CBE Faculty Candidate Seminar: Decomposition: Exploiting Structure in Chemical Systems to Solve Challenging Decision-Making Problems”

Abstract:

Computational optimal decision-making tools are essential for ensuring that systems are designed, operated, and controlled in an economic and sustainable manner. Using optimization to make decisions for chemical and energy systems is particularly challenging due to the inherent presence of nonlinear process physics, both integer and continuous decisions, uncertainties in important parameters, and multiple relevant time scales. This talk addresses the method of decomposition, which solves large, computationally challenging decision-making problems through a set of smaller, easier-to-solve subproblems. The first half of this talk addresses the problem of identifying smaller subproblems that make the large problem easy to solve. An algorithmic framework for automatically doing so using community detection, a concept from network theory, is presented. The superiority of using community-based decompositions to solve optimization problems, compared to other intuition-based decompositions, is showcased through an optimal model predictive control case study. The ability of the algorithm to identify subproblems when an intuitive decomposition does not exist is also demonstrated. The second part of the talk addresses the challenge of coordinating subproblems to arrive at a solution of the original problem. Here, a branch-and-price algorithm which can solve certain classes of nonconvex mixed integer nonlinear programs (the most challenging type of optimization problem to solve) to global optimality is presented. The applicability of this algorithm to many problems of chemical engineering interest, including process design under uncertainty, multiperiod capacity planning, dynamic facility location, and task assignment to process units, is demonstrated.