Basic Approaches

1. System Architecting
2. Clustering
3. Cognitive maps
4. Optimal Decomposition of Design Problems (Automotive Research Center, Dept. of ME, Univ. of Michigan)
5. Modularity in Engineering and Management
6. Decomposition in linear programming:
(i) Dantzig-Wolfe decomposition (column generation),
(ii) Benders's decomposition (row generation),
(iii) Kornai-Liptak decomposition (two-level planning)
(iii) column generation (delayed column generation)
7. Partitining of graph/network
8. Design of optimal 'hierarchy'
9. Design of ontology
10. Expert based procedures
11. Design Structure Matrix (DSM, static, time-based):
11a. Basic approach as Design Structure Matrix (DSM) methods (components of a system and relationaship between them):
(i) product architecture DSM models,
(ii) organization architecture DSM models,
(iii) process architectures DSM models,
(iv) multidomain architecture MDM models.
11b. Other approaches:
(i) The Dependency Structure Matrix
(ii) The Problem Solving Matrix (PSM),
(iii) Design Precedence Matrix

Basic Hierarchical System Models

1. Set of clusters
2. Tree (forest, polytree)
3. Hierarchy, organic hierarchy, 'optimal' hierarchy, morphological hierarchy
4. Diagram, flowchart
5. Statechart (and its versions)
6. Graph, oriented (directed) graph, hypergraph
7. Network, multi-layer network
8. Ontology
9. Design Structure Matrix (DSM) (and its versions)
10. Finite automata
11. Petri nets
12. Hybrid models

Some Web-based Resources

I. Systems Architecting
1. Wikipedia site on Systems Architecture
2. Viterbi School of Engineering (Univ. of Southern California), About Systems Architecting
3. Gaudi System Architecting homepage
4. Course on Systems Architecture in MIT (Prof. Edward Crawley, MIT Course Number ESD.34, MIT Open CourseWare)
5. Course on Advanced Systems Architecture in MIT (Dr. Joel E. Whitney, Joel Moses, Dr. Christopher L. Magee; MIT Course Number ESD.342, MIT Open CourseWare)
II. System Hierarchy
1. Wikipedia site on Hierarchy
III. Decomposition
1. Wikipedia site on Decomposition
2. Wikipedia site on Decomposition in CS
3. Wikipedia site on Dantzig-Wolfe decomposition
4. Wikipedia site on Benders' decomposition
IV. Clustering
1. Wikipedia site on Cluster Analysis
2. Wikipedia site on Hierarchical Clustering
3. Prof. Boris Mirkin (Birkbeck College, London Univ., UK)


  • ACM Computing Surveys
  • ACM Trans. on Information Systems
  • Advanced Engineering Informatics
  • J. of Systems Architecture (Embedded Software Design) (Elsevier)
  • AI Magazine
  • AIAA Journal
  • Annals of Operations Research
  • Automation and Remote Control
  • Bell System Technical Journal
  • Communications of the ACM
  • Computational Optimization and Applicaitons
  • Data and Knowledge Engineering
  • Decision Sciences
  • Engineering Optimization
  • European J. of Operaitonal Research
  • Fuzzy Systems
  • IEEE Trans. on PAMI
  • IEEE Trans. on SMC
  • IEEE Trans. on KDE
  • IEEE Intelligent Systems
  • IEEE Expert
  • IEEE Trans. on Fuzzy Systems
  • Information Sciences (Elsevier)
  • Int. J. of General Systems
  • Journal of Classification
  • J. of Machine Learning Research
  • J. of Mechanical Design
  • J. of the ORS
  • Machine Learning
  • Operations Research
  • Organizational Science
  • Pattern Recognition
  • SIAM J. on Matrix Analysis and Applicaitons
  • SIAM J. on Scientific Computing
  • Structural and Multidisciplinary Optimization
  • The Computer Journal
  • Transportation Science


  • Basic Papers on Decomposition in Linear Programming
    1. G.B. Dantzig, P. Wolfe, Decomposition principle for linear programs. Operations Research. Vol. 8, 101-111, 1960.
    2. J.F. Benders, Partitioning procedures for solving mixed variables programming problems. Numerische Matematik, vol. 4, 238-252, 1962.
    3. J. Kornai, T. Liptak, Two-level planning. Econometrica, vol. 33, 141-169, 1965.
    4. Leon S. Lasdon, Optimization Theory for Large Systems. (reprint of the 1970 Macmillan ed.). Dover Publications, Mineola, New York, 2002.
    5. Dimitris Bertsimas, John N. Tsitsiklis, Linear Optimization, Athena Scientific. 1997.

