Multidisciplinary design optimization with quasiseparable subsystems

Numerous hierarchical and nonhierarchical decomposition strategies for the optimization of large scale systems, comprised of interacting subsystems, have been proposed. With a few exceptions, all of these strategies lack a rigorous theoretical justification. This paper focuses on a class of quasiseparable optimization problems narrow enough for a rigorous decomposition theory, yet general enough to encompass many large scale engineering design problems. The subsystems for these problems involve local design variables and global system variables, but no variables from other subsystems. The objective function is a sum of a global system criterion and the subsystems' criteria. The essential idea is to give each subsystem a budget and global system variable values, and then ask the subsystems to independently maximize their constraint margins. Using these constraint margins, a system optimization then adjusts the values of the system variables and subsystem budgets. The subsystem margin problems are totally independent, always feasible, and could even be done asynchronously in a parallel computing context. An important detail is that the subsystem tasks, in practice, would be to construct response surface approximations to the constraint margin functions, and the system level optimization would use these margin surrogate functions. The purpose of the present paper is to present a decomposition strategy in a general context, provide rigorous theory justifying the decomposition, and give some simple illustrative examples.