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Journal of Computer Science and Technology ›› 2019, Vol. 34 ›› Issue (6): 1241-1257.

• Artificial Intelligence and Pattern Recognition •

### Large-Scale Estimation of Distribution Algorithms with Adaptive Heavy Tailed Random Projection Ensembles

Momodou L. Sanyang1,2, Ata Kabán1, Member, IEEE

1. 1 School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, U. K.;
2 School of Information Technology and Communication, University of The Gambia, Serekunda, The Gambia
• Received:2018-09-06 Revised:2019-09-13 Online:2019-11-16 Published:2019-11-16
• About author:Momodou L. Sanyang received his Ph.D. degree in computer science from the University of Birmingham, Birmingham, in 2017. Prior to that, he received his B.Sc. degree in mathematics and physics from the University of The Gambia (UTG), Serekunda, The Gambia, in 2006, and his M.Sc. degree in information systems and applications from the "National" Tsing Hua University, Hsinchu, in 2010. He is currently a senior lecturer in computer science at the University of The Gambia (UTG), and a honorary research fellow at the University of Birmingham, UK. His research interests include machine learning and data mining, dimensionality reduction, random projections, evolutionary computation and black box optimisation in high-dimensional settings.
• Supported by:
The work of Momodou L. Sanyang was partly funded by a Ph.D. scholarship from the Islamic Development Bank. The work of Ata Kabán is funded by the Engineering and Physical Sciences Research Council of UK under Fellowship Grant EP/P004245/1.

We present new variants of Estimation of Distribution Algorithms (EDA) for large-scale continuous optimisation that extend and enhance a recently proposed random projection (RP) ensemble based approach. The main novelty here is to depart from the theory of RPs that require (sub-)Gaussian random matrices for norm-preservation, and instead for the purposes of high-dimensional search we propose to employ random matrices with independent and identically distributed entries drawn from a t-distribution. We analytically show that the implicitly resulting high-dimensional covariance of the search distribution is enlarged as a result. Moreover, the extent of this enlargement is controlled by a single parameter, the degree of freedom. For this reason, in the context of optimisation, such heavy tailed random matrices turn out to be preferable over the previously employed (sub-)Gaussians. Based on this observation, we then propose novel covariance adaptation schemes that are able to adapt the degree of freedom parameter during the search, and give rise to a flexible approach to balance exploration versus exploitation. We perform a thorough experimental study on high-dimensional benchmark functions, and provide statistical analyses that demonstrate the state-of-the-art performance of our approach when compared with existing alternatives in problems with 1 000 search variables.

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