A novel feasibility analysis approach based on dimensionality reduction and shape reconstruction

Optimal and feasible operation of process plants demand accurate knowledge of the effect of parameter uncertainty on process design and operation. There has been considerable effort towards accurate representation of the feasible operation range and different metrics have been proposed in literature to quantify the operational flexibility. While these methods are largely successful in addressing convex problems, their applicability becomes restricted for general nonconvex problems. The feasibility analysis technique proposed in this paper considers the feasible region as an object, and applies surface reconstruction ideas to capture and define the shape of the object. The procedure starts by first sampling the feasible region to have a representation of the feasible space, an a shape is then constructed with the sampled points, thus generating a polygonal representation of the feasible parameter space. With this information at hand, any point can be checked for its feasibility by applying the point-in-polygon algorithm. The proposed method is general, and can be applied to any convex, non-convex even disjoint problems without any further modifications.