A Hypergraph Framework for Optimal Model-Based Decomposition ofDesign Problems

Abstract

Decomposition of large engineering system models is desirable since increased model size reduces reliability and speed of numerical solution algorithms. The article presents a methodology for optimal model-based decomposition (OMBD) of design problems, whether or not initially cast as optimization problems. The overall model is represented by a hypergraph and is optimally partitioned into weakly connected subgraphs that satisfy decomposition constraints. Spectral graph-partitioning methods together with iterative improvement techniques are proposed for hypergraph partitioning. A known spectral K-partitioning formulation, which accounts for partition sizes and edge weights, is extended to graphs with also vertex weights. The OMBD formulation is robust enough to account for computational demands and resources and strength of interdependencies between the computational modules contained in the model.