Exact reliability optimization for series‐parallel graphs using convex envelopes

Given its wide spectrum of applications, the classical problem all-terminal network reliability evaluation remains a highly relevant in design. The associated optimization -- to find with best possible under multiple constraints presents an even more complex challenge, which has been addressed scientific literature but usually strong assumptions over failures probabilities and/or topology. In this work, we propose novel framework for design that are independent not necessarily identical. We leverage linear-time procedure series-parallel graphs Satyanarayana and Wood(1985) formulate as mixed-integer nonlinear problem. To solve nonconvex problem, use convex envelopes bilinear functions, introduce custom cutting planes, new family expressions appear reliability. Furthermore, exploit refinements produced by spatial branch-and-bound locally strengthen our relaxations. Our experiments show that, using framework, one can efficiently obtain optimal solutions challenging instances