Sparse, Continuous Policy Representations for Uniform Online Bin Packing via Regression of Interpolants

  • John H. Drake
  • Jerry Swan
  • Geoff Neumann
  • Ender Özcan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10197)

Abstract

Online bin packing is a classic optimisation problem, widely tackled by heuristic methods. In addition to human-designed heuristic packing policies (e.g. first- or best- fit), there has been interest over the last decade in the automatic generation of policies. One of the main limitations of some previously-used policy representations is the trade-off between locality and granularity in the associated search space. In this article, we adopt an interpolation-based representation which has the jointly-desirable properties of being sparse and continuous (i.e. exhibits good genotype-to-phenotype locality). In contrast to previous approaches, the policy space is searchable via real-valued optimization methods. Packing policies using five different interpolation methods are comprehensively compared against a range of existing methods from the literature, and it is determined that the proposed method scales to larger instances than those in the literature.

Keywords

Hyper-heuristics Online bin packing CMA-ES Heuristic generation Sparse policy representations Metaheuristics Optimisation 

References

  1. 1.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, Hoboken (1990)MATHGoogle Scholar
  2. 2.
    Csirik, J., Woeginger, G.J.: On-line packing and covering problems. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 147–177. Springer, Heidelberg (1998). doi: 10.1007/BFb0029568 CrossRefGoogle Scholar
  3. 3.
    Coffman Jr., E.G., Csirik, J., Galambos, G., Martello, S., Vigo, D.: Bin packing approximation algorithms: survey and classification. In: Pardalos, P.M., Du, D.Z., Graham, R.L. (eds.) Handbook of Combinatorial Optimization, pp. 455–531. Springer, New York (2013)CrossRefGoogle Scholar
  4. 4.
    Lee, C.C., Lee, D.T.: A simple on-line bin-packing algorithm. J. ACM 32(3), 562–572 (1985)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Sinuany-Stern, Z., Weiner, I.: The one dimensional cutting stock problem using two objectives. J. Oper. Res. Soc. 45(2), 231–236 (1994)CrossRefMATHGoogle Scholar
  6. 6.
    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, vol. 146, pp. 449–468. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Woodward, J.R., Swan, J.: The automatic generation of mutation operators for genetic algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2012), pp. 67–74. ACM (2012)Google Scholar
  8. 8.
    Drake, J.H., Hyde, M., Ibrahim, K., Ozcan, E.: A genetic programming hyper-heuristic for the multidimensional knapsack problem. Kybernetes 43(9/10), 1500–1511 (2014)CrossRefGoogle Scholar
  9. 9.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: Automatic heuristic generation with genetic programming: evolving a jack-of-all-trades or a master of one. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2007), pp. 1559–1565. ACM (2007)Google Scholar
  10. 10.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: Automating the packing heuristic design process with genetic programming. Evol. Comput. 20(1), 63–89 (2012)CrossRefGoogle Scholar
  11. 11.
    Özcan, E., Parkes, A.J.: Policy matrix evolution for generation of heuristics. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2011), pp. 2011–2018. ACM (2011)Google Scholar
  12. 12.
    Johnson, D.S., Demers, A., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput. 3(4), 299–325 (1974)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Asta, S., Özcan, E., Parkes, A.J.: CHAMP: creating heuristics via many parameters for online bin packing. Expert Syst. Appl. 63, 208–221 (2016)CrossRefGoogle Scholar
  14. 14.
    Yarimcam, A., Asta, S., Özcan, E., Parkes, A.J.: Heuristic generation via parameter tuning for online bin packing. In: IEEE Symposium on Evolving and Autonomous Learning Systems (EALS 2014), pp. 102–108. IEEE (2014)Google Scholar
  15. 15.
    Burke, E.K., Hyde, M.R., Kendall, G.: Evolving bin packing heuristics with genetic programming. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 860–869. Springer, Heidelberg (2006). doi: 10.1007/11844297_87 CrossRefGoogle Scholar
  16. 16.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.R.: The scalability of evolved on line bin packing heuristics. In: 2007 IEEE Congress on Evolutionary Computation, pp. 2530–2537. IEEE (2007)Google Scholar
  17. 17.
    Ross, P., Schulenburg, S., Marín-Blázquez, J.G., Hart, E.: Hyper-heuristics: learning to combine simple heuristics in bin-packing problems. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2002), pp. 942–948 (2002)Google Scholar
  18. 18.
    López-Ibáñez, M., Dubois-Lacoste, J., Cáceres, L.P., Birattari, M., Stützle, T.: The irace package: iterated racing for automatic algorithm configuration. Oper. Res. Perspect. 3, 43–58 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Parkes, A.J., Özcan, E., Hyde, M.R.: Matrix analysis of genetic programming mutation. In: Moraglio, A., Silva, S., Krawiec, K., Machado, P., Cotta, C. (eds.) EuroGP 2012. LNCS, vol. 7244, pp. 158–169. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29139-5_14 CrossRefGoogle Scholar
  20. 20.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover Publications, New York (1965)MATHGoogle Scholar
  21. 21.
    Cleveland, W.S.: Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74(368), 829–836 (1979)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Texts in Applied Mathematics. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  23. 23.
    Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)CrossRefGoogle Scholar
  24. 24.
    Rechenberg, I.: Evolutionsstrategie: optimierung technischer systeme nach prinzipien der biologischen evolution. Number 15 in Problemata. Frommann-Holzboog, Stuttgart-Bad Cannstatt (1973)Google Scholar
  25. 25.
    Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. (TOMACS) 8(1), 3–30 (1998)CrossRefMATHGoogle Scholar
  26. 26.
    Luke, S.: Essentials of Metaheuristics, 2nd edn. Lulu, Raleigh (2013)Google Scholar
  27. 27.
    Asta, S., Özcan, E.: A tensor analysis improved genetic algorithm for online bin packing. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 799–806. ACM, New York (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • John H. Drake
    • 1
  • Jerry Swan
    • 2
  • Geoff Neumann
    • 3
  • Ender Özcan
    • 4
  1. 1.Operational Research GroupQueen Mary University of LondonLondonUK
  2. 2.Department of Computer ScienceUniversity of YorkYorkUK
  3. 3.Computing Science and MathematicsUniversity of StirlingStirlingUK
  4. 4.School of Computer ScienceUniversity of NottinghamNottinghamUK

Personalised recommendations