The environmental and economic impact of structural optimization


According to the well-known mathematician Leonhard Euler: “Nothing takes place within the universe in which the rule of maximum or minimum does not appear.” The development of optimization algorithms can be traced back to the days of Kepler, Newton, Lagrange and Cauchy and the concept of minimization much earlier to the days of Euclid. However, despite these early developments, very little progress on their use was achieved until the middle of twentieth century when digital computers made possible the application of the optimization algorithms and motivated further research, producing massive literature on the subject and development of new optimization techniques. Nevertheless, professional structural engineers and practitioners are highly sceptical in adopting such procedures in their professional life, while software applications implementing optimization techniques fall short of meeting their needs. Therefore, in this study the question that I will try to answer from an environmental and economic perspective is: “Is it worth performing structural optimization studies?” and will aim to prove that adopting optimization based design procedures will have drastic environmental impact and contribute on the economic development of the construction industry.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. A380 (2017) Accessed Dec 2017

  2. ACI 318-11 (2011) Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary (ACI 318R-11), American Concrete Institute (ACI) Committee, Farmington Hills

  3. ACI 318-14 (2014) Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318M-14), American Concrete Institute (ACI) Committee, Farmington Hills

  4. Aldwaik M, Adeli H (2016) Advances in optimization of highrise building structures. Struct Multidiscip Optim 50(6):899–919

    Article  Google Scholar 

  5. ANSI/AISC 341 (2010) Seismic Provisions for Structural Steel Buildings, AISC 341-10, American institute of steel construction Chicago

  6. ANSI/AISC 360 (2010) Specification for Structural Steel Buildings, AISC 360-10, American Institute of Steel Construction, Chicago

  7. Ansys (2017) Topology optimization: Accessed Dec 2017

  8. Argyris JH (1955) Energy theorems and structural analysis: a generalized discourse with applications on energy principles of structural analysis including the effects of temperature and non-linear stress-strain relations part I. General theory. Aircraft Engineering and Aerospace Technology 27(2):42–58

    Article  Google Scholar 

  9. ARUP (2017) Accessed Dec 2017

  10. Beghini LL, Beghini A, Katz N, Baker WF, Paulino GH (2014) Connecting architecture and engineering through structural topology optimization. Eng Struct 59:716–726

    Article  Google Scholar 

  11. Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21(9):1583–1599

    Article  MATH  Google Scholar 

  12. Cauchy A (1847) Methode generale pour la resolution des systemes d’equations simultanees. Comptes Rendus Hebd. Seances. Acad Sci 25:536–538

    Google Scholar 

  13. CCDI Group. (2017) China construction design international. Accessed Dec 2017

  14. CDP (2016) Carbon Disclosure Project (CDP) open data portal - Citywide Emissions Map, Retrieved Dec 1st 2017

  15. CEMBUREAU (2016) Cembureau-the European cement association, activity report 2016, Brussels, Accessed Dec 2017

  16. Cho YS, Kim JH, Hong SU, Kim Y (2012) LCA application in the optimum design of high rise steel structures. Renew Sust Energ Rev 16(5):3146–3153

    Article  Google Scholar 

  17. Code for Seismic Design of Buildings (2010) GB 50011-2010, National Standard of the People's Republic of China, Ministry of Housing and Urban-Rural Development of the Peoples' Republic of China, General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Beijing, [in Chinese]

  18. Committee of Steel Structure (2009) Standard specifications for steel and composite structures (design edition): I general provision, II structural planning, III design, Japan Society of Civil Engineers (JSCE), First Edition, [in Japanese]

  19. Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of American, Mathematical. Society 49:1–23

    MathSciNet  MATH  Google Scholar 

  20. Crow JM (2008) The concrete conundrum. Chemistry World 62-66

  21. Dantzig GB (1951) Maximization of a linear function of variables subject to linear inequalities. Activity Analysis of Production and Allocation. In: Koopman TC (ed) Cowles commission monograph, vol 13. John Wiley and Sons, New York

