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<p>This research examines the applicability of nature-inspired, population-based metaheuristic swarm intelligence algorithms for estimating resilient modulus (M<sub>R</sub>) of pavement subgrade soil. A dataset of 2,813 samples was systematically divided into training and testing subsets, including soil, stress, moisture, and environmental variables. Three machine learning (ML) models—Multivariate Adaptive Regression Splines (MARS), Extreme Learning Machine (ELM), and Deep Neural Network (DNN)—were developed to predict M<sub>R</sub> values. To enhance prediction accuracy, a swarm intelligence-based approach, Grey Wolf Optimizer (GWO), was used to optimize and combine outputs of the individual ML models. Reliability and robustness were evaluated using 10-fold cross-validation, Shapley Additive Explanation (SHAP) analysis, partial dependence plots (PDP), and error box plots. Generalization capability was further assessed with an independent experimental dataset of 40 M<sub>R</sub> specimens. Results demonstrate that the GWO-DNN model outperformed the others, achieving the highest prediction accuracy (R² = 0.971, RMSE = 4.05&#xa0;MPa). For practical use, a graphical user interface (GUI) was developed for direct M<sub>R</sub> estimation. This study advances data-driven geo-transportation engineering by improving M<sub>R</sub> estimation efficiency and sustainability.</p>

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A Grey Wolf Optimized Deep Learning Framework for Robust Prediction of Subgrade Resilient Modulus

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Aman Mishra,
  • Laxmikant Yadu,
  • Shrabony Adhikary

摘要

This research examines the applicability of nature-inspired, population-based metaheuristic swarm intelligence algorithms for estimating resilient modulus (MR) of pavement subgrade soil. A dataset of 2,813 samples was systematically divided into training and testing subsets, including soil, stress, moisture, and environmental variables. Three machine learning (ML) models—Multivariate Adaptive Regression Splines (MARS), Extreme Learning Machine (ELM), and Deep Neural Network (DNN)—were developed to predict MR values. To enhance prediction accuracy, a swarm intelligence-based approach, Grey Wolf Optimizer (GWO), was used to optimize and combine outputs of the individual ML models. Reliability and robustness were evaluated using 10-fold cross-validation, Shapley Additive Explanation (SHAP) analysis, partial dependence plots (PDP), and error box plots. Generalization capability was further assessed with an independent experimental dataset of 40 MR specimens. Results demonstrate that the GWO-DNN model outperformed the others, achieving the highest prediction accuracy (R² = 0.971, RMSE = 4.05 MPa). For practical use, a graphical user interface (GUI) was developed for direct MR estimation. This study advances data-driven geo-transportation engineering by improving MR estimation efficiency and sustainability.