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A hybrid iterated local search heuristic for the maximum weight independent set problem

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Abstract

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.

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Notes

  1. The source code of our ILS-VND algorithm is publicly available at: https://sites.google.com/site/nogueirabruno/software/ils-mwis.tar.gz.

  2. http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/.

  3. http://www.cs.hbg.psu.edu/txn131/clique.html.

  4. http://iridia.ulb.ac.be/~fmascia/maximum_clique/BHOSLIB-benchmark.

  5. dmclique, http://lcs.ios.ac.cn/~caisw/Resource/DIMACS%20machine%20benchmark.tar.gz.

  6. http://www.info.univ-angers.fr/pub/hao/clique.html.

  7. http://users.aalto.fi/~pat/cliquer.html.

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Authors and Affiliations

  1. Unidade Acadêmica de Garanhuns, Universidade Federal Rural de Pernambuco, Garanhuns, Brazil

    Bruno Nogueira & Rian G. S. Pinheiro

  2. Departamento de Sistemas de Computação, Universidade Federal da Paraíba, João Pessoa, Brazil

    Anand Subramanian

Authors
  1. Bruno Nogueira
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  2. Rian G. S. Pinheiro
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  3. Anand Subramanian
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Correspondence to Bruno Nogueira.

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Nogueira, B., Pinheiro, R.G.S. & Subramanian, A. A hybrid iterated local search heuristic for the maximum weight independent set problem. Optim Lett 12, 567–583 (2018). https://doi.org/10.1007/s11590-017-1128-7

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  • DOI: https://doi.org/10.1007/s11590-017-1128-7

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