Abstract
One of the challenges for modern search methods is resolving multidimensional tasks where optimization parameters are hundreds, thousands and more. Many evolutionary, swarm and adaptive methods, which perform well on numerical test with up to 10 dimensions are suffering insuperable stagnation when are applied to the same tests extended to 50, 100 and more dimensions. This article presents an original investigation on Free Search, Differential Evolution and Particle Swarm Optimization applied to multidimensional versions of several heterogeneous real-value numerical tests. The aim is to identify how dimensionality reflects on the search space complexity, in particular to evaluate relation between tasks’ dimensions’ number and corresponding iterations’ number required by used methods for reaching acceptable solution with non-zero probability. Experimental results are presented and analyzed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
MacNish, C., Yao, X.: Direction matters in high-dimensional optimisation. In: IEEE Congress on Evolutionary Computation, pp. 2372–2379 (2008)
Eberhart R., Kennedy J.: Particle swarm optimisation. In: Proceedings of the 1995 IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE Press (1995)
Keane, A.J.: A brief comparison of some evolutionary optimization methods. In: Rayward-Smith, V.J., Osman, I.H., Reeves, C.R., Smith, G.D. (eds.) Modern Heuristic Search Methods, pp. 255–272. John Wiley, Chichester (1996)
Penev, K.: Free search of real value or how to make computers think. St. Qu, UK (2008). ISBN 978-0-9558948-0-0
Liu, P., Lau, F., Lewis, M.J., Wang, C.: A new asynchronous parallel evolutionary algorithm for function optimization. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 401–410. Springer, Heidelberg (2002)
Liu, P., Lewis, M.J.: Communication aspects of an asynchronous parallel evolutionary algorithm In: Proceedings of the Third International Conference on Communications in Computing, Las Vegas, NV, 24–27 June 2002, pp. 190–195
Storn, R.: Constrained optimisation. Dr. Dobb’s J. pp. 119–123 (1994)
Yanga, Z., Tanga, K., Yaoa, X.: Large scale evolutionary optimization using cooperative coevolution. Inf. Sci. 178(15), 2985–2999 (2008)
Yang, Z., Tang, K., Yao, X.: Differential evolution for high-dimensional function optimization. In: IEEE Congress on Evolutionary Computation (2007)
Noman, N., Iba, H.: Enhancing differential evolution performance with local search for high dimensional function optimization. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 967–974 (2005)
Hendtlass, T.: Particle swarm optimization and high dimensional problem spaces. In: IEEE Congress on Evolutionary Computation (CEC 2009), pp. 1988–1994 (2009)
Hedar, A.-R.: Test functions for unconstrained global optimization. http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/Page2376.htm. Accessed 4 April 2013
Vasileva, V., Penev, K.: Free search and particle swarm optimization applied to non-constrained test. In: Proceedings of Optimization of Mobile Communications Networks, pp. 20–27 (2013). ISBN 978-0-9563140-4-8
Eberhart, R., Shi, Y.: Comparing inertia weights and construction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, pp. 84–89 (2000)
Penev, K.: Adaptive intelligence - essential aspects. J. Inf. Technol. Control VII(4), 8–17 (2009). ISSN 1312–2622
Acknowledgements
I would like to thank to my students Asim Al Nashwan, Dimitrios Kalfas, Georgius Haritonidis, and Michael Borg for the design, implementation and overclocking of desktop PC used for completion of the experiments presented in this article.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Penev, K. (2014). Free Search in Multidimensional Space. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-662-43880-0_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43879-4
Online ISBN: 978-3-662-43880-0
eBook Packages: Computer ScienceComputer Science (R0)