For a reliable optimal molecular design, imprecision associated with property-prediction models cannot be neglected. This study presents a novel sampling approach to stochastic optimization, incorporating property-prediction uncertainty effects in a robust, generalized optimization framework. Detailed uncertainty analysis addresses, through nine case studies, various issues in computer-aided molecular design under uncertainty. Results indicate that property-prediction uncertainty can significantly impact the optimal molecular designs. Additional complex cases with nonlinear or black-box models, nonlinear objective function and constraints, and nonstable distribution for model parameter uncertainty representation highlight the flexibility and versatility of this approach. Sensitivity analysis of uncertainties in the model parameters was also made possible in this generalized framework. Uncertainties, the focus of any future research, were identified through this critical model. Increased computational efficiency of this approach and wider applicability to solve problems involving various kinds of objective functions Lend constraints, and different forms of uncertainties, is illustrated in the context of polymer design case studies.