Skip to main content

Modified Choice Function Heuristic Selection for the Multidimensional Knapsack Problem

  • Conference paper

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 329))

Abstract

Hyper-heuristics are a class of high-level search methods used to solve computationally difficult problems, which operate on a search space of low-level heuristics rather than solutions directly. Previous work has shown that selection hyper-heuristics are able to solve many combinatorial optimisation problems, including the multidimensional 0-1 knapsack problem (MKP). The traditional framework for iterative selection hyper-heuristics relies on two key components, a heuristic selection method and a move acceptance criterion. Existing work has shown that a hyper-heuristic using Modified Choice Function heuristic selection can be effective at solving problems in multiple problem domains. Late Acceptance Strategy is a hill climbing metaheuristic strategy often used as a move acceptance criteria in selection hyper-heuristics. This work compares a Modified Choice Function - Late Acceptance Strategy hyper-heuristic to an existing selection hyper-heuristic method from the literature which has previously performed well on standard MKP benchmarks.

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   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
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. Burke, E.K., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Woodward, J.: A Classification of Hyper-heuristic Approaches. In: Handbook of Metaheuristics, 2nd edn., pp. 449–468. Springer (2010)

    Google Scholar 

  2. Burke, E.K., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Qu, R.: Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society 64(12), 1695–1724 (2013)

    Article  Google Scholar 

  3. Sörensen, K., Glover, F.: Metaheuristics. In: Encyclopedia of Operations Research and Management Science, pp. 960–970. Springer (2013)

    Google Scholar 

  4. Drake, J.H., Kililis, N., Özcan, E.: Generation of vns components with grammatical evolution for vehicle routing. In: Krawiec, K., Moraglio, A., Hu, T., Etaner-Uyar, A.Ş., Hu, B. (eds.) EuroGP 2013. LNCS, vol. 7831, pp. 25–36. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Jackson, W.G., Özcan, E., Drake, J.H.: Late acceptance-based selection hyper-heuristics for cross-domain heuristic search. In: Proceedings of the 13th Annual Workshop on Computational Intelligence (UKCI 2013), pp. 228–235. IEEE Press, Surrey (2013)

    Chapter  Google Scholar 

  6. Fisher, H., Thompson, G.: Probabilistic learning combinations of local job-shop scheduling rules. In: Factory Scheduling Conference, Carnegie Institute of Technology (1961)

    Google Scholar 

  7. Burke, E.K., Kendall, G., Soubeiga, E.: A tabu-search hyperheuristic for timetabling and rostering. Journal of Heuristics 9(6), 451–470 (2003)

    Article  Google Scholar 

  8. Gibbs, J., Kendall, G., Özcan, E.: Scheduling english football fixtures over the holiday period using hyper-heuristics. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part I. LNCS, vol. 6238, pp. 496–505. Springer, Heidelberg (2010)

    Google Scholar 

  9. López-Camacho, E., Terashima-Marín, H., Ross, P.: A hyper-heuristic for solving one and two-dimensional bin packing problems. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2011), pp. 257–258. ACM, Dublin (2011)

    Google Scholar 

  10. Kiraz, B., Uyar, A.S., Özcan, E.: Selection hyper-heuristics in dynamic environments. Journal of the Operational Research Society 64(12), 1753–1769 (2013)

    Article  Google Scholar 

  11. Drake, J.H., Özcan, E., Burke, E.K.: Controlling crossover in a selection hyper-heuristic framework. Technical Report No. NOTTCS-TR-SUB-1104181638-4244, School of Computer Science, University of Nottingham (2011)

    Google Scholar 

  12. Drake, J.H., Hyde, M., Ibrahim, K., Özcan, E.: A genetic programming hyper-heuristic for the multidimensional knapsack problem. In: Proceedings of the 11th IEEE International Conference on Cybernetic Intelligent Systems (CIS 2012), pp. 76–80. IEEE Press, Limerick (2012)

    Google Scholar 

  13. Özcan, E., Bilgin, B., Korkmaz, E.E.: A comprehensive analysis of hyper-heuristics. Intelligent Data Analysis 12(1), 3–23 (2008)

    Google Scholar 

  14. Cowling, P., Kendall, G., Soubeiga, E.: A hyperheuristic approach to scheduling a sales summit. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 176–190. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Bilgin, B., Özcan, E., Korkmaz, E.E.: An experimental study on hyper-heuristics and exam timetabling. In: Burke, E.K., Rudová, H. (eds.) PATAT 2007. LNCS, vol. 3867, pp. 394–412. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Özcan, E., Bykov, Y., Birben, M., Burke, E.K.: Examination timetabling using late acceptance hyper-heuristics. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), pp. 997–1004. IEEE Press, Trondheim (2009)

    Chapter  Google Scholar 

  17. Burke, E.K., Kendall, G., Misir, M., Özcan, E.: Monte carlo hyper-heuristics for examination timetabling. Annals of Operations Research 196(1), 73–90 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Drake, J.H., Özcan, E., Burke, E.K.: An improved choice function heuristic selection for cross domain heuristic search. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part II. LNCS, vol. 7492, pp. 307–316. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Ochoa, G., Hyde, M.: The cross-domain heuristic search challenge (CHeSC 2011) (2011), http://www.asap.cs.nott.ac.uk/chesc2011/

  20. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Co., New York (1979)

    MATH  Google Scholar 

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

    Article  Google Scholar 

  22. Glover, F., Kochenberger, G.: Benchmarks for “the multiple knapsack problem” (n.d.), http://hces.bus.olemiss.edu/tools.html

  23. Burke, E.K., Bykov, Y.: A late acceptance strategy in hill-climbing for exam timetabling problems. In: Proceedings of the International Conference on the Practice and Theory of Automated Timetabling (PATAT 2008), Montreal, Canada (2008) Extended Abstract

    Google Scholar 

  24. Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4(1), 63–86 (1998)

    Article  MATH  Google Scholar 

  25. Özcan, E., Basaran, C.: A case study of memetic algorithms for constraint optimization. Soft Computing 13(8-9), 871–882 (2009)

    Article  Google Scholar 

  26. Pirkul, H.: A heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Research Logistics 34(2), 161–172 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  27. Freville, A., Plateau, G.: An efficient preprocessing procedure for the multidimensional 0-1 knapsack problem. Discrete Applied Mathematics 49(1-3), 189–212 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  28. Akçay, Y., Li, H., Xu, S.H.: Greedy algorithm for the general multidimensional knapsack problem. Annals of Operations Research 150(1), 17–29 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Volgenant, A., Zoon, J.A.: An improved heuristic for multidimensional 0-1 knapsack problems. Journal of the Operational Research Society 41(1), 963–970 (1990)

    Article  MATH  Google Scholar 

  30. Magazine, M.J., Oguz, O.: A heuristic algorithm for the multidimensional zero-one knapsack problem. European Journal of Operational Research 16(3), 319–326 (1984)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John H. Drake .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Drake, J.H., Özcan, E., Burke, E.K. (2015). Modified Choice Function Heuristic Selection for the Multidimensional Knapsack Problem. In: Sun, H., Yang, CY., Lin, CW., Pan, JS., Snasel, V., Abraham, A. (eds) Genetic and Evolutionary Computing. Advances in Intelligent Systems and Computing, vol 329. Springer, Cham. https://doi.org/10.1007/978-3-319-12286-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12286-1_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12285-4

  • Online ISBN: 978-3-319-12286-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics