Hybrid and individual least square support vector regression methods for estimating the optimal moisture content of stabilized soil

The Optimum moisture content \((OMC)\) $(OMC)$ is a pivotal factor in the composition of embankment fill soil materials employed in transportation construction. This article introduces a groundbreaking methodology for the anticipation of \(OMC\) $\mathit{OMC}$ in soil-stabilizer blends through the utilization of one of the Machine Learning \((ML)\) $(ML)$ models, including Least Square Support Vector Regression \((LSSVR)\) $(LSSVR)$ analysis. Furthermore, this study pioneers the creation of dedicated \(LSSVR\) $\mathit{LSSVR}$ prediction models meticulously tailored to ensure the utmost precision in \(OMC\) $\mathit{OMC}$ estimation. To fortify the model’s accuracy, the research incorporates two ingenious meta-heuristic algorithms, namely the Beluga Whale Optimization \((BWO)\) $(BWO)$ and the Sooty Tern Optimization Algorithm \((STO)\) $(STO)$ . These algorithms serve a dual purpose by corroborating the models’ reliability and by validating them against an expansive array of \(OMC\) $\mathit{OMC}$ samples extracted from diverse soil types derived from comprehensive stabilization test results previously documented. The outcomes of this rigorous analysis unveil the emergence of three distinct models: \(LSST\) $\mathit{LSST}$ , \(LSBW\) $\mathit{LSBW}$ , and an individual \(LSSV\) $\mathit{LSSV}$ model. The analyses of developed models have been applied with R², RMSE, MAE, SI, NRMSE, a20-index, RSR, VAF, IOA, and PI to determine the suitable model for OMC prediction. As a result, the \(LSST\) $\mathit{LSST}$ model surfaces as a standout performer, boasting an extraordinary R² value of \(0.993\) $0.993$ alongside an exceptionally low \(RMSE\) $\mathit{RMSE}$ value of \(0.613\) $0.613$ . These results not only substantiate the precision and consistency of the \(LSST\) $\mathit{LSST}$ model but also underscore its potency in prognosticating soil stabilization outcomes. In essence, this approach presents a promising way for precisely predicting \(OMC\) $\mathit{OMC}$ within soil stabilization blends across a spectrum of engineering applications.