Hybrid whale optimization algorithm with gathering strategies for high-dimensional problems

• A novel two-stage individual-based Whale Optimization Algorithm is proposed. • Opposition learning and grey wolf optimizer are added to raise solution diversity. • A big parameter value and differential disturbance are adopted in the first stage. • Historical agent best solutions and a global-best way are used in the second stage. • Experiments are carried on high-dimensional functions and fuzzy C-means clustering. In order to solve the problems, such as insufficient search ability and low search efficiency, of Whale Optimization Algorithm (WOA) in solving high-dimensional problems, a novel Hybrid WOA with Gathering strategies (HWOAG) is proposed in this paper. Firstly, an individual-based updating way is used in HWOAG instead of the dimension-based updating one of WOA to reduce the computational complexity and to be more suitable for high-dimensional problems. Secondly, a random opposition learning strategy is embedded into the individual-based WOA to form an opposition learning WOA (OWOA), and Grey Wolf Optimizer (GWO) is integrated into OWOA to form an OWOA with GWO (OWOAG) so as to improve the global search ability of WOA. Finally, two standalone OWOAGs are formulated to balance exploration and exploitation better. The two OWOAGs adopt strategies such as switching parameter tuning, random differential disturbance and global-best spiral operator to get stronger search ability. A lot of experimental results on high-dimensional (i.e. 1000-, 2000-, 4000- and 8000- dimensional) benchmark functions and clustering datasets for Fuzzy C-Means (FCM) optimization show that HWOAG has stronger search ability and higher search efficiency than WOA and quite a few state-of-the-art algorithms and that all the strategies gathered to WOA are effective. The source codes of the proposed algorithm HWOAG are available at https://github.com/kangzhai/HWOAG .