Abstract
In order to improve the behavior of Particle Swarm Optimization (PSO), the classical method is often extended by additional operations. Here, we are interested in how much “PSO” remains in this case, and how often the extension takes over the computation. We study the variant of PSO that applies random velocities (then called forced moves) as soon as the so-called potential of the swarm falls below a certain bound. We show experimentally that the number of iterations the swarm actually deviates from the classical PSO behavior is small as long as the particles are sufficiently far away from any local optimum. As soon as the swarm comes close to a local optimum, the number of forced moves increases significantly and approaches a value that depends on the swarm size and the problem dimension, but not on the actual fitness function, an observation that can be used as a stopping criterion. Additionally, we provide an explanation for the observed phenomenon in terms of the swarm’s potential.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6, 58–73 (2002); doi:10.1109/4235.985692
Lehre, P.K., Witt, C.: Finite first hitting time versus stochastic convergence in particle swarm optimisation (2011). http://arxiv.org/abs/1105.5540
Schmitt, M., Wanka, R.: Particle swarm optimization almost surely finds local optima. In: Proc. 15th Genetic and Evolutionary Computation Conference (GECCO), pp. 1629–1636 (2013); doi:10.1145/2463372.2463563
Schmitt, M., Wanka, R.: Particles prefer walking along the axes: Experimental insights into the behavior of a particle swarm. In: Companion of Proc. 15th Genetic and Evolutionary Computation Conference (GECCO), pp. 17–18 (2013); doi:10.1145/2464576.2464583
Shi, X.H., Liang, Y.C., Leeb, H.P., Lu, C., Wang, Q.: Particle swarm optimization-based algorithms for TSP and generalized TSP. Information Processing Letters, (103), 169–176 (2007); doi:10.1016/j.ipl.2007.03.010
Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.-P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, KanGAL Report Number 2005005 (Kanpur Genetic Algorithms Laboratory, IIT Kanpur) (2005)
van den Bergh, F., Engelbrecht, A.P.: A new locally convergent particle swarm optimiser. In: Proc. IEEE Int. Conf. on Systems, Man and Cybernetics (SMC) vol. 3, pp. 94–99 (2002); doi:10.1109/ICSMC.2002.1176018
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bassimir, B., Schmitt, M., Wanka, R. (2014). How Much Forcing Is Necessary to Let the Results of Particle Swarms Converge?. In: Siarry, P., Idoumghar, L., Lepagnot, J. (eds) Swarm Intelligence Based Optimization. ICSIBO 2014. Lecture Notes in Computer Science(), vol 8472. Springer, Cham. https://doi.org/10.1007/978-3-319-12970-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-12970-9_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12969-3
Online ISBN: 978-3-319-12970-9
eBook Packages: Computer ScienceComputer Science (R0)