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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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%.

Original languageEnglish
Pages (from-to)83-109
Number of pages27
JournalOptimization and Engineering
Issue number1-2
StatePublished - Mar 2011


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


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