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How effective is Cauchy-EDA in high dimensions?

Abstract
We consider the problem of high dimensional blackbox optimisation via Estimation of Distribution Algorithms (EDA) and the use of heavy-tailed search distributions in this setting. Some authors have suggested that employing a heavy tailed search distribution, such as a Cauchy, may make EDA better explore a high dimensional search space. However, other authors have found Cauchy search distributions are less effective than Gaussian search distributions in high dimensional problems. In this paper, we set out to resolve this controversy. To achieve this we run extensive experiments on a battery of high-dimensional test functions, and develop some theory which shows that small search steps are always more likely to move the search distribution towards the global optimum than large ones and, in particular, large search steps in high-dimensional spaces nearly always do badly in this respect. We hypothesise that, since exploration by large steps is mostly counterproductive in high dimensions, and since the fraction of good directions decays exponentially fast with increasing dimension, instead one should focus mainly on finding the right direction in which to move the search distribution. We propose a minor change to standard Gaussian EDA which implicitly achieves this aim, and our experiments on a sequence of test functions confirm the good performance of our new approach.
Type
Conference Contribution
Type of thesis
Series
Citation
Sanyang, M. L., Durrant, R. J., & Kaban, A. (2016). How effective is Cauchy-EDA in high dimensions? In Proceedings of IEEE Congress on Evolutionary Computation 2016 (CEC2016). Conference held at Vancouver Convention Centre, Vancouver, Canada: IEEE.
Date
2016
Publisher
IEEE
Degree
Supervisors
Rights
This is an author’s accepted version of an article accepted to be include in the Proceedings of IEEE Congress on Evolutionary Computation 2016 (CEC2016). © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.