    Google Scholar 

  22. Dapogny C, Faure A, Michailidis G, Allaire G, Couvelas A, Estevez R (2017) Geometric constraints for shape and topology optimization in architectural design. Comput Mech 59(6):933–965

    MathSciNet  Article  MATH  Google Scholar 

  23. EC2 (2004) Eurocode 2: Design of concrete structures - part 1-1: general rules and rules for buildings. European Committee for Standardisation Brussels, Belgium: the European standard EN 1992–1-1

  24. Edisonian Approach (2017) For more information about the Edisonian approach, visit Accessed Dec 2017)

  25. EUROFER (2017) Eurofer-the European steel association, annual report 2017, Brussels, Accessed Dec 2017)

  26. Eurostat (2017) PRODCOM (PRODuction COMmunautaire) - Statistics by Products", Community Production for mining, quarrying and manufacturing: sections B and C of the Statistical Classification of Economy Activity in the European Union (NACE 2). Retrieved 1st December 2017

  27. Ferreiro-Cabello J, Fraile-Garcia E, Martinez de Pison Ascacibar E, Martinez de Pison Ascacibar FJ (2016) Minimizing greenhouse gas emissions and costs for structures with flat slabs. J Clean Prod 137:922–930

    Article  Google Scholar 

  28. Focus Economics (2017) Policy interest rates for 2016, Accessed Dec 2017

  29. Foley CM, Pezeshk S, Alimoradi A (2007) Probabilistic performance-based optimal design of steel moment-resisting frames. I: formulation. J Struct Eng 133(6):757–766

    Article  Google Scholar 

  30. Frangopol DM, Maute K (2003) Life-cycle reliability-based optimization of civil and aerospace structures. Comput Struct 81(7):397–410

    Article  Google Scholar 

  31. Global Steel (2014) Planning to profit from opportunity: preparing for future demand, Ernst & Young-Building a better working world, Accessed Dec 2017

  32. Hammond G, Jones C (2008) Inventory of carbon energy (ICE), Department of Mechanical Engineering, University of Bath, Version 6(1)

  33. IPCC (2007) Climate change 2007: synthesis report. In: Core Writing Team, Pachauri RK, Reisinger A (Eds.) Contribution of working groups I, II and III to the fourth assessment report of the intergovernmental panel on climate change. IPCC, Geneva, Switzerland, pp. 104.

  34. ISO 14040 (2006) Environmental management - life cycle assessment-principles and framework. International Organization for Standardization (ISO), Geneva

    Google Scholar 

  35. Karush W (1939) Minima of functions of several variables with inequalities as side conditions. MS thesis, Department of Mathematics, University of Chicago, Chicago

  36. Kaveh A, Zakian P (2013) Optimal design of steel frames under seismic loading using two meta-heuristic algorithms. J Constr Steel Res 82:111–130

    Article  Google Scholar 

  37. Mavrokapnidis, D., Mitropoulou, C.C., Lagaros, N.D., Environmental assessment of optimized tall buildings᾽ struc-tural systems, 18th Panhellenic Conference on Concrete, Conference Proceedings, Athens, Greece, March 29-31, 2018

  38. Kroiss M, Cremers L, Evangelou V (2013) Conceptual car design at BMW with focus on NVH performance, 5th ANSA & μETA International Conference, Thessaloniki

  39. Kuhn HW, Tucker AW (1951) Non-linear programming. In: Neyman J (ed) Proceedings of the second Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, pp 481–493

    Google Scholar 

  40. Lagaros ND (2014) A general purpose real-world structural design optimization computing platform. Struct Multidiscip Optim 49:1047–1066

    Article  Google Scholar 

  41. Lagaros ND, Karlaftis MG (2016) Life-cycle cost structural design optimization of steel wind towers. Comput Struct 174:122–132

    Article  Google Scholar 

  42. Load Code for the Design of Building Structures (2012) GB 50009-2012, National Standard of the People's Republic of China, Ministry of Housing and Urban-Rural Development of the Peoples' Republic of China, General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Beijing, [in Chinese]

  43. MacNamara S, Guest JK (2012) Topology optimization: the use of cutting edge numerical methods in teaching structures to architects, 119th ASEE Annual Conference and Exposition, Conference Proceedings, San Antonio

