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A Hybrid GRASP/VND Heuristic for the Design of Highly Reliable Networks

  • Mathias Bourel
  • Eduardo Canale
  • Franco Robledo
  • Pablo Romero
  • Luis Stábile
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11299)

Abstract

There is a strong interplay between network reliability and connectivity theory. In fact, previous studies show that the graphs with maximum reliability, called uniformly most-reliable graphs, must have the highest connectivity. In this paper, we revisit the underlying theory in order to build uniformly most-reliable cubic graphs. The computational complexity of the problem promotes the development of heuristics. The contributions of this paper are three-fold. In a first stage, we propose an ideal Variable Neighborhood Descent (VND) which returns the graph with maximum reliability. This VND works in exponential time. In a second stage, we propose a hybrid GRASP/VND approach that trades quality for computational effort. A construction phase enriched with a Restricted Candidate List (RCL) offers diversification. Our local search phase includes a factor-2 algorithm for an Integer Linear Programming (ILP) model. As a product of our research, we recovered previous optimal graphs from the related literature in the field. Additionally, we offer new candidates of uniformly most-reliable graphs with maximum connectivity and maximum number of spanning trees.

Keywords

Network optimization Maximum reliability Heuristics GRASP VND ILP 

Notes

Acknowledgements

This work is partially supported by Project 395 CSIC I+D Sistemas Binarios Estocásticos Dinámicos.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mathias Bourel
    • 1
  • Eduardo Canale
    • 1
  • Franco Robledo
    • 1
  • Pablo Romero
    • 1
  • Luis Stábile
    • 1
  1. 1.Facultad de IngenieríaUniversidad de la RepúblicaMontevideoUruguay

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