Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering

David Bernal Neira
Nonlinear discrete optimization problems arise in many different disciplines, given the modeling versatility associated with nonlinear constraints and discrete decision variables. In Process Systems Engineering, such problems appear in applications ranging from optimal process design and synthesis, process planning, scheduling, and control, and molecular design. Albeit their many applications that arise from its universal modeling capabilities, finding optimal solutions to these optimization
more » ... blems is a challenging task, given the computational complexity associated with their solution. The design of novel algorithms and the correct modeling of these problems arise among the different ways to overcome this complexity. In particular, tackling these problems with the correct combination of mathematical modeling and solution procedure is an efficient strategy to address them. The objective of this Thesis is to propose new solutions and modeling methods for nonlinear discrete optimization problems, which lead to improvements with respect to the existing solution approaches. We initially pose the discrete nonlinear optimization problems in the context of Mathematical Programming. The problems that we consider solving here can be classified as Mixed-Integer Nonlinear Programming (MINLP) problems. In Chapter 2 we provide a review on the different solution algorithms and existing software to deterministically solve a subclass of MINLP problems called convex MINLP. Among those algorithms, we consider the Outer-approximation (OA) method, which decomposes the MINLP into a Mixed-Integer Nonlinear Programming (MILP) problem and a Nonlinear Programming (NLP) problem. We perform a large computational study comparing the performance of more than sixteen different software implementations, solvers, by solving over 350 convex MINLP problems from benchmark library MINLPLib. This large study allowed us to identify how the different solvers perform based on features from the problem to be solved. Chapter 3 presents the implementati [...]
doi:10.1184/r1/19146305.v1 fatcat:dvqfoztozjes7ejmoldd2smrha