Advanced Computational Models for Multistage Stochastic Optimization of Process Systems with Renewable Resources

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

ABSTRACT PI: Ignacio E. Grossmann Institution: Carnegie Mellon University Proposal Number: 0521769 Title: Advanced Computational Models for Multistage Stochastic Optimization of Process Systems with Renewable Resources Handling uncertainties in the design of process systems under multiperiod operation is becoming an increasingly important issue, particularly when dealing with systems such as bioprocesses where there are significant uncertainties in the availability and quality of the feedstocks and in the yields of the process units. A major objective of this project is to develop novel computational models for the stochastic optimization of process systems that involve exogenous and endogenous uncertainties. Examples of the former include demands or feed compositions, whereas examples of the latter include yields or other process parameters. The specific goal of the research is to develop novel models and effective solution methods for multistage stochastic optimization where the structure of scenario trees are functions of design decisions given endogenous uncertainties. To overcome the computationally challenging computations the PI intends to investigate a novel disjunctive programming formulation that expresses in closed form the dependency of the scenario tree with the design decisions. Based on that model, he intends to investigate a computational procedure based on a Lagrangean branch and cut method for solving linear stochastic problems. The method will rely on the use of grid computing using master-worker algorithms to exploit the subproblems that can be solved independently as part of the decomposition. The extension of this computational method to bilinear models will also be investigated. This computational technique will be applied to two problems. The first one deals with the design of biorefineries (biomass conversion systems) in which there are uncertainties in the availability and quality of food residues (raw materials) and in the yields of conversion in the various processes that are involved. The second application deals with the synthesis of integrated process water systems in which there are uncertainties in the concentration of contaminants and in the recoveries of treatment units. The first application will be modeled as a linear stochastic programming problem, while the second one is a nonlinear stochastic problem that involves bilinearities. Broader impact: This research has the potential not only of expanding the scope and significance of stochastic optimization, but also for greatly improving the design of bioprocesses and process water systems. The research results and computational tools will be made available through the internet. The PI also intends to develop two design case studies that will be disseminated to process design instructors through CACHE. He believes that these case studies will have significant impact in undergraduate education as they will expose the students to biorefineries, process water systems and techniques for handling uncertainties. Finally, in order to promote interest in high schools in applied mathematics and processes based on renewable resources, he plans to perform outreach activities through the Steinbrenner Institute for Environmental Education at Carnegie Mellon where students can be exposed to simplified versions of the case studies.