The simulation-based and computationally expensive problem tackled in this paper addresses COVID-19 vaccines allocation in Malaysia. The multi-objective formulation considers simultaneously the total number of deaths, peak hospital occupancy and relaxation of mobility restrictions. Evolutionary algorithms have proven their capability to handle multi-to-many objectives but require a high number of computationally expensive simulations. The available techniques to raise the challenge rely on the joint use of surrogate-assisted optimization and parallel computing to deal with computational expensiveness. On the one hand, the simulation software is imitated by a cheap-to-evaluate surrogate model. On the other hand, multiple candidates are simultaneously assessed via multiple processing cores. In this study, we compare the performance of recently proposed surrogate-free and surrogate-based parallel multi-objective algorithms through the application to the COVID-19 vaccine distribution problem.