  • Books
    1. Grady Booch, Object-oriented Analysis and Design, 2nd ed., Redwood Citam CA, Benjamin/Cummings, 1994.
    2. Tom DeMarco, Structured Analysis and System Specification. Yourdanmm New York, 1978.
    3. Jan Dietz, Enterprise Ontology - Theory and Methodology. Springer, 2006.
    4. Steven D. Eppinger, Tyson R. Browning, Design Structure Matrix Methods and Applications. The MIT Press, 2012.
    5. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Company, San Francisco, 1979.
    6. A.D. Gordon, Classification. 2nd ed., Chapman & Hall/CRC, London/Boca Raton, FL, 1999.
    7. Y.Y. Haimes, K. Tarvainen, T. Shima, J. Thadathil, Hierarchical Multiobjective Analysis of Large-Scale Systems. Hemisphere Pub. Corp., New York, 1990
    8. D.M. Himmelblau, Morphology of Decomposition. In: Himmelblau, D.M., (Ed.), Decomposition of Large-Scale Problem. New York: North Holland, pp. 1-13, 1973.
    9. F. Hoppner, F. Klawonn, R. Kruse, T. Runkler, Fuzzy Cluster Analysis. New York, Wiley, 1999.
    10. N. Jardine, R. Sibson, Mathematical Taxonomy. J.Wiley & Sons, London, 1971.
    11. T. Kophonen, Self-organizing Maps. Springer, 1995.
    12. M.Sh. Levin, Composite Systems Decisions. Springer, 2006.
    13. M.Sh. Levin, Decision Support Technology for Modular Systems. Electronic book. 341 pp. (in Russian). 2013.
    14. M.Sh. Levin, Modular System Design and Evaluation. Springer, 373 p., 2015 (Due: Sep. 2014).
    15. Mark W. Maier, Eberhardt Rechtin, The Art of Systems Architecting. 3rd ed., Boca Raton, CRC Press, 2009.
    16. Oded Maimon, Lior Rokach, Decomposition Methodology for Knoweldge Discovery and Data Mining. World Scientific, 2005.
    17. J.G. March, H.A. Simon, Organizations. 2nd ed., Wiley-Blackwell, 1993.
    18. M.D. Mesarovic, D. Macko, Y. Takahara, Theory of Hierarchical, Multilevel Systems. New York and London: Academic Press, 1970.
    19. B.G. Mirkin, Mathematical Classification and Clustering. Boston: Kluwer, 1996.
    20. Boris G. Mirkin, Clustering for Data Mining: A Data Recovery Approach. Chapman & Hall/CRC, New York, 2005.
    21. B. Mirkin, F.R. McMorris, F.S. Robets, A. Rzhetsky, (eds), Mathematical Hierarchies and Biology. DIMACS Ser. in Discrete Math. and Theoretical Comput. Sci., AMS, Providence, 1996.
    22. Gerrit Muller, Systems Architecting: A Business Perspective. CRC Press,2012.
    23. R. de Neufville, Architecting/Designing Engineering Systems Using Real Options. ESD Internal Symposium, MIT, Engineering Systems Division, Cambridge, MA, 2002.
    24. E. Rechtin, Systems Architecting: Creating & Building Complex Systems. Englewood Cliffs, NJ, PTR Prentice-Hall, 1991.
    25. C.J. van Rijsbergen, Information Retrieval. 2nd ed., Butterworths, London, 1979.
    26. J. Van Ryzin, Ed. Classification and Clustering. New York: Academic Press, 1977.
    27. G. Salton, M.J. McGill, Introduction to Modern Retrieval. McGraw-Hill, 1983.
    28. Dimitrios Serpanos, Tilman Wolf, Architecture of Network Systems. Morgan Kaufmann. 2011.
    29. P.H.A. Sneath, R.R. Sokol, Numerical Taxonomy: The Principles and Practice of Numerical Classification. W.H. Freeman and Company, San Francisco, 1973.
    30. Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra (eds.), Modular Ontologies. Concepts, Theories and Techniques for Knowledge Modularization. LNCS 5445, Springer, 2009.
    31. A.S. Tanenbaum, Computer Networks. 4th ed., Prentice Hall PTR, NJ, 2002.
    32. A.S. Tanenbaum, Structured Computer Organization. 5th ed., Prentice Hall, NJ, 2006.

