Analysis of Decomposability and Complexity for Design Problems in the Context of Decomposition

The current practice in problem decomposition assumes that (1) design problems can be rationally decomposed a priori and (2) decomposition can usefully result in complexity reduction a priori. However, this assumption is not always true in reality. In response to this concern, this paper introduces the notions of decomposability and complexity to problem decomposition. In particular, a full scale of decomposability analysis and complexity analysis in the context of decomposition are presented along with approaches and algorithms. These new analyses not only address the viability and validity of decomposition, but also help achieve an optimal number of sub-problems during decomposition, which is usually determined by trial and error or a priori. Further, a procedure that is able to combine these new analyses into our two-phase decomposition framework is described. This effort leads to an enhanced decomposition method that is able to find the most appropriate decomposition solution to a complex design problem.