Nature-inspired hybrid techniques of IWO, DA, ES, GA, and ICA, validated through a k-fold validation process predicting monthly natural gas consumption

Abstract

Current study aimed to combine the multi-layer Perceptron (MLP) neural network technique with five metaheuristic computational algorithms, namely invasive weed optimization (IWO-MLP), dragonfly algorithm (DA-MLP), evolution strategy (ES-MLP), genetic algorithm (GA-MLP), and imperialist competitive algorithm (ICA-MLP) for estimating the monthly natural gas consumption (NGC). For the case of this study, the NGC data was collected from the United States (U.S.) was chosen. To achieve this, a dataset composed of eight independent factors, namely, dry gas production, NGPL production, gross withdrawals, supplemental gaseous fuels, net storage withdrawals, marketed production, net imports, and balancing items, along with a dependent variable of natural gas consumption is provided. Out of 39 samples, a 3-fold ratio is taken to select the datasets of training and testing randomly. During the calculation phase, and through a trial and error procedure, the optimal parameters of the MLP, IWO-MLP, DA-MLP, ES-MLP, GA-MLP, ICA-MLP networks are taken into consideration. To assess the reliability of the proposed technique with the real collected data, three well-known statistical criteria, including mean square error (MSE) and root mean square error (RMSE) as well as coefficient of determination (R²), are introduced. These indices help to measure the level of accuracy of the used models. It is found that the IWO can be a better predictive network comparing to other hybridized techniques reducing the error performance of the MLP method. The predicted results reveal that hybridizing optimization algorithms could improve the prediction accuracy and helps the MLP to perform more efficiently. The recorded in testing MSE for the IWO-MLP, DA-MLP, ES-MLP, GA-MLP, ICA-MLP prediction techniques (i.e., used for U.S. natural gas consumption estimation) were found 0.000013, 0.002358, 0.024744, 0.013244, and 0.048572, respectively. In the sense of U.S. natural gas consumption prediction, the training R2 value to 0.9999, 0.9996, 0.9971, 0.9996, and 1.0000 and testing R2 value of 0.9999, 0.9995, 0.9956, 0.9984, and 0.8115 show that the outputs of the ensemble models are more correlated with the real data.