Rao algorithms are a new class of population-based metaheuristics that have shown promise in several technical and scientific research domains. Unlike other well-known heuristics, Rao algorithms are metaphor less and parameter less methods thus do not require tuning of algorithm-specific parameters. The present study attempts to apply Rao algorithms to the well-known complicated discrete combinatorial optimization problem viz. the permutation flow shop scheduling problem (PFSP) for the first time in literature. The objective is to minimize makespan. To make Rao algorithms adaptive to PFSP, encoding and decoding mechanism is presented. Random rank vectors and largest order value (LOV) rule are utilized in generation of the initial solution, perturbation, and updating the solutions. Computational results are compared with publicly available benchmarks to showcase the feasibility of the proposed approach. Results reveal that Rao methods have considerable potential to solve discrete combinatorial optimization problems such as flow shop scheduling problems in the present case.