Grey wolf optimizer (GWO) is a novel nature-inspired algorithm, and it has the characteristics of strong local search ability but weak global search ability when dealing with some large-scale problems. So a GWO based on random opposition learning, strengthening hierarchy of grey wolves and modified evolutionary population dynamics (EPD), named as RSMGWO, is proposed. Firstly, a search way based on strengthening hierarchy of grey wolves is added; each grey wolf uses two kinds of updating modes, including a global-best search way based on random dimensions and the original search way of GWO, to improve the optimization performance. Secondly, a modified EPD is embedded to improve the optimization performance further. Finally, a random opposition learning strategy is merged to avoid falling into local optima. Experimental results on 19 different (especially large scale) dimensional benchmark functions and multi-layer perceptron (MLP) optimization for cancer identification show that compared with GWO and quite a few state-of-the-art algorithms, RSMGWO is able to provide more competitive results, in terms of both accuracy and convergence.