(756d) Tight Reformulation of Transshipment Model for Heat Integration Problems

Heat integration is essential for improving energy efficiency and reducing operating cost in power, refinery and chemical plants, and it is also important in the integration of advanced fossil energy systems to reduce CO₂ emissions. The transshipment model is widely used in the synthesis of heat exchange network due to its compact formulation, where linear programming (LP) version of transshipment model minimizes the utility cost, and mixed-integer linear programming (MILP) version of transshipment model further minimizes the number of heat exchangers based on the results of LP model [1]. However, the MILP transshipment model becomes computationally expensive to solve for large-scale problems because of its large LP relaxation gap. The current MILP transshipment model can only practically solve problems with size up to 15 hot streams and 15 cold streams, which limits its applicability to real problems. Another reason for this performance is the fact that in the objective for the minimum number of units, all binaries are multiplied by a coefficient of one, which tends to introduce degeneracies.

In this work, we present several reformulations and computational strategies for solving the MILP transshipment model. The MILP model is reformulated in several ways to obtain tighter relaxations. First, the heat exchange rate is disaggregated for all temperature intervals like in the lot sizing problem [2], which in fact gives rise to the MILP transportation model [3], in which tighter upper bounds for the heat exchanges can be used. Second, special integer cuts are added to constrain the matches and to reduce non-optimal matches between hot and cold streams. Finally, as an alternative solution strategy, Generalized Benders decomposition is applied to the MILP problem, treating the binaries as complicating variables which gives rise to LP subproblems which can be solved very fast. This in turn allows the generation of multiple cuts. Furthermore, we strengthen the MILP master problem with the addition of surrogate constraints from the LP transshipment model to improve the lower bound predicted by the MILP master problem to reduce the solution time of the MILP. Computational results are presented for large problems showing that the computational time for solving the MILP transshipment model can be significantly reduced applying some of the above approaches. This study also finds that problems with dissimilar FCps, like many industrial problems, are in fact solved faster than those with similar FCps, which tend to be academic examples.

Reference

[1]   Papoulias SA, Grossmann IE. A structural optimization approach to process synthesis – II. Heat recovery networks. Computers and Chemical Engineering. 1983;7(6):707-721.

[2]   Barany I, van Roy TJ, Wolsey LA. Strong formulations for multi-item capacitated lot sizing. Management Science. 1984;30(10):1255-1261.

[3]   Cerda J, Westerburg AW. Synthesizing heat exchanger networks having restricted stream/stream matches using transportation problem formulations. Chemical Engineering Science. 1983;38(10):1723-1740.