  • Basic Surveys
    1. R.A. Botafogo, E. Rivlin, B. Shneiderman, Structural analysis of hypertexts: Identifying hierarchies and useful metrics. ACM Trans. on Information Systems, 10(2), 83-110, 1992.
    2. T.R. Browning, Applying the design structure matrix to system decomposition and integration problems: a review. IEEE Trans on Engineering Management, 48(3), 292-306, 2001.
    3. M. Chiang, S.H. Low, A.R. Calderbank, J.C. Doyle, Layering as optimization decomposition: A mathematical theory of network architecture. Proc. of the IEEE, 95(1), 255--312, Jan. 2007.
    4. O. Corcho, M. Fernandez-Lopez, A. Gomez-Perez, Methodologies, tools and languages for building ontologies: Where is their meeting point? Data & Knowledge Engineering, 46(1) (2003) 41-64.
    5. J. Current, C. ReVelle, J. Cohon, The hierarchical network design problem. EJOR, 27(1), 57-66, 1986.
    6. J.L. England, Hierarchies, theories, and methodologies. In: R. Trappl (Ed.) Cybernetics and Systems'88, Kluwer, 271-278, 1988.
    7. C.W. Holsapple, K.D. Joshi, A collaborative approach to ontology design. Commun. of the ACM, 45(2), 42-47, 2002.
    8. A.K. Jain, M.N. Murty, P.J. Flynn, Data clustering: a review. ACM Computing Surveys, 31(3), 264-323, 1999.
    9. C. Kemp, J.B. Tenenbaum, The discovery of structural form. PNAS, 105(31), 10687-10692, 2008.
    10. Mark W. Maier, Architectinrg principles for systems-of-systems. Systems Engineering, 1(4), 267-284, 1998.
    11. N.F. Michelena and P.Y. Papalambros, A Hypergraph Framework to Optimal Model-Based Decomposition of Design Problems. Computational Optimization and Applications, 8(2), pp. 173-196, Sept. 1997.
    12. M. Minsky, A framework for representing knowledge. In: Winston P.H. (ed) The Psychology of Computer Vision. McGraw-Hill, New York, pp. 211-277, 1975.
    13. B. Mirkin, I. Muchnik, Combinatorial Optimization in Clustering, in D.-Z. Du, P. Pardalos (Eds.), Handbook of Combinatorial Optimization. Vol. 2, Bostron, Kluwer Academic Publishers, 261-329, 1998.
    14. J. Moses, Architecting engineering systems. In: van de Poel I., D Goldberg D.E. (eds) Philosophy and Engineering, Series Philosophy of Engineeirng and Technology, vol. 2, Springer, pp. 275-284, 2010.
    15. J.H. Muller and J. Spinrad, Incremental Modular Decomposition. J. of the ACM, Vol. 36, pp. 1-19, 1989.
    16. M.E.J. Newman, The structure and function of complex network. SIAM Review, 42(2), 167-256, 2003.
    17. N.F. Noy, C. Hafner, The state of the art in ontology design: A survey and comparative review. AI Magazine, 18(3), 53-74, 1997.
    18. P.Y. Papalambros and N.F. Michelena, Model-Based Partitioning in Optimal Design of Large Engineering Systems. In: N. Alexandrov and M.Y. Hussani (Eds.) Multidisciplinary Design Optimization: State-of-the-Art, Philadelphia: SIAM, pp. 209-226, 1997.
    19. Christine Parent, Stefano Spaccapietra (eds.), An Overview of Modularity. In: Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra (eds.), Modular Ontologies. LNCS 5445, Springer, 5-24, 2009.
    20. H. Pirkul, J. Current, V. Nagarajan, The hierarchical network design problem: A new formulation and solution procedures. Transportation Science, 25(3), 175-182, 1991.
    21. M. Uschold, M. Gruninger, Ontologies: Principles, methods and applications. Knowledge Eng. Rev., 11(2), 93-136, June 1996.
    22. H.J. Waller, The synthesis of hierarchical structures: Techniques and applications. Decision Sciences, 7(4), 659-674, Oct. 1976.
    23. A.M. Costa, A survey on Benders decomposition applied to fixed-charge network design problems. Comput. and Oper. Research, 32, 1429-1450, 2005.

