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Crossover Operator Using Knowledge Transfer for the Firefighter Problem

  • Krzysztof MichalakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11314)

Abstract

This paper concerns the Firefighter Problem (FFP) which is a graph-based problem in which solutions can be represented as permutations. A new crossover operator is proposed that uses a machine learning model to decide how to combine two parent solutions of the FFP into an offspring. The operator works on two parent permutations and the machine learning model provides information which parent to select the next permutation element from, when constructing a new solution. Training data is collected during a training run in which transpositions are applied to solutions found by an evolutionary algorithm for a small problem instance. The machine learning model is trained to classify pairs of graph vertices into two classes corresponding to which vertex should be placed earlier in the permutation.

In the experiments the machine learning model was trained on a set of FFP instances with 1000 vertices. Subsequently, the proposed operator was used for solving FFP instances with up to 10000 vertices. The experiments, in which the proposed operator was compared against a set of other crossover operators, shown that the proposed operator is able to effectively use knowledge gathered when solving smaller instances for solving larger instances of the same problem.

Keywords

Knowledge-based optimization Graph problems REDS graphs 

Notes

Acknowledgment

This work was supported by the Polish National Science Centre under grant no. 2015/19/D/HS4/02574. Calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl), grant No. 407.

References

  1. 1.
    Torrey, L., Shavlik, J.: Transfer learning. In: Olivas, E.S., et al. (eds.) Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, vol. 2. Information Science Reference - Imprint of: IGI Publishing, Hershey (2009)Google Scholar
  2. 2.
    Yosinski, J., Clune, J., Bengio, Y., Lipson, H.: How transferable are features in deep neural networks? In: Proceedings of the 27th International Conference on Neural Information Processing Systems, NIPS 2014, vol. 2, pp. 3320–3328. MIT Press, Cambridge (2014)Google Scholar
  3. 3.
    Hartnell, B.: Firefighter! An application of domination. In: 20th Conference on Numerical Mathematics and Computing (1995)Google Scholar
  4. 4.
    Michalak, K.: Estimation of distribution algorithms for the firefighter problem. In: Hu, B., López-Ibáñez, M. (eds.) EvoCOP 2017. LNCS, vol. 10197, pp. 108–123. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-55453-2_8CrossRefGoogle Scholar
  5. 5.
    Vogl, T., Mangis, J., Rigler, A., Zink, W., Alkon, D.: Accelerating the convergence of the backpropagation method. Biol. Cybern. 59, 257–263 (1988)CrossRefGoogle Scholar
  6. 6.
    Bridle, J.S.: Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In: Soulié, F.F., Hérault, J. (eds.) Neurocomputing. NATO ASI Series, vol. 68, pp. 227–236. Springer, Heidelberg (1990).  https://doi.org/10.1007/978-3-642-76153-9_28CrossRefGoogle Scholar
  7. 7.
    Antonioni, A., Bullock, S., Tomassini, M.: REDS: an energy-constrained spatial social network model. In: Lipson, H., et al. (eds.) ALIFE 2014. MIT Press (2014)Google Scholar
  8. 8.
    Michalak, K.: The Sim-EA algorithm with operator autoadaptation for the multiobjective firefighter problem. In: Ochoa, G., Chicano, F. (eds.) EvoCOP 2015. LNCS, vol. 9026, pp. 184–196. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-16468-7_16CrossRefGoogle Scholar
  9. 9.
    Moller, M.F.: A scaled conjugate gradient algorithm for fast supervised learning. Neural Netw. 6, 525–533 (1993)CrossRefGoogle Scholar
  10. 10.
    Arlot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40–79 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Information Technologies, Institute of Business InformaticsWroclaw University of EconomicsWroclawPoland

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