In this study, we have formulated a general geometric based shortcut method that can be used for multi-feed multi-component columns. Simulated annealing algorithm is used to obtain the solution. This method can be used to find the minimum reflux ratio, minimum number of stages at total reflux, and number of stages at given reflux ratio, as well as the reflux ratio with given number of stages. Reliable solutions were obtained for different types of splits in both single-feed columns and double-feed columns. This method serves as the basis for developing a general method for estimating minimum reflux for other more complex columns. 2008 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.