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Variable neighborhood search for metric dimension and minimal doubly resolving set problems

Author

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  • Mladenović, Nenad
  • Kratica, Jozef
  • Kovačević-Vujčić, Vera
  • Čangalović, Mirjana

Abstract

In this paper, two similar NP-hard optimization problems on graphs are considered: the metric dimension problem and the problem of determining a doubly resolving set with the minimum cardinality. Both are present in many diverse areas, including network discovery and verification, robot navigation, and chemistry. For each problem, a new mathematical programming formulation is proposed. For solving more realistic large-size instances, a variable neighborhood search based heuristic is designed. An extensive experimental comparison on five different types of instances indicates that the VNS approach consistently outperforms a genetic algorithm, the only existing heuristic in the literature designed for solving those problems.

Suggested Citation

  • Mladenović, Nenad & Kratica, Jozef & Kovačević-Vujčić, Vera & Čangalović, Mirjana, 2012. "Variable neighborhood search for metric dimension and minimal doubly resolving set problems," European Journal of Operational Research, Elsevier, vol. 220(2), pages 328-337.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:328-337
    DOI: 10.1016/j.ejor.2012.02.019
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    References listed on IDEAS

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    1. Mladenovic, Nenad & Urosevic, Dragan & Pérez-Brito, Dionisio & García-González, Carlos G., 2010. "Variable neighbourhood search for bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 200(1), pages 14-27, January.
    2. András Sebő & Eric Tannier, 2004. "On Metric Generators of Graphs," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 383-393, May.
    3. Tatjana Davidović & Pierre Hansen & Nenad Mladenović, 2005. "Permutation-Based Genetic, Tabu, And Variable Neighborhood Search Heuristics For Multiprocessor Scheduling With Communication Delays," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 297-326.
    4. Ilic, Aleksandar & Urosevic, Dragan & Brimberg, Jack & Mladenovic, Nenad, 2010. "A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 206(2), pages 289-300, October.
    5. Muller, Laurent Flindt & Spoorendonk, Simon & Pisinger, David, 2012. "A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times," European Journal of Operational Research, Elsevier, vol. 218(3), pages 614-623.
    6. Jozef Kratica & Vera Kovačević-Vujčić & Mirjana Čangalović, 2009. "Computing the metric dimension of graphs by genetic algorithms," Computational Optimization and Applications, Springer, vol. 44(2), pages 343-361, November.
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    Cited by:

    1. Xiao, Yiyong & Zhang, Renqian & Zhao, Qiuhong & Kaku, Ikou & Xu, Yuchun, 2014. "A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 102-114.
    2. González, Antonio & Hernando, Carmen & Mora, Mercè, 2018. "Metric-locating-dominating sets of graphs for constructing related subsets of vertices," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 449-456.

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