This study seeks to integrate Random Key Genetic Algorithm (RKGA) and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to compute makespan and solve the Flow Shop Scheduling Problem (FSSP). FSSP is considered as a Multi Criteria Decision Making Problem (MCDM) by setting machines as criteria and jobs as alternatives. RKGA is employed to determine the best weights for the criteria that directly affect the robustness of the solution. The proposed methodology is presented with illustrative example and applied to benchmark problems. The solutions are compared to well-known construction heuristics. The proposed methodology provides the best or reasonable solutions in acceptable computational times.