Optimization Letters

, Volume 12, Issue 3, pp 567–583 | Cite as

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

  • Bruno Nogueira
  • Rian G. S. Pinheiro
  • Anand Subramanian
Original Paper


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.


Maximum weight independent set Maximum weight clique Minimum weight vertex cover Iterated local search Metaheuristics 


  1. 1.
    Karp, R.: Reducibility among combinatorial problems. In: Miller, R., Thatcher, J. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, Berlin (1972)CrossRefGoogle Scholar
  2. 2.
    Ay, F., Kellis, M., Kahveci, T.: Submap: aligning metabolic pathways with subnetwork mappings. J. Comput. Biol. 18(3), 219–235 (2011)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chou, J., Kim, J., Rotem, D.: Energy-aware scheduling in disk storage systems, in 2011 31st International Conference on Distributed Computing Systems (ICDCS), IEEE, pp. 423–433 (2011)Google Scholar
  4. 4.
    Pardalos, P.M., Desai, N.: An algorithm for finding a maximum weighted independent set in an arbitrary graph. Int. J. Comput. Math. 38(3–4), 163–175 (1991)CrossRefzbMATHGoogle Scholar
  5. 5.
    Babel, L.: A fast algorithm for the maximum weight clique problem. Computing 52(1), 31–38 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Östergård, P.R.: A new algorithm for the maximum-weight clique problem. Nord. J. Comput. 8(4), 424–436 (2001)MathSciNetGoogle Scholar
  7. 7.
    Warrier, D., Wilhelm, W.E., Warren, J.S., Hicks, I.V.: A branch-and-price approach for the maximum weight independent set problem. Networks 46(4), 198–209 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Yamaguchi, K., Masuda, S.: A new exact algorithm for the maximum weight clique problem, in 23rd international conference on circuit/systems, computers and communications (ITC-CSCC08), Vol. 65, p. 68 (2008)Google Scholar
  9. 9.
    Nayeem, S.M.A., Pal, M.: Genetic algorithmic approach to find the maximum weight independent set of a graph. J. Appl. Math. Comput. 25(1–2), 217–229 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Pullan, W.: Approximating the maximum vertex/edge weighted clique using local search. J. Heuristics 14(2), 117–134 (2008)CrossRefzbMATHGoogle Scholar
  11. 11.
    Pullan, W.: Optimisation of unweighted/weighted maximum independent sets and minimum vertex covers. Discrete Optim. 6(2), 214–219 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wu, Q., Hao, J.-K., Glover, F.: Multi-neighborhood tabu search for the maximum weight clique problem. Ann. Oper. Res. 196(1), 611–634 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Benlic, U., Hao, J.-K.: Breakout local search for maximum clique problems. Comput. Oper. Res. 40(1), 192–206 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wang, Y., Hao, J.-K., Glover, F., Lü, Z., Wu, Q.: Solving the maximum vertex weight clique problem via binary quadratic programming. J. Comb. Optim. 32(2), 531–549 (2016). doi: 10.1007/s10878-016-9990-2
  15. 15.
    Lourenço, H.R., Martin, O.C., Stützle, T.: Handbook of Metaheuristics. Ch. Iterated Local Search, Framework and Applications. Springer, Berlin (2010)Google Scholar
  16. 16.
    Hansen, P., Mladenović, N., Brimberg, J., Prez, J.: Handbook of Metaheuristics. Ch. Variable Neighborhood Search. Springer, Berlin (2010)Google Scholar
  17. 17.
    Bastos, L., Ochi, L.S., Protti, F., Subramanian, A., Martins, I.C., Pinheiro, R.G.S.: Efficient algorithms for cluster editing. J. Comb. Optim. 31(1), 347–371 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Andrade, D.V., Resende, M.G., Werneck, R.F.: Fast local search for the maximum independent set problem. J. Heuristics 18(4), 525–547 (2012)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Bruno Nogueira
    • 1
  • Rian G. S. Pinheiro
    • 1
  • Anand Subramanian
    • 2
  1. 1. Unidade Acadêmica de GaranhunsUniversidade Federal Rural de PernambucoGaranhunsBrazil
  2. 2.Departamento de Sistemas de ComputaçãoUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations