The volumetric flexibility index (FIv) of a chemical system can be viewed geometrically as the ratio between the hypervolume of feasible region and that of a hypercube bounded by the expected upper and lower limits of uncertain process parameters. Although several methods have already been developed to compute FIv, none of them are effective for solving the high-dimensional problems defined in nonconvex, non-simply connected or disconnected regions. While the available shortcut approaches are not accurate enough, successful tuning of the algorithmic parameters is mandatory for producing credible estimates with the more elaborate existing strategies. The above practical issues in volume estimation are thoroughly addressed in the present research. The most critical step in the proposed procedure is to characterize the feasible region accurately. To this end, the domain boundaries in parameter space are first identified with the feasible proximity points obtained by following a random line search algorithm. The Delaunay triangulation technique is then implemented to generate simplexes on the basis of such near-boundary points. By checking the centroids of these simplexes, the infeasible ones may be identified and eliminated. Finally, the hypervolumes of all feasible simplexes are summed to determine the volumetric flexibility index. Extensive case studies with 2-7 uncertain parameters have been carried out to show the superior capabilities of the proposed computation strategies. (C) 2016 Elsevier Ltd. All rights reserved.