On the Latent Structure of the bbob-biobj Test Suite

Landscape analysis is a popular method for the characterization of black-box optimization problems. It consists of a sequence of operations that, from a limited sample of solutions, approximate and describe the hypersurfaces formed by characteristic problem properties. The hypersurfaces, called problem landscapes, are described by sets of carefully crafted features that ought to capture their characteristic properties. In this way, arbitrary optimization problems with potentially very different technical parameters, such as search space dimensionality, are projected into specific feature spaces where they can be further studied. The representation of a problem in a feature space can be used, for example, to find similar problems and identify metaheuristic optimization algorithms that have the best track record on the same type of tasks. Because of that, the quality and properties of problem representation in the feature spaces gain importance. In this work, we study the representation properties of the popular bbob-biobj test suite in the space of bi-objective features, analyze the structure naturally emerging in the feature space, and analyze the high-level properties of the projection. The obtained results clearly demonstrate the discrepancies between the latent structure of the test suite and its expert perception.