A TUNABLE REAL-WORLD MULTI-FUNNEL BENCHMARK PROBLEM FOR EVOLUTIONARY OPTIMIZATION - And Why Parallel Island Models Might Remedy the Failure of CMA-ES on It

Christian L. Müeller, Ivo F. Sbalzarini

Abstract

A common shortcoming in the Evolutionary Computation (EC) community is that the publication of many search heuristics is not accompanied by rigorous benchmarks on a balanced set of test problems. A welcome effort to promote such test suites are the IEEE CEC competitions on real-valued black-box optimization. These competitions prescribe carefully designed synthetic test functions and benchmarking protocols. They do, however, not contain tunable real-world examples of the important class of multi-funnel functions. We argue that finding minimum-energy configurations of 38-atom Lennard-Jones (LJ38) clusters could serve as such a benchmark for real-valued, single-objective evolutionary optimization. We thus suggest that this problem be included in EC studies whenever general-purpose optimizers are proposed. The problem is tunable from a single-funnel to a double-funnel topology. We show that the winner of the CEC 2005 competition, the Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), works on the single-funnel version of this test case, but fails on the double-funnel version. We further argue that this performance loss of CMA-ES can be relaxed by using parallel island models. We support this hypothesis by simulation results of a parallel island CMA-ES, the Particle Swarm CMA-ES, on a subset of the multi-funnel functions in the CEC 2005 benchmark.

References

  1. Alba, E. (2005). Parallel Metaheuristics: A New Class of Algorithms. Wiley-Interscience.
  2. Auger, A. and Hansen, N. (2005). A restart CMA evolution strategy with increasing population size. In Proc. IEEE Congress on Evolutionary Computation (CEC 2005), volume 2, pages 1769-1776.
  3. Clark, P. L. (2004). Protein folding in the cell: reshaping the folding funnel. Trends Biochem. Sci., 29(10):527- 534.
  4. Doye, J. (2000). Effect of compression on the global optimization of atomic clusters. Phys. Rev. E, 62(6, Part B):8753-8761.
  5. Doye, J. P. K., Miller, M. A., and Wales, D. J. (1999). The double-funnel energy landscape of the 38-atom Lennard-Jones cluster. J. Chem. Phys., 110(14):6896- 6906.
  6. Hansen, N. (2007). The CMA Evolution Strategy: A Tutorial. http://www.lri.fr/ hansen/cmatutorial.pdf.
  7. Hansen, N. and Kern, S. (2004). Evaluating the CMA Evolution Strategy on Multimodal Test Functions. In Lect. Notes Comput. Sc., volume 3242 of Parallel Problem Solving from Nature - PPSN VIII, pages 282-291.
  8. Hansen, N. and Ostermeier, A. (2001). Completely Derandomized Self-Adaption in Evolution Strategies. Evolutionary Computation, 9(2):159-195.
  9. Lunacek, M., Whitley, D., and Sutton, A. (2008). The Impact of Global Structure on Search. In Lect. Notes Comput. Sc., volume 5199 of Parallel Problem Solving from Nature - PPSN X, pages 498-507.
  10. Müller, C. L., Baumgartner, B., and Sbalzarini, I. F. (2009). Particle swarm CMA evolution strategy for the optimization of multi-funnel landscapes. In Proc. IEEE Congress on Evolutionary Computation (CEC 2009), pages 2685-2692.
  11. Steinhardt, P. J., Nelson, D. R., and Ronchetti, M. (1983). Bond-orientational order in liquids and glasses. Phys. Rev. B, 28(2):784-805.
  12. Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y.-P., Auger, A., and Tiwari, S. (2005). Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Technical report, Nanyang Technological University, Singapore.
  13. Sutton, A. M., Whitley, D., Lunacek, M., and Howe, A. (2006). PSO and multi-funnel landscapes: how cooperation might limit exploration. In Proc. ACM Genetic and Evolutionary Computation Conference (GECCO'06), pages 75-82. ACM.
  14. Wales, D. (2004). Energy Landscapes : Applications to Clusters, Biomolecules and Glasses (Cambridge Molecular Science). Cambridge University Press.
  15. Wales, D. J. and Doye, J. P. K. (1997). Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms. J. Phys. Chem. A, 101(28):5111-5116.
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in Harvard Style

L. Müeller C. and F. Sbalzarini I. (2009). A TUNABLE REAL-WORLD MULTI-FUNNEL BENCHMARK PROBLEM FOR EVOLUTIONARY OPTIMIZATION - And Why Parallel Island Models Might Remedy the Failure of CMA-ES on It . In Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009) ISBN 978-989-674-014-6, pages 248-253. DOI: 10.5220/0002335202480253


in Bibtex Style

@conference{icec09,
author={Christian L. Müeller and Ivo F. Sbalzarini},
title={A TUNABLE REAL-WORLD MULTI-FUNNEL BENCHMARK PROBLEM FOR EVOLUTIONARY OPTIMIZATION - And Why Parallel Island Models Might Remedy the Failure of CMA-ES on It},
booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)},
year={2009},
pages={248-253},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002335202480253},
isbn={978-989-674-014-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)
TI - A TUNABLE REAL-WORLD MULTI-FUNNEL BENCHMARK PROBLEM FOR EVOLUTIONARY OPTIMIZATION - And Why Parallel Island Models Might Remedy the Failure of CMA-ES on It
SN - 978-989-674-014-6
AU - L. Müeller C.
AU - F. Sbalzarini I.
PY - 2009
SP - 248
EP - 253
DO - 10.5220/0002335202480253