Novel formulations of flexibility index and design centering for design space definition

Abstract

Design space definition is one of the key issues in pharmaceutical research and development. Flexibility index and design centering are two complementary ways to estimate a candidate design space. In this study, we first propose a novel formulation of flexibility index based on a direction search method, which is applied to any shape of the design space. Next, we propose two design centering methods. The vertex direction search method is first developed as a single-level optimization model, which is rigorous for convex regions. Next, based on the proposed flexibility index model, a derivative-free optimization (DFO) method is developed for solving the bi-level optimization models involved in design centering problems, which is applicable not only to convex but also to nonconvex problems. In order to find near global solutions, latin hypercube sampling (LHS) is used to generate multiple starting points for the DFO solver. The solution yields the optimal nominal point, which is the candidate point with the largest flexibility index. Several case studies demonstrate the performance of the proposed methods.