Abstract
This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization.
Work partially funded by FUI of System@tic Paris-Region ICT cluster through contract DGT 117 407 Complex Systems Design Lab (CSDL).
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
Addis, B., Cassioli, A., Locatelli, M., Schoen, F.: Global optimization for the design of space trajectories. Optimization On Line, 11 (2008)
Auger, A., Hansen, N.: A restart CMA evolution strategy with increasing population size. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), pp. 1769–1776. IEEE Press (2005)
García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC 2005 special session on real parameter optimization. Journal of Heuristics 15, 617–644 (2009)
Hansen, N.: Compilation of results on the 2005 CEC benchmark function set (May 2006)
Hansen, N.: Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed. In: Rothlauf, F. (ed.) GECCO Companion, pp. 2389–2396. ACM (2009)
Hansen, N.: References to CMA-ES applications (2009), http://www.lri.fr/~hansen/cmaapplications.pdf
Hansen, N., Auger, A., Finck, S., Ros, R.: Real-parameter black-box optimization benchmarking 2012: Experimental setup. Technical report, INRIA (2012)
Hansen, N., Finck, S., Ros, R., Auger, A.: Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions. Technical Report RR-6829, INRIA (2009) (updated, February 2010)
Hansen, N., Kern, S.: Evaluating the CMA Evolution Strategy on Multimodal Test Functions. 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. 282–291. Springer, Heidelberg (2004)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)
Hansen, N., Ros, R.: Benchmarking a weighted negative covariance matrix update on the BBOB-2010 noiseless testbed. In: GECCO 2010: Proceedings of the 12th Annual Conference Comp. on Genetic and Evolutionary Computation, pp. 1673–1680. ACM, New York (2010)
Jastrebski, G.A., Arnold, D.V.: Improving evolution strategies through active covariance matrix adaptation. In: IEEE Congress on Evolutionary Computation, CEC 2006, pp. 2814–2821 (2006)
Loshchilov, I., Schoenauer, M., Sebag, M.: Black-box Optimization Benchmarking of NIPOP-aCMA-ES and NBIPOP-aCMA-ES on the BBOB-2012 Noiseless Testbed. In: GECCO 2012: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation. ACM (page to appear, 2012)
Loshchilov, I., Schoenauer, M., Sebag, M.: Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy. In: GECCO 2012 Proceedings. ACM (page to appear, 2012)
Stracquadanio, G., La Ferla, A., De Felice, M., Nicosia, G.: Design of robust space trajectories. In: Research and Development in Intelligent Systems XXVIII, pp. 341–354. Springer (2011)
Vinko, T., Izzo, D.: Global Optimisation Heuristics and Test Problems for Preliminary Spacecraft Trajectory Design. Technical Report GOHTPPSTD, European Space Agency (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Loshchilov, I., Schoenauer, M., Sebag, M. (2012). Alternative Restart Strategies for CMA-ES. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32937-1_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-32937-1_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32936-4
Online ISBN: 978-3-642-32937-1
eBook Packages: Computer ScienceComputer Science (R0)