This study addresses critical challenges in multivariate optimization by: (1) developing efficient strategies for optimizing nonlinear response functions in high-dimensional parameter spaces, (2) quantifying comparative performance of traditional versus statistical design methodologies, (3) establishing mathematical frameworks for parameter interactions, and (4) validating results through comprehensive statistical analysis. A dual-phase optimization framework combined One-Variable-At-a-Time (OVAT) screening with Central Composite Design-based Response Surface Methodology (CCD-RSM). Five parameters were evaluated using rotatable CCD (α= 2.378) with 50 design points. Statistical analysis included analysis of variance (ANOVA), regression modeling, interaction quantification, and cross-validation. CCD-RSM demonstrated superior performance with model predictability improving from R2 = 0.892 (OVAT) to R2 = 0.947 (p < 0.0001). Optimal parameter combinations maximized response values from 4.0 to 9.2 units (130% improvement), outperforming OVAT predictions by 5.4%. Critical parameter interactions were quantified, revealing significant negative carbon-nitrogen interaction (β= –0.67, p < 0.001) and quadratic effects. Temperature emerged as the dominant factor (β= 1.42, p < 0.0001). Model validation confirmed excellent predictive capability (r = 0.973) with normal residuals and minimal multicollinearity. Statistical design methodology achieved 15% higher optimization performance and 30% fewer experimental evaluations compared to traditional approaches. The framework successfully quantified parameter interactions missed by univariate methods while maintaining statistical rigor. This research provides reproducible protocols applicable to engineering design, process optimization, and machine learning applications, representing significant advancement in optimization theory and practice.
Hussein et al. (Thu,) studied this question.