Learning Multimodal Parameters: A Bare-Bones Niching Differential Evolution Approach

Most learning methods contain optimization as a substep, where the nondifferentiability and multimodality of objectives push forward the interplay of evolutionary optimization algorithms and machine learning models. The recently emerged evolutionary multimodal optimization (MMOP) technique enables the learning of diverse sets of effective parameters for the models simultaneously, providing new opportunities to the applications requiring both accuracy and diversity, such as ensemble, interactive, and interpretive learning. Targeting at locating multiple optima simultaneously in the multimodal landscape, this paper develops an efficient neighborhood-based niching algorithm. Bare-bones differential evolution is used as the baseline. Further, using Gaussian mutation with local mean and standard deviations, the neighborhoods capture niches that match well with the contours of peaks in the landscape. To increase diversity and enhance global exploration, the proposed algorithm embeds a diversity preserving operator to reinitialize converged or overlapped neighborhoods. The experimental results verify that the proposed algorithm has superior and consistent performance for a wide range of MMOP problems. Further, the algorithm has been successfully applied to train neural network ensembles, which validates its effectiveness and benefits of learning multimodal parameters.