Abstract - Sahinidis - 9704643 There are two approaches to process synthesis and optimization - heuristic and analytical. Heuristics offer fast solutions but do not guarantee optimality. Analytical integer programming approaches offer rigor but suffer combinatorial explosion of computational requirements (i.e. as the problems become larger, the solutions become computationally too large for most systems). This project will pursue analytical investigations as a theoretical means to characterize the behavior of heuristics and optimization algorithms and produce a framework that combines the strengths of the two approaches while eliminating their weaknesses. Preliminary results demonstrate the proposed paradigm in the context of the multi-period capacity expansion problem for chemical process networks. The multi-period aspects of it makes this problem similar to discrete-time scheduling. The same problem requires optimizing a superstructure as in synthesis problems. Analytical investigations for this problem lead to the development of a heuristic which is proved to be asymptotically optimal under standard assumptions about the problem parameters. In the more general scope of process synthesis and operations, analytical investigations present a large array of opportunities. The work planned will deal explicitly with problems in (I) multi-period process operations, (ii) synthesis of heat exchanger networks, and (iii) synthesis of separation networks. The PI's efforts will be directed towards (1) determining the computational complexity of these problems, (2) analyzing the worst case and expected behavior of existing heuristics, and (3) developing new, mathematical programming-based, polynomial time heuristics that are optimal in a statistical sense.
