Optimization and Engineering

, Volume 12, Issue 1–2, pp 83–109 | Cite as

Practical optimization of group piles using discrete Lagrange multiplier method

  • Jin-Hung Hwang
  • Ming-Chien Chung
  • Der-Shin Juang
  • Yu-Da Lyu
  • C. Hsein Juang


This paper presents a practical methodology for designing group piles of a bridge foundation that can minimize the construction cost. The constraint functions for the designed pile group are constructed according to the design code currently adopted in local engineering practice. A new procedure based on the discrete Lagrange multiplier (DLM) method is proposed for searching the optimal solution. Seven real-world design cases are used to test the validity and the performance of the proposed procedure and algorithm, in which the DLM solutions are compared with the global optimum solutions obtained by the exhaustive searching method (ESM). Vast improvement in the computational efficiency is achieved, as the DLM method can find local minimum solutions in less than 2.0 to 4.0 minutes whereas the time required with the ESM is 10,000 to 25,000 times longer. In the case studies presented, the construction costs in conjunction with the use of the DLM method differ from the global minimum costs by less than 6.0%, but the savings over the original designs can be as high as 13% to 56%.


Group pile design Bridge pier foundation Practical design Code based design Discrete Lagrange multiplier method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Chan CM, Zhang LM, Ng JTM (2009) Optimization of pile groups using hybrid genetic algorithms. J Geotech Geoenviron Eng 135(4):497–505 CrossRefGoogle Scholar
  2. Chang YL (1937) Discussion on lateral pile-loading tests. Trans ASCE 102:272–278 Google Scholar
  3. Chow YK, Thevendran V (1987) Optimization of pile groups. Comput Geotech 4(1):43–58 CrossRefGoogle Scholar
  4. Chung MC (2006) Optimum design of piled foundations. PhD Dissertation, Department of Civil Engineering, National Central University, Jhong-li, Taiwan Google Scholar
  5. Hanna AM, Morcous G, Helmy M (2004) Efficiency of pile groups installed in cohesionless soil using artificial neural networks. Can Geotech J 41(6):1241–1249 CrossRefGoogle Scholar
  6. Hoback AS, Truman KZ (1993) Least weight design of steel pile foundations. Eng Struct 15(5):379–385 CrossRefGoogle Scholar
  7. Huang Z, Hinduja S (1986) Shape optimization of a foundation for a large machine tool. Int J Mach Tool Des Res 26(2):85–97 CrossRefGoogle Scholar
  8. Hurd AJ, Truman KZ (2006) Optimization method of pile foundations. In: Proceedings of an international conference on advances in engineering structures, mechanics & construction, Waterloo, Ontario, Canada, 14–17 May, pp 653–661 Google Scholar
  9. Japan Road Association (2002a) Specifications for highway bridges part IV: substructures. Tokyo, Japan Google Scholar
  10. Japan Road Association (2002b) Specifications for highway bridges part V: seismic design. Tokyo, Japan Google Scholar
  11. Kim KN, Lee SH, Kim KS, Chung CK, Kim MM, Lee HS (2001) Optimal pile arrangement for minimizing differential settlements in piled raft foundations. Comput Geotech 28:235–253 CrossRefGoogle Scholar
  12. Kim HT, Koo HK, Kang IK (2002) Genetic algorithm-based optimum design of piled raft foundations with model tests. J Southeast Asian Geotech Soc 33(1):1–11 Google Scholar
  13. Liu JL (1992) The method for calculating the separate synthetic pile group coefficients of lateral bearing capacity. J Soil Rock Eng 14(3):9–19 Google Scholar
  14. Ng JTM, Chan CM, Zhang LM (2005) Optimum design of pile groups in nonlinear soil using genetic algorithms. In: Proceedings of the 8th international conference on the application of artificial intelligence to civil, structural and environmental engineering, Rome, Italy, 30 August–2 September, 2005, paper 35. doi: 10.4203/ccp.82.35
  15. The Chinese Institute of Civil and Hydraulic Engineering (2005) Design code and commentary to concrete engineering (DCCCE). Scientific & Technical Publishing, Taiwan Google Scholar
  16. Valliappan S, Tandjiria V, Khalili N (1999) Design of raft-pile foundation using combined optimization and finite element approach. Int J Numer Anal Methods Geomech 23(10):1043–1065 zbMATHCrossRefGoogle Scholar
  17. Yang KJ, Han LA (1997) Pile engineering. China Communications Press, Beijing, pp 13–77 Google Scholar
  18. Shang Y, Wah BW (1998) A discrete Lagrangian-based global search method for solving satisfiability problems. J Glob Optim 12(1):61–99 MathSciNetzbMATHCrossRefGoogle Scholar
  19. Wu Z (1998) The discrete Lagrangian theory and its application to solve nonlinear discrete constrain optimization problems. Master Thesis, Department of Computer Science, University of Illinois at Urbana-Champaign Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jin-Hung Hwang
    • 1
  • Ming-Chien Chung
    • 2
  • Der-Shin Juang
    • 1
  • Yu-Da Lyu
    • 1
  • C. Hsein Juang
    • 3
  1. 1.Department of Civil EngineeringNational Central UniversityJhong-liTaiwan, China
  2. 2.SINOTECH Engineering Consultants Inc.TaipeiTaiwan, ROC
  3. 3.Department of Civil EngineeringClemson UniversityClemsonUSA

Personalised recommendations