Skip to main content

Combining Incomplete Search and Clause Generation: An Application to the Orienteering Problems with Time Windows

  • Conference paper
  • First Online:
Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Abstract

In this paper, we present a hybrid optimization architecture which combines on one side incomplete search processes that are often used to quickly find good-quality solutions to large-size problems, and on the other side clause generation techniques that are known to be efficient to boost systematic search. In this architecture, clauses are generated once a locally optimal solution is found. We introduce a generic component to store these clauses generated step-by-step. This component is able to prune neighborhoods by answering queries formulated by the incomplete search process. We define three versions of this clause basis manager and then experiment with an Operations Research problem known as the Orienteering Problem with Time Windows (OPTW) to show the efficiency of the approach.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://www.mech.kuleuven.be/en/cib/op.

  2. 2.

    Github URL of the source code: https://github.com/thtran97/kb_ls_cpp.

  3. 3.

    https://github.com/msoos/cryptominisat.

  4. 4.

    https://github.com/ivmai/cudd.

References

  1. Audemard, G., Lagniez, J.M., Mazure, B., Saïs, L.: Integrating conflict driven clause learning to local search. In: 6th International Workshop on Local Search Techniques in Constraint Satisfaction (LSCS 2009) (2009)

    Google Scholar 

  2. Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39071-5_23

    Chapter  MATH  Google Scholar 

  3. Bellman, R.: Dynamic programming treatment of the travelling salesman problem. J. ACM (JACM) 9(1), 61–63 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. Comput. IEEE Trans. 100(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  5. Crawford, J.: Solving satisfiability problems using a combination of systematic and local search. In: Second Challenge on Satisfiability Testing organized by Center for Discrete Mathematics and Computer Science of Rutgers University (1996)

    Google Scholar 

  6. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electron. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)

    Article  MATH  Google Scholar 

  8. Gillard, X., Schaus, P.: Large neighborhood search with decision diagrams. In: International Joint Conference on Artificial Intelligence (2022)

    Google Scholar 

  9. Glover, F., Laguna, M.: Tabu search. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 2093–2229. Springer, Boston (1998). https://doi.org/10.1007/978-1-4613-0303-9_33

    Chapter  Google Scholar 

  10. Golden, B.L., Levy, L., Vohra, R.: The orienteering problem. Naval Res. Logistics (NRL) 34(3), 307–318 (1987)

    Article  MATH  Google Scholar 

  11. Gunawan, A., Lau, H.C., Vansteenwegen, P.: Orienteering problem: a survey of recent variants, solution approaches and applications. Eur. J. Oper. Res. 255(2), 315–332 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hentenryck, P.V., Michel, L.: Constraint-Based Local Search. The MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  13. Hirsch, E., Kojevnikov, A.: UnitWalk: a new SAT solver that uses local search guided by unit clause elimination. Ann. Math. Artif. Intell. 43, 91–111 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hooker, J., Ottosson, G.: Logic-based Benders’ decomposition. Math. Program. Ser. B 96, 33–60 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ignatiev, A., Semenov, A.: DPLL+ROBDD derivation applied to inversion of some cryptographic functions. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 76–89. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21581-0_8

    Chapter  MATH  Google Scholar 

  16. Kantor, M.G., Rosenwein, M.B.: The orienteering problem with time windows. J. Oper. Res. Soc. 43(6), 629–635 (1992)

    Article  MATH  Google Scholar 

  17. Li, X.Y., Stallmann, M.F., Brglez, F.: QingTing: a fast SAT solver using local search and efficient unit propagation. In: Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT 2003) (2003)

    Google Scholar 

  18. Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Handbook of Satisfiability, pp. 133–182. IOS Press (2021)

    Google Scholar 

  19. Mazure, B., Sais, L., Grégoire, É.: Boosting complete techniques thanks to local search methods. Ann. Math. Artif. Intell. 22(3), 319–331 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proceedings of the 38th annual Design Automation Conference, pp. 530–535 (2001)

    Google Scholar 

  21. Nadel, A., Ryvchin, V.: Efficient SAT solving under assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_19

    Chapter  MATH  Google Scholar 

  22. Pesant, G., Gendreau, M.: A constraint programming framework for local search methods. J. Heuristics 5(3), 255–279 (1999)

    Article  MATH  Google Scholar 

  23. Pisinger, D., Ropke, S.: Large neighborhood search. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics. ISORMS, vol. 272, pp. 99–127. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-91086-4_4

    Chapter  Google Scholar 

  24. Prestwich, S.: The relation between complete and incomplete search. In: Blum, C., Aguilera, M.J.B., Roli, A., Sampels, M. (eds.) Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 114, pp. 63–83. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78295-7_3

    Chapter  Google Scholar 

  25. Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proceedings of 1993 International Conference on Computer Aided Design (ICCAD), pp. 42–47. IEEE (1993)

    Google Scholar 

  26. Savelsbergh, M.W.: Local search in routing problems with time windows. Ann. Oper. Res. 4(1), 285–305 (1985)

    Article  MathSciNet  Google Scholar 

  27. Schmid, V., Ehmke, J.F.: An effective large neighborhood search for the team orienteering problem with time windows. In: ICCL 2017. LNCS, vol. 10572, pp. 3–18. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68496-3_1

    Chapter  Google Scholar 

  28. Schutt, A., Feydy, T., Stuckey, P., Wallace, M.: Solving RCPSP/max by lazy clause generation. J. Sched. 16(3), 273–289 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  30. Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: 12th International Conference on Theory and Applications of Satisfiability Testing (SAT), pp. 244–257 (2009)

    Google Scholar 

  31. Vansteenwegen, P., Souffriau, W., Berghe, G.V., Van Oudheusden, D.: Iterated local search for the team orienteering problem with time windows. Comput. Oper. Res. 36(12), 3281–3290 (2009)

    Article  MATH  Google Scholar 

  32. Vansteenwegen, P., Souffriau, W., Van Oudheusden, D.: The orienteering problem: a survey. Eur. J. Oper. Res. 209(1), 1–10 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Trong-Hieu Tran .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tran, TH., Pralet, C., Fargier, H. (2023). Combining Incomplete Search and Clause Generation: An Application to the Orienteering Problems with Time Windows. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-33271-5_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33270-8

  • Online ISBN: 978-3-031-33271-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics