Abstract
This paper reveals the surprising result that a single-parent non-elitist evolution strategy (ES) can be locally faster than the (1+1)-ES. The result is brought about by mirrored sampling and sequential selection. With mirrored sampling, two offspring are generated symmetrically or mirrored with respect to their parent. In sequential selection, the offspring are evaluated sequentially and the iteration is concluded as soon as one offspring is better than the current parent. Both concepts complement each other well. We derive exact convergence rates of the (1,λ)-ES with mirrored sampling and/or sequential selection on the sphere model. The log-linear convergence of the ES is preserved. Both methods lead to an improvement and in combination the (1,4)-ES becomes about 10% faster than the (1+1)-ES. Naively implemented into the CMA-ES with recombination, mirrored sampling leads to a bias on the step-size. However, the (1,4)-CMA-ES with mirrored sampling and sequential selection is unbiased and appears to be faster, more robust, and as local as the (1+1)-CMA-ES.
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.
Similar content being viewed by others
References
Arnold, D.V., Salomon, R.: Evolutionary gradient search revisited. IEEE Transactions on Evolutionary Computation 11(4), 480–495 (2007)
Arnold, D.V., Van Wart, D.C.S.: Cumulative step length adaptation for evolution strategies using negative recombination weights. 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. 545–554. Springer, Heidelberg (2008)
Auger, A., Brockhoff, D., Hansen, N.: Mirrored sampling and sequential selection for evolution strategies. Research Report RR-7249, INRIA Saclay—Île-de-France (June 2010)
Auger, A., Hansen, N.: Reconsidering the progress rate theory for evolution strategies in finite dimensions. In: Keijzer, et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 445–452. ACM Press, New York (2006)
Auger, A., Hansen, N.: Benchmarking the (1+1)-CMA-ES on the BBOB-2009 noisy testbed. In: Rothlauf, F., et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2009), Companion Material, pp. 2467–2472. ACM Press, New York (2009)
Hansen, N.: An analysis of mutative σ-self-adaptation on linear fitness functions. Evolutionary Computation 14(3), 255–275 (2006)
Hansen, N.: The CMA evolution strategy: a comparing review. In: Lozano, J., Larranaga, P., Inza, I., Bengoetxea, E. (eds.) Towards a New Evolutionary Computation. Advances on Estimation of Distribution Algorithms, pp. 75–102. Springer, Heidelberg (2006)
Hansen, N., Finck, S., Ros, R., Auger, A.: Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions. Tech. Rep. RR-6829, INRIA (2009), http://coco.gforge.inria.fr/bbob2010-downloads (updated February 2010)
Hansen, N., Finck, S., Ros, R., Auger, A.: Real-parameter black-box optimization benchmarking 2009: Noisy functions definitions. Tech. Rep. RR-6869, INRIA (2009), http://coco.gforge.inria.fr/bbob2010-downloads (updated February 2010)
Igel, C., Suttorp, T., Hansen, N.: A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies. In: Keijzer, et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 453–460. ACM Press, New York (2006)
Teytaud, O., Gelly, S., Mary, J.: On the ultimate convergence rates for isotropic algorithms and the best choices among various forms of isotropy. 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. 32–41. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brockhoff, D., Auger, A., Hansen, N., Arnold, D.V., Hohm, T. (2010). Mirrored Sampling and Sequential Selection for Evolution Strategies. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-15844-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15843-8
Online ISBN: 978-3-642-15844-5
eBook Packages: Computer ScienceComputer Science (R0)