Advertisement

Learning a Stopping Criterion for Local Search

  • Alejandro ArbelaezEmail author
  • Barry O’Sullivan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10079)

Abstract

Local search is a very effective technique to tackle combinatorial problems in multiple areas ranging from telecommunications to transportations, and VLSI circuit design. A local search algorithm typically explores the space of solutions until a given stopping criterion is met. Ideally, the algorithm is executed until a target solution is reached (e.g., optimal or near-optimal). However, in many real-world problems such a target is unknown. In this work, our objective is to study the application of machine learning techniques to carefully craft a stopping criterion. More precisely, we exploit instance features to predict the expected quality of the solution for a given algorithm to solve a given problem instance, we then run the local search algorithm until the expected quality is reached. Our experiments indicate that the suggested method is able to reduce the average runtime up to 80% for real-world instances and up to 97% for randomly generated instances with a minor impact in the quality of the solutions.

Keywords

Local Search Problem Instance Travel Salesman Problem Local Search Algorithm Average Runtime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by DISCUS (FP7 Grant Agreement 318137) and Science Foundation Ireland (SFI) Grant No. 10/CE/I1853. The Insight Centre for Data Analytics is also supported by SFI under Grant Number SFI/12/RC/2289.

References

  1. 1.
    Davey, R., Grossman, D., Rasztovits-Wiech, M., Payne, D., Nesset, D., Kelly, A., Rafel, A., Appathurai, S., Yang, S.H.: Long-reach passive optical networks. J. Lightwave Technol. 27(3), 273–291 (2009)CrossRefGoogle Scholar
  2. 2.
    Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: Constraint-based local search for the distance- and capacity-bounded network design problem. In: ICTAI 2014, Limassol, Cyprus, November 10–12, 2014, pp. 178–185 (2014)Google Scholar
  3. 3.
    Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: Constraint-based local search for edge disjoint rooted distance-constrainted minimum spanning tree problem. In: CPAIOR 2015, pp. 31–46 (2015)Google Scholar
  4. 4.
    Arbelaez, A., Mehta, D., O’Sullivan, B.: Constraint-based local search for finding node-disjoint bounded-paths in optical access networks. In: CP 2015, pp. 499–507 (2015)Google Scholar
  5. 5.
    Helsgaun, K.: An effective implementation of the lin-kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126(1), 106–130 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Croes, G.A.: A method for solving traveling salesman problems. Oper. Res. 6, 791–812 (1958)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hoos, H., Stütze, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, New York (2005)Google Scholar
  8. 8.
    Larochelle, H., Bengio, Y.: Classification using Discriminative Restricted Boltzmann Machines. In: ICML 2008, Helsinki, Finland, ACM 536–543., June 2008Google Scholar
  9. 9.
    Al-Shahib, A., Breitling, R., Gilbert, D.R.: Predicting protein function by machine learning on amino acid sequences - a critical evaluation. BMC Genomics 8(2), 78 (2007)CrossRefGoogle Scholar
  10. 10.
    Gelly, S., Silver, D.: Combining Online and Offline Knowledge in UCT. In: ICML 2007. vol. 227, pp. 273–280. ACM, Corvalis, Oregon, USA, June 2007Google Scholar
  11. 11.
    Rish, I., Brodie, M., Ma, S., et al.: Adaptive diagnosis in distributed dystems. IEEE Trans. Neural Netw. 16, 1088–1109 (2005)CrossRefGoogle Scholar
  12. 12.
    Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. AI Mag. 35(3), 48–60 (2014)Google Scholar
  13. 13.
    Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: Satzilla: portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. 32, 565–606 (2008)zbMATHGoogle Scholar
  14. 14.
    Battiti, R., Tecchiolli, G.: The reactive tabu search. INFORMS J. Comput. 6(2), 126–140 (1994)CrossRefzbMATHGoogle Scholar
  15. 15.
    Hutter, F., Xu, L., Hoos, H.H., Leyton-Brown, K.: Algorithm runtime prediction: methods & evaluation. Artif. Intell. 206, 79–111 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kahavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: IJCAI 1995, pp. 1137–1145 (1995)Google Scholar
  17. 17.
    Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The weka data mining software: an update. SIGKDD Explor. 11, 10–18 (2009)CrossRefGoogle Scholar
  18. 18.
    Ribeiro, C.C., Rosseti, I., Souza, R.C.: Effective probabilistic stopping rules for randomized metaheuristics: GRASP Implementations. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 146–160. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-25566-3_11 CrossRefGoogle Scholar
  19. 19.
    Bontempi, G.: An optimal stopping strategy for online calibration in local search. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 106–115. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-25566-3_8 CrossRefGoogle Scholar
  20. 20.
    Pardalos, P.M., Romeijn, H.E.: Handbook of Global Optimization. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  21. 21.
    Boender, C.G.E., Kan, A.H.G.R.: Bayesian stopping rules for multistart global optimization methods. Math. Program. 37(1), 59–80 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Orsenigo, C., Vercellis, C.: Bayesian stopping rules for greedy randomized procedures. J. Global Optim. 36(3), 365–377 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Dorea, C.C.Y.: Stopping rules for a random optimization method. SIAM J. Control Optim. 4, 841–850 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Hart, W.E.: Sequential stopping rules for random optimization methods with applications to multistart local search. SIAM J. Optim. 9(1), 270–290 (1998)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Insight Centre for Data Analytics, Department of Computer ScienceUniversity College CorkCorkIreland

Personalised recommendations