Abstract
When a simple real-valued estimation of distribution algorithm (EDA) with Gaussian model and maximum likelihood estimation of parameters is used, it converges prematurely even on the slope of the fitness function. The simplest way of preventing premature convergence by multiplying the variance estimate by a constant factor k each generation is studied. Recent works have shown that when increasing the dimensionality of the search space, such an algorithm becomes very quickly unable to traverse the slope and focus to the optimum at the same time. In this paper it is shown that when isotropic distributions with Gaussian or Cauchy distributed norms are used, the simple constant setting of k is able to ensure a reasonable behaviour of the EDA on the slope and in the valley of the fitness function at the same time.
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
Preview
Unable to display preview. Download preview PDF.
References
Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms. GENA. Kluwer Academic Publishers, Dordrecht (2002)
Larrañaga, P., Lozano, J.A., Bengoetxea, E.: Estimation of distribution algorithms based on multivariate normal distributions and gaussian networks. Technical Report KZZA-IK-1-01, Dept. of Computer Science and Artificial Intelligence, University of Basque Country (2001)
Bosman, P.A.N., Thierens, D.: Expanding from discrete to continuous estimation of distribution algorithms: The IDEA. In: PPSN VI: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, London, UK, pp. 767–776. Springer, Heidelberg (2000)
Rudlof, S., Köppen, M.: Stochastic hill climbing by vectors of normal distributions. In: First Online Workshop on Soft Computing, Nagoya, Japan (1996)
Ahn, C.W., Ramakrishna, R.S., Goldberg, D.E.: Real-coded bayesian optimization algorithm: Bringing the strength of BOA into the continuous world. In: Deb, K., Poli, R., Banzhaf, W., Beyer, H.-G., Burke, E.K., Darwan, P.J., Dasgupta, D., Floreano, D., Foster, J.A., Harman, M., Holland, O., Lanzi, P.L., Spector, L., Tettamanzi, A., Thierens, D., Tyrrell, A.M. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 840–851. Springer, Heidelberg (2004)
Yuan, B., Gallagher, M.: On the importance of diversity maintenance in estimation of distribution algorithms. In: Beyer, H.G., O’Reilly, U.M. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference GECCO 2005, vol. 1, pp. 719–726. ACM Press, New York (2005)
Ocenasek, J., Kern, S., Hansen, N., Koumoutsakos, P.: A mixed bayesian optimization algorithm with variance adaptation. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 352–361. Springer, Heidelberg (2004)
Grahl, J., Minner, S., Rothlauf, F.: Behaviour of UMDAc with truncation selection on monotonous functions. In: IEEE Congress on Evolutionary Computation, CEC 2005, vol. 3, pp. 2553–2559 (2005)
Gonzales, C., Lozano, J., Larranaga, P.: Mathematical modelling of UMDAc algorithm with tournament selection. International Journal of Approximate Reasoning 31(3), 313–340 (2002)
Grahl, J., Bosman, P.A.N., Rothlauf, F.: The correlation-triggered adaptive variance scaling IDEA. In: Proceedings of the 8th annual conference on Genetic and Evolutionary Computation Conference - GECCO 2006, pp. 397–404. ACM Press, New York (2006)
Bosman, P.A.N., Grahl, J., Rothlauf, F.: SDR: A better trigger for adaptive variance scaling in normal EDAs. In: GECCO 2007: Proceedings of the 9th annual conference on Genetic and Evolutionary Computation, pp. 492–499. ACM Press, New York (2007)
Yuan, B., Gallagher, M.: A mathematical modelling technique for the analysis of the dynamics of a simple continuous EDA. In: IEEE Congress on Evolutionary Computation, CEC 2006, Vancouver, Canada, pp. 1585–1591. IEEE Press, Los Alamitos (2006)
Pošík, P.: Gaussian EDA and truncation selection: Setting limits for sustainable progress. In: IEEE SMC International Conference on Distributed Human-Machine Systems, DHMS 2008, Athens, Greece. IEEE, Los Alamitos (2008)
Pošík, P.: Truncation selection and gaussian EDA: Bounds for sustainable progress in high-dimensional spaces. In: Giacobini, M., Brabazon, A., Cagnoni, S., Di Caro, G.A., Drechsler, R., Ekárt, A., Esparcia-Alcázar, A.I., Farooq, M., Fink, A., McCormack, J., O’Neill, M., Romero, J., Rothlauf, F., Squillero, G., Uyar, A.Ş., Yang, S. (eds.) EvoWorkshops 2008. LNCS, vol. 4974, pp. 525–534. Springer, Heidelberg (2008)
Beyer, H.G., Deb, K.: On self-adaptive features in real-parameter evolutionary algorithms. IEEE Trans. on Evol. Comp. 5(3), 250–270 (2001)
Grahl, J., Bosman, P.A.N., Minner, S.: Convergence phases, variance trajectories, and runtime analysis of continuous EDAs. In: GECCO 2007: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pp. 516–522. ACM Press, New York (2007)
Rudolph, G.: Local convergence rates of simple evolutionary algorithms with cauchy mutations. IEEE Transactions on Evolutionary Computation 1, 249–258 (1997)
Obuchowicz, A.: Multidimensional mutations in evolutionary algorithms based on real-valued representation. Int. J. Systems Science 34(7), 469–483 (2003)
Hansen, N., Gemperle, F., Auger, A., Koumoutsakos, P.: When do heavy-tail distributions help? In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 62–71. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pošík, P. (2008). Preventing Premature Convergence in a Simple EDA Via Global Step Size Setting. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_55
Download citation
DOI: https://doi.org/10.1007/978-3-540-87700-4_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87699-1
Online ISBN: 978-3-540-87700-4
eBook Packages: Computer ScienceComputer Science (R0)