Evolutionary Learning of Fire Fighting Strategies

  • Martin Kretschmer
  • Elmar Langetepe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10764)


The dynamic problem of enclosing an expanding fire can be modelled by a simple discrete variant in a grid graph. While the fire expands to all neighbouring cells in any time step, the fire fighter is allowed to block c cells in the average outside the fire in the same time interval. It was shown that the success of the fire fighter is guaranteed for \(c>1.5\) but no strategy can enclose the fire for \(c\le 1.5\). For achieving such a critical threshold the correctness (sometimes even optimality) of strategies and lower bounds have been shown by integer programming or by direct but often very sophisticated arguments. We investigate the problem whether it is possible to find or to approach such a threshold and/or optimal strategies by means of evolutionary algorithms, i.e., we just try to learn successful strategies for different constants c and have a look at the outcome. We investigate the variant of protecting a highway with still unknown threshold and found interesting strategic paradigms.


Dynamic environments Fire fighting Evolutionary strategies Threshold approximation 



The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.


  1. 1.
    Beyer, H.-G., Schwefel, H.-P., Wegener, I.: How to analyse evolutionary algorithms. Theoret. Comput. Sci. 287(1), 101–130 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Chrobak, M., Larmore, L.L.: An optimal on-line algorithm for k-servers on trees. SIAM J. Comput. 20(1), 144–148 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoret. Comput. Sci. 276(1), 51–81 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Feldheim, O.N., Hod, R.: 3/2 firefighters are not enough. Discret. Appl. Math. 161(1–2), 301–306 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Finbow, S., MacGillivray, G.: The firefighter problem: a survey of results, directions and questions. Australas. J. Comb. 43(57–77), 6 (2009)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Fogarty, P.: Catching the fire on grids. Ph.D. thesis, The University of Vermont (2003)Google Scholar
  7. 7.
    Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press, Piscataway (1995)zbMATHGoogle Scholar
  8. 8.
    Gilbers, A., Klein, R.: A new upper bound for the VC-dimension of visibility regions. Comput. Geom. 47(1), 61–74 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. University of Michigan Press, Ann Arbor (1975)zbMATHGoogle Scholar
  10. 10.
    Klein, R., Langetepe, E.: Computational geometry column 63. SIGACT News 47(2), 34–39 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ng, K., Raff, P.: Fractional firefighting in the two dimensional grid. Technical report, DIMACS Technical Report 2005-23 (2005)Google Scholar
  12. 12.
    Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Number 15 in Problemata. Frommann-Holzboog, Stuttgart-Bad Cannstatt (1973)Google Scholar
  13. 13.
    Schwefel, H.-P.: Numerical Optimization of Computer Models. Wiley, New York (1981)zbMATHGoogle Scholar
  14. 14.
    Wang, P., Moeller, S.A.: Fire control on graphs. J. Comb. Math. Comb. Comput. 41, 19–34 (2002)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BonnBonnGermany

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