Advances in global optimization
Optimization is an active area of research and an important computational tool in many fields of science and engineering. While many effective global optimization algorithms have been developed over the past decades, there is still a need for improved robustness, reliability and efficiency. Examples where improvements in robustness, reliability and efficiency are needed include finding the global minimum of molecular modeling problems and finding all physically relevant solutions for mathematical models of chemical engineering applications. This dissertation describes two novel advanced global optimization tools—a multi-scale terrain/funneling methodology and logarithmic barrier-terrain method—that provide improved robustness, reliability and computational efficiency for solving complex optimization problems. ^ The multi-scale global optimization approach based on terrain/funneling is somewhat specific to problems in molecular modeling such as finding the molecular conformation of Lennard-Jones clusters, the conformation of n-alkane molecules, and the determination of crystal structures of solid materials because it makes use of the funnel structure of the potential energy landscapes in molecular modeling. Numerical results in this dissertation provide strong evidence that the multi-scale terrain/funneling method is a powerful global optimization method for reliably and efficiently solving molecular conformation problems with a large number of unknown variables.^ A barrier-terrain methodology is proposed as a natural extension to the original terrain method of Lucia and Yang for finding all physically relevant solutions of complex optimization problems in process engineering. This work clearly shows that all stationary and singular points to optimization problems do not necessarily lie in the same valley and are not necessarily smoothly connected. The key contribution of this phase of the thesis rests on the novel idea of using logarithmic barrier functions to create smooth connections between distinct valleys so that the terrain method can be used to explore the entire feasible region and find all physically relevant solutions. A barrier-terrain algorithm is described and details for a small example are presented to elucidate the underlying key ideas. The proposed barrier-terrain methodology is used to successfully solve a challenging collocation model for a spherical catalyst pellet problem with 20 variables and multiple solutions. ^
Rajeswar R Gattupalli,
"Advances in global optimization"
Dissertations and Master's Theses (Campus Access).