A heuristic Lagrangean approach for the synthesis of multiperiod heat exchanger networks

In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem size grows quickly with the number of streams and the number of periods resulting in a large scale problem to solve. In order to reduce the problem to a manageable size, we propose a specialized heuristic algorithm that relies on the concept of Lagrangean decomposition. We present an iterative scheme where feasible solutions are postulated from the Lagrangean decomposition subproblems, and the Lagrangean multipliers are updated through a subgradient method. Numerical examples are used to illustrate the proposed approach and the solutions are compared with the full space solutions with no decomposition. In general, slightly better solutions are found but in the terms of computational effort, its use is only justified as the problem size is increased.