Optimized sequencing of analysis components in multidisciplinary systems
 A. S. Shaja,
 K. Sudhakar
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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 supercomponent 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 onehopsequence. The onehopsequencing 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. Onehopsequence 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.
Inside
Within this Article
 Introduction
 Basic ideas in sequencing
 Aggregations
 Aggregations within aggregations
 Quantifying iterations for convergence
 Simple aggregations: sequencing insights
 Recursive simple aggregations
 Overlapping aggregations
 Possible looping structures
 Execution time for a network of components
 Proposed method of sequencing: the complete picture
 Conclusions
 References
 References
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 Title
 Optimized sequencing of analysis components in multidisciplinary systems
 Journal

Research in Engineering Design
Volume 21, Issue 3 , pp 173187
 Cover Date
 20100701
 DOI
 10.1007/s0016300900825
 Print ISSN
 09349839
 Online ISSN
 14356066
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Sequencing
 Graph
 Strongly connected component
 Extended Tarjan depth first search
 Aggregation
 Iteration
 Industry Sectors
 Authors

 A. S. Shaja ^{(1)}
 K. Sudhakar ^{(1)}
 Author Affiliations

 1. Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India