A multiobjective optimization model is presented in this paper for the Autonomous Straddle Carriers Scheduling (ASCS) problem in automated container terminals, which is more practical than the single objective model. The model considers three objectives [i.e., Straddle Carriers (SCs) traveling time, SC waiting time and finishing time of high-priority container-transferring jobs], and their weighted sum is investigated as the representative example. The presented model is formulated as a pickup and delivery problem with time windows in the form of binary integer programming. An exact algorithm based on Branch-and-Bound with Column Generation (BBCG) is employed for solving the multiobjective ASCS problem. Based on the map of an actual fully automated container terminal, simulation results are compared with the single-objective scheduling to demonstrate the effectiveness and flexibility of the presented multiobjective model, as well as the efficacy of the BBCG algorithm for autonomous SC scheduling.