Decomposition theory for multidisciplinary design optimization problems with mixed integer 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 are essentially heuristic in nature. Recent work considered a class of optimization problems, called quasiseparable, 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 present paper extends the quasiseparable necessary conditions for continuous variables to include discrete subsystem variables, although the continuous necessary and sufficient conditions do not extend to include integer variables.