  • Papers
    1. C.L. Blorbaum, P. Hajela, J. Sobieszczanski-Sobieski, Non-hierarchic system decomposition in structural optimization. Engineering Optimization, 19(3), 171-186, 1992.
    2. I.S. Dhillon, Co-clustering documents and words using Bipartite Spectral Graph Partitioning. In: Proc. of the Seventh ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, ACM, 269-274, 2001.
    3. S.D. Eppinger, D. E. Whitney, R.P. Smith, D.A. Gebala, A Model-Based Method for Organizing Tasks in Product Development. Research in Engineering Design, 6(1), 1-13, 1994.
    4. A. Fernandez, S. Gomez, Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms. J. of Classification, 25(1), 43-65, 2008.
    5. P. Geyer, Component-oriented decomposition for multidisciplinary design optimization in building design. Advanced Engineering Informatics, 23(1), 12-31, 2009.
    6. M.D. Guenov, S.G. Barker, Application of axiomatic design and design structure matrix to the decomposition of engineering systems. Systems Engineering, 8(1), 29-40, 2005.
    7. R.T. Haftka, L.T. Watson, Decomposition theory for multidisciplinary design optimization with mixed integer quasiseparable subsystems. Optimization and Engineering, 7(2), 135-149, 2006.
    8. Y.Y. Haimes, Hierarchical holographic modeling. IEEE Trans. SMC, 11(9), 606-617, 1981.
    9. D. Harel, STATECHARTS: A visual formalism for complex systems. Science of Computer Programming, 8(3), 231-274, 1987.
    10. Bruce Hendrickson, Robert W. Leland, A Multi-level Algorithm for Partitining Graphs. SC, 95, 28, 1995.
    11. I. Jonyer, D.J. Cook, L.B. Holder, Graph-based hierarchical conceptual clustering. J. of Machine Learning Res., 2, 19-43, 2001.
    12. George Karypis, Vipin Kumar, A fast and high quality multilevel scheme for partitioning irregular graph. SIAM J. on Scientific Computing, 20(1), 359-392, 1998.
    13. B.W. Kernighan, S. Lin, An efficient heuristic procedure for partitioning graph. Bell System Technical Journal, 29(2), 291-307, 1970.
    14. V. Krishnan, S.D. Eppinger, D.E. Whitney, A model-based framework to overlap product development activity. Management Sciecne, 43(4), 437-451, 1997.
    15. W.P. Ledet, D.M. Himmelblau, Decomposition procedures for the solving of large scale systems. Advances in Chemical Engineering, 8, 185-254, 1970.
    16. M.Sh. Levin, Towards hierarchical clustering. In: V. Diekert, M. Volkov, A. Voronkov, (Eds.), CSR 2007, LNCS 4649, Springer, 205-215, 2007.
    17. M.F. Lopez, A. Gomez-Perez, J.P. Sierra, A.P. Sierra, Building a chemical ontology using methodology and the ontology design environment. IEEE Intelligent Systems, 14(1), 37-46, 1999.
    18. N.F. Michelena and P.Y. Papalambros, Optimal Model-based Decomposition of Powertrain System Design. J. of Mechanical Design. Vol. 117, pp. 499-505, 1995.
    19. N.F. Michelena, P.Y. Papalambros, A network reliability approach to optimal decomposition of design problems. J. of Mechanical Design, vol. 2, 195-204, 1995.
    20. S. Mishin, Optimal organizational hierarchies in firms. J. of Business Economics and Management, 8(2), 79-99, 2007.
    21. G.E. Moiseenko, Optimal Dividing of System into Subsystems. Automation and Remote Control, No. 7, pp. 103-112, 1977 (in Russian)
    22. Alex Pothen, Horst D. Somin, Kang-Pu Paul Liou, Partitioning sparse matrices with eigenvectors of graphs. SIAM J. on Matrix Analysis and Applications, 11(3), 430-452, 1990.
    23. J. Rasmussen, The role of hierarchical knowledge representation in decision making and system management. IEEE Trans. SMC, 15(2), 234-243, 1985.
    24. J.E. Renaud, G.A. Gabriele, Approximation in non-hierarchic system optimization. AIAA Journal, 32(1), 198-205, 1994.
    25. J. Shankar, C.J. Ribbens, R.T. Haftka, L.T. Watson, Computational study of a nonhierarchic decomposition algorithm. Computational Optimization and Applications, vol. 2, 273-293, 1993.
    26. S. Tosserams, A.T. Hofkamp, L.F. Etman, J.E. Rooda, A specification language for problem partitioning in decomposition-based design optimization. Structural and Multidisciplinary Optimization. Vol. 42, 707-723, 2010.
    27. David M. Sharman, Ali A. Yassine, Characterizing Complex Product Architectures. Systems Engineering, 7(1), 35-60, 2004.
    28. J. Shi, J. Malik, Normalized cuts and image segmentation. IEEE Trans. PAMI, 22(8), 888-905, May 2000.
    29. Manuel E. Sosa, Steven D. Eppinger, Craig M. Rowles, A Network Approach to Define Modularity of Components in Complex Products. J. of Mechanical Design, 129(11), 1118-1129, 2007.
    30. D.V. Steward, Partitioning and tearing systems of equations. SIAM J. on Numerical Analysis, 2(2), 345-365, 1965.
    31. D.V. Steward, The Design Structure System: A Method for Managing the Design of Complex Systems. IEEE Trans. on Engineering Management, 28(3), 71-74, 1981.
    32. A.A. Voronin, S.P. Mishin, Algorithms to seek the optimal structure of the organizational system. Autom. & Remote Control, 63(5), 803-814, 2002.
    33. B. Wang, F. Madani, X. Wang, L. Wang, C. White, Design Structure Matrix. In: Planning and Roadmapping Technolopgical Innovations, Springer, 53-65, 2014.
    34. Ali Yassine, Dan Braha, Complex Concurrent Engineering and the Design Structure Matrix Method. Concurrent Engineering: Research and Applicaitopns, 11(3), 165-176, Sept. 2003.
    35. L. Yelowitz, An efficient algorithm for constructing hierarchical graphs. IEEE Trans. SMC, 6(4), 327-329, Apr. 1976.
    36. U. Brandes, D. Delling, M. gaertler, R. Gorke, M. Hoefer, Z. Nikoloski, D. Wagner, In finding graph clustering with maximum modularity. In: A. Brandstadt, D. Kratach, H. Muller (Eds.), Proc. of 33rd Int. Conf. 'Workshop on Graph-Theoretic Concepts in Computer Science' Workshop WG 2007, LNCS 4769, Springer, 121-132, 2007.
    37. J. Carriere, Rick Kazman, Research report. Interacting with huge hierarchies: beyond cone trees. In: Proc. on Informaion Visualization, IEEE, 74-81, 1995.

