Nonlinear and mixed-integer optimization in chemical process network systems

The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the Process Synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process owsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process owsheets. The mathematical model-ing of the superstructure has a mixed set of binary and continuous variables and results in a mixed-integer optimization model. Due to the nonlinearity of chemical models, these problems are generally classiied as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms for MINLP problems are outlined in this paper: Generalized Benders Decomposition (GBD), Outer Approximation (OA), Generalized Cross Decomposition (GCD), Extended Cutting Plane (ECP), Branch and Bound (BB), and Feasibility Approach (FA), with particular emphasis on the Generalized Benders Decomposition. Recent developments for the global optimization of nonconvex MINLPs are then introduced. In particular, two branch-and-bound approaches are discussed: the Special structure Mixed Integer Nonlinear BB (SMIN-BB), where the binary variables should participate linearly or in mixed-bilinear terms, and the General structure Mixed Integer Nonlinear BB (GMIN-BB), where the continuous relaxation of the binary variables must lead to a twice-diierentiable problem. Both algorithms are based on the BB global optimization algorithm for nonconvex continuous problems. Once some of the theoretical issues behind local and global optimization algorithms for MINLPs have been exposed, attention is directed to their practical use. The algorithmic framework MINOPT is discussed as a computational tool for the solution of process synthesis problems. It is an implementation of a number of local optimization algorithms for the solution of MINLPs. The synthesis problem for a heat exchanger network is then presented to demonstrate the application of some local MINLP algorithms and the global optimization SMIN-BB algorithm.