The facility layout problem (FLP) is a combinatorial optimization problem. The performance of the layout design is significantly impacted by diverse, multiple factors. The use of algorithmic or procedural design methodology in ranking and identification of efficient layout is ineffective. In this context, this study proposes a three-stage methodology where data envelopment analysis (DEA) is augmented with unsupervised and supervised machine learning (ML). In stage 1, unsupervised ML is used for the clustering of the criteria in which the layouts need to be evaluated using homogeneity. Layouts are generated using simulated annealing, chaotic simulated annealing, and hybrid firefly algorithm/chaotic simulated annealing meta-heuristics. In stage 2, the nonparametric DEA approach is used to identify efficient and inefficient layouts. Finally, supervised ML utilizes the performance frontiers from DEA (efficiency scores) to generate a trained model for getting the unique rankings and predicted efficiency scores of layouts. The proposed methodology overcomes the limitations associated with large datasets that contain many inputs / outputs from the conventional DEA and improves the prediction accuracy of layouts. A Gaussian distribution product demand dataset for time period T = 5 and facility size N = 12 is used to prove the effectiveness of the methodology.