In the flowshop problem, one has to schedule jobs, where each job has to follow the same route of machines. The goal is to find a job order that minimizes some criteria. The permutation flowshop, also called PFSP, is a common (and fundamental) variant that imposes the machines to process jobs in the same order (thus, a permutation of jobs is enough to describe a solution). The permutation flowshop has been one of the most studied problems in the literature [35, 30] and has been considered on various industrial applications [16, 42]. We may also note that the permutation flowshop is at the origin of multiple other variants, for instance, the blocking permutation flowshop [45], the multiobjective permutation flowshop [20], the distributed permutation flowshop [11], the no-idle permutation flowshop [31], the permutation flowshop with buffers [28] and many others. Regarding the criteria to minimize, we study in this paper, two of the most studied objectives: the makespan (minimizing the completion time of the last job on the last machine) and the flowtime (minimizing the sum of completion times of each job on the last machine).