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In many recent works, the potential of Exploratory Landscape Analysis (ELA)features to numerically characterize, in particular, single-objectivecontinuous optimization problems has been demonstrated. These numericalfeatures provide the input for all kinds of machine learning tasks oncontinuous optimization problems, ranging, i.a., from High-level PropertyPrediction to Automated Algorithm Selection and Automated AlgorithmConfiguration. Without ELA features, analyzing and understanding thecharacteristics of single-objective continuous optimization problems would beimpossible.  Yet, despite their undisputed usefulness, ELA features suffer from severaldrawbacks. These include, in particular, (1.) a strong correlation betweenmultiple features, as well as (2.) its very limited applicability tomulti-objective continuous optimization problems. As a remedy, recent worksproposed deep learning-based approaches as alternatives to ELA. In these works,e.g., point-cloud transformers were used to characterize an optimizationproblem's fitness landscape. However, these approaches require a large amountof labeled training data.  Within this work, we propose a hybrid approach, Deep-ELA, which combines (thebenefits of) deep learning and ELA features. Specifically, we pre-trained fourtransformers on millions of randomly generated optimization problems to learndeep representations of the landscapes of continuous single- andmulti-objective optimization problems. Our proposed framework can either beused out-of-the-box for analyzing single- and multi-objective continuousoptimization problems, or subsequently fine-tuned to various tasks focussing onalgorithm behavior and problem understanding.

Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised  Pretrained Transformers for Single- and Multi-Objective Continuous  Optimization Problems