Design space description through adaptive sampling and symbolic computation

Design space definition is one of the key parts in pharmaceutical research and development. In this article, we propose a novel solution strategy to explicitly describe the design space without recourse decisions. First, to smooth the boundary, the Kreisselmeier-Steinhauser (KS) function is applied to aggregate all inequality constraints. Next, for creating a surrogate polynomial model of the KS function, we focus on finding sampling points on the boundary of KS space. After performing Latin hypercube sampling (LHS), two methods are presented to efficiently expand the boundary points, that is, line projection to the boundary through any two feasible LHS points and perturbation around the adaptive sampling points. Finally, a symbolic computation method, cylindrical algebraic decomposition, is applied to transform the surrogate model into a series of explicit and triangular subsystems, which can be converted to describe the KS space. Two case studies show the efficiency of the proposed algorithm.