  44. Mavrokapnidis, D., Mitropoulou, C.C., Lagaros, N.D., Environmental assessment of optimized tall buildings᾽ structural systems, 18th Panhellenic Conference on Concrete, Conference Proceedings, Athens, Greece, March 29-31, 2018

  45. MIDAS NFX (2017) Topology optimization capability: Accessed Dec 2017

  46. OCP (2017) The world’s first optimization computing platform for structural engineering, Accessed Dec 2017

  47. OptiStruct (2017) Accessed Dec 2017

  48. PCA (2017) America’s Cement Manufacturers – How concrete is made, Accessed Dec 2017

  49. Quaranta G, Fiore A, Marano GC (2014) Optimum design of prestressed concrete beams using constrained differential evolution algorithm. Struct Multidiscip Optim 49(3):441–453

    Article  Google Scholar 

  50. Rahmatalla S, Swan CC (2003) Form finding of sparse structures with continuum topology optimization. J Struct Eng 129(12):1707–1716

    Article  Google Scholar 

  51. Ramesh T, Prakash R, Shukla KK (2010) Life cycle energy analysis of buildings: an overview. Energy and Buildings 42(10):1592–1600

    Article  Google Scholar 

  52. Rozvany GIN (1989) Structural design via optimality criteria. Kluwer, Dordrecht

    Google Scholar 

  53. Russo L (2004) The forgotten revolution: how science was born in 300BC and why it had to be reborn. Springer, Berlin

    Google Scholar 

  54. Schmit LA (1960) Structural design by systematic synthesis, proceedings of the 2nd conference on electronic computation. ASCE, New York, pp 105–122

    Google Scholar 

  55. SCIA Engineer Optimizer (2017) Automatic Optimization of Civil Engineering Structures, Accessed Dec 2017

  56. de Souza RR, Fadel Miguel LF, Lopez RH, Miguel LFF, Torii AJ (2016) A procedure for the size, shape and topology optimization of transmission line tower structures. Eng Struct 111:162–184

    Article  Google Scholar 

  57. The World Bank (2017) World Bank national accounts data and OECD National Accounts data files, GDP in USD for 2016, Retrieved Dec 1st 2017

  58. Tosca (2017) Accessed Dec 2017

  59. UNEP (2016) United Nations Environment Programme, Towards zero-emission efficient and resilient buildings, Global Status Report 2016, prepared by the GABC on the occasion of the 22nd Conference of Parties (COP22) to the United Nations Framework Convention on Climate Change (UNFCCC), Accessed Dec 2017

  60. USGS (2017) US Geological Survey - National Minerals Information Center: Cement Statistics and Information,, (retrieved 1 December 2017)

  61. Veselago VG (2002) Formulating Fermat's principle for light traveling in negative refraction materials. Physics-Uspekhi 45(10):1097–1099

    Article  Google Scholar 

  62. WSA (2017a) 50 years of the World Steel Association 1967–2017, World Steel in Figures 2017, Accessed Dec 2017)

  63. WSA (2017b) Worldsteel Short Range Outlook 2017–2018, World Steel Association, Accessed Dec 2017

  64. Yeo D, Gabbai RD (2011) Sustainable design of reinforced concrete structures through embodied energy optimization. Energy and Buildings 43(8):2028–2033

    Article  Google Scholar 

Download references


This research has been supported by the OptArch project: “Optimization Driven Architectural Design of Structures” (No: 689983) belonging to the Marie Skłodowska-Curie Actions (MSCA) Research and Innovation Staff Exchange (RISE) H2020-MSCA-RISE-2015.

Author information



Corresponding author

Correspondence to Nikos D. Lagaros.

Additional information

Responsible Editor: Ming Zhou

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lagaros, N.D. The environmental and economic impact of structural optimization. Struct Multidisc Optim 58, 1751–1768 (2018).

Download citation


  • Structural optimization
  • Life cycle assessment
  • Structural engineering practice
  • Material usage
  • Environmental and economic impact