ABSTRACT: Mathematical programming methods have been widely adopted for process design and operation, as they provide systematic means to find optimal or feasible design/operation decisions that may not be easily seen from qualitative or simple quantitative analysis. However, mathematical programming formulations of process design and operation problems are usually nonconvex, implying that an optimal, or even a feasible solution, is difficult to obtain. When uncertainties in the problem (e.g., material qualities and prices) need to be explicitly addressed, the problem is usually cast a large-scale nonconvex mixed-integer nonlinear programming (MINLP) or continuous nonlinear programming (NLP) problem, and the large problem size brings more challenges for numerical optimization. This presentation discusses global optimization of large-scale nonconvex MINLP and NLP for process design and operation under uncertainty. The presentation includes two parts. In the first part, we introduce a new decomposition-based global optimization method, called joint decomposition, which can exploit the decomposable structure of the problem for efficient global optimization. The method is motivated by the fact that, classical decomposition based optimization methods either need to solve complicated subproblems or cannot guarantee finding an optimal solution. Joint decomposition combines the classical Lagrangian decomposition and generalized Benders decomposition in a novel way, such that solution of difficult subproblems is delayed as much as possible, and when the difficult subproblems need to be solved, they have been updated into easier subproblems (according to the solutions of already solved easy subproblems). In the second part, we discuss the potential benefits of a good problem formulation for global optimization. We focus on a natural gas production network problem, for which nonconvex pressure-flow equations need to be considered in optimization. It will be shown that, with mild assumptions, a highly nonconvex MINLP formulation can be equivalently reformulated into a less nonconvex and better structured MINLP, which can be solved much more efficiently via decomposition based global optimization. This reformulation strategy is not limited to natural gas production networks; for example, it can be applied to water networks where similar pressure-flow relations exist. Computational study results will be presented to demonstrate the benefits of the new global optimization method and the reformulation strategy.
Bio-sketch:
Xiang Li is an assistant professor in the Department of Chemical Engineering at Queen’s University, in Ontario, Canada. He received bachelor’s degree in Industrial Automation, master’s degree in Systems Engineering, both from Zhejiang University, and Ph.D. degree in Chemical Engineering from McMaster University under the supervision of Prof. Thomas Marlin. He later became a postdoc at MIT, working under Prof. Paul Barton on global optimization for energy systems under uncertainty. His current research interests include supply chain management, planning and scheduling, energy systems engineering, stochastic programming, global optimization, and model predictive control. He is a recipient of discovery grant with early career researcher supplement, from Natural Sciences and Engineering Research Council of Canada.