Parallel peaks: A visualization method for benchmark studies of multimodal optimization

Multimodal optimization has attracted increasing interest recently. Despite the emergence of various multimodal optimization algorithms during the last decade, little work has been dedicated to the development of benchmark tools. In this paper, we propose a visualization method for benchmark studies of multimodal optimization, called parallel peaks. Inspired by parallel coordinates, the proposed parallel peaks method is capable of visualizing both distribution information and convergence information of a given candidate solution set inside a 2D coordinate plane. To the best of our knowledge, this is the first visualization method in the multimodal optimization area. Our empirical results demonstrate that the proposed parallel peaks method can be robustly used to visualize candidate solutions sets with a range of properties, including high-accuracy solutions sets, high-dimensional solution sets and solution sets with a large number of optima. Additionally, by visualizing the populations obtained during the optimization process, it can also be used to investigate search behaviors of multimodal optimization algorithms.