Journal of Global Optimization

, Volume 69, Issue 2, pp 461–484 | Cite as

A certified Branch & Bound approach for reliability-based optimization problems

  • Benjamin MartinEmail author
  • Marco Correia
  • Jorge Cruz


Reliability-based optimization problems are optimization problems considering a constraint that measures reliability of the modelled system: the probability of a safety event with respect to controllable decision variables and uncertain random variables. Most solving approaches use approximate techniques for evaluating this reliability constraint. As a consequence, the reliability of the computed optimal decision is not guaranteed. In this paper, we investigate an interval-based Branch & Bound for solving globally reliability-based optimization problems with numerical guarantee. It combines an interval Branch & Bound framework with a certified reliability analysis technique. This technique considers the reliability constraint and induced safety region modelled within Probabilistic Continuous Constraint Programming paradigm. The certified reliability analysis is numerically handled by an interval quadrature algorithm. In addition, a new interval quadrature function for two random variables, based on linear models of the safety region is described. Two implementations of the Branch & Bound, which differ on how the certified reliability analysis is handled throughout the optimization process, are presented. A numerical study of these two variants shows the relevance of the interval linear model-based quadrature function.


Reliability-based optimization Branch & Bound Interval analysis Probabilistic constraints 



The authors are thankful to the Portuguese Foundation for Science and Technology for having Granted this work through the Project PROCURE (Probabilistic Constraints for Uncertainty Reasoning in Science and Engineering Applications), Ref. PTDC/EEI-CTP/1403/2012. The authors are also thankful to the anonymous referees for their useful remarks improving the quality of the paper.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.NOVA-LINCSUniversidade Nova de LisboaLisbonPortugal
  2. 2.LIXÉcole PolytechniquePalaiseauFrance

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