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Solving the Multi-dimensional Multi-choice Knapsack Problem with the Help of Ants

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6234))

Abstract

In this paper, we have proposed two novel algorithms based on Ant Colony Optimization (ACO) for finding near-optimal solutions for the Multi-dimensional Multi-choice Knapsack Problem (MMKP). MMKP is a discrete optimization problem, which is a variant of the classical 0-1 Knapsack Problem and is also an NP-hard problem. Due to its high computational complexity, exact solutions of MMKP are not suitable for most real-time decision-making applications e.g. QoS and Admission Control for Adaptive Multimedia Systems, Service Level Agreement (SLA) etc. Although ACO algorithms are known to have scalability and slow convergence issues, here we have augmented the traditional ACO algorithm with a unique random local search, which not only produces near-optimal solutions but also greatly enhances convergence speed. A comparative analysis with other state-of-the-art heuristic algorithms based on public MMKP dataset shows that, in all cases our approaches outperform others. We have also shown that our algorithms find near optimal (within 3% of the optimal value) solutions within milliseconds, which makes our approach very attractive for large scale real time systems.

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References

  1. Akbar, M.M., Rahman, M.S., Kaykobad, M., Manning, E.G., Shoja, G.C.: Solving the multidimensional multiple-choice knapsack problem by constructing convex hulls. Comput. Oper. Res. 33(5), 1259–1273 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alaya, I., Solnon, C., Ghèdira, K.: Ant algorithm for the multi-dimensional knapsack problem. In: International Conference on Bioinspired Optimization Methods and their Applications (BIOMA 2004), pp. 63–72 (2004)

    Google Scholar 

  3. Beasley, J.: OR-Library: Distributing test problems by electronic mail. The Journal of the Operational Research Society 41(11), 1069–1072 (1990)

    Google Scholar 

  4. Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm intelligence: From natural to artificial systems. J. Artificial Societies and Social Simulation 4(1) (2001)

    Google Scholar 

  5. Dorigo, M., Di Caro, G.: The ant colony optimization meta-heuristic: New ideas in optimization. McGraw-Hill Ltd., UK (1999)

    Google Scholar 

  6. Dorigo, M., Di Caro, G., Gambardella, L.M.: Ant algorithms for discrete optimization. Artificial Life 5(2), 137–172 (1999)

    Article  Google Scholar 

  7. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evolutionary Computation 1(1), 53–66 (1997)

    Article  Google Scholar 

  8. Fidanova, S.: Aco algorithm for mkp using different heuristic information. In: Dimov, I.T., Lirkov, I., Margenov, S., Zlatev, Z. (eds.) NMA 2002. LNCS, vol. 2542, pp. 438–444. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Gambardella, L.M., Taillard, É., Agazzi, G.: Macs-vrptw: A multiple colony system for vehicle routing problems with time windows. In: New Ideas in Optimization, pp. 63–76. McGraw-Hill, New York (1999)

    Google Scholar 

  10. Gambardella, L.M., Taillard, É., Dorigo, M.: Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society 50, 167–176 (1999)

    MATH  Google Scholar 

  11. Hifi, M., Michrafy, M., Sbihi, A.: A reactive local search-based algorithm for the multiple-choice multi-dimensional knapsack problem. Comput. Optim. Appl. 33(2-3), 271–285 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hifi, M., Michrafy, M., Sbihi, A.: Heuristic algorithms for the multiple-choice multidimensional knapsack problem. Journal of the Operational Research Society 55, 1323–1332 (2004)

    Article  MATH  Google Scholar 

  13. Hiremath, C.: New heuristic and metaheuristic approaches applied to the multiple-choice multidimensional knapsack problem. Ph.D. thesis, Wright State University (2008)

    Google Scholar 

  14. Ji, J., Huang, Z., Liu, C., Liu, X., Zhong, N.: An Ant Colony Optimization Algorithm for Solving the Multidimensional Knapsack Problems. In: Proceedings of the 2007 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, pp. 10–16. IEEE Computer Society, Los Alamitos (2007)

    Chapter  Google Scholar 

  15. Khan, S., Li, K.F., Manning, E.G., Akbar, M.M.: Solving the knapsack problem for adaptive multimedia systems. Studia Informatica Universalis 2, 157–178 (2003)

    Google Scholar 

  16. Khan, S.: Quality Adaptation in a Multisession Multimedia System: Model, Algorithms and Architecture. Ph.D. thesis, Department of Electrical and Computer Engineering, University of Victoria, ph.D. Dissertation (1998)

    Google Scholar 

  17. Leguizamon, G., Michalewicz, Z.: A new version of ant system for subset problems. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 2 (1999)

    Google Scholar 

  18. Maniezzo, V., Colorni, A.: The ant system applied to the quadratic assignment problem. IEEE Trans. on Knowl. and Data Eng. 11(5), 769–778 (1999)

    Article  Google Scholar 

  19. Moser, M., Jokanovic, D., Shiratori, N.: An algorithm for the multidimensional multiple-choice knapsack problem. IEICE transactions on fundamentals of electronics, communications and computer sciences 80(3), 582–589 (1997)

    Google Scholar 

  20. Parra-Hernandez, R., Dimopoulos, N.J.: A new heuristic for solving the multichoice multidimensional knapsack problem. IEEE Transactions on Systems, Man, and Cybernetics, Part A 35(5), 708–717 (2005)

    Article  Google Scholar 

  21. Parsons, S.: Ant colony optimization by marco dorigo and thomas stützle. Knowledge Eng. Review 20(1), 92–93 (2005)

    MathSciNet  Google Scholar 

  22. Stützle, T., Hoos, H.H.: Max–min ant system. Future Generation Computer Systems 16, 889–914 (2000)

    Article  Google Scholar 

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Iqbal, S., Bari, M.F., Rahman, M.S. (2010). Solving the Multi-dimensional Multi-choice Knapsack Problem with the Help of Ants. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2010. Lecture Notes in Computer Science, vol 6234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15461-4_27

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  • DOI: https://doi.org/10.1007/978-3-642-15461-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15460-7

  • Online ISBN: 978-3-642-15461-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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