The Frequency Assignment Problem (fap) is one of the key issues in the design of Global System for Mobile Communications (gsm) networks. The formulation of the fap used here focuses on aspects that are relevant to real gsm networks. In this paper, we adapt a parallel model to tackle a multiobjectivised version of the fap. It is a hybrid model which combines an island-based model and a hyperheuristic. The main aim of this paper is to design a strategy that facilitates the application of the current best-behaved algorithm. Specifically, our goal is to decrease the user effort required to set its parameters. At the same time, the usage of such an algorithm in parallel environments was enabled. As a result, the time required to attain high-quality solutions was decreased. We also conduct a robustness analysis of this parallel model. In this analysis we study the relationship between the migration stage of the parallel model and the quality of the resulting solutions. In addition, we also carry out a scalability study of the parallel model. In this case, we analyse the impact that the migration stage has on the scalability of the entire parallel model. Computational results with several real network instances have validated our proposed approach. The best-known frequency plans for two real-world network instances are improved with this strategy.