Multimodal optimization problem (MMOP) is one of the most common problems in engineering practices that requires multiple optimal solutions to be located simultaneously. An efficient algorithm for solving MMOPs should balance the diversity and convergence of the population, so that the global optimal solutions can be located as many as possible. However, most of existing algorithms are easy to be trapped into local peaks and cannot provide high-quality solutions. To better deal with MMOPs, considerations on the solution quality angle and the evolution stage angle are both taken into account in this paper and a multi-angle hierarchical differential evolution (MaHDE) algorithm is proposed. Firstly, a fitness hierarchical mutation (FHM) strategy is designed to balance the exploration and exploitation ability of different individuals. In the FHM strategy, the individuals are divided into two levels (i.e., low/high-level) according to their solution quality in the current niche. Then, the low/high-level individuals are applied to different guiding strategies. Secondly, a directed global search (DGS) strategy is introduced for the lowlevel individuals in the late evolution stage, which can improve the population diversity and provide these low-level individuals with the opportunity to research the global peaks. Thirdly, an elite local search (ELS) strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy. Extensive experiments are developed to verify the performance of MaHDE on the widely used MMOPs test functions i.e., CEC'2013. Experimental results show that MaHDE generally outperforms the compared state-of-the-art multimodal algorithms. INDEX TERMS Multi-angle hierarchical, two-stage search, differential evolution, multimodal optimization problems I. INTRODUCTION Multimodal optimization problems (MMOPs), as one kind of challenging and interesting optimization problems, have attracted increasing attentions in recent years [1]−[4]. MMOPs are an important problem area as it widely exists in many real-world applications [5], such as virtual camera composition problems [6], metabolic network modeling problems [7], laser pulse shaping problems [8], job scheduling problems [9][10], and neutral network problems [11]. These MMOPs are required the algorithms to locate the global peaks as many as possible and refine the accuracy of the found solutions as high as possible, so that the high-quality decisions can be finally made. In detail, MMOP is a kind of complex optimization problem that requires the algorithm to not only locate multiple global peaks simultaneously, but also achieve certain accuracy of solutions on the global peaks. In fact, the algorithm for MMOPs faces the problem of how to improve the