It is known that there exist a combinatorially large number of multicomponent distillation column configurations for a given feed and given product specifications. In the accompanying part I of the paper, we classified configurations into basic configurations (those that use (n - 1) columns for an n-component feed mixture) and non-basic configurations (those that use more than (n - I) columns for the same feed). As n exceeds four, the number of non-basic configurations greatly exceeds the number of basic configurations and have a huge impact on the size of the search space. However, through extensive calculations for a four-component feed, we have found that a non-basic configuration never has a lower heat duty than the lowest heat duty basic configuration. While prior researchers have proposed a mathematical formulation that could be used to generate only the set of basic configurations, we present an alternative supernetwork model to achieve this goal. We show how the supernetwork call be reduced to a binary integer program (BIP). and how all feasible configurations call be drawn for a given application using a Suitable solver. We present different solution techniques, including parallel algorithms based on the fact that the evaluation of the performance for each configuration is independent of any other configuration. Through such a procedure, all applicable basic configurations can be rank listed for a given application according to a chosen criterion. We also extend the supernetwork formulation to a unified non-convex MINLP that can be used in a flexible way to find the best candidate configurations for a given application. We show the power of our search formulation in accommodating general separation techniques other than distillation, Such as membranes, adsorption, etc. (C) 2009 Elsevier Ltd. All rights reserved.