Towards Basin Identification Methods with Robustness Against Outliers

An important subtask in multimodal optimization is the identification of the attraction basins of individual optima. The knowledge about these basins can, for example, be used to start an appropriate number of local searches or to classify the problem instance in an exploratory landscape analysis before the optimization is started. In a black-box setting, the identification process necessarily needs a sample of evaluated solutions as input data. As these evaluations are expensive, it would be desirable to reuse previously acquired samples, if existing. In this case, arbitrary mixture distributions of the data must be assumed. Unfortunately, there is no basin identification method currently available that is robust to spatial outliers in the sample and at the same time can provide a ranking and/or a clustering of all the solutions. Topographical selection, which is based on a k-nearest-neighbor graph, is robust against outliers, but does not provide clustering information and determines the number of selected solutions on its own. Nearest-better clustering, on the other hand, can provide a hierarchical clustering but is not very robust to outliers. In this work, we adopt ideas from density-based clustering to develop a new basin identification method. The core idea is to use the number of neighbors within the distance to the nearest-better neighbor as a selection criterion. Experiments show that the new method combines the desirable features of the existing ones.