Particle Swarm Optimization with Reduction for Global Optimization Problems
This paper presents an algorithm of particle swarm
optimization with reduction for global optimization problems. Particle
swarm optimization is an algorithm which refers to the collective
motion such as birds or fishes, and a multi-point search algorithm
which finds a best solution using multiple particles. Particle
swarm optimization is so flexible that it can adapt to a number
of optimization problems. When an objective function has a lot of
local minimums complicatedly, the particle may fall into a local
minimum. For avoiding the local minimum, a number of particles are
initially prepared and their positions are updated by particle swarm
optimization. Particles sequentially reduce to reach a predetermined
number of them grounded in evaluation value and particle swarm
optimization continues until the termination condition is met. In order
to show the effectiveness of the proposed algorithm, we examine the
minimum by using test functions compared to existing algorithms.
Furthermore the influence of best value on the initial number of
particles for our algorithm is discussed.
[1] E. Aiyoshi and K. Yasuda, Metaheuristics and Applications, Ohmsha,
2007.
[2] H. Kitano, Genetic Algorithm vol.4, Sangyotosho, 2000.
[3] K. Price, R. Storn, and J. Lampinen, Differential Evolution, Springer-
Verlag, 2005.
[4] J. Kennedy and R. Eberhart Particle swarm optimization, IEEE Proc.
Int. Conf. Neural Networks, pp.1942-1948, 1995.
[5] S. Kinoshita, A. Ishigame and K. Yasuda, Particle swarm optimization
with hierarchical structure, The Institute of Electrical Engineers of
Japan, vol.130, pp.100-107, 2009.
[6] W. Langdon and R. Poli, Evolving problems to learn about particle
swarm optimization and other search algorithms, IEEE Trans. Evolutionary
Computation, vol.11, no.5, pp.561-578, 2007.
[7] J. Liang, A. Qin, P. Suganthan, and S. Baskar, Comprehensive learning
particle swarm optimization for global optimization of multimodal
functions, IEEE Trans. Evolutionary Computation, vol.10, no.3, pp.281-
295, 2006.
[8] K. Parsopoulos and M. Vrahatis, On the computation of all global minimizers
through particle swarm optimization. IEEE Trans. Evolutionary
Computation, vol.8, no.3, pp.211-224, 2004.
[9] Y. Shi, Particle swarm optimization, IEEE Connections, vol.2, no.1,
pp.8-13, 2004.
[10] S. Tsuda, T. Liu, and M. Maeda, Solution search algorithm of particle
swarm optimization with perturbation term, ICIC Express Letters, vol.5,
no.5, pp.1515-1521, 2011.
[11] S. Wu and T. Chow, Self-organizing and self-evolving neurons: A new
neural network for optimization, IEEE Trans. Neural Networks, vol.18,
no.2, pp.385-396, 2007.
[12] W. Yeh, Y. Lin, Y. Chung, and M. Chih, A particle swarm optimization
approach based on monte carlo simulation for solving the complex network
reliability problem, IEEE Trans. Reliability, vol.59, no.1, pp.212-
221, 2010.
[13] R. Reed, Pruning algorithmsÔÇöA survey, IEEE Trans. Neural Networks,
vol.4, pp.740-747, 1993.
[14] M. Ishikawa, Structural learning with forgetting, Neural Networks, vol.9,
pp.509-521, 1996.
[15] M. Maeda, N. Shigei, and H. Miyajima, Adaptive vector quantization
with creation and reduction grounded in the equinumber principle, Journal
of Advanced Computational Intelligence and Intelligent Informatics,
vol.9, pp.599-606, 2005.
[16] M. Maeda, N. Shigei, H. Miyajima, and K. Suzaki, Reduction models
in competitive learning founded on distortion standards, Journal of Advanced
Computational Intelligence and Intelligent Informatics, vol.12,
pp.314-323, 2008.
[1] E. Aiyoshi and K. Yasuda, Metaheuristics and Applications, Ohmsha,
2007.
