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Two‐node‐connected star problem
Author(s) -
Recoba Rodrigo,
Robledo Franco,
Romero Pablo,
Viera Omar
Publication year - 2018
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12362
Subject(s) - grasp , node (physics) , computer science , graph , star (game theory) , heuristic , integer programming , maxima and minima , mathematical optimization , core (optical fiber) , linear programming , greedy randomized adaptive search procedure , mathematics , theoretical computer science , algorithm , mathematical analysis , telecommunications , structural engineering , engineering , programming language
In this study, a two‐node‐connected star problem (2NCSP) is introduced. We are given a simple graph and internal and external costs for each link of the graph. The goal is to find the minimum‐cost spanning subgraph, where the core is two‐node‐connected and the remaining external nodes are connected to the core. First, we show that the 2NCSP belongs to the class of NP‐hard computational problems. Therefore, a greedy randomized adaptive search procedure (GRASP) heuristic is developed, enriched with a variable neighborhood descent (VND). The neighborhood structures include exact integer linear programming models to find the best paths and two‐node‐connected replacements, as well as a shaking operation in order to prevent being trapped in a local minima. The ring star problem (RSP) represents a relevant model in network optimization, where the core is a ring instead of an arbitrary two‐node‐connected graph. We contrast our GRASP/VND methodology with a previous reference work on the RSP in order to highlight the effectiveness of our heuristic. The heuristic is competitive, and the best results produced for several instances so far are under study. In this study, a discussion of the results and trends for future work are provided.