Robust D-Optimal Mixture Designs Under Manufacturing Tolerances via Multi-Objective NSGA-II

Abstract

This study proposes a multi-objective optimization framework for generating statistically efficient and operationally robust designs in constrained mixture experiments with irregular experimental regions. In industrial settings, manufacturing variability from batching inaccuracies, raw material inconsistencies, or process drift can degrade nominally optimal designs. Traditional methods focus on nominal efficiency but neglect robustness, and few explicitly incorporate percentile-based criteria. To address this limitation, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was employed to simultaneously maximize nominal D-efficiency and the 10th-percentile D-efficiency (R-D10), a conservative robustness metric representing the efficiency level exceeded by 90% of perturbed implementations. Six design generation methods were evaluated across seven statistical criteria using two case studies: a constrained concrete formulation and a glass chemical durability study. NSGA-II designs consistently achieved top rankings for D-efficiency, R-D10, A-efficiency, and G-efficiency, while maintaining competitive IV-efficiency and scaled prediction variance (SPV) values. Robustness improvements were notable, with R-D10 by 1.5–5.1% higher than the best alternative. Fraction of design space plots further confirmed its resilience, demonstrating low variance and stable performance across the design space.