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The associated optimization problem\u2014to find a network with the best possible reliability under multiple constraints\u2014presents 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\u2010time evaluation procedure for network reliability in the series\u2010parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed\u2010integer 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\u2010and\u2010bound 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.<\/jats:p>","DOI":"10.1002\/net.22089","type":"journal-article","created":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T08:58:41Z","timestamp":1643273921000},"page":"235-248","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact reliability optimization for series\u2010parallel graphs using convex envelopes"],"prefix":"10.1002","volume":"80","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2866-3730","authenticated-orcid":false,"given":"Javiera","family":"Barrera","sequence":"first","affiliation":[{"name":"Faculty of Engineering and Sciences Universidad Adolfo Ib\u00e1\u00f1ez Santiago Chile"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3404-8294","authenticated-orcid":false,"given":"Eduardo","family":"Moreno","sequence":"additional","affiliation":[{"name":"Faculty of 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