In this study novel integrative machine learning models embedded with the firefly algorithm (FA) were developed and employed to predict energy dissipation on block ramps. The used models include multi-layer perceptron neural network (MLPNN), adaptive neuro-fuzzy inference system (ANFIS), group method of data handling (GMDH), support vector regression (SVR), linear equation (LE), and nonlinear regression equation (NE). The investigation focused on the evaluation of the performance of standard and integrative models in different runs. The performances of machine learning models and the nonlinear equation are higher than the linear equation. The results also show that FA increases the performance of all applied models. Moreover, the results indicate that the ANFIS-FA is the most stable integrative model in comparison to the other embedded methods and reveal that GMDH and SVR are the most stable technique among all applied models. The results also show that the accuracy of the LE-FA technique is relatively low, RMSE=0.091. The most accurate results provide SVR-FA, RMSE=0.034.