Landscape analysis aims to characterise optimisation problems based on their objective (or fitness) function landscape properties. The problem search space is typically sampled, and various landscape features are estimated based on the samples. One particularly salient set of features is information content, which requires the samples to be sequences of neighbouring solutions, such that the local relationships between consecutive sample points are preserved. Generating such spatially correlated samples that also provide good search space coverage is challenging. It is therefore common to first obtain an unordered sample with good search space coverage, and then apply an ordering algorithm such as the nearest neighbour to minimise the distance between consecutive points in the sample. However, the nearest neighbour algorithm becomes computationally prohibitive in higher dimensions, thus there is a need for more efficient alternatives. In this study, Hilbert space-filling curves are proposed as a method to efficiently obtain high-quality ordered samples. Hilbert curves are a special case of fractal curves, and guarantee uniform coverage of a bounded search space while providing a spatially correlated sample. We study the effectiveness of Hilbert curves as samplers, and discover that they are capable of extracting salient features at a fraction of the computational cost compared to Latin hypercube sampling with post-factum ordering. Further, we investigate the use of Hilbert curves as an ordering strategy, and find that they order the sample significantly faster than the nearest neighbour ordering, without sacrificing the saliency of the extracted features.
Towards Explainable Exploratory Landscape Analysis: Extreme Feature Selection for Classifying BBOB Functions
Thales Research & Technology（泰雷兹研究与技术公司）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；CNRS（法国国家科学研究中心）；Sorbonne Université（索邦大学）
Exploratory Landscape Analysis is Strongly Sensitive to the Sampling Strategy
Thales Research & Technology（泰雷兹研究与技术公司）；CNRS（法国国家科学研究中心）；École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）；Sorbonne Université（索邦大学）
Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised Pretrained Transformers for Single- and Multi-Objective Continuous Optimization Problems
Paderborn University（帕德博恩大学）；TU Dresden（德累斯顿工业大学）；ScaDS.AI Dresden/Leipzig（德累斯顿/莱比锡数据科学与人工智能中心）；University of Twente（特文特大学）
The Importance of Landscape Features for Performance Prediction of Modular CMA-ES Variants
Jožef Stefan Institute（约泽夫·斯蒂芬研究所）；Jožef Stefan International Postgraduate School（约泽夫·斯蒂芬国际研究生院）；Leiden Institute for Advanced Computer Science（莱顿高级计算机科学研究所）；Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）
Does Dimensionality Reduction via Random Projections Preserve Landscape Features?
Leiden Institute of Advanced Computer Science, Leiden University（莱顿高级计算机科学研究所，莱顿大学）；RTWH Aachen University（亚琛工业大学）；Institute for Clarity in Documentation（文档清晰研究所）；Inria Paris-Rocquencourt（巴黎-罗quentourt研究所）；Rajiv Gandhi University（拉贾·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕勒研究实验室）
