The operating cost of a multicomponent distillation system comprises two major aspects: the overall heat duty requirement and the temperature levels at which the heat duties are generated and rejected. The second aspect, often measured by the thermodynamic efficiency of the distillation system, can be quantified by its total exergy loss. In this article, we introduce a global optimization framework for determining the minimum total exergy loss required to distill any ideal or near-ideal multicomponent mixture using a sequence of columns. Desired configurations identified by this new framework tend to use milder-temperature reboilers and condensers and are thus attractive for applications such as heat pump assisted distillation. Through a case study of shale gas separations, we demonstrate the effectiveness of this framework and present various useful physical insights for designing energy efficient distillation systems.