In response to frequently changing demands on gaseous products of cryogenic air separation units, an automatic load change (ALC) system is desired to optimally change the products and recycle rates under widely variable load conditions. However, due to the complex heat integration in the process, simulation and optimization of cryogenic air separation units (ASUs) often fails to converge with traditional Newton-based algorithms. A homotopy-based backtracking method (HBM) is presented and applied to the process operation of a cryogenic ASU under wide changes in load conditions. Different from traditional process simulation, a load vector is introduced to denote the variation of the operation point due to the load change. The HBM solves the process in a way that heads toward the target and backtracks at failure. The results show that a large number of operating points that failed to converge with traditional algorithms can be successfully optimized with the proposed method. (C) 2009 Elsevier B.V. All rights reserved.