Real-Valued Multimodal Fitness Landscape Characterization for Evolution

This paper deals with the characterization of the fitness landscape of multimodal functions and how it can be used to choose the most appropriate evolutionary algorithm for a given problem. An algorithm that obtains a general description of real valued multimodal fitness landscapes in terms of the relative number of optima, their sparseness, the size of their attraction basins and the evolution of this size when moving away from the global optimum is presented and used to characterize a set of well-known multimodal benchmark functions. To illustrate the relevance of the information obtained and its relationship to the performance of evolutionary algorithms over different fitness landscapes, two evolutionary algorithms, Differential Evolution and Covariance Matrix Adaptation, are compared over the same benchmark set showing their behavior depending on the multimodal features of each landscape.