Generating Robust Optimal Mixture Designs Due to Missing Observation Using a Multi-Objective Genetic Algorithm

Abstract

Missing observation is a common problem in scientific and industrial experiments, particularly in a small-scale experiment. They often present significant challenges when experiment repetition is infeasible. In this research, we propose a multi-objective genetic algorithm as a practical alternative for generating optimal mixture designs that remain robust in the face of missing observation. Our algorithm prioritizes designs that exhibit superior D-efficiency while maintaining a high minimum D-efficiency due to missing observations. The focus on D-efficiency stems from its ability to minimize the impact of missing observations on parameter estimates, ensure reliability across the experimental space, and maximize the utility of available data. We study problems with three mixture components where the experimental region is an irregularly shaped polyhedral within the simplex. Our designs have proven to be D-optimal designs, demonstrating exceptional performance in terms of D-efficiency and robustness to missing observations. We provide a well-distributed set of optimal designs derived from the Pareto front, enabling experimenters to select the most suitable design based on their priorities using the desirability function.

Keywords

• genetic algorithm
• multi-objective functions
• missing observation
• mixture experiment
• D-efficiency