The convergence of electrification and automated driving will introduce opportunities to improve the operation and energy-efficiency of transportation systems. This paper discusses the challenges of dispatching autonomous electric vehicles (AEVs) in a ride-hailing fleet and their interactions with charging infrastructure. An integrated decision-making framework for dispatching and charging has been proposed using system optimization approaches. An agent-based platform has been developed for simulating and testing the proposed methods. A case study using New York City taxi data has been performed with different fleet sizes, dispatching strategies, and charging networks. Advantages of optimization-based approaches for AEV fleet management have been studied and demonstrated, for example, for a fleet of 1,750 AEVs to meet 100,000 daily requests, optimization-based centralized fleet management would result in 14% more ride requests satisfied and 43% fewer zero-occupancy miles traveled than if AEVs make independent decisions based on heuristic strategy. Benefits on reducing fleet size and charging downtime from optimization approaches are also comprehensively illustrated.