Due to rising energy costs, there is an increasing need to include the goal of energy conservation as an integral part of process synthesis. This paper discusses the problem of finding the optimum sequence of distillation columns for separating a multicomponent mixture, when heat exchange is permitted between the columns. The major difficulties are associated with the nonserial nature of the problem, the large combinatorial variety and the size of the optimization task. The synthesis strategy presented here overcomes these problems by the use of a bounding technique together with the Lagrangian theory from nonlinear programming. Accurate lower bounds on the optimal costs permit the elimination of nonoptimal sequences with minimal computational effort.