What does this research mean for the field?

Integrating the Rao-1 metaheuristic optimization algorithm with machine learning models significantly enhances the predictive accuracy of soil compaction parameters, specifically maximum dry density and optimum moisture content. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to develop a robust framework for predicting maximum dry density and optimum moisture content using machine learning techniques.

July 10, 2026Open Access

Metaheuristic optimized hybrid machine learning framework for predicting soil compaction parameters

BABayram AteşKaradeniz Technical University JTJun Jiat TiangMultimedia University MEMohammad Azım EırgashKaradeniz Technical University

Key Points

This research aims to develop a robust framework for predicting maximum dry density and optimum moisture content using machine learning techniques.
Hybrid modeling framework integrating Rao-1 optimization, ANN, RF, and GB models
Dataset of 397 soil samples characterized by gradation properties and Atterberg limits used for development and validation
Rao-1 algorithm applied to optimize weights and hyperparameters for enhanced predictive accuracy.
ANN model predictions of MDD improved R^2 from 0.8512 to 0.9277 with RMSE reduction from 0.4327 to 0.2865.
RF and GB models achieved R^2 values of 0.9176 and 0.9213, respectively, with notable performance increases.
OMC prediction improved R^2 from 0.8234 to 0.9245 with RMSE reduced from 0.4677 to 0.3071 using the Rao-1 optimized ANN.

Abstract

Accurate prediction of maximum dry density (MDD) and optimum moisture content (OMC) is critical for effective compaction control and earthwork design in geotechnical engineering. Conventional laboratory compaction tests are time-consuming and resource-intensive, motivating the adoption of reliable data-driven prediction models. In this study, a hybrid modeling framework integrating the Rao-1 metaheuristic optimization algorithm with Artificial Neural Network (ANN), Random Forest (RF), and Gradient Boosting (GB) models is proposed for predicting MDD and OMC. A dataset comprising 397 soil samples, characterized by gradation properties and Atterberg limits, is utilized for model development and validation. The Rao-1 algorithm is employed to optimize network weights and model hyperparameters, aiming to enhance convergence behavior and predictive accuracy. Comparative results reveal that Rao-1 optimization consistently enhances model performance across all algorithms and target variables. For MDD prediction, the ANN model achieves an increase in R 2 from 0.8512 to 0.9277, accompanied by a reduction in RMSE from 0.4327 to 0.2865. Similarly, the RF and GB models show notable improvements, with optimized R 2 values reaching 0.9176 and 0.9213, respectively. For OMC prediction, the Rao-1 optimized ANN exhibits the highest accuracy, improving R 2 from 0.8234 to 0.9245 and reducing RMSE from 0.4677 to 0.3071, while optimized RF and GB models also demonstrate substantial error reductions. Furthermore, SHapley Additive exPlanations (SHAP) and the Cosine Amplitude Method (CAM) were integrated to enhance model interpretability, enabling transparent evaluation of feature contributions and providing deeper insight into the influence of geotechnical parameters. Overall, the proposed Rao-1–based hybrid framework significantly enhances predictive accuracy and error minimization compared to conventional models. The results confirm the robustness and effectiveness of Rao-1 optimization in data-driven soil compaction modeling, offering a practical decision-support tool for process innovation and the preliminary estimation of compaction parameters, rather than replacing standardized laboratory testing.

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