  • Electronic Preprints
    1. M.Sh. Levin, Towards design of hierarchy (research survey). Electronic preprint. 36 pp., Dec. 8, 2012. [math.OC]

  • Technical Reports
    1. J. Sobieszczanski-Sobieski, Optimization by decomposition: A step from hierarchic to non-hierarchic systems. Tech. Rep., NASA Langley Research Center, Hampton, VA, Sept. 1988.
    2. C.M. Fiduccia, R.M. Mattheyses, A lienar time heuristic for improving network partitions. Technical Report 82CRD130, GE Corporate Research, 1982.

  • PhD Theses
    1. James Richard Tebboth, A computational study of Dantzig-Wolfe decomposition. PhD thesis, Univ. of Buckingham, UK, 2001.
    2. E.M. Voorhees, The effectiveness and effciency of agglomerative hierarchic clustering in document retrieval. PhD thesis, Cornell Univ., 1986.
    3. Gunnar Erixon, Modular Function Deployment - A Method for Product Modularization. PhD Thesis, The Royal Institute of Technology, Stockholm, 2008. TRITA-MSM R-98-1
    4. Manuel E. Sosa, Analyzing the Effect of Product Architecture on Technical Communication in Product Development Organization. PhD thesis, MIT, Cambridge, June 2000.
    5. Jason E. Bartolomei, Quantitative Knowledge Construction for Engineering Systems: Extending the Design Structure matrix Methodology in Scope and Procedure. PhD thesis, Engineering Systems Division, MIT, Cambridge, June 2007.
    6. O. Dong, Predicting and managing system interactions at early phase of the product development process. PhD thesis, MIT, Cambridge, 2002.
    7. B. Koo, Meta-Language for Systems Architecting. PhD thesis, Engineering Systems Division, MIT, Cambridge, 2005.
    8. Katja Holtta-Otto, Modular Product Platform Design. PhD Thesis. Dept. of Mechanical Engineering, Helsinki University of Technology, 2005.
    9. Gerrit J. Muller, CAFCR: A Multi-view Method for Embedded Systems Architecting: Balancing Genericity and Specificity. PhD Thesis, Tehcnical Univ. of Eindhoven, The Netherlands, March 2013.

  • MS Theses
    1. J. Schatzmann, Using self-organizing maps to visualize clusters and trends in multidimensional data sets. MS thesis, Imperial College, London, UK, 2003.
    2. V. Jakobsen, Data clustering with viuslaization. MS thesis, Univ. of Bergen, Norway, 2010.
    3. Craig M. Rowles, System Integration Analysis of a Large Commercial Aircraft Engine. MS thesis, MIT, Cambridge, Febr. 1999.
    4. O. Dong, Representing information flow and knowledge management in product design using the design strcuture matrix. MS thesis, MIT, Cambridge, 1999.