Abstract
Avoiding conflicting elements is a natural constraint that appears in several graph problems making them more challenging and close to real applications. Minimum Conflict-Free Spanning Tree (MCFST) is a variant of the classic Minimum Spanning Tree (MST) problem, where we are asked to find (if any) the spanning tree avoiding pairs of conflicting edges (conflict-free) of minimum cost. Although it is well known that MST is polynomial-time solvable, the MCFST problem is \(\mathcal{N}\mathcal{P}\)-hard. In this paper, we present a GRASP with adaptive memory (GRASP-AM) for Minimum Conflict-Free Spanning Tree. Adaptive memory (AM) is used in the constructive phase to decide which set of edges generates good solutions. Furthermore, we show how to implement the local search adopted in the GRASP-AM efficiently. Experimental results on a well-known benchmark indicate that our proposal outperforms the best existing heuristic for the problem. In particular, our GRASP-AM was able to find all known optimal solutions and to improve best-known solutions.
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The instances are available at: http://ic.ufal.br/professor/rian/Instances/Instances-MCFST-Zhang.zip and the source code of our GRASP-AM is available at: http://ic.ufal.br/professor/rian/Code/MCFST.zip.
Notes
The instances are available at: http://ic.ufal.br/professor/rian/Instances/Instances-MCFST-Zhang.zip and the source code of our GRASP-AM is available at: http://ic.ufal.br/professor/rian/Code/MCFST.zip.
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Acknowledgements
We would like to thank Prof. Marco Aurélio Lopes Barbosa for providing the source codes of ILS and the instances. The authors would like to thank the Coordination for the Improvement of Higher Education Personnel—Brazil (CAPES), National Council for Scientific and Technological Development—Brazil (CNPq), Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro—(FAPERJ).
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This work was supported by FAPERJ, CNPq and CAPES.
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Author Barros BJS declares that he has no conflict of interest. Author Pinheiro RGS declares that he has no conflict of interest. Author Souza US declares that he has no conflict of interest. Author Ochi LS declares that he has no conflict of interest.
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da Silva Barros, B.J., Pinheiro, R.G.S., Souza, U.S. et al. Using adaptive memory in GRASP to find minimum conflict-free spanning trees. Soft Comput 27, 4699–4712 (2023). https://doi.org/10.1007/s00500-022-07602-x
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DOI: https://doi.org/10.1007/s00500-022-07602-x