Research On Large-Scale Optimization For Process Systems

Process optimization has emerged as one of the most valuable techniques for system design, analysis and operation. Currently, the rapid trends toward increased model detail and rigor, dynamic optimization, on-line optimization, and scheduling accelerate the need to optimize very large systems of equations with many degrees of freedom. The large-scale optimization of process systems, however, continues to present a major challenge both in academia and in process industries. This dissertation details the investigation, development and implementation of efficient algorithms and techniques for large-scale optimization of process systems. The main contributions are as follows: 1) A new strategy is developed for the optimization of large-scale process problems, in particular those nonlinear constrained problems arising in chemical process industries. The proposed method applies first/second derivative and sparse matrix techniques in conjunction with Sequential Quadratic Programming (SQP), allowing the nature sparse structure of optimization problems to be preserved and exploited. It is a two-phase procedure in which there is a preprocessing computation before the optimization. In the preprocessing phase, the sparsity patterns of Jacobian and Hessian elements are obtained from a proposed sparse structure identification algorithm. Each nonzero element in those matrices is examined and classified as constant or nonconstant. All the constant elements are stored as global variables and are computed only once during the optimization, leading to a significant time saving. In the optimization phase, a sparsity preserving approximation to the true Lagrangian Hessian is built in the full space of variables to provide more accurate curvature information for QP sub-problems, which improves both the reliability and efficiency of SQP method. In addition, sparse matrix techniques are introduced in each phase throughout the whole optimization procedure of SQP, especially in the QP sub-problems. Numerical experiments on a distillation process optimization problem as well as a variety of Iv scalable problems demonstrate the efficiency of our strategy. The significant enhancement in speed on those test problems with distinct difference in size (100 - 900 variables), together with the great reduction in storage requirements for large matrices, shows that the strategy is particularly well suited for large-scale process optimization problems. 2) A novel automatic differentiation (AD) algorithm is presented to generate analytical derivative expressions. Considering the accurate gradient information provided and potential advantage in sparsity pattern detection, analytical derivative expressions are preferable in process simulation and optimization. However, AD algorithms currently in use only provide numerical derivatives. In this dissertation, the conventional AD is extended to a new variant based on a detailed investigation of the data structure. The extended automatic differentiation (XAD) is able to generate both analytical and numerical derivatives simultaneously. Further, to generate derivatives more efficiently, the sparsity in derivative matrices are exploited by incorporating advanced matrix compression algorithms into XAD. Numerical results demonstrate tremendous speed improvement in derivative generation by the resulting XAD. Also, fewer...