Advancing Robust Optimization for Process Systems Engineering Applications

Abstract

Robust optimization is a popular method for incorporating parameter uncertainty into optimization models. Whether parameters represent the price of a feedstock or product, the operability of an edge in a network, or length of time required for a unit operation, the actual realization of a parameter can have a tremendous impact on the optimal solution of a model. Robust optimization centers on the use of uncertainty sets, which represent the possible parameter realizations which must be considered. In many cases, this uncertainty set may be directly imposed onto a constraint using duality theory, providing deterministic robust counterparts. In other cases, algorithmic developments are required to tractably solve robust optimization problems, which may occur in multiple stages.

This dissertation seeks to expand the theory and application of robust optimization for problems in process systems engineering. Theoretically, this focuses on decreasing the conservatism and increasing the applicability of robust optimization methods. This is addressed first through the development of new, tight bounds on the probability of constraint violation. These probabilistic bounds use the available information regarding the uncertain parameter distributions to determine the likelihood that a constraint becomes infeasible, using either the size of the uncertainty set a priori or the optimal solution values a posteriori. Then, new uncertainty sets are also derived for the case when both bounded and unbounded parameters exist in the same constraint, a previously unaddressed area of robust optimization.

Robust optimization is also shown to be effective in two major application areas. First, it is applied to process synthesis and global optimization of liquid transportation fuel refineries from natural gas and biomass, when feedstock prices, product prices, and investment costs are uncertain. The impact of parameter uncertainty on plant topologies and the probabilistic guarantees on profits are seen through multiple case studies. Finally, two-stage robust optimization is also applied to resilient network design, for which edges in a network may fail at random, rendering flow impossible along that edge. In these cases, a tailored column and constraint generation algorithm is developed to solve the two-stage problem, for which the relatively complete recourse assumption does not hold.