# Optimized sequencing of analysis components in multidisciplinary systems

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DOI: 10.1007/s00163-009-0082-5

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- Shaja, A.S. & Sudhakar, K. Res Eng Design (2010) 21: 173. doi:10.1007/s00163-009-0082-5

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## Abstract

System analysis of complex engineering systems is synthesized from a collection of analysis components that have data dependencies on each other. Sequencing interdependent analysis components in order to reduce the execution time has been addressed by multidisciplinary design optimization researchers. Representation of interdependency of analysis components is accomplished as a design structure matrix or as a graph made of nodes and edges. Sequencing of interdependent analysis components that form a directed acyclic graph is trivial. Aggregation (i.e., group of components) of some of the components into a single super-component that can render a directed cyclic graph to a directed acyclic graph is important in sequencing. Identification of components that form an aggregation is the first step in sequencing. We argue that the best form of aggregation is the strongly connected component of the graph. Challenge essentially is in sequencing within aggregations. An aggregation having n components presents a search space of n! candidate sequences. The current state of the art is to use evolutionary algorithms for this search. An aggregation requires repeated traversal (cycle/loop) of components within it for convergence. The central aim of sequencing is to reduce/minimize the overall execution time for achieving convergence through iterations. Several objective functions have been proposed for the associated optimization problems like minimize the number of feedback paths, minimize the weighted sum of feedback paths, minimize feedback and crossovers, etc. These are proxy objectives as they are not backed by mathematically established relation between the proxy objective and the aim. An objective method of predicting the number of iterations based on the sensitivity of components is proposed here. It is shown that the best sequence that takes least time to execute has a particular ordering of components, which we call one-hop-sequence. The one-hop-sequencing of components is easily achieved using a small extension to Tarjans depth first search algorithm, a standard tool in graph theory. Extended TDFS does not use sensitivity information and is much faster than evolutionary algorithms that use sensitivity information. System analysis can have simple aggregation, recursive aggregations (i.e., aggregation within aggregation) or overlapping aggregations. One-hop-sequence is shown to be the best sequence for all three cases. After sequencing of the components is done, we investigate whether an inner aggregation must retain its loop or it must be severed for speed up. This step uses sensitivity information and can offer further speed up. The proposed methodology is implemented as a tool named CASeq. Ideas discussed here may be useful to other design structure matrix applicable domains like software design, systems engineering, organizational design, product development, multidisciplinary design, product architecture, project management, building construction, manufacturing and so on.