A decomposition synthesis methodology for optimal systems design

Solving an optimal design problem (ODP) by decomposition methods involves partitioning a given ODP into several smaller problems and coordinating their solutions to obtain the solution to the original problem. In general, casting a given general design problem (GDP) as an optimization model is subjective. Therefore, one may seek to synthesize an ODP by defining the appropriate model functions so that the resulting model can be directly partitioned and solved in a decomposed form.; The method by which such a subjective selection can be made so that the resulting optimal design model can be directly partitioned into an appropriate decomposed form is presented in this thesis. This process is termed decomposition synthesis. A particular methodology for synthesizing hierarchically decomposed optimal design models using a bipartite graph partitioning technique is presented, and explained using examples. Formal definitions of decomposition concepts and types are developed to describe the methodology rigorously.; Given a GDP there are many ways of synthesizing a decomposable ODP. Thus, introducing suitable criteria an optimal decomposition synthesis process can be defined in a manner analogous to optimal partitioning formulations. An integer linear programming (ILP) formulation and solution techniques for synthesizing hierarchically decomposed optimal design problems is presented in this thesis. The implementation of the ILP is explained first using simple examples, and its use as a decomposition synthesis tool of large systems is further demonstrated using the examples of an automotive powertrain design and brake system design problems.; Once a decomposed ODP is obtained it is necessary to use a coordination scheme to obtain the optimal solution to the overall problem. An implementation of a sensitivity-based coordination strategy to obtain the optimal solution to a hierarchically decomposed optimal design problem is illustrated using the example of an automotive electric hybrid powertrain. Results obtained using the coordination scheme are validated with those obtained without decomposition. The results clearly demonstrate how the synthesis methodology provides a general technique for optimally partitioning a large system design problem, and a method for composing a meaningful ODP from it for solution by decomposition methods.