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• Vehicle route, speed and departure time are optimized for shared autonomous electric vehicles (SAEVs) service. • A mixed-integer linear model is formulated for a time-dependent vehicle routing problem for SAEVs service. • Realistic energy consumption and congestion is considered in route optimization. • Adaptive large neighborhood search algorithm (ALNS) is proposed, and is embedded with departure time and speed optimization. Shared autonomous electric vehicles (SAEVs) are expected to become a popular choice for urban transportation in the future. A solution to a vehicle routing problem that considers congestion and energy consumption of SAEVs is proposed to assist green transportation under poor traffic conditions. In addition to routing the fleet of SAEVs to serve customers, the proposed method also determines the vehicle speed in each arc and the departure time at each node by minimizing the cost considering the travel distance, energy consumption, and travel time. In the time-dependent vehicle routing problem with departure time and speed optimization for SAEV service (SAEV-TD-VRP-DSO), the electric vehicles (EVs) exchange batteries at battery swapping stations (BSSs), and the corresponding vehicle routing method also includes recharge scheduling. We develop a mixed-integer linear model (MILP) to formulate the SAEV-TD-VRP-DSO and show that the state-of-the-art commercial optimization solver (CPLEX) can only solve a few instances (no more than 8 requests). Thus, an adaptive large neighborhood search (ALNS) algorithm is proposed to find near-optimal solutions for larger-size instances. The removal and insertion operators of ALNS help optimize the node sequences. A departure time and speed optimization procedure (DSOP) is employed to optimize the speed and departure time in each arc. The good performance of the proposed algorithm is demonstrated using instance sets. The optimization results of a case study in the Yanta Administrative District in Xi'an, China, show that speed and departure time optimization result in 24.99% cost savings. The sensitivity analysis results provide the SAEV operators with alternative cost-saving solutions. Empty vehicles traveling at a slower speed can reduce energy cost. The total cost of operating vehicles with passengers can be reduced by avoiding congestion and utilizing larger capacity batteries (32 kWh or more) and a lower minimum battery level (0.2-0.3). [ABSTRACT FROM AUTHOR]