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

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


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.


Network optimization Maximum reliability Heuristics GRASP VND ILP 



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
    Email author
  1. 1.Facultad de IngenieríaUniversidad de la RepúblicaMontevideoUruguay

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