Optimal engineering design via Benders' decomposition Articles uri icon

publication date

  • November 2013

start page

  • 273

end page

  • 293


  • 1


  • 210

International Standard Serial Number (ISSN)

  • 0254-5330

Electronic International Standard Serial Number (EISSN)

  • 1572-9338


  • The optimal engineering design problem consists in minimizing the expected total cost of an infrastructure or equipment, including construction and expected repair costs, the latter depending on the failure probabilities of each failure mode. The solution becomes complex because the evaluation of failure probabilities using First-Order Reliability Methods (FORM) involves one optimization problem per failure mode. This paper formulates the optimal engineering design problem as a bi-level problem, i.e., an optimization problem constrained by a collection of other interrelated optimization problems. The structure of this bi-level problem is advantageously exploited using Benders' decomposition to develop and report an efficient algorithm to solve it. An advantage of the proposed approach is that the design optimization and the reliability calculations are decoupled, resulting in a structurally simple algorithm that exhibits high computational efficiency. Bi-level problems are non-convex by nature and Benders algorithm is intended for convex optimization. However, possible non-convexities can be detected and tackled using simple heuristics. Its practical interest is illustrated through a realistic but simple case study, a breakwater design example with two failure modes: overtopping and armor instability.


  • Civil and Construction Engineering
  • Environment
  • Materials science and engineering


  • benders decomposition; breakwater design; civil engineering examples; forms; optimal design