Skip to main content
Springer Nature Link
Log in

Merging Variables: One Technique of Search in Pseudo-Boolean Optimization

  • Conference paper
  • First Online:
Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

  • 628 Accesses

Abstract

In the present paper we describe new heuristic technique, which can be applied to the optimization of pseudo-Boolean functions including Black-Box functions. This technique is based on a simple procedure which consists in transition from the optimization problem over Boolean hypercube to the optimization problem of auxiliary function in a specially constructed metric space. It is shown that there is a natural connection between the points of the original Boolean hypercube and points from new metric space. For a Boolean hypercube with fixed dimension it is possible to construct a number of such metric spaces. The proposed technique can be considered as a special case of Variable Neighborhood Search, which is focused on pseudo-Boolean optimization. Preliminary computational results show high efficiency of the proposed technique on some reasonably hard problems. Also it is shown that the described technique in combination with the well-known (1+1)-Evolutionary Algorithm allows to decrease the upper bound on the runtime of this algorithm for arbitrary pseudo-Boolean functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Appl. Math. 123(1–3), 155–225 (2002)

    Article  MathSciNet  Google Scholar 

  2. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  3. Burke, E., Kendall, G. (eds.): Search Methodologies, 2nd edn. Springer, New York (2014). https://doi.org/10.1007/978-1-4614-6940-7

    Book  Google Scholar 

  4. McWilliams, F., Sloan, N.: The Theory of Error-Correcting Codes. North Holland, Amsterdam (1983)

    Google Scholar 

  5. Luke, S.: Essentials of Metaheuristics, 2nd edn. George Mason University, Fairfax (2015)

    Google Scholar 

  6. Rudolph, G.: Convergence properties of evolutionary algorithms. Ph.D. thesis, Hamburg (1997)

    Google Scholar 

  7. Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theor. Comput. Sci. 276(1–2), 51–81 (2002)

    Article  MathSciNet  Google Scholar 

  8. Stanley, R.: Enumerative Combinatorics. Cambridge University Press, Cambridge (2011)

    Book  Google Scholar 

  9. Feller, W.: An Introduction to Probability Theory and its Applications, 3rd edn. Wiley, Hoboken (1970)

    MATH  Google Scholar 

  10. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  Google Scholar 

  11. Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)

    Article  MathSciNet  Google Scholar 

  12. Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2016)

    Article  MathSciNet  Google Scholar 

  13. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Dordrecht (1997)

    Book  Google Scholar 

  14. Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. JSAT 2(1–4), 1–26 (2006)

    MATH  Google Scholar 

  15. Rivest, R.L.: The MD4 message digest algorithm. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 303–311. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-38424-3_22

    Chapter  Google Scholar 

  16. Otpuschennikov, I., Semenov, A., Gribanova, I., Zaikin, O., Kochemazov, S.: Encoding cryptographic functions to SAT using TRANSALG system. In: The 22nd European Conference on Artificial Intelligence (ECAI 2016). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 1594–1595. IOS Press (2016)

    Google Scholar 

  17. Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere et al. [2], pp. 131–153

    Google Scholar 

  18. Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: The 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), pp. 1173–1178 (2003)

    Google Scholar 

  19. Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_24

    Chapter  Google Scholar 

  20. Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling, YalSAT entering the SAT competition 2017. In: Balyo, T., Heule, M.J.H., Järvisalo, M. (eds.) SAT Competition 2017, vol. B-2017-1, pp. 14–15 (2017)

    Google Scholar 

  21. Ahuja, R.K., Ergun, O., Orlin, J.B., Punnen, A.P.: A survey of very large-scale neighborhood search techniques. Discrete Appl. Math. 123(1–3), 75–102 (2002)

    Article  MathSciNet  Google Scholar 

  22. Avella, P., D’Auria, B., Salerno, S., Vasil’ev, I.: A computational study of local search algorithms for italian high-school timetabling. J. Heuristics 13(6), 543–556 (2007)

    Article  Google Scholar 

  23. Doerr, B.: Analyzing randomized search heuristics via stochastic domination. Theor. Comput. Sci. 773, 115–137 (2019)

    Article  MathSciNet  Google Scholar 

  24. Li, C., Manya, F.: MaxSAT. In: Biere et al. [2], pp. 613–632

    Google Scholar 

  25. Ansótegui, C., Heymann, B., Pon, J., Sellmann, M., Tierney, K.: Hyper-reactive tabu search for MaxSAT. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P.M. (eds.) LION 12 2018. LNCS, vol. 11353, pp. 309–325. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05348-2_27

    Chapter  Google Scholar 

  26. Bouhmala, N., Øvergård, K.I.: Combining genetic algorithm with variable neighborhood search for MAX-SAT. In: Zelinka, I., Vasant, P., Duy, V.H., Dao, T.T. (eds.) Innovative Computing, Optimization and Its Applications. SCI, vol. 741, pp. 73–92. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66984-7_5

    Chapter  Google Scholar 

  27. Buzdalov, M., Doerr, B.: Runtime analysis of the (1 + (\(\lambda \), \(\lambda \))) genetic algorithm on random satisfiable 3-CNF formulas. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2017), pp. 1343–1350. ACM Press (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ISDCT SB RAS, Irkutsk, Russia

    Alexander A. Semenov

Authors
  1. Alexander A. Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander A. Semenov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Semenov, A.A. (2019). Merging Variables: One Technique of Search in Pseudo-Boolean Optimization. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-33394-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics