ABSTRACT

This chapter presents an effective computation strategy for evaluating the volumetric flexibility index (FIv) of high-dimensional systems with enhanced accuracy. By integrating several software tools, computation of the volumetric FIv requires a sequential implementation of five distinct steps. They are: placement of boundary points with a random line search; generation of simplexes using the Delaunay triangulation strategy; removal of infeasible simplexes; calculation of total hypervolume, and evaluation of volumetric FIv. The random nature of the line search provides a more precise characterization of the feasible region without a priori information of its geometric properties. By Delaunay triangulation, the hypervolumes of disjoint nonsimply connected and/or nonconvex regions can be computed accurately and efficiently. A heuristic rule is also suggested to facilitate proper selection of the number of boundary points. Finally, the effectiveness of the proposed computation strategy has been clearly demonstrated in a series of simple examples.