Soft Computing

, Volume 21, Issue 17, pp 4901–4915 | Cite as

Large neighborhood search for the most strings with few bad columns problem

  • Evelia Lizárraga
  • Maria J. Blesa
  • Christian Blum
  • Günther R. Raidl
Focus

Abstract

In this work, we consider the following NP-hard combinatorial optimization problem from computational biology. Given a set of input strings of equal length, the goal is to identify a maximum cardinality subset of strings that differ maximally in a pre-defined number of positions. First of all, we introduce an integer linear programming model for this problem. Second, two variants of a rather simple greedy strategy are proposed. Finally, a large neighborhood search algorithm is presented. A comprehensive experimental comparison among the proposed techniques shows, first, that larger neighborhood search generally outperforms both greedy strategies. Second, while large neighborhood search shows to be competitive with the stand-alone application of CPLEX for small- and medium-sized problem instances, it outperforms CPLEX in the context of larger instances.

Keywords

Most strings with few bad columns Integer linear programming Large neighborhood search 

References

  1. Boucher C, Landau GM, Levy A, Pritchard D, Weimann O (2013) On approximating string selection problems with outliers. Theor Comput Sci 498:107–114MathSciNetCrossRefMATHGoogle Scholar
  2. Gusfield D (1997) Algorithms on strings, trees, and sequences. Computer science and computational biology. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  3. Hsu WJ, Du MW (1984) Computing a longest common subsequence for a set of strings. BIT Numer Math 24(1):45–59. doi:10.1007/BF01934514 MathSciNetCrossRefMATHGoogle Scholar
  4. Landau GM, Schmidt JP, Sokol D (2001) An algorithm for approxixmate tandem repeat. J Comput Biol 8(1):1–18CrossRefGoogle Scholar
  5. Lizárraga E, Blesa MJ, Blum C, Raidl GR (2015) On solving the most strings with few bad columns problem: an ILP model and heuristics. In: Proceedings of INISTA 2015—international symposium on innovations in intelligent systems and applications, IEEE Press, pp 1–8Google Scholar
  6. López-Ibáñez M, Dubois-Lacoste J, Stützle T, Birattari M (2011) The \(\sf irace\) package, iterated race for automatic algorithm configuration. Technical Report TR/IRIDIA/2011-004, IRIDIA, Université libre de Bruxelles, BelgiumGoogle Scholar
  7. Meneses C, Oliveira C, Pardalos P (2005) Optimization techniques for string selection and comparison problems in genomics. IEEE Eng Med Biol Mag 24(3):81–87CrossRefGoogle Scholar
  8. Mousavi S, Babaie M, Montazerian M (2012) An improved heuristic for the far from most strings problem. J Heuristics 18:239–262CrossRefGoogle Scholar
  9. Pappalardo E, Pardalos PM, Stracquadanio G (2013) Optimization approaches for solving string selection problems. SpringerBriefs in optimization. Springer, New YorkCrossRefMATHGoogle Scholar
  10. Pisinger D, Ropke S (2010) Large neighborhood search. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics, International series in operations research and management science, vol 146. Springer, New York, pp 399–419Google Scholar
  11. Rajasekaran S, Hu Y, Luo J, Nick H, Pardalos PM, Sahni S, Shaw G (2001) Efficient algorithms for similarity search. J Comb Optim 5(1):125–132MathSciNetCrossRefMATHGoogle Scholar
  12. Rajasekaran S, Nick H, Pardalos PM, Sahni S, Shaw G (2001) Efficient algorithms for local alignment search. J Comb Optim 5(1):117–124MathSciNetCrossRefMATHGoogle Scholar
  13. Smith T, Waterman M (1981) Identification of common molecular subsequences. J Mol Biol 147(1):195–197CrossRefGoogle Scholar
  14. Voß S, Fink A, Duin C (2005) Looking ahead with the pilot method. Ann Oper Res 136(1):285–302MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Evelia Lizárraga
    • 1
  • Maria J. Blesa
    • 1
  • Christian Blum
    • 2
  • Günther R. Raidl
    • 3
  1. 1.Computer Science DepartmentUniversitat Politècnica de Catalunya – BarcelonaTechBarcelonaSpain
  2. 2.Artificial Intelligence Research Institute (IIIA-CSIC)BellaterraSpain
  3. 3.Institute of Computer Graphics and AlgorithmsTU WienViennaAustria

Personalised recommendations