Reliable Network Design Problem under Node Failure with Benders Decomposition

Abstract

The design of telecommunication network with capacity constraints of links, routers and ports of routers is considered in this paper. Specially, we limit each demand flow traversed through a pre-speci fi ed maximal number of links (called hops) under node failure scenarios in IP layer network. Such a design must be the most cost-effec tive and ensure that feasible flows continue to exist even when any relay node of the network fail s . We propose a reliable mixed-integer programming (MIP) model with multi-scenario constraints to optimally design a mini mum-cost survivable IP network that continues to support a good communication under any node failure scena rio. Then we transform the MIP model into many single scenario models, that is, simplified MIPs, nonlinear programming (NLP) models and MIP models under Benders decomposition Then we transform the MIP model into many single scenario models, that is, simplified MIPs, nonlinear programming (NLP) models and MIP mod els under Benders decomposition. Three heuristic methods are proposed to solve these models including branch-and-bound algorithm, global algorithm for NLP, and heuristic algorithm based on benders decomposition. We mainly study the application of Benders decomposition method, where dual model and bounding procedures are given for each MIP model under Benders decomposition at each scenario. The results of our computational experiments validate the effectiveness of the proposed models and algorithms.