TLA: Topological Landscape Analysis for Single-Objective Continuous Optimization Problem Instances

The characterization of problem instances in numerical optimization is a prerequisite for automated algorithm selection and configuration, as well as the evaluation of the quality of benchmark suites. While several approaches to feature construction for single-objective optimization problems have already been proposed, each of them have their limitations. For this reason, in this paper, we propose Topological Landscape Analysis (TLA), a novel approach for generating features for single-objective optimization problems, which is based on the principles of Topological Data Analysis. We evaluate the proposed TLA approach by showing that the obtained features can be used to distinguish problem classes in the benchmark suite from the Genetic and Evolutionary Computation Conference Black-box Optimization Benchmarking workshop.