Free-floating bike sharing is an innovative and sustainable travel mode, where shared bikes can be picked up and returned at any proper place on the streets and not just at docking stations. Nevertheless, in these systems, two major problems arise. One is the imbalance of free-floating shared bikes (FFSB) between zones due to one-way trips, the other is the damaged bikes that must be brought for repair. In this study, a modeling framework for dynamic relocating operational and damaged bikes is proposed that starts with predicting the number and location of shared bikes using deep learning algorithms. The demand forecasting model adopts the Encoder-Decoder architecture embedded with the attention mechanism to further enhance the model's prediction ability and flexibility. Then, a data-driven optimization model for FFSB relocations is presented, where the multi-period optimization is applied to dynamically plan the relocation activities throughout the day. A new hybrid metaheuristic algorithm that incorporates variable neighborhood search (VNS) and enhanced simulated annealing (ESA) algorithm is developed for solving the relocating problem, in which satisfactory performance is observed from the numerical example. We test the proposed framework with the real-world FFSB data from Beijing, China. The results show that relocating both operational and damaged bikes timely decreases the probability of users finding damaged bikes in the system, but leads to higher relocation costs. For peak-hours, considering only the operational bikes for relocation is the most effective strategy given the limited relocation resources. It is urgent at those times of the day to focus on providing bikes to clients where they are undersupplied.