Research Of Dynamic Optimization Methods For Industrial Applications

As moderm process industries becoming finer and facing ever-tighter performance specifications, more and more attention has been paid to dynamic optimization methods in both academic and industrial areas home and abroad, where dynamic optimization is employed to manage bottleneck problems, exploite potentiality and improve producing efficiency of industrial process.In this work, an overview of dynamic optimization and its research status quo at home and abroad is given. More attention is paid to the research and improvement of the orthogonal collocation approach and the control parameterization approach, as well as the solution of the important fixed boundary problem in practical industries, for which several novel and effective algorithms are designed. The main contributions of the present work are as follows:(1) In order to solve the instability problems caused by singular arcs and high degree DAE in the process of dynamic optimization, an improved orthogonal collocation algorithm is presented. Boundary constraints for control variables at the finite element knots are introduced, and the lengths limits of the finite elements are designed, so as to enhance the convergence stability of conventional orthogonal collocation approach. And several classical benchmark examples with varying degree of complexities are provided to demonstrate the advantages of the presented approach in solution stability, accuracy and efficiency, as compared to the research results reported in the literature.(2) Based on the analysis of the online application of the control parameterization approach, an improved strategy is presented, which for the first time combined the control parameterization approach with PRP~+ conjugate method and strong Wolfe line search. Furthermore, a special scheme is introduced to tackle the boundary constraints of control variables, so as to overcome the shortcomings of conventional gradient methods in application. A variety of classical benchmark problems are provided to illustrate that the proposed algorithm has satisfying solution performance, and is preferable to many established methods reported in the literature, especially in improving solution precision meanwhile, reducing computational cost.(3) In order to solve the fixed boundary dynamic optimization problems, an effective constraint-preferred strategy is presented, which uses a bilevel programming framework to transform the original problem into two optimization problems without boundary constraints, where the inner part of the bilevel framework aims to solve the boundary constraints, and the outer part searches the optimal solution of the objective function. Moreover, an effective PRP conjugate gradient method based constraint-preferred algorithm and an effective two point gradient method based constraint-preferred algorithm are proposed respectively. The detailed reseach results of several classical industrial dynamic optimization problems indicate that the proposed algorithms can overcome the ill-conditioning problems of the penalty function method, and have marked superiority not only on its convergence robustness but also on their solution accuracy and efficiency.