The goal of the berth allocation problem under time-dependent limitations is to assign and schedule incoming vessels to berthing positions taking into account tidal and water depth constraints. In order to solve this problem, we propose a POPMUSIC approach (Partial Optimization Metaheuristic Under Special Intensification Conditions) which includes the resolution of an appropriate mathematical programming formulation as an embedded procedure. This method is tested over realistic problem instances proposed in the literature. The computational experiments as well as the comparison with a reference algorithm for this problem reported in the related literature reveal that our approach is suitable to be used in real-world environments.