Skip to main content

Solving Multidimensional 0–1 Knapsack Problem with an Artificial Fish Swarm Algorithm

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7335))

Abstract

The multidimensional 0–1 knapsack problem is a combinatorial optimization problem, which is NP-hard and arises in many fields of optimization. Exact as well as heuristic methods exist for solving this type of problem. Recently, a population-based artificial fish swarm algorithm was proposed and applied in an engineering context. In this paper, we present a binary version of the artificial fish swarm algorithm for solving multidimensional 0–1 knapsack problem. Infeasible solutions are made feasible by a decoding algorithm. We test the presented method with a set of benchmark problems and compare the obtained results with other methods available in literature. The tested method appears to give good results when solving these problems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akçay, Y., Li, H., Xu, S.H.: Greedy algorithm for the general multidimensional knapsack problem. Ann. Oper. Res. 150, 17–29 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Balev, S., Yanev, N., Fréville, A., Andonov, R.: A dynamic programming based reduction procedure for the multidimensional 0–1 knapsack problem. Eur. J. Oper. Res. 186, 63–76 (2008)

    Article  MATH  Google Scholar 

  3. Battiti, R., Tecchiolli, G.: Local search with memory: benchmarking RTS. OR Spektrum 17, 67–86 (1995)

    Article  MATH  Google Scholar 

  4. Beasley, J.E.: OR-Library; Distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990), http://people.brunel.ac.uk/~mastjjb/jeb/info.html

    Google Scholar 

  5. Boyer, V., Elkihel, M., Baz, D.E.: Heuristics for the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. 199, 658–664 (2009)

    Article  MATH  Google Scholar 

  6. Cabot, A.V.: An enumeratuion algorithm for knapsack problems. Oper. Res. 18, 306–311 (1970)

    Article  MATH  Google Scholar 

  7. Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 4, 63–86 (1998)

    Article  MATH  Google Scholar 

  8. Deep, K., Bansal, J.C.: A socio-cognitive particle swarm optimization for multi-dimensional knapsack problem. In: Proceedings of the First International Conference on Emerging Trends in Engineering and Technology, pp. 355–360 (2008)

    Google Scholar 

  9. Djannaty, F., Doostdar, S.: A hybrid genetic algorithm for the multidimensional knapsack problem. Int. J. Contemp. Math. Sci. 3(9), 443–456 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Drexl, A.: A simulated annealing approach to the multiconstraint zero–one knapsack problem. Computing 40, 1–8 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fernandes, E.M.G.P., Martins, T.F.M.C., Rocha, A.M.A.C.: Fish swarm intelligent algorithm for bound constrained global optimization. In: Aguiar, J.V. (ed.) CMMSE 2009, pp. 461–472 (2009)

    Google Scholar 

  12. Fontanari, J.F.: A statistical analysis of the knapsack problem. J. Phys. A: Math. Gen. 28, 4751–4759 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fréville, A., Plateau, G.: The 0–1 bidimensional knapsack problem: Towards an efficient high-level primitive tool. J. Heuristics 2, 147–167 (1996)

    Article  MATH  Google Scholar 

  14. Fréville, A.: The multidimensional 0–1 knapsack problem: An overview. Eur. J. Oper. Res. 155, 1–21 (2004)

    Article  MATH  Google Scholar 

  15. Gavish, B., Pirkul, H.: Efficient algorithms for solving multiconstraint zero–one knapsack problems to optimality. Math. Program. 31, 78–105 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gilmore, P.C., Gomory, R.E.: The theory and computation of knapsack functions. Oper. Res. 14, 1045–1075 (1966)

    Article  MathSciNet  Google Scholar 

  17. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  18. Hanafi, S., Fréville, A.: An efficient tabu search approach for the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. 106, 659–675 (1998)

    Article  MATH  Google Scholar 

  19. He, J., Miao, Z., Zhang, Z., Shi, X.: Solving multidimensional 0–1 knapsack problem by tissue P systems with cell division. In: Proceedings of the Fourth International Conference on Bio-Inspired Computing BIC–TA 2009, pp. 249–253 (2009)

    Google Scholar 

  20. Hill, R.R., Cho, Y.K., Moore, J.T.: Problem reduction heuristic for the 0–1 multidimensional knapsack problem. Comput. Oper. Res. 39, 19–26 (2012)

