This work investigates the dynamical weighted deployment of mobile fog computing devices to support a mobile edge computing environment, in which each edge device is associated with a weight to reflect its importance based on the application. Since edge devices are mobile and could be switched off, it is challenging to dynamically optimize the deployment to adapt to dynamic change. This work further models the problem mathematically and solves it by a bat-inspired algorithm (BA), which searches the optimal solutions by simulating the food-searching behavior of bats via echolocation. Furthermore, three local search methods designed specifically for this problem are integrated into the BA, and a dynamic local search selection mechanism is proposed to adjust the probabilities of choosing the three local search methods iteratively in the BA main loop. Simulation results show outperformance of the proposed BA over the BA without local search and the previous approach.