A Quasi-Sequential Approach To Large-Scale Dynamic Process Optimization Problems

Modelling and optimization based on rigorous mathematical model equations have significantly become a major technology area in the process industries. Many system engineering companies and academic organization have put a lot of research efforts to study in depth on the process modelling and optimization, and hope to make great progress. However, the discretized optimization problems based on rigorous and mathematical model often own the characteristics that are many model equations, multi-variables and high nonlinearity. There exists great difficulty to solve such optimizations, and store such numbers of variables. Solution of this large-scale optimization problem with general optimization approach can be inefficient. Even though the solution could be found, the computation efficiency, convergence rate and initial-value sensitivity were unsuitable for demand of modern process industries. Therefore, it is a crucial research work to develop efficient approach for the large-scale optimization problems in modern process industries.Methods that apply NLP solvers to large-scale dynamic optimization normally can be separated into sequential approach and simultaneous approach. Sequential approaches have some advantages that are few degrees of freedom in NLP, feasible path method and employment of normal simulation solvers. But it cannot handle problems with path constraints efficiently. Simultaneous approach directly couple the solution of model equations with the optimization problem, the model equations are solved only once at the optimal point. Moreover, it has the advantage for problems with path constraints. Its disadvantage arises from the need to solve large nonlinear programming problems, specialized methods and mathematical analyses are required to solve them efficiently. In this dissertation, a novel sequential approach based on SQP, namely quasi-sequential approach, is presented for solving dynamic process optimization problems. It possesses advantages of both the simultaneous and the sequential approach. Furthermore, following the quasi-sequential approach, a program QSOPT is developed. QSOPT is compared with recently developed IPOPT (based on simultaneous approach). The comparative results show that the quasi-sequential approach is well suited for solving highly nonlinear optimal control problems. This is especially the case for highly nonlinear large-scale problems where the dynamic model equations may be violated by large values during the course of NLP solution.The main research works and contributions of this dissertation are as follows:1. A novel sequential approach based on SQP, namely quasi-sequential approach, is proposed for solving dynamic process optimization problems. It possesses advantages of both the simultaneous and the sequential approach. In the quasi-sequential approach, as in the simultaneous approach, both state and control variables are discretized using collocation on finite elements, so that path constraints can be guaranteed inside each element. On the other hand, the state variables are solved in a similar manner as in the sequential approach, this eliminates the discretized differential algebraic equations (DAEs) and state variables, so that the problem is reduced to a smaller problem only with inequality constraints and control variables. Quasi-sequential approach does not need complex mathematics derivation in order to reduce optimization problem to smaller one as simultaneous approach does. It is straightforward optimization approach and easy to be applied in engineering field.2. The different performance of optimization approaches is studied by comparing the solution path and step length of line search. The comparison results show that the quasi-sequential approach is well suitable to solve some process optimization problems, for example optimal control problem. The equality constraints are not included in SQP in the quasi-sequential approach and the merit function for line search only consists of the objective function, so that the strict descent requirement for merit function in line search is relieved. Compared with simultaneous approach, the quasi-sequential method takes larger step length and this leads to fewer SQP iterations. Numerical experiments show that quasi-sequential approach performs better than simultaneous approach while solving highly nonlinear large-scale problems where the dynamic model equations may be violated by large values during the course of solution by NLP. Moreover, quasi-sequential approach has advantage for general inequality constrained problems.3. A criterion, which is used to choose approach for a practical optimization problem, is given by analyzing the arithmetic operations of solution course and computational efficiency. By calculating the arithmetic operations of both quasi-sequential and simultaneous approach for a practical equality constrained optimization problem, the criterion can be used to decide which one is suitable for solving it. The example of CSTR optimal control problem is used todemonstrate its validity.4. The effect of process model structure on computation cost of optimization approach in solving optimization problem is exploited. The optimization approach can be more efficient by considering the sparsity of the DAE system. A program QSOPT based on quasi-sequential approach is developed, and used to calculate two typical chemical engineering examples: One is the CSTR optimal control; the other is optimization operation and parameter estimation of heat-integrated distillation system. From the computational results, it can be concluded that this quasi-sequential approach is able to solve large-scale dynamic optimization problems containing path constraints on state variables quickly.The dissertation is concluded with a summary and prospect of future researches.