    Article  MathSciNet  Google Scholar 

  21. Jiang, M., Wang, Y., Pfletschinger, S., Lagunas, M.A., Yuan, D.: Optimal Multiuser Detection with Artificial Fish Swarm Algorithm. In: Huang, D.-S., Heutte, L., Loog, M. (eds.) ICIC 2007, Part 22. CCIS, vol. 2, pp. 1084–1093. Springer, Heidelberg (2007)

    Google Scholar 

  22. Jiang, M., Mastorakis, N., Yuan, D., Lagunas, M.A.: Image Segmentation with Improved Artificial Fish Swarm Algorithm. In: Mastorakis, N., Mladenov, V., Kontargyri, V.T. (eds.) ECC 2008. LNEE, vol. 28, pp. 133–138. Springer, Heidelberg (2009)

    Google Scholar 

  23. Khuri, S., Bäck, T., Heitkötter, J.: The zero/one multiple knapsack problem and genetic algorithm. In: Proceedings of the 1994 ACM Symposium on Applied Computing, pp. 188–193 (1994)

    Google Scholar 

  24. Kong, M., Tian, P., Kao, Y.: A new ant colony optimization algorithm for the multidimensional knapsack problem. Comput. Oper. Res. 35, 2672–2683 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. Li, H., Jiao, Y.-C., Zhang, L., Gu, Z.-W.: Genetic Algorithm Based on the Orthogonal Design for Multidimensional Knapsack Problems. In: Jiao, L., Wang, L., Gao, X.-b., Liu, J., Wu, F. (eds.) ICNC 2006, Part I. LNCS, vol. 4221, pp. 696–705. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  26. Michalewicz, Z.: Genetic Algorithms+Data Structures=Evolution Programs. Springer, Berlin (1996)

    MATH  Google Scholar 

  27. Petersen, C.C.: Computational experience with variants of the Balas algorithm applied to the selection of R&D projects. Manag. Sci. 13(9), 736–750 (1967)

    Article  Google Scholar 

  28. Rocha, A.M.A.C., Martins, T.F.M.C., Fernandes, E.M.G.P.: An augmented Lagrangian fish swarm based method for global optimization. J. Comput. Appl. Math. 235, 4611–4620 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. Rocha, A.M.A.C., Fernandes, E.M.G.P., Martins, T.F.M.C.: Novel Fish Swarm Heuristics for Bound Constrained Global Optimization Problems. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part III. LNCS, vol. 6784, pp. 185–199. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  30. Sakawa, M., Kato, K.: Genetic algorithms with double strings for 0–1 programming problems. Eur. J. Oper. Res. 144, 581–597 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  31. Schilling, K.E.: The growth of m–constraint random knapsacks. Eur. J. Oper. Res. 46, 109–112 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shih, W.: A branch and bound method for the multiconstraint zero–one knapsack problem. J. Oper. Res. Soc. 30, 369–378 (1979)

    MATH  Google Scholar 

  33. Soyster, A.L., Lev, B., Slivka, W.: Zero–one programming with many variables and few constraints. Eur. J. Oper. Res. 2, 195–201 (1978)

    Article  MATH  Google Scholar 

  34. Vasquez, M., Vimont, Y.: Improved results on the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. 165, 70–81 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  35. Veni, K.K., Balachandar, S.R.: A new heuristic approach for large size zero–one multi knapsack problem using intercept matrix. Int. J. Comput. Math. Sci. 4(5), 259–263 (2010)

    Google Scholar 

  36. Wang, C.-R., Zhou, C.-L., Ma, J.-W.: An improved artificial fish swarm algorithm and its application in feed-forward neural networks. In: Proceedings of the 4th ICMLC, pp. 2890–2894 (2005)

    Google Scholar 

  37. Wang, X., Gao, N., Cai, S., Huang, M.: An Artificial Fish Swarm Algorithm Based and ABC Supported QoS Unicast Routing Scheme in NGI. In: Min, G., Di Martino, B., Yang, L.T., Guo, M., Rünger, G. (eds.) ISPA Workshops 2006. LNCS, vol. 4331, pp. 205–214. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  38. Weingartner, H.M., Ness, D.N.: Methods for the solution of the multidimensional 0/1 knapsack problem. Oper. Res. 15, 83–103 (1967)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Azad, M.A.K., Rocha, A.M.A.C., Fernandes, E.M.G.P. (2012). Solving Multidimensional 0–1 Knapsack Problem with an Artificial Fish Swarm Algorithm. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2012. ICCSA 2012. Lecture Notes in Computer Science, vol 7335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31137-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31137-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31136-9

  • Online ISBN: 978-3-642-31137-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics