Approximation algorithms for the minimum number of matches problem in heat exchanger network synthesis

Although the use of heuristics has been prevalent in the process synthesis literature, their justification has been exclusively based on empirical evidence obtained through computational testing. As a result, heuristics currently in use offer no guarantee of optimality. Optimization algorithms, on the other hand, offer rigor but suffer from the combinatorial explosion of computational requirements necessary to produce an optimal solution. Recognizing this gap between heuristic and optimization approaches in process synthesis, we propose the use of analytical techniques in the development and assessment of heuristics. The primary purpose of this paper is to introduce the analysis of algorithm performance into the field of process synthesis and develop the first approximation algorithms for process synthesis. Approximation algorithms are heuristics with guaranteed performance. In the context of the classical matches problem in heat exchanger network synthesis, we develop approximation algorithms based on primal rounding, dual rounding, Lagrangean relaxation rounding, primal-dual approximation, and greedy approximation. We provide an analytical characterization of the worst-case behavior of these as well as any heuristic that may be devised for the matches problem. In computational experiments with a test set of 29 problems from the literature, we find that the developed suite of algorithms performs much better than its theoretical worst-case bound and provides solutions that average within 25% of optimality. On the other hand, five of these test problems are beyond the capabilities of current state-of-the-art optimization software. Finally, we pose a number of interesting research challenges in this area.