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Author (up) Barrera, J.; Moreno, E.; Munoz, G.; Romero, P. doi  openurl
  Title Exact reliability optimization for series-parallel graphs using convex envelopes Type
  Year 2022 Publication Networks Abbreviated Journal Networks  
  Volume 80 Issue 2 Pages 235-248  
  Keywords convex envelopes; network reliability; nonlinear optimization; reliability optimization; series-parallel graphs  
  Abstract Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem-to find a network with the best possible reliability under multiple constraints-presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.  
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  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0028-3045 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000749651100001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1513  
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