In the context of increasingly competitive shipbuilding, the flexible multi-level picking system, composed of high-rise shelves, Automated Guided Vehicles (AGVs), and picking stations, has been of gradual interest because of its advantages in operation efficiency, system flexibility, and system robustness. Compared with other simple-level systems, the flexible multi-level picking system has a more complex coupling temporal relationship, which makes the scheduling optimization of shipbuilding automated collaborative order picking (SACOP) extremely difficult. In order to avoid the dilemma of finding a feasible and optimal collaborative scheduling scheme under the constraints of a complex temporal relationship, this paper proposed a multi-AGV-driven pallet-picking scheduling optimization (MADPSO) method, which takes the AGV scheduling scheme as the direct solution and modifies it to a feasible solution under the reasonably designed interaction strategy of stacker, AGV, and the interaction strategy of picking station, AGV. Furthermore, taking the minimum energy consumption and operation time as the optimization objectives, a multi-objective optimization mathematical model was established to describe MADPSO, and an improved NSGA-III algorithm was designed to solve the problem. Finally, several experiments were conducted in various scenarios and verified that using MADPSO can achieve a comprehensive optimization index improvement of 52.02–75.66% compared with traditional picking methods, which has a certain reference significance for shipyards.