In the standard grey wolf optimizer (GWO), the search wolf must wait to update its current position until the comparison between the other search wolves and the three leader wolves is completed. During this waiting period, the standard GWO is seen as the static GWO. To get rid of this waiting period, two dynamic GWO algorithms are proposed: the first dynamic grey wolf optimizer (DGWO1) and the second dynamic grey wolf optimizer (DGWO2). In the dynamic GWO algorithms, the current search wolf does not need to wait for the comparisons between all other search wolves and the leading wolves, and its position can be updated after completing the comparison between itself or the previous search wolf and the leading wolves. The position of the search wolf is promptly updated in the dynamic GWO algorithms, which increases the iterative convergence rate. Based on the structure of the dynamic GWOs, the performance of the other improved GWOs is examined, verifying that for the same improved algorithm, the one based on dynamic GWO has better performance than that based on static GWO in most instances.