### Abstract

This article presents a network design problem with relays considering the two-edge network connectivity. The problem arises in telecommunications and logistic networks where a constraint is imposed on the distance that a commodity can travel on a route without being processed by a relay, and the survivability of the network is critical in case of a component failure. The network design problem involves selecting two-edge disjoint paths between source and destination node pairs and determining the location of relays to minimize the network design cost. The formulated problem is solved by a hybrid approach of a genetic algorithm (GA) and a Lagrangian heuristic such that the GA searches for two-edge disjoint paths for each commodity, and the Lagrangian heuristic is used to determine relays on these paths. The performance of the proposed hybrid approach is compared to the previous approaches from the literature, with promising results.

Original language | English (US) |
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Pages (from-to) | 130-145 |

Number of pages | 16 |

Journal | Engineering Optimization |

Volume | 46 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2 2014 |

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### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Control and Optimization
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics