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 flowsheets 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 flowsheets. The mathematical modeling 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 classified as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms, developed for the solution of this class of problems, are presented in this pap...

The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...

I am deeply grateful to my research advisor, Dr. Karlene A. Hoo, for her guid-ance and support during the four years that I was her graduate student. She has shown extreme patience in helping me understand the concepts of process control and optimization. I am also thankful to her for due diligence in proofreading all of my manuscripts and this dissertation. Her financial support also is appreciated for my studies and travel to the national meeting of the American Institute of Chemical Engineering conference and technical workshops. This work would not have been possible without my parents and their constant love and support. This work is dedicated to them. I would like to thank Dr. Uzi Mann for being on my committee and providing me with the project that ultimately became central to my dissertation. I take away the need to always define the problem. Thanks also go to Dr. Gary Gladysz, for providing me with a rewarding in-ternship at Los Alamos National Laboratory and for his service on my committee; and to Dr. Naz Karim for agreeing to serve on my committee. My academic career here has been enriched by many things including the industrial sponsors of the TTU Process Control and Optimization Consortium; and the faculty, helpful staff, and graduate students within our research group

. 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 flowsheets 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 flowsheets. The mathematical modeling 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 classified as Mixed-Integer Nonlinear Programming (MINLP) problems. A number of local optimization algorithms for MINLP problems are outlined in this paper: Generalized Benders Decompositi...

Many practical optimal control problems include discrete decisions. These may be either time–independent parameters or time–dependent control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed–integer linear programs, as well as in continuous optimal control problems, the combination of the two is yet an open field of research. We consider the question of lower bounds that can be obtained by a relaxation of the integer requirements. For general nonlinear mixed–integer programs such lower bounds typically suffer from a huge integer gap. We convexify (with respect to binary controls) and relax the original problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear integer problem. Building on this theoretical result we present a novel algorithm to solve mixed–integer optimal control problems, with a focus on discrete–valued control functions. Our algorithm is based on the direct multiple shooting method, an adaptive refinement of the underlying control discretization grid and tailored heuristic integer methods. Its applicability is shown by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits.