Improving global optimization methods for dynamic process models

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Many applications in engineering, chemistry, and physics involve systems with time-varying behavior. These dynamic systems include batch processes for production of high-value specialty chemicals, bioproducts, and pharmaceuticals from lower-value raw materials through complex systems of chemical reactions, automatic control policies that maintain safety and quality by preventing systems from drifting off-course, biological processes such as cell growth, and robotics. The goal of the proposed research program is to improve global optimization methods for process models of dynamic systems. Global optimization of a system involves determining parameters or operating conditions that produce the best possible performance, and verifying that no alternative would perform better. This task is mathematically challenging, since it requires extracting global knowledge about a complicated system's behavior, while rigorously excluding suboptimal parameters from consideration. Dynamic behavior introduces further obstacles into optimization methods, by making local knowledge of the system more difficult to acquire. As a result, current methods for global dynamic optimization are restricted to small systems in practice. Nevertheless, several practical problems require global optimization of dynamic systems, including verification that safety constraints are satisfied robustly, verification that a process model describes the underlying system adequately, and improvement of economic performance.The proposed program of research pursues two avenues for improving global dynamic optimization methods. First, new techniques will be developed to furnish superior global bounding information, to reduce the number of iterations required by an overarching optimization method. Second, new numerical methods will be developed process this bounding information more efficiently, to speed up the overarching method. These avenues will be pursued by exploiting untapped synergies between several recent and independent advances in global optimization and model development, including a numerical method developed in my postdoctoral work for extracting useful global bounding information. This research will allow more dynamic models to be optimized in practice, with far-reaching impact across the practical science and engineering applications mentioned above. In particular, this work will provide techniques for improving the economic performance of batch chemical processes in the specialty chemical and pharmaceutical sectors of Canada. More robust automatic control policies will also be enabled, and the design of safe, environmentally friendly chemical processes will be aided. Ultimately, the long-term goal of the proposed research program is to develop new theoretical and numerical tools to foster further advances in global optimization for practical applications.