Abstract
It has been observed that in many real-world large scale problems only few variables have a major impact on the function value: While there are many inputs to the function, there are just few degrees of freedom. We refer to such functions as having a low intrinsic dimension. In this paper we devise an Estimation of Distribution Algorithm (EDA) for continuous optimisation that exploits intrinsic dimension without knowing the influential subspace of the input space, or its dimension, by employing the idea of random embedding. While the idea is applicable to any optimiser, EDA is known to be remarkably successful in low dimensional problems but prone to the curse of dimensionality in larger problems because its model building step requires large population sizes. Our method, Random Embedding in Estimation of Distribution Algorithm (REMEDA) remedies this weakness and is able to optimise very large dimensional problems as long as their intrinsic dimension is low.
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
References
Bergstra, J., Bengio, Y.: Random search for hyper-parameter optimization. Mach. Learn. Res. 13, 281–305 (2012)
Bosman, P.: On empirical memory design, faster selection of Bayesian factorizations and parameter-free Gaussian EDAs. In: Proceedings of Genetic and Evolutionary Computation Conference (GECCO), pp. 389–396. ACM (2009)
Constantine, P.: Active subspace methods in theory and practice: applications to kriging surfaces. SIAM J. Sci. Comput. 36(4), 1500–1524 (2013)
Davidson, K.R., Szarek, S.J.: Local operator theory, random matrices and banach spaces. In: Handbook of the Geometry of Banach Spaces, vol. 1. pp. 317–366 (2001)
Dong, W., Chen, T., Tino, P., Yao, X.: Scaling up estimation of distribution algorithm for continuous optimisation. IEEE Trans. Evol. Comput. 17(6), 797–822 (2013)
Dong, W., Yao, X.: Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms. Inf. Sci. 178, 3000–3023 (2008)
Hansen, N.: The CMA evolution strategy: a comparing review. In: Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.) Towards a New Evolutionary Computation: Advances in the Estimation of Distribution Algorithms. Studies in Fuzziness and Soft Computing, vol. 192. Springer, Heidelberg (2006)
Hutter, F.: Automated configuration of algorithms for solving hard computational problems. Ph.D. thesis (2009)
Kabán, A., Bootkrajang, J., Durrant, R.J.: Towards large scale continuous EDA: a random matrix theory perspective. Evol. Comput. (2015). MIT Press
Ros, R., Hansen, N.: A simple modification in CMA-ES achieving linear time and space complexity. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 296–305. Springer, Heidelberg (2008)
Sanyang, M.L., Kaban, A.: Multivariate cauchy EDA optimisation. In: Corchado, E., Lozano, J.A., Quintián, H., Yin, H. (eds.) IDEAL 2014. LNCS, vol. 8669, pp. 449–456. Springer, Heidelberg (2014)
Sanyang, M.L., Kabán, A.: Heavy tails with parameter adaptation in random projection based continuous EDA. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2074–2081 (2015)
Yang, Z., Chen, W., Weise, T., Tang, K.: Large-scale global optimization using cooperative co-evolution with variable interaction learning. In: Parallel Problem Solving from Nature (PPSN), vol. 11, pp. 300–309 (2010)
Wang, Z., Zoghi, M., Hutter, F., Matheson, D., de Freitas, N.: Bayesian optimization in a billion dimensions via random embeddings. In: IJCAI (2013)
Weicker, K., Weicker, N.: On the improvement of co-evolutionary optimizers by learning variable inter-dependencies. In: Proceedings of Congress on Evolutionary Computation, vol. 3 (1999)
Tang, K., Yang, Z., Yao, X.: Multilevel cooperative co-evolution for large scale optimization. In: IEEE World Congress on Computational Intelligence 2008 (CEC 2008) (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Sanyang, M.L., Kabán, A. (2016). REMEDA: Random Embedding EDA for Optimising Functions with Intrinsic Dimension. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_80
Download citation
DOI: https://doi.org/10.1007/978-3-319-45823-6_80
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45822-9
Online ISBN: 978-3-319-45823-6
eBook Packages: Computer ScienceComputer Science (R0)