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The efficiency of a hybrid systems method which combined artificial neural networks (ANNs) as a modeling tool and genetic algorithms (GAs) as an optimizing method for input variables used in ANN modeling was assessed. Hence, as a new technique, it was applied for the prediction and optimization of the plant hormones concentrations and combinations for  in vitro  proliferation of Garnem (G × N15) rootstock as a case study. Optimizing hormones combination was surveyed by modeling the effects of various concentrations of cytokinin–auxin, i.e., BAP, KIN, TDZ, IBA, and NAA combinations (inputs) on four growth parameters (outputs), i.e., micro-shoots number per explant, length of micro-shoots, developed callus weight (CW) and the quality index (QI) of plantlets. Calculation of statistical values such as R 2  (coefficient of determination) related to the accuracy of ANN-GA models showed a considerably higher prediction accuracy for ANN models, i.e., micro-shoots number:  R  2  = 0.81, length of micro-shoots:  R  2  = 0.87, CW:  R  2  = 0.88, QI:  R  2  = 0.87. According to the results, among the input variables, BAP (19.3), KIN (9.64), and IBA (2.63) showed the highest values of variable sensitivity ratio for proliferation rate. The GA showed that media containing 1.02 mg/l BAP in combination with 0.098 mg/l IBA could lead to the optimal proliferation rate (10.53) for G × N15 rootstock. Another objective of the present study was to compare the performance of predicted and optimized cytokinin–auxin combination with the best optimized obtained concentrations of our other experiments. Considering three growth parameters (length of micro-shoots, micro-shoots number, and proliferation rate), the last treatment was found to be superior to the rest of treatments for G × N15 rootstock  in vitro  multiplication. Very little difference between the ANN predicted and experimental data confirmed high capability of ANN-GA method in predicting new optimized protocols for plant  in vitro  propagation.

frontiers in plant science

Mathematical Modeling and Optimizing of in Vitro Hormonal Combination for G × N15 Vegetative Rootstock Proliferation Using Artificial Neural Network-Genetic Algorithm (ANN-GA)