Paper Info
Title
Optimal engineering design via Benders' decomposition.
Abstract
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.
Year
DOI
Venue
2013
10.1007/s10479-011-0890-7
Annals OR
Keywords
Field
DocType
Benders decomposition,Breakwater design,Civil engineering examples,FORMs,Optimal design
Failure mode and effects analysis,Mathematical optimization,Optimal design,Heuristics,Engineering design process,SIMPLE algorithm,Convex optimization,Optimization problem,Engineering optimization,Mathematics
Journal
Volume
Issue
ISSN
210
1
0254-5330
Citations 
PageRank 
References 
0
0.34
12
Authors
3
Name
Order
Citations
PageRank
Roberto Mínguez1439.56
Antonio Conejo218924.33
Enrique Castillo355559.86