Matrix-based decomposition algorithms for engineering applications: the survey and generic framework

This paper focuses on the issue of matrix-based decomposition, which has already been recognised as an effective means to address a system's complexity. For instance, a Design Structure Matrix (DSM) has been applied to tackle the complexity involved in product architecture and project management. As matrix-based decomposition has been studied and applied in different engineering contexts, the corresponding algorithms are rather scattered and often address only specific, context-dependent problems. Therefore, this paper is intended to contribute to matrix-based decomposition in two aspects. First, the research efforts in different domains are surveyed to identify the fundamental algorithmic techniques that are relevant to matrix-based decomposition. Second, a generic framework that allows the customisation of algorithms is proposed as an integrated tool to address different problems in matrix-based decomposition. Four matrix examples have been used to illustrate the framework's feasibility and applicability. The example results support that the proposed framework is capable of addressing four common matrix types in engineering applications, namely, symmetric DSM, non-symmetric DSM, directed DSM and rectangular matrix.