This paper presents an effective evolutionary hybrid for solving the permutation flowshop scheduling problem. Based on a memetic algorithm, the procedure uses a construction component that generates initial solutions through the use of a novel reblocking mechanism operating according to a biased random sampling technique. This component is aimed at forcing the operations having smaller processing times to appear on the critical path. The goal of the construction component is to fill an initial pool with high-quality solutions for a memetic algorithm that looks for even higher-quality solutions. In the memetic algorithm, whenever a crossover operator and possibly a mutation are performed, the offspring genome is fine-tuned by a combination of 2-exchange swap and insertion local searches. The same with the employed construction method; in these local searches, the critical path notion has been used to exploit the structure of the problem. The results of computational experiments on the benchmark instances indicate that these components have strong synergy, and their integration has created a robust and effective procedure that outperforms several state-of-the-art procedures on a number of the benchmark instances. By deactivating different components enhancing the evolutionary module of the procedure, the effects of these components have also been examined.