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Large-Scale Estimation of Distribution Algorithms with Adaptive Heavy Tailed random Pro jection ensembles

Journal of Computer Science & Technology 2019年第6期34卷 1241-1257页

作者： Momodou L.Sanyang Ata Kabán School of Computer Science University of BirminghamEdgbastonBirmingham B152TTU.K. School of Information Technology and Communication University of The GambiaSerekundaThe Gambia

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 1000 search variables.

关键词： covariance adaptation estimation of distribution algorithm random projection ensemble t-distribution

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