Boundary search and simplex decomposition method for MDO problems with a convex or star-like state parameter region

Abstract

One major challenge in multidisciplinary design optimization (MDO) is the presence of couplings among state parameters, which demands an iterative and often expensive system analysis (SA) process for each function evaluation in optimization. This paper offers a new perspective and proposes a corresponding method for solving MDO problems. The proposed method, named the boundary search and simplex decomposition method (BSSDM), geometrically captures the relation among coupled state parameters with a feasible state parameter region. Given the feasible state parameter region, the SA can be avoided during the optimization of the system objective function. To identify the feasible state parameter region, a search strategy is developed to find boundary points of the region. In the boundary search process, a collaboration model (CM) is applied to maintain the feasibility of samples with respect to the SA. In search of the system optimum in the feasible region, a robust simplex decomposition algorithm is developed for convex and star-like feasible state parameter regions. The BSSDM is tested with two numerical cases, one of which is an MDO problem constrained by a convex state parameter region, and the other is a SA problem with a star-like state parameter region. All results are then validated, and the results show the promising capability of the proposed BSSDM.