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.

中文翻译：

---

具有自适应重尾随机投影系综的分布算法的大规模估计

我们提出了用于大规模连续优化的分布估计算法 (EDA) 的新变体，这些变体扩展和增强了最近提出的基于随机投影 (RP) 集成的方法。这里的主要新颖之处在于背离需要（亚）高斯随机矩阵进行范数保持的 RP 理论，而是为了高维搜索的目的，我们建议使用具有独立且同分布的条目的随机矩阵t 分布。我们分析表明，搜索分布的隐式产生的高维协方差因此被放大。此外，这种放大的程度由一个参数控制，即自由度。为此，在优化的背景下，事实证明，这种重尾随机矩阵比以前使用的（亚）高斯矩阵更可取。基于这一观察，我们提出了新的协方差适应方案，该方案能够在搜索过程中适应自由度参数，并提供一种灵活的方法来平衡探索与开发。我们对高维基准函数进行了彻底的实验研究，并提供了统计分析，与 1000 个搜索变量的问题中的现有替代方案相比，证明了我们的方法的最新性能。并产生一种灵活的方法来平衡探索与开发。我们对高维基准函数进行了彻底的实验研究，并提供了统计分析，与 1000 个搜索变量的问题中的现有替代方案相比，证明了我们的方法的最新性能。并产生一种灵活的方法来平衡探索与开发。我们对高维基准函数进行了彻底的实验研究，并提供了统计分析，与 1000 个搜索变量的问题中的现有替代方案相比，证明了我们的方法的最新性能。