Heavy Tails with Parameter Adaptation in Random Projection based Continuous EDA

In this paper, we present a new variant of EDA for high dimensional continuous optimisation, which extends a recently proposed random projections (RP) ensemble based approach by employing heavy tailed random matrices. In particular, we use random matrices with i.i.d. t-distributed entries. The use of t-distributions may look surprising in the context of random projections, however we show that the resulting ensemble covariance is enlarged when the degree of freedom parameter is lowered. Based on this observation, we develop an adaptive scheme to adjust this parameter during evolution, and this results in a flexible means of balancing exploration and exploitation of the search process. A comprehensive set of experiments on high dimensional benchmark functions demonstrate the usefulness of our approach.