Logical Architecture Optimization via a Markov chain based Hierarchical Clustering Method

Due to the growing complexity of engineering systems, optimization of logical architectures is becoming fundamental in the economy of the Systems Engineering process. Clusters of functions that are highly interacting with each other should be identified, while minimizing dependencies across the resulting modules. To this purpose, one can consider the Design Structure Matrix (DSM) describing relation between functions and permute its rows and columns to recover a block-diagonal structure with single or double border, with blocks corresponding to clusters of functions and borders to bus-like elements. This paper proposes a method to achieve this by partitioning the nodes of an undirected graph representation of the DSM. More precisely, starting from the DSM structure, a Markov chain is introduced by associating probabilities to transitions between nodes, which are then clustered based on the similarity among the probability distributions originating from them using a hierarchical clustering scheme. Interestingly, the method does not require any prior knowledge of system structure (e.g. the number of clusters), and it is computationally less demanding than competing algorithms.