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Implementing Artificial Immune Systems for the Linear Ordering Problem

  • Pavel Krömer
  • Jan Platoš
  • Václav Snášel
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 188)

Abstract

Linear Ordering Problem (LOP) is a well know NP-hard combinatorial optimization problem attractive for its complexity, rich library of test data, and variety of real world applications. This study investigates the bio-inspired Artificial Immune Systems (AIS) as a pure metaheuristic soft computing solver of the LOP. The well known LOP library LOLIB was used to compare the results obtained by AIS and other pure soft computing metaheuristics.

Keywords

linear ordering problem artificial immune systems pure metaheuristics soft computing 

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References

  1. 1.
    Abraham, A.: Editorial - hybrid soft computing and applications. International Journal of Computational Intelligence and Applications 8(1) (2009)Google Scholar
  2. 2.
    Affenzeller, M., Winkler, S., Wagner, S., Beham, A.: Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications. Chapman & Hall/CRC (2009)Google Scholar
  3. 3.
    Campos, V., Glover, F., Laguna, M., Martí, R.: An experimental evaluation of a scatter search for the linear ordering problem. J. of Global Optimization 21(4), 397–414 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    Chira, C., Pintea, C.M., Crisan, G.C., Dumitrescu, D.: Solving the linear ordering problem using ant models. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, GECCO 2009, pp. 1803–1804. ACM, New York (2009)CrossRefGoogle Scholar
  5. 5.
    Corchado, E., Arroyo, A., Tricio, V.: Soft computing models to identify typical meteorological days. Logic Journal of the IGPL 19(2), 373–383 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dyer, J.D., Hartfield, R.J., Dozier, G.V., Burkhalter, J.E.: Aerospace design optimization using a steady state real-coded genetic algorithm. Applied Mathematics and Computation 218(9), 4710–4730 (2012)MATHCrossRefGoogle Scholar
  7. 7.
    Engelbrecht, A.: Computational Intelligence: An Introduction, 2nd edn. Wiley, New York (2007)Google Scholar
  8. 8.
    Hart, E., Timmis, J.: Application areas of ais: The past, the present and the future. Applied Soft Computing 8(1), 191–201 (2008)CrossRefGoogle Scholar
  9. 9.
    Huang, G., Lim, A.: Designing a hybrid genetic algorithm for the linear ordering problem. In: GECCO, pp. 1053–1064 (2003)Google Scholar
  10. 10.
    Krömer, P., Platos, J., Snasel, V.: Differential evolution for the linear ordering problem implemented on cuda. In: Smith, A.E. (ed.) Proceedings of the 2011 IEEE Congress on Evolutionary Computation, June 5-8, pp. 790–796. IEEE Computational Intelligence Society, IEEE Press, New Orleans (2011)Google Scholar
  11. 11.
    Krömer, P., Platoš, J., Snášel, V.: Modeling permutations for genetic algorithms. In: Proceedings of the International Conference of Soft Computing and Pattern Recognition (SoCPaR 2009), pp. 100–105. IEEE Computer Society (2009)Google Scholar
  12. 12.
    Krömer, P., Snášel, V., Platoš, J.: Evolving feasible linear ordering problem solutions. In: CSTST 2008: Proceedings of the 5th International Conference on Soft Computing as Transdisciplinary Science and Technology, pp. 337–342. ACM, New York (2008)CrossRefGoogle Scholar
  13. 13.
    Krömer, P., Snášel, V., Platoš, J., Husek, D.: Genetic Algorithms for the Linear Ordering Problem. Neural Network World 19(1), 65–80 (2009)Google Scholar
  14. 14.
    Lozano, M., Herrera, F., Cano, J.: Replacement Strategies to Maintain Useful Diversity in Steady-State Genetic Algorithms, pp. 85–96 (2005)Google Scholar
  15. 15.
    Martí, R., Reinelt, G.: The Linear Ordering Problem - Exact and Heuristic Methods in Combinatorial Optimization. Applied Mathematical Sciences, vol. 175. Springer, Heidelberg (2011)MATHGoogle Scholar
  16. 16.
    Martí, R., Reinelt, G., Duarte, A.: A benchmark library and a comparison of heuristic methods for the linear ordering problem. In: Computational Optimization and Applications, pp. 1–21 (2011)Google Scholar
  17. 17.
    Mitchell, J.E., Borchers, B.: Solving linear ordering problems with a combined interior point/simplex cutting plane algorithm. Tech. rep., Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180–3590 (September 1997), http://www.math.rpi.edu/~mitchj/papers/combined.ps; accepted for publication in Proceedings of HPOPT 1997, Rotterdam, The Netherlands
  18. 18.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)MATHGoogle Scholar
  19. 19.
    Reinelt, G.: The Linear Ordering Problem: Algorithms and Applications, Research and Exposition in Mathematics, vol. 8. Heldermann Verlag, Berlin (1985)Google Scholar
  20. 20.
    Schiavinotto, T., Stützle, T.: Search Space Analysis of the Linear Ordering Problem. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 322–333. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Schiavinotto, T., Stützle, T.: The linear ordering problem: Instances, search space analysis and algorithms. Journal of Mathematical Modelling and Algorithms 3(4), 367–402 (2004)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Sedano, J., Curiel, L., Corchado, E., de la Cal, E., Villar, J.R.: A soft computing method for detecting lifetime building thermal insulation failures. Integr. Comput.-Aided Eng. 17(2), 103–115 (2010)Google Scholar
  23. 23.
    Snášel, V., Krömer, P., Platoš, J.: Differential Evolution and Genetic Algorithms for the Linear Ordering Problem. In: Velásquez, J.D., Ríos, S.A., Howlett, R.J., Jain, L.C. (eds.) KES 2009, Part I. LNCS, vol. 5711, pp. 139–146. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Snyder, L.V., Daskin, M.S.: A random-key genetic algorithm for the generalized traveling salesman problem. European Journal of Operational Research 174(1), 38–53 (2006)MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Timmis, J., Hone, A., Stibor, T., Clark, E.: Theoretical advances in artificial immune systems. Theoretical Computer Science 403(1), 11–32 (2008)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Timmis, J., Andrews, P.S., Hart, E.: Special issue on artificial immune systems. Swarm Intelligence 4(4), 245–246 (2010)CrossRefGoogle Scholar
  27. 27.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (2002)CrossRefGoogle Scholar
  28. 28.
    Yu, H.: Optimizing task schedules using an artificial immune system approach. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, GECCO 2008, pp. 151–158. ACM, New York (2008)CrossRefGoogle Scholar
  29. 29.
    Zhao, S.Z., Iruthayarajan, M.W., Baskar, S., Suganthan, P.: Multi-objective robust pid controller tuning using two lbests multi-objective particle swarm optimization. Information Sciences 181(16), 3323–3335 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pavel Krömer
    • 1
    • 2
  • Jan Platoš
    • 1
    • 2
  • Václav Snášel
    • 1
    • 2
  1. 1.Department of Computer Science, FEECSVŠB – Technical University of OstravaOstravaCzech Republic
  2. 2.IT4Innovations, Center of ExcellenceVŠB – Technical University of OstravaOstravaCzech Republic

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