Advertisement

Simheuristics for the Multiobjective Nondeterministic Firefighter Problem in a Time-Constrained Setting

  • Krzysztof MichalakEmail author
  • Joshua D. Knowles
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9598)

Abstract

The firefighter problem (FFP) is a combinatorial problem requiring the allocation of ‘firefighters’ to nodes in a graph in order to protect the nodes from fire (or other threat) spreading along the edges. In the original formulation the problem is deterministic: fire spreads from burning nodes to adjacent, unprotected nodes with certainty.

In this paper a nondeterministic version of the FFP is introduced where fire spreads to unprotected nodes with a probability \({P_{sp}}\) (lower than 1) per time step. To account for the stochastic nature of the problem the simheuristic approach is used in which a metaheuristic algorithm uses simulation to evaluate candidate solutions. Also, it is assumed that the optimization has to be performed in a limited amount of time available for computations in each time step.

In this paper online and offline optimization using a multipopulation evolutionary algorithm is performed and the results are compared to various heuristics that determine how to place firefighters. Given the time-constrained nature of the problem we also investigate for how long to simulate the spread of fire when evaluating solutions produced by an evolutionary algorithm. Results generally indicate that the evolutionary algorithm proposed is effective for \({P_{sp}} \ge 0.7\), whereas for lower probabilities the heuristics are competitive suggesting that more work on hybrids is warranted.

Keywords

Graph-based optimization Nondeterministic firefighter problem Simheuristics 

References

  1. 1.
    Blum, C., Blesa, M.J., García-Martínez, C., Rodríguez, F.J., Lozano, M.: The firefighter problem: application of hybrid ant colony optimization algorithms. In: Blum, C., Ochoa, G. (eds.) EvoCOP 2014. LNCS, vol. 8600, pp. 218–229. Springer, Heidelberg (2014)Google Scholar
  2. 2.
    Comellas, F., Mitjana, M.: Broadcasting in small-world communication networks. In: Kaklamanis, C., Kirousis, L. (eds.) 9th International Colloquium on Structural Information and Communication Complexity, pp. 73–85. Carleton Scientific, Waterloo (2002)Google Scholar
  3. 3.
    Develin, M., Hartke, S.G.: Fire containment in grids of dimension three and higher. Discrete Appl. Math. 155(17), 2257–2268 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Feldheim, O.N., Hod, R.: 3/2 firefighters are not enough. Discrete Appl. Math. 161(1–2), 301–306 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    García-Martínez, C., et al.: The firefighter problem: empirical results on random graphs. Comput. Oper. Res. 60, 55–66 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hartnell, B.: Firefighter! an application of domination. In: 20th Conference on Numerical Mathematics and Computing (1995)Google Scholar
  7. 7.
    Hu, B., Windbichler, A., Raidl, G.R.: A new solution representation for the firefighter problem. In: Ochoa, G., Chicano, F. (eds.) EvoCOP 2015. LNCS, vol. 9026, pp. 25–35. Springer, Heidelberg (2015)Google Scholar
  8. 8.
    Juan, A.A.: A review of simheuristics: extending metaheuristics to deal with stochastic combinatorial optimization problems. Oper. Res. Perspect. 2, 62–72 (2015)CrossRefGoogle Scholar
  9. 9.
    Kumar, R., et al.: Stochastic models for the web graph. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, FOCS 2000, pp. 57–65. IEEE Computer Society (2000)Google Scholar
  10. 10.
    Li, H., Zhang, Q.: Multiobjective optimization problems with complicated pareto sets, MOEA/D and NSGA-II. IEEE Trans. Evolut. Comput. 13(2), 284–302 (2009)CrossRefGoogle Scholar
  11. 11.
    Michalak, K.: Auto-adaptation of genetic operators for multi-objective optimization in the firefighter problem. In: Corchado, E., Lozano, J.A., Quintián, H., Yin, H. (eds.) IDEAL 2014. LNCS, vol. 8669, pp. 484–491. Springer, Heidelberg (2014)Google Scholar
  12. 12.
    Michalak, K.: Sim-EA: an evolutionary algorithm based on problem similarity. In: Corchado, E., Lozano, J.A., Quintián, H., Yin, H. (eds.) IDEAL 2014. LNCS, vol. 8669, pp. 191–198. Springer, Heidelberg (2014)Google Scholar
  13. 13.
    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, Heidelberg (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Information Technologies, Institute of Business InformaticsWroclaw University of EconomicsWroclawPoland
  2. 2.School of Computer ScienceUniversity of BirminghamBirminghamUK

Personalised recommendations