 1.7202 w1,1 (2) b2 -0.99 w1,2 (1) RBF w2,1 (2) b1,2 1.4020 0.8584 0.8424 5%) 69 w3,1 (2) w1,3 (1) -1.2511 0.9417 2.1611 b1,3 607 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.
  • 5. 5%) 362 5%) 3625%) @ 5%) 0 . 1 * randn
  • 6. 5%) 5%) 8 5%) 8 608 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.
  • 7. 5%) 5%)
  • 8. 8 8 8 8 3625%) 609 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.
  • 9. 8 3625%) 5%) 8 5%) 8 362 3625%)5%) 5%) 5 PSO-RBF 5%) 5%) 6 5%) 3625%) 5%) 3625%) 5%) 5%) 3625%) 5%) 5%) 3625%) 3625%) [1] L 5%) 362 @ L @ 362 5%)
  • 10. @ 5%)
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  • 12. 5%) [6] Kennedy J, Eberhart R C, “Particle swarm optimization,” Proc. IEEE International Conf. on Neural Networks. Piscataway: 5%) IEEE, Perth, 1995, pp 1942-1948. 5%) [7] Eberhart R C, Shi Y, “Particle swarm optimization: developments, 5%) applications and resources,” Proc. Congress on Evolutionary Computation. Piscataway: IEEE, Soul, 2001. 81-86 [8] Wang L, Kang Q, Wu Q.D, “Nature-inspired computation: effective realization of artificial intelligence,” System 362 Engineering Theory and Practice, 2007, 27 (5): 126-13 610 Authorized licensed use limited to: IEEE Xplore. Downloaded on April 7, 2009 at 13:18 from IEEE Xplore. Restrictions apply.