In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize, in particular, single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks on continuous optimization problems, ranging, i.a., from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems would be impossible. Yet, despite their undisputed usefulness, ELA features suffer from several drawbacks. These include, in particular, (1.) a strong correlation between multiple features, as well as (2.) its very limited applicability to multi-objective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, e.g., point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. Specifically, we pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multi-objective optimization problems. Our proposed framework can either be used out-of-the-box for analyzing single- and multi-objective continuous optimization problems, or subsequently fine-tuned to various tasks focussing on algorithm behavior and problem understanding.

翻译：在近期多项研究中，探索性景观分析（ELA）特征在数值化表征单目标连续优化问题方面的潜力已得到充分验证。这些数值特征为连续优化问题的各类机器学习任务（如高层属性预测、自动化算法选择与自动化算法配置等）提供了输入基础。没有ELA特征，分析并理解单目标连续优化问题的特性将无从实现。然而，尽管其具有公认的实用性，ELA特征仍存在若干缺陷，主要包括：(1) 多个特征之间存在强相关性，以及 (2) 在多目标连续优化问题中的适用性非常有限。作为解决方案，近期研究提出了基于深度学习的方法作为ELA的替代方案。在这些工作中，例如采用点云Transformer来表征优化问题的适应度景观。然而，这类方法需要大量标注训练数据。本研究提出了一种混合方法Deep-ELA，深度融合了深度学习与ELA特征的优势。具体而言，我们基于数百万随机生成的优化问题对四个Transformer模型进行预训练，以学习连续单目标和多目标优化问题景观的深层表征。所提出的框架既可开箱即用地分析单目标和多目标连续优化问题，亦可针对聚焦算法行为与问题理解的各种任务进行后续微调。