Execution sequence planning of computational models based on incidence matrix and design structure matrix

Based on incidence matrix (IM) and design structure matrix (DSM), an algorithm is proposed to obtain an optimal execution sequence of computational models in order to reduce computational cost and design time. The IM describes the relationship between design variables and equations/models. The DSM has been used to express the dependency relationships between the computational models and also, after manipulation, to produce the solution process. The designer specifies the independent (known) design variables first. Then the variable flow is modeled by using the IM. It determines how the data flows through the models, and also identifies any strongly connected models (SCM). The second step is to arrange all equations/models hierarchically in order to reduce the feedback loops in each of the identified SCMs. A GA-based algorithm is applied for resolving the couplings. Subsequently each SCM is grouped into a macro model to form a global DSM. The global DSM is further rearranged to obtain a lower triangular matrix which defines the final model execution sequence. A simple aircraft sizing example is presented to illustrate the proposed method and algorithm.