The increasingly growing data traffic has posed great challenges for mobile operators to increase their data processing capacity, which incurs a significant energy consumption and deployment cost. With the emergence of the Cloud Radio Access Network (C-RAN) architecture, the data processing units can now be centralized in data centers and shared among base stations. By mapping a cluster of base stations with complementary traffic patterns to a data processing unit, the processing unit can be fully utilized in different periods of time, and the required capacity to be deployed is expected to be smaller than the sum of capacities of single base stations. However, since the traffic patterns of base stations are highly dynamic in different time and locations, it is challenging to foresee and characterize the traffic patterns in advance to make optimal clustering schemes. In this paper, we address these issues by proposing a deep-learning-based C-RAN optimization framework. First, we exploit a Multivariate Long Short-Term Memory (MuLSTM) model to learn the temporal dependency and spatial correlation among base station traffic patterns, and make accurate traffic forecast for a future period of time. Afterwards, we build a weighted graph to model the complementarity of base stations according to their traffic patterns, and propose a Distance-Constrained Complementarity-Aware (DCCA) algorithm to find optimal base station clustering schemes with the objectives of optimizing capacity utility and deployment cost. We evaluate the performance of our framework using data in two months from real-world mobile networks in Milan and Trentino, Italy. Results show that our method effectively increases the average capacity utility to 83.4% and 76.7%, and reduces the overall deployment cost to 48.4% and 51.7% of the traditional RAN architecture in the two datasets, respectively, which consistently outperforms the state-of-the-art baseline methods