With the increasing volume of shipping containers, container multimodal transport and port scheduling have attracted much attention. The allocation and dispatching of handling equipment to minimize completion time and energy consumption have always been a focus of research. This paper considers a scheduling problem at an automated land-maritime multimodal container terminal with multi-size containers, in which operating facilities and equipment such as quay cranes, vehicles, yard cranes, and external container trucks are involved. Moreover, the diversity of container sizes and the location of handshake areas in yards are concerned. A mixed integer programming model is established to schedule all operating facilities and equipment. To solve the mathematical model is a NP-hard problem, which is difficult to be solved by conventional methods. Then we propose a heuristic algorithm which merges multiple targets into one and designs an improved genetic algorithm based on the heuristic combination strategy in which 20-ft containers are paired-up to the same yard before allocation. After that, some experiments are designed to prove the effectiveness of the model and the algorithm. The effect of configurations on efficiency and energy consumption under different conditions is discussed, and the influences of different parameters and the proportion of 20-ft containers are also compared. Furthermore, the influence of locations of handshake area with different yard quantities are compared. To conclude, there is an optimal number of equipment to be allocated. If few equipment is used, the operation time will be prolonged; if too many, the energy consumption will be increased. When the yard operation is the bottleneck, the handover location should be in the centre, otherwise other locations might be feasible. When the proportion of 20-ft containers that can be combined is large, the method proposed in this paper has advantages over traditional methods. The proposed algorithm has made a breakthrough in improving efficiency and reducing energy consumption.