Abstract
Large scale problems need to be decomposed for tractability purposes. The decomposition process needs to be carefully managed to minimize the interdependencies between sub-problems. A measure of partitioning quality is introduced and its application in problem classification is highlighted. The measure is complexity based (real complexity) and can be employed for both disjoint and overlap decompositions. The measure shows that decomposition increases the overall complexity of the problem, which can be taken as the measure’s viability indicator. The real complexity can also indicate the decomposability of the design problem, when the complexity of the whole after decomposition is less than the complexity sum of sub-problems. As such, real complexity can specify the necessary paradigm shift from decomposition based problem solving to evolutionary and holistic problem solving.
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References
Chen, L., Li, S.: Analysis of Decomposability and Complexity for Design Problems in the Context of Decomposition. Journal of Mechanical Design 127, 545–557 (2005)
Summers, J.D., Shah, J.: Developing Measures of Complexity for Engineering Design. In: ASME Design Engineering Technical Conferences DETC 2003, Chicago, Illinois (2003)
Zdrahal, Z., Motta, E.: Case-Based Problem Solving Methods for Parametric Design Tasks. In: Smith, I., Faltings, B.V. (eds.) EWCBR 1996. LNCS, vol. 1168, pp. 473–486. Springer, Heidelberg (1996)
Prasad, B.: Concurrent Engineering Fundamentals: Integrated Product and Process Organisation. Prentice Hall, New Jersey (1996)
Browning, T.R.: Applying the Design Structure Matrix to System Decomposition and Integration Problems: A Review and New Directions. IEEE Transactions on Engineering Management 48 (2001)
Michelena, N.F., Papalambros, P.Y.: A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems. Computational Optimization and Applications 8, 173–196 (1997)
Pimmler, T.U., Eppinger, S.D.: Integration Analysis of Product Decompositions. In: ASME Design Theory and Methodology Conference, Minneapolis, MN (1994)
Alexander, C.: Notes on the Synthesis of Form. Harvard University Press, Cambridge (1964)
Browning, T.: Designing System Development Projects for Organizational Integration. Systems Engineering 2, 217–225 (1999)
Simon, H.: Sciences of the Artificial. M.I.T. Press, Cambridge (1969)
Kusiak, A.: Engineering Design: Products, Processes, and Systems. Academic Press, London (1999)
Chen, L., Ding, Z., Simon, L.: A Formal Two-Phase Method for Decomposition of Complex Design Problems. Journal of Mechanical Design 127, 184–195 (2005)
Bar-Yam, Y.: When Systems Engineering Fails – Toward Complex Systems Engineering. In: International Conference on Systems, Man & Cybernetics, vol. 2, pp. 2021–2028. IEEE Press, Piscataway (2003)
Altus, S., Kroo, I.M., Gage, P.J.: A Genetic Algorithm for Scheduling and Decompostion of Multidisciplinary Design Problems. Journal of Mechanical Design 118, 486–489 (2003)
Cameron, P.J.: Automorphisms of Graphs. In: Beineke, L.W., Wilson, R.J. (eds.) Topics in Algebraic Graph Theory, pp. 137–155. Cambridge University Press, Cambridge (2004)
Alpert, C.J., Kahngb, A.B., Yao, S.-Z.: Spectral partitioning with multiple eigenvectors. Discrete Applied Mathematics 90, 3–26 (1999)
Spielman, D.A., Teng, S.-H.: Spectral Partitioning Works: Planar Graphs and Finite Element Meshes. In: IEEE Symposium on Foundations of Computer Science (1996)
Chan, P., Schlag, M., Zien, J.: Spectral K-Way Ratio-Cut Partitioning and Clustering. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 13, 1088–1096 (1994)
Ding, C., He, X., Zha, H.: A Min-Max Cut Algorithm for Graph Partitioning and Data Clustering. In: IEEE International Conference on Data Mining, San Jose, CA (2001)
White, S., Smyth, P.: A spectral Clustering Approach to Finding Communities in Graphs. In: 5th SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, Newport Beach, CA (2005)
Shi, J., Malik, J.: Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 888–905 (2000)
Cheng, C., Hu, T.: The Optimal Partitioning of Networks: Technical Report. University of California, San Diego (1989)
Yeh, C., Cheng, C., Lin, T.: A Probabilistic Multicommodity-Flow Solution to Circuit Clustering Problems. In: IEEE Int. Conf. Computer-Aided Design ICCAD 1992, Santa Clara, CA (1992)
Verma, D., Meila, M.: A Comparison of Spectral Clustering Algorithms. Technical Report. University of Washington (2003)
Bashir, H., Thomson, V.: Metrics for Design Projects: A Review. Design Studies 20, 263–277 (1999)
McCabe, T.: A Complexity Measure. IEEE Transactions on Software Engineering 2, 308–320 (1976)
Edmonds, B.: Syntactic Measures of Complexity. PhD. University of Manchester, Manchester, UK (1999)
Erdi, P.: Complexity Explained. Springer, Heidelberg (2008)
Marczyk, J., Deshpande, B.: Measuring and Tracking Complexity in Science. In: 6th International Conference on Complex Systems, Boston, MA (2006)
Boschetti, F., Prokopenko, M., Macreadie, I., et al.: Defining and Detecting Emergence in Complex Networks. In: 9th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, Melbourne, Australia, pp. 573–580 (2005)
Ulrich, K.T., Eppinger, S.D.: Product Design and Development. Mc Graw-Hill/Irwin (2004)
Braha, D., Maimon, O.: The Measurement of a Design Structural and Functional Complexity. IEEE Transactions on Systems, Man, and Cybernetics-Part A 28, 527–535 (1998)
Browning, T.R., Deyst, J.J., Eppinger, S.D.: Adding Value in product Developement by Creating Information and Reducing Risk. IEEE Transactions on Engineering Management 49, 443–458 (2002)
Smith, R.P., Eppinger, S.D.: Identifying Controlling Features of Design Iteration. Managment Science 43, 276–293 (1997)
Roemer, T., Ahmadi, R.: Concurrent Crashing and Overlapping in Product Development. Operations Research 52, 606–622 (2004)
Krishnan, V., Eppinger, S., Whitney, D.: A Model-Based Framework to Overlap Product Development Activities. Management Science 43, 437–451 (1997)
Clark, K.B., Fujimoto, T.: Overlapping Problem Solving in Product Development, pp. 127–152. Managing International Manufacturing, Amsterdam (1989)
Ikeda, M., Siljak, D.D., White, D.E.: Decentralized Control with -Overlapping Information Sets. Journal of Optimization Theory and Applications 34, 279–310 (1981)
Eppinger, S.D., Whitney, D., Yassine, A., et al.: Information Hiding in Product Development: The Design Churn Effect. Research in Engineering Design 14, 145–161 (2003)
Klir, G.J. (ed.): Facets of Generalized Uncertainty-Based Information. Springer, Heidelberg (2003)
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Efatmaneshnik, M., Reidsema, C., Marczyk, J., Balaei, A.T. (2010). Immune Decomposition and Decomposability Analysis of Complex Design Problems with a Graph Theoretic Complexity Measure. In: Szczerbicki, E., Nguyen, N.T. (eds) Smart Information and Knowledge Management. Studies in Computational Intelligence, vol 260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04584-4_2
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DOI: https://doi.org/10.1007/978-3-642-04584-4_2
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