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A Modified Shuffled Frog Leaping Algorithm with Genetic Mutation for Combinatorial Optimization

  • Kaushik Kumar Bhattacharjee
  • Sarada Prasad Sarmah
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7654)

Abstract

In this work, we propose modified versions of shuffled frog leaping algorithm (SFLA) to solve multiple knapsack problems (MKP). The proposed algorithm includes two important operations: repair operator and genetic mutation with a small probability. The former is utilizing the pseudo-utility to repair infeasible solutions, and the later can effectively prevent the algorithm from trapping into the local optimal solution. Computational experiments with a large set of instances show that the proposed algorithm can be an efficient alternative for solving 0/1 multidimensional knapsack problem.

Keywords

Genetic mutation metaheuristics multidimensional knapsack problem repair operator shuffled frog leaping algorithm 

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References

  1. 1.
    Osrio, M., Glover, F., Hammer, P.: Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions. Technical Report HCES-08-00, Hearing Center for Enterprise Science (2000)Google Scholar
  2. 2.
    Nemhauser, G., Ullmann, Z.: Discrete dynamic programming and capital allocation. Management Science 15(9), 494–505 (1969)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Balas, E.: An additive algorithm for solving linear programs with zero-one variables. Operations Research 13(4), 517–546 (1965)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Crama, Y., Mazzola, J.: On the strength of relaxations of multidimensional knapsack problems. INFOR 32(4), 219–225 (1994)MATHGoogle Scholar
  5. 5.
    Arntzen, H., Hvattum, L.M., Lokketangen, A.: Adaptive memory search for multidemand multidimensional knapsack problems. Computers and Operations Research 33(9), 2508–2525 (2006)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Egeblad, J., Pisinger, D.: Heuristic approaches for the two- and three-dimensional knapsack packing problem. Computers and Operations Research 36(4), 1026–1049 (2009)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hua, Z., Huang, F.: A variable-grouping based genetic algorithm for large-scale integer programming. Information Sciences 176(19), 2869–2885 (2006)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Ke, L., Feng, Z., Ren, Z., Wei, X.: An ant colony optimization approach for the multidimensional knapsack problem. Journal of Heuristics 16(1), 65–83 (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Zhao, Q., Zhang, X., Xiao, R.: Particle swarm optimization algorithm for partner selection in virtual enterprise. Progress in Natural Science 18(11), 1445–1452 (2008)CrossRefGoogle Scholar
  10. 10.
    Eusuff, M.M., Lansey, K., Pasha, F.: Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization. Engineering Optimization 38(2), 129–154 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhang, X., Hu, X., Cui, G., Wang, Y., Niu, Y.: An improved shuffled frog leaping algorithm with cognitive behavior. In: Proc. 7th World Congr. Intelligent Control and Automation 2008 (2008)Google Scholar
  12. 12.
    Elbeltagi, E., Hegazy, T., Grierson, D.: Comparison among five evolutionary based optimization algorithms. Adv. Eng. Informat. 19(1), 43–53 (2005)CrossRefGoogle Scholar
  13. 13.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc. IEEE Conf. Neural Networks, vol. 4, pp. 1942–1948 (1995)Google Scholar
  14. 14.
    Eusuff, M., Lansey, K.: Optimization of water distribution network design using the shuffled frog leaping algorithm. Journal of Water Resource Plan Management 129, 210–225 (2003)CrossRefGoogle Scholar
  15. 15.
    Pirkul, H.: A heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Research Logistics 34, 161–172 (1987)CrossRefMATHGoogle Scholar
  16. 16.
    Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4(1), 63–86 (1998)CrossRefMATHGoogle Scholar
  17. 17.
    Beasley, J.E.: Or-library: Distributing test problems by electronic mail. Journal of Operational Research Society 41(11), 1069–1072 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kaushik Kumar Bhattacharjee
    • 1
  • Sarada Prasad Sarmah
    • 1
  1. 1.Deptt. of Industrial Engineering and ManagementIndian Institute of Technology KharagpurKharagpurIndia

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