A novel framework for flexibility assessment in design spaces defined by a set of affine bounds

A novel framework for flexibility assessment in the context of system design is proposed. We deal with the case when the design space is bounded by a set of affine bounds defining a convex-hull. For this class of problems several flexibility metrics can be calculated, which are related to the minimum/maximum distances between any point in the design space and the less/most distant points at its bounds, respectively. In the first case, the distance functions are obtained via projection to individual bounds, and in the second case, the distance functions are defined via the Euclidean distance to the corners of convex hulls. These two sets of functions can then be used separately to calculate the minimum/maximum of the complete set of minimum/maximum distance functions over the full design space. This approach effectively enables the definition of four multi-parametric programming problems, and deliver four flexibility maps from their solutions. Flexibility maps based on the average of the two sets of distance functions are also delivered. This offers a plethora of complementary metrics for flexibility assessment, which extend beyond the classic approach based on the definition of feasible boxes. From the full set of solutions enabled by this framework, the minimum–minimum and maximum–maximum distance-based flexibility maps stand out as the extreme and most useful cases for flexibility assessment; the initial experimentation with these maps suggest that the average-minimum and particularly the average-maximum distance cases also provide useful information as an overall score on flexibility for any points within the design space.