Efficient Global Dynamic Optimization using Dynamic Cut Generation and Domain Reduction Techniques

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Dynamic optimization is a computational approach used to optimally control dynamic processes. Effective dynamic optimization codes have become a key enabling technology in many industries, leading to substantial gains in profitability, efficiency, and safety. However, dynamic optimization problems commonly exhibit multiple sub-optimal local solutions. Use of these sub-optimal solutions instead of the desired globally optimal solution can lead to significant economic loss and performance degradation in many applications; this can even produce expensive or dangerous unreliable conclusions. This project aims to develop more efficient global optimization algorithms for types of problems that arise in a broad spectrum of applications in the chemical, pharmaceutical and aerospace industries.This project aims to increase the efficiency of global dynamic optimization (GDO) codes by developing cut generation and domain reduction techniques in the branch and bound (B&B) algorithm for solving nonconvex algebraic optimization problems. Cut generation refers broadly to methods that strengthen the convex relaxation of a nonconvex problem by imposing constraints that are redundant in the original model, but not in the relaxation. In contrast, domain reduction refers to methods that tighten the bounds on the decision variables in a B&B node using the problem constraints or a known feasible objective value. Research into such techniques for GDO is very well motivated by analogy to standard nonlinear programs (NLPs). Prior work on GDO has focused on relaxation methods that can be considered dynamic extensions of the most basic methods used for NLPs (specifically those based on factorable decomposition, such as McCormick relaxations). However, B&B codes based solely on these techniques are extremely inefficient in most cases. In contrast, modern B&B codes, which routinely solve problems with hundreds of decisions, utilize a rich toolbox of cut generation and domain reduction techniques. This strongly suggests that analogous techniques for dynamic problems will profoundly impact the efficiency of GDO algorithms. In addition to training graduate students, the proposed research will involve training of undergraduate researchers through Clemson's Creative Inquiry Program and rising high school seniors through Clemson's six-week Summer Program for Research Interns. The project also includes the development of a half-day long hands-on research activity for educating women and minorities about career opportunities in STEM fields, hosted by Clemson's Women in Science and Engineering (WISE) Program and the Programs for Educational Enrichment and Retention (PEER).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.