An accurate penalty-based approach for reliability-based design optimization

Fan Li, Teresa Wu, Mengqi Hu, Jin Dong

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


A typical reliability-based design optimization (RBDO) problem is usually formulated as a stochastic optimization model where the performance of a system is optimized with the reliability requirements being satisfied. Most existing RBDO methods divide the problem into two sub-problems: one relates to reliability analysis, the other relates to optimization. Traditional approaches nest the two sub-problems with the reliability analysis as the inner loop and the optimization as the outer loop. Such nested approaches face the challenge of prohibitive computational expense that drives recent research focusing on decoupling the two loops or even fundamentally transforming the two-loop structure into one deterministic optimization problem. While promising, the potential issue in these computationally efficient approaches is the lowered accuracy. In this paper, a new decoupled approach, which performs the two loops sequentially, is proposed. First, a deterministic optimization problem is solved to locate the means of the uncertain design variables. After the mean values are determined, the reliability analysis is performed. A new deterministic optimization problem is then restructured with a penalty added to each limit-state function to improve the solution iteratively. Most existing research on decoupled approaches linearizes the limit-state functions or introduces the penalty into the limit-state functions, which may suffer the approximation error. In this research, the penalty term is introduced to change the right hand side (RHS) value of the deterministic constraints. Without linearizing or transforming the formulations of limit-state function, this penalty-based approach effectively improves the accuracy of RBDO. Comparison experiments are conducted to illustrate how the proposed method obtains improved solutions with acceptable computational cost when compared to other RBDO approaches collected from literature.

Original languageEnglish (US)
Pages (from-to)87-98
Number of pages12
JournalResearch in Engineering Design
Issue number2
StatePublished - Apr 2010


  • First-order reliability method (FORM)
  • Most probable point (MPP)
  • Probabilistic optimization
  • Reliability-based design optimization (RBDO)
  • Uncertainty

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Architecture
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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