Theoretical Analysis on Sequential Multidisciplinary Design Optimization Architecture

In the past few decades, multidisciplinary design optimization (MDO) has become a very important research topic along with the increase of the system complexity. In an MDO problem, it is very typical that multiple disciplines are involved, making the problem coupled and complex. Monolithic and distributed architectures have been proposed for solving MDO problems. However, efficient architectures are still needed. In the prior work, a sequential multidisciplinary design optimization (S-MDO) architecture was proposed that has a distributed structure that decomposes the original MDO problem into several subproblems. However, in the original S-MDO work, the theoretical behaviors were not analyzed because its mathematical representations were not clear. In this article, we present a clear mathematical representation of the S-MDO architecture and conduct theoretical analysis on the S-MDO architecture to explain its performance in solving MDO problems. The optimality condition of the S-MDO architecture is derived and summarized as a theorem and a proposition. To demonstrate the general formulation of solving an MDO problem using the S-MDO architecture and validate the correctness of the optimality condition, we use it to obtain the Pareto frontier of a benchmark MDO problem. From the spread of the obtained Pareto frontier, we can conclude that the S-MDO architecture performs well, as long as the global optimum of each disciplinary subproblem can be found.