An abductive approach to Design Structure Matrix (DSM) partitioning using frequency domain scoring

Abstract

A key benefit of the DSM representation is that it gives a visual interpretation of relationships between its elements. The array format allows us to sort the elements using clustering algorithms which try to group the relationships into modules which are as independent as possible. There are a number of clustering algorithms available which may each end up sorting the DSMs differently using different objectives, for example, activities in a time-based DSM can be sequenced to reduce iterations or to improve concurrency. However, most of these algorithms take a deductive approach which results in only one 'optimal' output. If an abductive approach is used instead, multiple solutions can be generated for the user to evaluate, some which may provide insight on useful configurations that he or she may have overlooked. In electrical engineering, we often make use of transforms to convert time domain signals into frequency domain signals in order to glean additional information which may not have been initially apparent. In this respect, using a frequency domain transform on a DSM matrix gives us additional insights into the relationships represented. An example of one such insight would be into the sorted-ness of a DSM to which module cuts can be defined. By applying a frequency transform to a pixel representation of the DSM and examining the transform coefficients, we gain an understanding of what image patterns exist in the DSM. Rules pertaining to these coefficients could then be defined which would classify a DSM as well sorted (with the dependencies being grouped up) or being unsorted (with the dependencies being scattered). This thesis demonstrates the above technique to rank each permutation of an 8x8 matrix on their conformance to certain rules or behaviors in order to filter out useful configurations in an abductive approach. When comparing the highest-ranking hypotheses against the optimal result from other clustering and sequencing algorithms, this algorithm performed on par with them to reduce external dependencies and iterations respectively. The frequency based scoring was also shown to be a useful metric when determining the optimal module cut of a system.