Assessing basin identification methods for locating multiple optima

Abstract

Basin identification is an important ingredient in global optimization algorithms for the efficient use of local searches. An established approach for this task is obtaining topographical information about the objective function from a discrete sample of the search space and representing it in a graph structure. So far, different variants of this approach are usually assessed by evaluating the performance of a whole optimization algorithm using them as components. In this work, we compare two approaches on their own, namely topographical selection and nearest-better clustering, regarding their ability to identify the distinct attraction basins of multimodal functions. We show that both have different strengths and weaknesses, as their behavior is very dependent on the problem instance.