Computational complexity of heat exchanger network synthesis

Heat exchanger network synthesis (HENS) has been the subject of a significa nt amount of research over the last 40 years. While significant progress ha s been made towards solving the problem, its computational complexity is no t known, i.e., it is not known whether a polynomial algorithm might exist f or the problem or not. This issue is addressed in this paper through a comp utational complexity analysis. We prove that HENS is, NP-hard, thus refuting the possibility for the exist ence of a computationally efficient (polynomial) exact solution algorithm f or this problem. While this complexity characterization may not be surprisi ng, our analysis shows that HENS is NP-hard in the strong sense. Therefore, HENS belongs to a particularly difficult class of hard optimization proble ms. Further, via restriction to the 3-partition problem, our complexity pro ofs reveal that even the following simple HENS subproblems are. NP-hard in the strong sense: (a) the minimum number of matches target problem, (b) the matches problem with only one temperature interval, uniform cost coefficie nts, and uniform heat requirements of all cold streams. These results facilitate the computational complexity analysis of more comp lex HENS problems and provide new insights to structural properties of the problem. They also provide motivation for the development of specialized op timization algorithms and approximation schemes. (C) 2001 Elsevier Science Ltd. All rights reserved.