Bi-level Decomposition Method For Solving Multidisciplinary Design Optimization Problems

Multidisciplinary design optimization (MDO) problems are engineering design prob-lems that require take into account the interaction between several disciplines. Multi-disciplinary design optimization problems are common in the areas of aerospace, civil engineering, automobiles and electronics design and so on. Due to the organizational structure of MDO problems, decomposition algorithm is generally considered to be a feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems with one subproblem per discipline, and a coordinat-ing master problem. A feasible and effective approach for MDO problems is the bi-level decomposition algorithm. Some famous bi-level decomposition algorithms are the collab-orative optimization (CO) method, the inexact penalty decomposition method (IPD) and the exact penalty decomposition method (EPD). In the inexact penalty decomposition method, large values of the penalty parameters will lead to ill-conditioning and affect the numerical performance. In this thesis, we propose two new bi-level decomposition algorithms based on the penalty decomposition methods.In Chapter 1, we give a brief introduction to the basic notions and research back-ground of multidisciplinary design optimization problems, and we also summarize the developments of research on multidisciplinary design optimization problems and bi-level decomposition algorithms. Finally, we outline the contents which are studied in this thesis.In Chapter 2, we introduce some relevant knowledge of this paper, including some symbols, definitions and conclusions.In Chapter 3, we propose an augmented Lagrangian decomposition method (ALPD) based on the inexact penalty decomposition method. In this method, to make the global variables converge to the objective variable, the augmented Lagrangian penalty function is used instead of the quadratic (inexact) penalty function to overcome the ill-conditioning in inexact penalty decomposition algorithm. Then we give the detailed augmented Lagrange algorithm. Furthermore, convergence analysis is presented and one numerical example is reported to show the effectiveness of the algorithm.In Chapter 4, based on the augmented Lagrangian decomposition penalty method and the exact penalty decomposition method, we propose a new bi-level decomposition algorithms that using a special kind of augmented Lagrangian function which is called sharp augmented Lagrangian penalty function. Sharp augmented Lagrangian penalty function satisfies the zero duality gap property, and its penalty parameter is not too large in parameter updating process. Then we give the detailed sharp augmented Lagrange algorithm. One numerical example is reported to show the effectiveness of the algorithm.In Chapter 5, we summarize the research in this thesis and make some suggestions for the further research.