The trend of global economic integration has fostered the prosperity of the maritime transportation industry, which has placed higher demands on the construction of automated container terminals, and the optimization of the integrated  berth allocation and crane assignment problems (BACAPs) is a key link of. Currently, population-based computational intelligence methods have attracted attention on BACAPs, but on small-scale case and simplified problem models. In this paper,  we propose a novel swarm optimization with intra- and inter-hierarchical competition (I2HCSO) for addressing large-scale BACAPs, which is a major challenge in container terminals. First, we construct a hierarchical model with better particles at higher hierarchy, and the population at different hierarchy are divided into several sub-swarm. Then, we design a intra- and inter-hierarchical competitive mechanism to balance the exploration and exploitation of the population, in which intra-hierarchical competition is carried out within sub-swarm at any hierarchy, whereas inter-hierarchical competition occurs in different sub-swarms of neighboring hierarchies. Third, we consider optimizing the priorities of vessels for efficient use of resources berth and crane for the first time in BACAPs, and employ ε-constraints to search for feasible regions. Additionally, we develop a local search operator as a repair strategy to improve the quality of the solution. Finally, we test I2HCSO in a set of cases consisting of 25 BACAPs. Compared with the several typical optimizers with experimental results, I2HCSO is more competitive on BACAPs with different scales.