Optimizing PGRs for in vitro shoot proliferation of pomegranate with bayesian-tuned ensemble stacking regression and NSGA-II: a comparative evaluation of machine learning models

Abstract

Background: The process of optimizing in vitro shoot proliferation is a complicated task, as it is influenced by interactions of many factors as well as genotype. This study investigated the role of various concentrations of plant growth regulators (zeatin and gibberellic acid) in the successful in vitro shoot proliferation of three Punica granatum cultivars ('Faroogh', 'Atabaki' and 'Shirineshahvar'). Also, the utility of five Machine Learning (ML) algorithms-Support Vector Regression (SVR), Random Forest (RF), Extreme Gradient Boosting (XGB), Ensemble Stacking Regression (ESR) and Elastic Net Multivariate Linear Regression (ENMLR)-as modeling tools were evaluated on in vitro multiplication of pomegranate. A new automatic hyperparameter optimization method named Adaptive Tree Pazen Estimator (ATPE) was developed to tune the hyperparameters. The performance of the models was evaluated and compared using statistical indicators (MAE, RMSE, RRMSE, MAPE, R and R²), while a specific Global Performance Indicator (GPI) was introduced to rank the models based on a single parameter. Moreover, Non‑dominated Sorting Genetic Algorithm‑II (NSGA‑II) was employed to optimize the selected prediction model.

Results: The results demonstrated that the ESR algorithm exhibited higher predictive accuracy in comparison to other ML algorithms. The ESR model was subsequently introduced for optimization by NSGA‑II. ESR-NSGA‑II revealed that the highest proliferation rate (3.47, 3.84, and 3.22), shoot length (2.74, 3.32, and 1.86 cm), leave number (18.18, 19.76, and 18.77), and explant survival (84.21%, 85.49%, and 56.39%) could be achieved with a medium containing 0.750, 0.654, and 0.705 mg/L zeatin, and 0.50, 0.329, and 0.347 mg/L gibberellic acid in the 'Atabaki', 'Faroogh', and 'Shirineshahvar' cultivars, respectively.

Conclusions: This study demonstrates that the 'Shirineshahvar' cultivar exhibited lower shoot proliferation success compared to the other cultivars. The results indicated the good performance of ESR-NSGA-II in modeling and optimizing in vitro propagation. ESR-NSGA-II can be applied as an up-to-date and reliable computational tool for future studies in plant in vitro culture.

Keywords: Evolutionary optimization algorithm; Hyperparameter tuning; Machine learning; Plant growth regulators; Pomegranate in vitro propagation.

Fig. 1

A schematic view of different factors that influence physiological disorders of in vitro plants

Fig. 2

In vitro propagation of pomegranate cultivar ‘Faroogh’. a Single-node explants, b shoot proliferation in mMS medium supplemented with 0.750 mg/L zeatin and 0.500 mg/L gibberellic acid, c shoot proliferation in control medium, and (d) shoots propagated in mMS medium supplemented with 0.750 mg/L zeatin and 0.500 mg/L gibberellic acid

Fig. 3

The schematic diagram of the step-by-step procedure of the present research includes (A) pomegranate micropropagation, B modeling growth parameters based on K-fold cross-validation and ATPE algorithm using MLs, and (C) optimization process of growth parameters via non-dominated sorting genetic algorithm-II (NSGA-II)

Fig. 4

The violin plots of the performance metrics of analyzed models on the observed value vs. the predicted values on in vitro pomegranate growth parameters including: A leave number, B proliferation, C explant survival, D shoot length

Fig. 5

Comparison between the predicted compressive strength via RF, XGB, SVR, ESR, and ENMLR models. A leave number, B proliferation, C explant survival, D shoot length of the pomegranate cultivar ‘Atabaki’

Fig. 6

Comparison between the predicted compressive strength via RF, XGB, SVR, ESR, and ENMLR models. A leave number, B proliferation, C explant survival, D shoot length of the pomegranate cultivar ‘Faroogh’

Fig. 7

Comparison between the predicted compressive strength via RF, XGB, SVR, ESR, and ENMLR models. A leave number, B proliferation, C explant survival, D shoot length of the pomegranate cultivar ‘Shirineshahvar’