We present a general Global Minimization Algorithm (GMA) to identify basic or thermally coupled distillation configurations that require the least vapor duty under minimum reflux conditions for separating any ideal or near-ideal multicomponent mixture into a desired number of product streams. In this algorithm, global optimality is guaranteed by modeling the system using Underwood equations and reformulating the resulting constraints to bilinear inequalities. The speed of convergence to the globally optimal solution is increased by using appropriate feasibility and optimality based variable-range reduction techniques and by developing valid inequalities. The GMA can be coupled with already developed techniques that enumerate basic and thermally coupled distillation configurations, to provide for the first time, a global optimization based rank-list of distillation configurations. (C) 2016 American Institute of Chemical Engineers