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Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –

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Abstract

The covariance matrix adaptation evolution strategy (CMA-ES) rates among the most successful evolutionary algorithms for continuous parameter optimization. Nevertheless, it is plagued with some drawbacks like the complexity of the adaptation process and the reliance on a number of sophisticatedly constructed strategy parameter formulae for which no or little theoretical substantiation is available. Furthermore, the CMA-ES does not work well for large population sizes. In this paper, we propose an alternative – simpler – adaptation step of the covariance matrix which is closer to the “traditional” mutative self-adaptation. We compare the newly proposed algorithm, which we term the CMSA-ES, with the CMA-ES on a number of different test functions and are able to demonstrate its superiority in particular for large population sizes.

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References

  1. Hansen, N., Ostermeier, A., Gawelczyk, A.: On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation. In: Eshelman, L.J. (ed.) Proc. 6th Int’l Conf. on Genetic Algorithms, pp. 57–64. Morgan Kaufmann Publishers, Inc., San Francisco (1995)

    Google Scholar 

  2. Hansen, N., Ostermeier, A.: Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation 9(2), 159–195 (2001)

    Article  Google Scholar 

  3. Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES). Evolutionary Computation 11(1), 1–18 (2003)

    Article  Google Scholar 

  4. Auger, A., Hansen, N.: A Restart CMA Evolution Strategy with Increasing Population Size. In: Congress on Evolutionary Computation, vol. 2, pp. 1769–1776. IEEE, Los Alamitos (2005)

    Google Scholar 

  5. Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.-P., Auger, A., Tiwari, S.: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Technical Report, Nanyang Tech. University, Singapore (2005)

    Google Scholar 

  6. Beyer, H.-G., Arnold, D.V.: Qualms Regarding the Optimality of Cumulative Path Length Control in CSA/CMA-Evolution Strategies. Evolutionary Computation 11(1), 19–28 (2003)

    Article  MathSciNet  Google Scholar 

  7. Beyer, H.-G., Olhofer, M., Sendhoff, B.: On the Behavior of (μ/μ I , λ)-ES Optimizing Functions Disturbed by Generalized Noise. In: De Jong, K., Poli, R., Rowe, J. (eds.) Foundations of Genetic Algorithms, 7, pp. 307–328. Morgan Kaufmann, San Francisco (2003)

    Google Scholar 

  8. Beyer, H.-G., Sendhoff, B.: Evolution Strategies for Robust Optimization. In: Congress on Evolutionary Computation (CEC), pp. 1346–1353. IEEE Press, Los Alamitos (2006)

    Google Scholar 

  9. Auger, A., Schoenauer, M., Vanhaecke, N.: LS-CMA-ES: A Second-Order Algorithm for Covariance Matrix Adaptation. In: Yao, X., et al. (eds.) Parallel Problem Solving from Nature 8, pp. 182–191. Springer, Berlin (2004)

    Google Scholar 

  10. Igel, C., Hansen, N., Roth, S.: Covariance Matrix Adaptation for Multi-Objective Optimization. Evolutionary Computation 15(1), 1–28 (2007)

    Article  Google Scholar 

  11. Arnold, D.V., Beyer, H.-G.: Performance Analysis of Evolutionary Optimization with Cumulative Step Length Adaptation. IEEE Transactions on Automatic Control 49(4), 617–622 (2004)

    Article  MathSciNet  Google Scholar 

  12. Beyer, H.-G., Sendhoff, B.: Robust Optimization - A Comprehensive Survey. Computer Methods in Applied Mechanics and Engineering 196(33–34), 3190–3218 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hansen, N., Kern, S.: Evaluating the CMA Evolution Strategy on Multimodal Test Functions. In: Yao, X., et al. (eds.) Parallel Problem Solving from Nature 8, pp. 282–291. Springer, Berlin (2004)

    Google Scholar 

  14. Amstrup, B., Tóth, G.J., Szabó, G., Rabitz, H., Lörincz, A.: Genetic Algorithm with Migration on Topology Conserving Maps for Optimal Control of Quantum Systems. J. Phys. Chem. 99, 5206–5213 (1995)

    Article  Google Scholar 

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Beyer, HG., Sendhoff, B. (2008). Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –. 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_13

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  • DOI: https://doi.org/10.1007/978-3-540-87700-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87699-1

  • Online ISBN: 978-3-540-87700-4

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