Abstract
An evolutionary algorithm (EA) is said to be spatially structured when its individuals are arranged in an incomplete graph and interact only with their neighbors. Previous studies argue that spatially structured EAs are less likely to converge prematurely to local optima. Furthermore, they have been initially designed for distributed computing and it is often claimed that their parallelization is simpler than the equivalent non-structured algorithm. However, most of the empirical studies on spatially structured EAs use a predefined and fixed population size, whereas the full potential of this or any other any kind of EA can only be explored if the population size is properly set. This paper investigates optimal population sizes of spatially structured EAs (cellular EAs, in particular) and the relationship between that size, convergence speed and the degree of the structuring network. EAs structured by regular graphs with different degrees have been tested on different types of fitness landscapes. We conclude that in most cases graphs with low degree require smaller populations to converge consistently to global optima. However, if the population size is properly set, EAs structured by graphs with higher degrees not only converge to global optima with high probability, but also converge faster.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. IEEE Trans. Evol. Comput. 6(5), 443–462 (2002)
Alba, E., Dorronsoro, B.: The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Trans. Evol. Comput. 9, 126–142 (2005)
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford (1996)
Cantú-Paz, E.: Migration policies, selection pressure, and parallel EAs. Journal of Heuristics 7(4), 311–334 (2001)
Fernandes, C.M., Laredo, J.L.J., Merelo, J.J., Cotta, C., Rosa, A.C.: Dynamic and Partially Connected Ring Topologies for Evolutionary Algorithms with Structured Populations, EvoApplications 2014: Applications of Evolutionary Computation, pp. 665–677 (2014)
Giacobini, M., Tomassini, M., Tettamanzi, A.: Takeover time curves in random and small-world structured populations. In: Proceedings of the 7th GECCO, pp. 1333–1340 (2005)
Giacobini, M., Tomassini, M., Tettamanzi, A.G.B., Alba, E.: Selection intensity in cellular evolutionary algorithms for regular lattices. IEEE Trans. Evol. Comput. 9, 489–505 (2005)
Laredo, J.L.J., Bouvry, P., González, D.L., Fernandéz de la Vega, F., Arenas, M.G., Merelo, J.J., Fernandes, C.M.: Designing robust volunteer-based evolutionary algorithms. Genet. Program Evol. Mach. 15(3), 221–244 (2014)
Payne, J.L, Eppstein, M.J.: Emergent mating topologies in spatially structured genetic algorithms. In: Proceedings of 8th GECCO, pp. 207–214 (2006)
Réka, A., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–94 (2000)
Sarma J., De Jong, K.: An analysis of the effect of the neighborhood size and shape on local selection algorithms. In: Proceedings of International Conference on Parallel Problem Solving from Nature IV, LNCS 1141, pp. 236–244. Springer (1996)
Sastry, K.: Evaluation-relaxation schemes for genetic and evolutionary algorithms. M.Sc. thesis, University of Illinois, Urbana, IL, USA (2001)
Tomassini, M.: Spatially Structured Evolutionary Algorithms. Springer, Heidelberg (2005)
Whitacre, J.M., Sarker, R.A., Pham, Q.: The self-organization of interaction networks for nature-inspired optimization. IEEE Trans. Evol. Comput. 12, 220–230 (2008)
Acknowledgements
First author wishes to thank FCT, Ministério da Ciência e Tecnologia, his Research Fellowship SFRH/BPD/111065/2015). This work was supported by FCT PROJECT [UID/EEA/50009/2013].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Fernandes, C.M., Laredo, J.L.J., Rosa, A.C. (2018). Spatially Structured Evolutionary Algorithms: Graph Degree, Population Size and Convergence Speed. In: Ivanović, M., Bădică, C., Dix, J., Jovanović, Z., Malgeri, M., Savić, M. (eds) Intelligent Distributed Computing XI. IDC 2017. Studies in Computational Intelligence, vol 737. Springer, Cham. https://doi.org/10.1007/978-3-319-66379-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-66379-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66378-4
Online ISBN: 978-3-319-66379-1
eBook Packages: EngineeringEngineering (R0)