No-Wait Flowshop Permutation Scheduling Problem (NWPFSP) is a scheduling problem that states that every job completed on machine n must be processed immediately on the next machine. The NWPFSP problem is an extension of the flowshop problem. This article proposes two new algorithms fire hawk optimization and beluga whale optimization, to solve the NWPFSP problem and minimize makespan. The two new algorithms developed to solve the NWPFSP problem are tested on three different cases. Each algorithm was run 30 times and was compared using an independent sample t-test. The results were also compared with the Campbell Dudek Smtih algorithm. In addition, the effectiveness of the FHO and BWO algorithms was assessed against the CDS algorithm using the Relative Error Percentage (REP) method. The results show that the FHO and BWO algorithms are better at solving NWPFSP problems when compared to the CDS algorithm. However, the BWO algorithm is more recommended in cases with large data because it can provide better results.