Development of a robust design optimization algorithm for hierarchical time series pharmaceutical problems

• There is room for improvement to simultaneously solve interdisciplinary optimization problems with drug development. • Customized experiments and estimation frameworks for representing pharmaceutical quality characteristics (i.e., time-oriented, multiple, and hierarchical responses) functional relationships between input factors and hierarchical time-oriented output responses are proposed. • Hierarchical time-oriented robust design optimization models (i.e., priority-based, weight-based, and integrated models) are proposed for these interdisciplinary pharmaceutical formulation problems. Experimental design and robust design (RD) methodologies have received attention from researchers to improve the performance of many different quality characteristics and solve problems at low costs. However, there is room for improvement to simultaneously solve interdisciplinary optimization problems associated with time-oriented, multiple, and hierarchical responses. This paper proposes a new RD modeling and optimization algorithm for drug development based on three research motivations: Firstly, customized experiments and estimation frameworks for representing pharmaceutical quality characteristics (i.e., time-oriented, multiple, and hierarchical responses) and functional relationships between input factors and hierarchical time-oriented output responses are proposed. Secondly, new hierarchical time-oriented robust design (HTRD) optimization models (i.e., priority-based, weight-based, and integrated models) are developed for these interdisciplinary pharmaceutical formulation problems. Finally, the pharmaceutical case study for drug formulation development is conducted for demonstration purposes. Based on the case study results, the proposed approach can provide optimal solutions with significantly small biases and variances.