Advertisement

A Quartile-Based Hyper-heuristic for Solving the 0/1 Knapsack Problem

  • Fernando Gómez-HerreraEmail author
  • Rodolfo A. Ramirez-Valenzuela
  • José Carlos Ortiz-BaylissEmail author
  • Ivan Amaya
  • Hugo Terashima-Marín
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10632)

Abstract

This research describes three novel heuristic-based approaches for solving the 0/1 knapsack problem. The knapsack problem, in its many variants, arises in many practical scenarios such as the selection of investment projects and budget control. As an NP-hard problem, it is not always possible to compute the optimal solution by using exact methods and, for this reason, the problem is usually solved by using heuristic-based strategies. In this document, we use information of the distributions of weight and profit of the items in the knapsack instances to design and implement new heuristic-based methods that solve those instances. The solution model proposed in this work is two-fold: the first part focuses on the generation of two new heuristics, while the second explores the combination of solving methods through a hyper-heuristic approach. The heuristics proposed, as well as the hyper-heuristic model, were tested on a heterogeneous set of knapsack problem instances and compared against four heuristics taken from the literature. One of the proposed heuristics proved to be highly competent with respect to heuristics available in the literature. By using the hyper-heuristic, a solver that dynamically selects heuristics based on the problem features, we improved the results obtained by the new heuristics proposed and, achieved the best results among all the methods tested in this investigation.

Keywords

Heuristics Hyper-heuristics Knapsack problem Quartile 

Notes

Acknowledgments

This research was supported in part by CONACyT Basic Science Projects under grant 241461 and ITESM Research Group with Strategic Focus in intelligent Systems.

References

  1. 1.
    Amuthan, A., Thilak, K.D.: Survey on Tabu search meta-heuristic optimization. In: 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES), pp. 1539–1543, October 2016Google Scholar
  2. 2.
    Banda, J., Velasco, J., Berrones, A.: A hybrid heuristic algorithm based on mean-field theory with a simple local search for the quadratic knapsack problem. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 2559–2565, June 2017Google Scholar
  3. 3.
    Barichard, V., Hao, J.K.: Genetic Tabu search for the multi-objective knapsack problem. Tsinghua Sci. Technol. 8(1), 8–13 (2003)zbMATHGoogle Scholar
  4. 4.
    Burke, E., Kendall, G.: Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques. Springer, Heidelberg (2005).  https://doi.org/10.1007/0-387-28356-0CrossRefzbMATHGoogle Scholar
  5. 5.
    Burke, E.K., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Woodward, J.R.: A classification of hyper-heuristic approaches. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, pp. 449–468. Springer, Boston (2010).  https://doi.org/10.1007/978-1-4419-1665-5_15CrossRefGoogle Scholar
  6. 6.
    Chou, Y.H., Yang, Y.J., Chiu, C.H.: Classical and quantum-inspired Tabu search for solving 0/1 knapsack problem. In: 2011 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1364–1369, October 2011Google Scholar
  7. 7.
    Cui, X., Wang, D., Yan, Y.: AES algorithm for dynamic knapsack problems in capital budgeting. In: 2010 Chinese Control and Decision Conference, pp. 481–485, May 2010Google Scholar
  8. 8.
    Dorigo, M., Stützle, T.: The Ant Colony Optimization Metaheuristic, pp. 25–64. MIT Press, Cambridge (2004)CrossRefGoogle Scholar
  9. 9.
    Gagliardi, E.O., Dorzán, M.G., Leguizamón, M.G., Peñalver, G.H.: Approximations on minimum weight pseudo-triangulation problem using ant colony optimization metaheuristic. In: 2011 30th International Conference of the Chilean Computer Science Society, pp. 238–246, November 2011Google Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  11. 11.
    Hifi, M., Otmani, N.: A first level scatter search for disjunctively constrained knapsack problems. In: 2011 International Conference on Communications, Computing and Control Applications (CCCA), pp. 1–6, March 2011Google Scholar
  12. 12.
    Jaszkiewicz, A.: On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment. IEEE Trans. Evol. Comput. 6(4), 402–412 (2002)CrossRefGoogle Scholar
  13. 13.
    Kiss, Z.I., Hosu, A.C., Varga, M., Polgar, Z.A.: Load balancing solution for heterogeneous wireless networks based on the knapsack problem. In: 2015 38th International Conference on Telecommunications and Signal Processing (TSP), pp. 1–6, July 2015Google Scholar
  14. 14.
    Kulkarni, A.J., Shabir, H.: Solving 0–1 knapsack problem using cohort intelligence algorithm. Int. J. Mach. Learn. Cybern. 7(3), 427–441 (2016)CrossRefGoogle Scholar
  15. 15.
    Lv, J., Wang, X., Huang, M., Cheng, H., Li, F.: Solving 0–1 knapsack problem by greedy degree and expectation efficiency. Appl. Soft Comput. J. 41, 94–103 (2016)CrossRefGoogle Scholar
  16. 16.
    Maashi, M., Özcan, E., Kendall, G.: A multi-objective hyper-heuristic based on choice function. Expert Syst. Appl. 41(9), 4475–4493 (2014)CrossRefGoogle Scholar
  17. 17.
    Naldi, M., Nicosia, G., Pacifici, A., Pferschy, U., Leder, B.: A simulation study of fairness-profit trade-off in project selection based on HHI and knapsack models. In: 2016 European Modelling Symposium (EMS), pp. 85–90, November 2016Google Scholar
  18. 18.
    Niar, S., Freville, A.: A parallel Tabu search algorithm for the 0–1 multidimensional knapsack problem. In: Proceedings 11th International Parallel Processing Symposium, pp. 512–516, April 1997Google Scholar
  19. 19.
    Ortiz-Bayliss, J.C., Terashima-Marín, H., Conant-Pablos, S.E.: Combine and conquer: an evolutionary hyper-heuristic approach for solving constraint satisfaction problems. Artif. Intell. Rev. 46(3), 327–349 (2016)CrossRefGoogle Scholar
  20. 20.
    Özcan, E., Bilgin, B., Korkmaz, E.E.: A comprehensive analysis of hyper-heuristics. Intell. Data Anal. 12(1), 3–23 (2008)CrossRefGoogle Scholar
  21. 21.
    Ren, Z., Jiang, H., Xuan, J., Hu, Y., Luo, Z.: New insights into diversification of hyper-heuristics. IEEE Trans. Cybern. 44(10), 1747–1761 (2014)CrossRefGoogle Scholar
  22. 22.
    Sapra, D., Sharma, R., Agarwal, A.P.: Comparative study of metaheuristic algorithms using knapsack problem. In: 2017 7th International Conference on Cloud Computing, Data Science Engineering - Confluence, pp. 134–137, January 2017Google Scholar
  23. 23.
    Terashima-Marín, H., Flores-Alvarez, E.J., Ross, P.: Hyper-heuristics and classifier systems for solving 2D-regular cutting stock problems. In: Proceedings of the 7th annual conference on Genetic and evolutionary computation, pp. 637–643. ACM (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Fernando Gómez-Herrera
    • 1
    Email author
  • Rodolfo A. Ramirez-Valenzuela
    • 1
  • José Carlos Ortiz-Bayliss
    • 1
    Email author
  • Ivan Amaya
    • 1
  • Hugo Terashima-Marín
    • 1
  1. 1.Escuela de Ingeniería y CienciasTecnologico de MonterreyMonterreyMexico

Personalised recommendations