Skip to main content
SpringerLink
Log in

Single-Branch Truss-Z (STZ)

  • Chapter
  • First Online:
Discrete Optimization in Architecture

Part of the book series: SpringerBriefs in Architectural Design and Technology ((BRIEFSARCHIDE))

Abstract

This chapter describes various methods of creating single-branch Truss-Z (STZ) structures. First, the alignment to the given path is described, followed by backtracking-based method illustrated with the Case Study I. Next, various evolutionary algorithms are implemented for optimization of STZ illustrated with the Case Study II.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ahmed S, Weber M, Liwicki M, Langenhan C, Dengel A, Petzold F (2014) Automatic analysis and sketch-based retrieval of architectural floor plans. Pattern Recognit Lett 35:91–100

    Article  Google Scholar 

  2. Albers S (1999) Online algorithms: a study of graph-theoretic concepts. In: Graph-theoretic concepts in computer science, pp 10–26

    Google Scholar 

  3. Albers S, Henzinger MR (1997) Exploring unknown environments. SIAM J Comput 416–425

    Google Scholar 

  4. Albers S, Kursawe K, Schuierer S (1998) Exploring unknown environments with obstacles. In: Proceeding 10th ACM-SIAM symposium discrete algorithms, pp 842–843

    Google Scholar 

  5. Ali MM, Golalikhani M, Zhuang J (2014) A computational study on different penalty approaches for solving constrained global optimization problems with the electromagnetism-like method. Optimization 63:403–419

    Article  MathSciNet  MATH  Google Scholar 

  6. Awerbuch B, Betke M, Rivest RL, Singh M (1999) Piecemeal graph exploration by a mobile robot. Inf Comput 152(2):155–172. doi:10.1006/inco.1999.2795, http://www.sciencedirect.com/science/article/pii/S0890540199927955

  7. Bar-Cohen Y (2005) Biomimetics: biologically inspired technologies. CRC Press

    Google Scholar 

  8. Barricelli NA (1957) Symbiogenetic evolution processes realized by artificial methods. Methodos 9(35–36):143–182

    Google Scholar 

  9. Barricelli NA et al (1954) Esempi numerici di processi di evoluzione. Methodos 6(21–22):45–68

    MathSciNet  Google Scholar 

  10. Betke M, Rivest RL, Singh M (1995) Piecemeal learning of an unknown environment. Mach Learn 18(2–3):231–254

    Google Scholar 

  11. Cook G et al (2009) Design of buildings and their approaches to meet the needs of disabled people

    Google Scholar 

  12. Crosby JL et al (1973) Computer simulation in genetics. Wiley, London

    MATH  Google Scholar 

  13. De Floriani L (1988) A variable resolution graph based model of three dimensional objects. Adv Eng Softw 10(3):143–158 (1978)

    Google Scholar 

  14. Deng X, Papadimitriou CH (1990) Exploring an unknown graph. In: 31st annual symposium on foundations of computer science, 1990. Proceedings. IEEE, pp 355–361

    Google Scholar 

  15. Deng X, Kameda T, Papadimitriou C (1998) How to learn an unknown environment. I: the rectilinear case. J ACM (JACM) 45(2):215–245

    Google Scholar 

  16. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numerische Mathematik 1(1):269–271

    Article  MathSciNet  MATH  Google Scholar 

  17. Fogel DB (1998) Evolutionary computation: the fossil record. Wiley-IEEE Press

    Google Scholar 

  18. Fomin FV, Kratsch D (2010) Exact exponential algorithms. Texts in theoretical computer science. An eatcs series

    Google Scholar 

  19. Fraser A (1957) Simulation of genetic systems by automatic digital computers. I. Introduction. Aust J Biol Sci 10:484–491

    Article  Google Scholar 

  20. Fraser A, Burnell D et al (1970) Computer models in genetics. Computer models in genetics

    Google Scholar 

  21. Graver JE, Servatius B, Servatius H (1993) Combinatorial rigidity. Am Math Soc 2

    Google Scholar 

  22. Hart PE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern 4(2):100–107

    Article  Google Scholar 

  23. Iványi P, Topping B (2002) A new graph representation for cable-membrane structures. Adv Eng Softw 33(5):273–279

    Article  MATH  Google Scholar 

  24. Jeronimidis G (2008) Bioinspiration for engineering and architecture materials–structures–function. In: Proceedings of the 28th annual conference of the ACADIA, Minneapolis

    Google Scholar 

  25. Kaveh A (1988) Topological properties of skeletal structures. Comput Struct 29(3):403–411

    Article  MathSciNet  MATH  Google Scholar 

  26. Kaveh A (2014) Computational structural analysis and finite element methods. Springer

    Google Scholar 

  27. Kaveh A, Koohestani K (2008) An efficient graph-theoretical force method for three-dimensional finite element analysis. Commun Numer Methods Eng 24(11):1533–1551

