Fast Solving Strategies For Dynamic Optimization With Differential-algebraic Equations

With the development of computer technology and the increasingly perfecting of non-linear programming (NLP) solution technology, dynamic optimization methods have at-tracted more and more attention in the process industries, machine control and other re-search areas. Since the simultaneous strategies adopt the idea that the continuous dynamic optimization problems are discretized into NLP problems and solved successively, the strategies can be executed easily and have extremely solution efficiency. The simultane-ous strategies gradually become more prospective. However, current simultaneous meth-ods still can not meet much application requirements, so need to be improved further to enhance the efficiency and practicality. This work mainly focuses on fast solving strategies for dynamic optimization with differential-algebraic equations (DAEs), including the next four aspects:1. It is analyzed deeply that the orthogonal collocation on finite element (OCFE) meth-ods are used to discretize the DAE optimization problems, and the equivalent con--ditions between direct and indirect discretization structures are proved theoretically. On this basis, combined with the specific collocation formulae for analysis and verifi-cation, it is concluded that the Lobatto formula has the best or better effects on many solution aspects. In addition, the nature of collocation discretization methods is dis-cussed further, and then the idea of basis function discretization are proposed. The feasibility of non-polynomial discretization is exemplified by radial basis function (RBF) methods.2. The nature of mnemonic enhancement optimization (MEO) is discussed, and it is pro-posed that the problems of advanced starting point (ASP) generated from empirical data are multivariate scatter data fitting problems in fact. Thus, the RBF interpolation principle is used to improve the MEO method, and the application results are signifi- cantly improved. Furthermore, an improved RBF-MEO method with error correction is proposed.3. In order to avoid the inherent deficiencies of RBF method, the support vector machine (SVM) is employed as an alternative to realize the functions of MEO. According to the fact that QP problems can not be solved quickly enough in the SVM, the Hessian matrix sparseness methods and the simultaneous strategy of multi-output problems are put forward, successfully raising the solution efficiency of the SVM. The SVM-MEO method is applied to solve the parametric dynamic optimization problems, and an efficient "partial MEO" is proposed.4. Since scarcity of research platform for dynamic optimization, a DAE optimization framework is built and successfully implemented in MATLAB and AMPL environ-ment. The platform adopts the modular design concept and divides the discrete for-mula into the model part and the method part. On this platform, the further research of discretization methods, model development and solver tools can be distributed. This section also includes standardization of dynamic optimization models and fast solution strategy based on discretization structure.