Multi-objective Deng's grey incidence analysis, orthogonal optimization, and artificial neural network modelling in hot-maceration-assisted extraction of African cucumber leaves (Momordica balsamina)

Due to the inherent multiple response characteristics in many biological and separation processes, parameter optimization and modelling is usually a daunting task. The integration of Deng's grey incidence model (GRA) and Taguchi optimization (TM) therefore helps in transforming multiple quality characteristics into a single response presented as the grey relational grade (GRG). This was applied to optimize the multiple quality response characteristics in the maceration-assisted extraction of African cucumber leaves. Two responses and five design factors were selected with L₁₆(2⁵) layout using signal-to-noise ratio as a point prediction feature. Under the optimized conditions, the optimum total phenolic content and antioxidant capacity of 0.8569 mg/ml gallic acid equivalence and 0.9259 mg/ml were achieved, respectively. The mass ratio was the highest contributor (38.2%), whereas the maceration time presented the least contribution (9.8%) to the cumulative response grade (GRG). In the neural network analysis, three models were deployed: Levenberg Marquardt backpropagation neural network (LMNN), gradient descent with adaptive learning rate neural network (GDALRNN), and the resilient back-propagation neural network (RPNN). A better prediction of hold-out data was achieved with the GDALRNN model, generating lesser absolute deviation error (MAD_GDALRNN = 0.099), root mean square error (RMSE_GDALRNN = 0.1033), relative mean bias error (rMBE_GDALRNN = − 0.24), and highest computational time (CT_GDALRNN = 8.8), which is expected of an effective model. Based on the GRG and the signal-to-noise ratio, the optimum conditions and the neural network model succinctly provided a benchmark for future assessment of complex relationship among extraction variables, which could form the basis for a potential future scale-up applications.