Random Filter Mappings as Optimization Problem Feature Extractors

Characterizing optimization problems and their properties addresses a key challenge in optimization and is crucial for tasks such as creating benchmarks, selecting algorithms, and configuring them. Although several techniques have been proposed for extracting features from single-objective optimization problems, the proposed approach offers an alternative look at these problems and their properties. We propose an approach for creating problem representations by utilizing domain-specific filters. These filters have randomly initialized weights and are applied to samples of the optimization problem to extract relevant properties. Proposed features are subsequently used to classify problem instances from the Comparing Continuous Optimizers benchmark demonstrating that problem instances of the same problem tend to be situated near each other in a high-dimensional feature space. Additionally, we demonstrate that the proposed feature extraction method can be used to recognize complex characteristics of optimization functions, including multimodality and the presence of global and funnel structures. We also explore the extent to which these identified features can assist in the selection of algorithms. Our findings reveal that these features are suitable for constructing meta-models for algorithm selection, provided that the problems encountered do not substantially differ from those seen in the training phase. The proposed approach offers a versatile tool for feature extraction, highlighting its applicability across multiple tasks within the domain of optimization.