[2] H. Kitano, Genetic Algorithm vol.4, Sangyotosho, 2000.
[3] K. Price, R. Storn, and J. Lampinen, Differential Evolution, Springer-
Verlag, 2005.
[4] J. Kennedy and R. Eberhart Particle swarm optimization, IEEE Proc.
Int. Conf. Neural Networks, pp.1942-1948, 1995.
[5] S. Kinoshita, A. Ishigame and K. Yasuda, Particle swarm optimization
with hierarchical structure, The Institute of Electrical Engineers of
Japan, vol.130, pp.100-107, 2009.
[6] W. Langdon and R. Poli, Evolving problems to learn about particle
swarm optimization and other search algorithms, IEEE Trans. Evolutionary
Computation, vol.11, no.5, pp.561-578, 2007.
[7] J. Liang, A. Qin, P. Suganthan, and S. Baskar, Comprehensive learning
particle swarm optimization for global optimization of multimodal
functions, IEEE Trans. Evolutionary Computation, vol.10, no.3, pp.281-
295, 2006.
[8] K. Parsopoulos and M. Vrahatis, On the computation of all global minimizers
through particle swarm optimization. IEEE Trans. Evolutionary
Computation, vol.8, no.3, pp.211-224, 2004.
[9] Y. Shi, Particle swarm optimization, IEEE Connections, vol.2, no.1,
pp.8-13, 2004.
[10] S. Tsuda, T. Liu, and M. Maeda, Solution search algorithm of particle
swarm optimization with perturbation term, ICIC Express Letters, vol.5,
no.5, pp.1515-1521, 2011.
[11] S. Wu and T. Chow, Self-organizing and self-evolving neurons: A new
neural network for optimization, IEEE Trans. Neural Networks, vol.18,
no.2, pp.385-396, 2007.
[12] W. Yeh, Y. Lin, Y. Chung, and M. Chih, A particle swarm optimization
approach based on monte carlo simulation for solving the complex network
reliability problem, IEEE Trans. Reliability, vol.59, no.1, pp.212-
221, 2010.
[13] R. Reed, Pruning algorithmsÔÇöA survey, IEEE Trans. Neural Networks,
vol.4, pp.740-747, 1993.
[14] M. Ishikawa, Structural learning with forgetting, Neural Networks, vol.9,
pp.509-521, 1996.
[15] M. Maeda, N. Shigei, and H. Miyajima, Adaptive vector quantization
with creation and reduction grounded in the equinumber principle, Journal
of Advanced Computational Intelligence and Intelligent Informatics,
vol.9, pp.599-606, 2005.
[16] M. Maeda, N. Shigei, H. Miyajima, and K. Suzaki, Reduction models
in competitive learning founded on distortion standards, Journal of Advanced
Computational Intelligence and Intelligent Informatics, vol.12,
pp.314-323, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64379", author = "Michiharu Maeda and Shinya Tsuda", title = "Particle Swarm Optimization with Reduction for Global Optimization Problems", abstract = "This paper presents an algorithm of particle swarm
optimization with reduction for global optimization problems. Particle
swarm optimization is an algorithm which refers to the collective
motion such as birds or fishes, and a multi-point search algorithm
which finds a best solution using multiple particles. Particle
swarm optimization is so flexible that it can adapt to a number
of optimization problems. When an objective function has a lot of
local minimums complicatedly, the particle may fall into a local
minimum. For avoiding the local minimum, a number of particles are
initially prepared and their positions are updated by particle swarm
optimization. Particles sequentially reduce to reach a predetermined
number of them grounded in evaluation value and particle swarm
optimization continues until the termination condition is met. In order
to show the effectiveness of the proposed algorithm, we examine the
minimum by using test functions compared to existing algorithms.
Furthermore the influence of best value on the initial number of
particles for our algorithm is discussed.", keywords = "Particle swarm optimization, Global optimization,Metaheuristics, Reduction.", volume = "5", number = "11", pages = "1783-5", }