    Article  MathSciNet  MATH  Google Scholar 

  28. Kaveh A, Ramachandran K (1984) Graph theoretical approach for bandwidth and frontwidth reductions. In: Proceedings 3rd international conference on space structures, pp 245–249

    Google Scholar 

  29. Kaveh A, Roosta G (1999) A graph theoretical method for frontwidth reduction. Adv Eng Softw 30(9):789–797

    Article  Google Scholar 

  30. Langenhan C, Weber M, Liwicki M, Petzold F, Dengel A (2013) Graph-based retrieval of building information models for supporting the early design stages. Adv Eng Inf 27(4):413–426

    Article  Google Scholar 

  31. Lee KY, Kwon OH, Lee JY, Kim TW (2003) A hybrid approach to geometric constraint solving with graph analysis and reduction. Adv Eng Softw 34(2):103–113

    Article  Google Scholar 

  32. Liu R, Baba T, Masumoto D (2004) Attributed graph matching based engineering drawings retrieval. In: Document analysis systems, Springer, pp 378–388

    Google Scholar 

  33. Michalewicz Z (2013) Genetic algorithms \(+\) data structures \(=\) evolution programs. Springer Science & Business Media

    Google Scholar 

  34. Michalewicz Z, Fogel DB (2013) How to solve it: modern heuristics. Springer Science & Business Media

    Google Scholar 

  35. Rechenberg I (1973) Evolutionsstrategie: Optimierung Technischer Systeme Nach Prinzipien Der Biologischen Evolution. Ph.D. thesis, Stuttgart (in German)

    Google Scholar 

  36. Recuero A, Río O, Alvarez M (2000) Heuristic method to check the realisability of a graph into a rectangular plan. Adv Eng Softw 31(3):223–231

    Article  MATH  Google Scholar 

  37. Shao W, Terzopoulos D (2007) Autonomous pedestrians. Graph Models 69(5):246–274

    Article  Google Scholar 

  38. Singh M, Khan I, Grover S (2011) Selection of manufacturing process using graph theoretic approach. Int J Syst Assur Eng Manag 2(4):301–311

    Article  Google Scholar 

  39. Sloan S (1986) An algorithm for profile and wavefront reduction of sparse matrices. Int J Numer Methods Eng 23(2):239–251

    Article  MathSciNet  MATH  Google Scholar 

  40. Sloan S (1989) A fortran program for profile and wavefront reduction. Int J Numer Methods Eng 28(11):2651–2679

    Article  MATH  Google Scholar 

  41. Tang J (2001) Mechanical system reliability analysis using a combination of graph theory and boolean function. Reliab Eng Syst Saf 72(1):21–30

    Article  Google Scholar 

  42. Thimm G, Britton G, Fok S (2004) A graph theoretic approach linking design dimensioning and process planning. Int J Adv Manuf Technol 24(3–4):261–271

    Article  Google Scholar 

  43. Vulpe A, Cărăusu A (1987) On some graph-theoretic concepts and techniques applicable in the reliability analysis of structural systems. In: Reliability and optimization of structural systems, Springer, pp 399–416

    Google Scholar 

  44. Zawidzki M (2010) Am i in a polygon? http://demonstrations.wolfram.com/AmIInAPolygon/, an interactive demonstration

  45. Zawidzki M (2010) Tiling a path with a single trapezoid along the given curve. http://demonstrations.wolfram.com/TilingAPathWithASingleTrapezoidAlongAGivenCurve/, an interactive demonstration

  46. Zawidzki M (2011a) Manually connecting two terminals with a path made of copies of a single trapezoid. http://demonstrations.wolfram.com/ManuallyConnectingTwoTerminalsWithAPathMadeOfCopiesOfASingle/, an interactive demonstration

  47. Zawidzki M (2011b) Tiling of a path with trapezoids in a constrained environment with backtracking algorithm. http://demonstrations.wolfram.com/TilingOfAPathWithTrapezoidsInAConstrainedEnvironmentWithBack/, an interactive demonstration

Download references

Author information

Authors and Affiliations

  1. MIT, Cambridge, MA, USA

    Machi Zawidzki

Authors
  1. Machi Zawidzki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Machi Zawidzki .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Author(s)

About this chapter

Cite this chapter

Zawidzki, M. (2017). Single-Branch Truss-Z (STZ). In: Discrete Optimization in Architecture. SpringerBriefs in Architectural Design and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-1109-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-1109-2_7

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-1108-5

  • Online ISBN: 978-981-10-1109-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation