| Process synthesis problems are typically difficult discrete optimization problems. Two distinct solution philosophies have emerged through the study of process systems engineering problems in recent years. Heuristics offer computationally efficient algorithms that produce solutions quickly, however they offer no guarantee of optimality. Optimization approaches offer rigor, but they suffer from the combinatorial explosion of computational requirements necessary to produce the optimal solution. Recognizing this gap between heuristic and optimization approaches in process systems engineering, the fundamental issues of introducing rigor in the use and practice of heuristics are addressed by solving discrete optimization problems in an approximate way to escape the curse of dimensionality, while avoiding a significant compromise of optimality.; Heat exchanger network synthesis (HENS) is a process systems engineering problem that has been the subject of a significant amount, of research over the last century. Nevertheless, there are three major unresolved issues in this area: (1) the computational complexity of the problem is not known; i.e., it is not known whether or not a polynomial algorithm might exist for the problem, (2) existing heuristics come with no guarantee of optimality, and (3) no complete formulation encompassing all possible network configurations exists. All three of these issues are addressed in this thesis.; Although exact algorithms have been successful in tackling HENS problems of small size, heuristics are required for large-scale problems, and nothing is known about the quality of the solutions provided by heuristics. Analytical investigations are suggested to characterize the behavior of both exact and heuristic solution methods as well as to provide a means to consolidate the strengths of both approaches and eliminate their weaknesses. |
