Modeling wheat yield with data-intelligent algorithms: artificial neural network versus genetic programming and minimax probability machine regression

In precision agriculture, data-intelligent algorithms applied for predicting wheat yield can generate crucial information about enhancing crop production and strategic decision-making. In this chapter, artificial neural network (ANN) model is trained with three neighboring station-based wheat yields to predict the yield for two nearby objective stations that share a common geographic boundary in the agricultural belt of Pakistan. A total of 2700 ANN models (with a combination of hidden neurons, training algorithm, and hidden transfer/output functions) are developed by trial-and-error method, attaining the lowest mean square error, in which the 90 best-ranked models for 3-layered neuronal network are utilized for wheat prediction. Models such as learning algorithms comprised of pure linear, tangent, and logarithmic sigmoid equations in hidden transfer/output functions, executed by Levenberg–Marquardt, scaled conjugate gradient, conjugate gradient with Powell-Beale restarts, Broyden–Fletcher–Goldfarb–Shanno quasi-Newton, Fletcher-Reeves update, one-step secant, conjugate gradient with Polak-Ribiére updates, gradient descent with adaptive learning, gradient descent with momentum, and gradient descent with momentum adaptive learning method are trained. For the predicted wheat yield at objective station 1 (i.e., Toba Taik Singh), the optimal architecture was 3-14-1 (input-hidden-output neurons) trained with the Levenberg–Marquardt algorithm and logarithmic sigmoid as activation and tangent sigmoid as output function, while at objective station 2 (i.e., Bakkar), the Levenberg–Marquardt algorithm provided the best architecture (3-20-1) with pure liner as activation and tangent sigmoid as output function. The results are benchmarked with those from minimax probability machine regression (MPMR) and genetic programming (GP) in accordance with statistical analysis of predicted yield based on correlations (r), Willmott's index (WI), Nash-Sutcliffe coefficient (EV), root mean-squared error (RMSE), and mean absolute error (MAE). For objective station 1, the ANN model attained the r value of approximately 0.983, with WI ≈ 0.984 and EV ≈ 0.962, while the MPMR model attained r ≈ 0.957, WI ≈ 0.544, and EV ≈ 0.527, with the results attained by GP model, r ≈ 0.982, WI ≈ 0.980, and EV ≈ 0.955. For optimal ANN model, a relatively low value of RMSE ≈ 192.02 kg/ha and MAE ≈ 162.75 kg/ha was registered compared with the MPMR (RMSE ≈ 614.46 kg/ha; MAE ≈ 431.29 kg/ha) and GP model (RMSE ≈ 209.25 kg/ha; MAE ≈ 182.84 kg/ha). For both objective stations, ANN was found to be superior, as confirmed by a larger Legates-McCabe's (LM) index used in conjunction with relative RMSE and MAE. Accordingly, it is averred that ANN is considered as a useful data-intelligent contrivance for predicting wheat yield by using nearest neighbor yield