A Functional Data Analysis-Based Framework for Modeling and Multi-Objective Optimization of Sustained-Release Drug Delivery Systems

Objectives: An integrated methodological framework was developed for modeling and multiobjective optimization of sustained-release drug delivery systems. Methods: The cumulative release percentage was fitted as a function curve, and functional principal component analysis was subsequently used to transform the function curves into functional principal component scores (FPCs). FPCs were then treated as dependent variables, while the proportions of the formulation factors were used as independent variables to construct Scheffé polynomial regression models. Finally, Non-dominated Sorting Genetic Algorithm III (NSGA-III) was applied to perform multi-objective optimization. Results: FPC1, FPC2, and FPC3 captured 95.18%, 4.39%, and 0.32% of the total variation, respectively. Corresponding Scheffé polynomial regression models were established, including quadratic models for FPC1 (adjusted R2 = 0.751, AIC = 168.557) and FPC2 (adjusted R2 = 0.592, AIC = 119.302), and a special cubic model for FPC3 (adjusted R2 = 0.597, AIC = 64.574). The NSGA-III algorithm generated a Pareto optimal set, yielding stable formulation compositions with mean (SD) values of X1 = 0.123 (0.015), X2 = 0.821 (0.032), X3 = 0.012 (0.017), and X4 = 0.045 (0.015). The corresponding FPCs were −41.787 (2.544), 10.009 (0.168), and 8.264 (0.010) for FPCs1–FPCs3, respectively. The reconstructed cumulative release percentages were 42.471 (1.661), 52.623 (2.868), 69.942 (1.200), 84.275 (1.010), and 93.330 (0.832), demonstrating good agreement with the target release profiles. Conclusions: The integrated FDA–Scheffé–NSGA-III framework provides a robust and effective approach for accurately modeling release behavior and optimizing sustained-release formulations.