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

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Evolutionary Computation in Combinatorial Optimization (EvoCOP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Notes

  1. 1.

    The term ‘locality’ is often used in this context in evolutionary computation.

  2. 2.

    https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/index.html.

References

  1. Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, Hoboken (1990)

    MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  4. Lee, C.C., Lee, D.T.: A simple on-line bin-packing algorithm. J. ACM 32(3), 562–572 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sinuany-Stern, Z., Weiner, I.: The one dimensional cutting stock problem using two objectives. J. Oper. Res. Soc. 45(2), 231–236 (1994)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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

    Chapter  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  Google Scholar 

  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

    Chapter  Google Scholar 

  20. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover Publications, New York (1965)

    MATH  Google Scholar 

  21. Cleveland, W.S.: Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74(368), 829–836 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  22. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Texts in Applied Mathematics. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  23. Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)

    Article  Google Scholar 

  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. 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)

    Article  MATH  Google Scholar 

  26. Luke, S.: Essentials of Metaheuristics, 2nd edn. Lulu, Raleigh (2013)

    Google Scholar 

  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 

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Correspondence to John H. Drake .

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Drake, J.H., Swan, J., Neumann, G., Özcan, E. (2017). Sparse, Continuous Policy Representations for Uniform Online Bin Packing via Regression of Interpolants. In: Hu, B., López-Ibáñez, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2017. Lecture Notes in Computer Science(), vol 10197. Springer, Cham. https://doi.org/10.1007/978-3-319-55453-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-55453-2_13

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