Proposal of distance-weighted exponential natural evolution strategies

This paper presents a new evolutionary algorithm for function optimization named the distance-weighted exponential natural evolution strategies (DX-NES). DX-NES remedies two problems of a conventional method, the exponential natural evolution strategies (xNES), that shows good performance when it does not need to move the distribution for sampling individuals down the slope to the optimal point. The first problem of xNES is that the search efficiency deteriorates while the distribution moves down the slope of an ill-scaled function because it degenerates before reaching the optimal point. The second problem is that the settings of learning rates are inappropriate because they do not taking account of some factors affecting the estimate accuracy of the natural gradient. We compared the performance of DX-NES with that of xNES and CMA-ES on typical benchmark functions and confirmed that DX-NES outperformed the xNES on all the benchmark functions and that DX-NES showed better performance than CMA-ES on the almost all functions except the fc-tablet function.

[1]  Kenneth D. Boese,et al.  Cost Versus Distance In the Traveling Salesman Problem , 1995 .

[2]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[3]  Shun-ichi Amari,et al.  Why natural gradient? , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[4]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[5]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[6]  Shigenobu Kobayashi,et al.  Latent variable crossover for k-tablet structures and its application to lens design problems , 2005, GECCO '05.

[7]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[8]  Isao Ono,et al.  Functionally specialized CMA-ES: a modification of CMA-ES based on the specialization of the functions of covariance matrix adaptation and step size adaptation , 2008, GECCO '08.

[9]  Tom Schaul,et al.  Natural Evolution Strategies , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[10]  Dirk Thierens,et al.  Enhancing the Performance of Maximum-Likelihood Gaussian EDAs Using Anticipated Mean Shift , 2008, PPSN.

[11]  Tom Schaul,et al.  Efficient natural evolution strategies , 2009, GECCO.

[12]  Isao Ono,et al.  Adaptation of expansion rate for real-coded crossovers , 2009, GECCO.

[13]  Tom Schaul,et al.  Stochastic search using the natural gradient , 2009, ICML '09.

[14]  Isao Ono,et al.  Bidirectional Relation between CMA Evolution Strategies and Natural Evolution Strategies , 2010, PPSN.

[15]  Tom Schaul,et al.  Exponential natural evolution strategies , 2010, GECCO '10.

[16]  Petr Posík,et al.  Stochastic local search in continuous domains: questions to be answered when designing a novel algorithm , 2010, GECCO '10.