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Evolutionary hyper-heuristics for tackling bi-objective 2D bin packing problems

  • Juan Carlos Gomez
  • Hugo Terashima-Marín
Article
Part of the following topical collections:
  1. Special Issue on Automated Design and Adaptation of Heuristics for Scheduling and Combinatorial Optimisation

Abstract

In this article, a multi-objective evolutionary framework to build selection hyper-heuristics for solving instances of the 2D bin packing problem is presented. The approach consists of a multi-objective evolutionary learning process, using specific tailored genetic operators, to produce sets of variable length rules representing hyper-heuristics. Each hyper-heuristic builds a solution to a given problem instance by sensing the state of the instance, and deciding which single heuristic to apply at each decision point. The hyper-heuristics consider the minimization of two conflicting objectives when building a solution: the number of bins used to accommodate the pieces and the total time required to do the job. The proposed framework integrates three well-studied multi-objective evolutionary algorithms to produce sets of Pareto-approximated hyper-heuristics: the Non-dominated Sorting Genetic Algorithm-II, the Strength Pareto Evolutionary Algorithm 2, and the Generalized Differential Evolution Algorithm 3. We conduct an extensive experimental analysis using a large set of 2D bin packing problem instances containing convex and non-convex irregular pieces, under many conditions, settings and using several performance metrics. The analysis assesses the robustness and flexibility of the proposed approach, providing encouraging results when compared against a set of well-known baseline single heuristics.

Keywords

Bin packing problem Evolutionary computation Hyper-heuristics Heuristics Multi-objective optimization Genetic algorithms 

Notes

Acknowledgements

This research was supported in part by CONACyT Basic Science Projects under Grants 99695 and 241461, ITESM Research Group with Strategic Focus in intelligent Systems, and by Universidad de Guanajuato Campus Irapuato-Salamanca.

References

  1. 1.
    J. de Armas, G. Miranda, C. León, Hyperheuristic encoding scheme for multi-objective guillotine cutting problems. In: GECCO, pp. 1683–1690 (2011). doi: 10.1145/2001576.2001803
  2. 2.
    R. Bai, T.V. Woensel, G. Kendall, E.K. Burke, A new model and a hyper-heuristic approach for two-dimensional shelf space allocation. 4OR 11(1), 31–35 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Rishinhaldar Boominathanperumal, S. Rajkumar, Bin packing problems: Comparative analysis of heuristic techniques for different dimensions. Int. J. Pharm. Technol. 8(2), 13,305–13,319 (2016)Google Scholar
  4. 4.
    E.K. Burke, M. Gendreau, M. Hyde, G. Kendall, G. Ochoa, E. zcan, R. Qu, Hyper-heuristics: a survey of the state of the art. J. Oper. Res. Soc. 64(12), 1695–1724 (2013). doi: 10.1057/jors.2013.71 CrossRefGoogle Scholar
  5. 5.
    E.K. Burke, E. Hart, G. Kendall, J. Newall, P. Ross, S. Schulenburg, Hyper-heuristics: An emerging direction in modern research technology. In: Handbook of Metaheuristics, pp. 457–474. Kluwer Academic Publishers (2003). doi: 10.1007/0-306-48056-5_16
  6. 6.
    E.K. Burke, M. Hyde, G. Kendall, J. Woodword, A genetic programming hyper-heuristic approach for evolving 2-d strip packing heuristics. IEEE Trans. Evolut. Comput. 14(6), 942–958 (2010)CrossRefGoogle Scholar
  7. 7.
    E.K. Burke, M.R. Hyde, G. Kendall, G. Ochoa, E. Özcan, J. Woodward, A Classification of Hyper-heuristic Approaches, International Series in Operations Research & Management Science, vol. 146, pp. 449–468. Springer US (2010). doi: 10.1007/978-1-4419-1665-5_15
  8. 8.
    E.K. Burke, M.R. Hyde, G. Kendall, J. Woodward, Automating the packing heuristic design process with genetic programming. Evol. Comput. 20(1), 63–89 (2012). doi: 10.1162/EVCO_a_00044 CrossRefGoogle Scholar
  9. 9.
    E.K. Burke, J.D.L. Silva, E. Soubeiga, Multi-Objective Hyper-Heuristic Approaches for Space Allocation and Timetabling, Operations Research/Computer Science Interfaces Series, vol. 32, chap. 6, pp. 129–158. Springer-Verlag (2005). doi: 10.1007/0-387-25383-1_6
  10. 10.
    C.A. Coello, D.A. Van Veldhuizen, G.B. Lamont (eds.), Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. (Springer Verlag, Syracuse, New York, 2007)zbMATHGoogle Scholar
  11. 11.
    A. Crispin, P. Clay, G. Taylor, T. Bayes, D. Reedman, Genetic algorithms applied to leather lay plan material utilization. Proc. Instit. Mech. Eng. Part B: J. Eng. Manuf. 217(12), 1753–1756 (2003). doi: 10.1243/095440503772680677 CrossRefGoogle Scholar
  12. 12.
    K. Deb, A. Pratap, S. Agrawal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  13. 13.
    K.A. Dowsland, W.B. Dowsland, Solution approaches to irregular nesting problems. Eur. J. Oper. Res. 84(3), 506–521 (1995). doi: 10.1016/0377-2217(95)00019-M CrossRefzbMATHGoogle Scholar
  14. 14.
    H. Dyckhoff, A typology of cutting and packing problems. Eur. J. Oper. Res. 44(2), 145–159 (1990). doi: 10.1016/0377-2217(90)90350-K MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    C. Fonseca, P. Fleming, Multiobjective optimization and multiple constraint handling in evolutionary algorithms. IEEE Trans. Man Syst. Cybern. Part A: Syst. Hum. 28(1), 26–37 (1998)CrossRefGoogle Scholar
  16. 16.
    M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York, 1979)zbMATHGoogle Scholar
  17. 17.
    J.C. Gomez, H. Terashima-Marín, Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems, Lecture Notes in Computer Science, vol. 6438, chap. 30, pp. 349–360. Springer Berlin Heidelberg (2010). doi: 10.1007/978-3-642-16773-7_30
  18. 18.
    J.C. Gomez, H. Terashima-Marín, Building general hyper-heuristics for multi-objective cutting stock problems. Computación y Sistemas 16(3), 321–334 (2012)Google Scholar
  19. 19.
    E.D. Goodman, A.Y. Tetelbaum, V.M. Kureichik, A genetic algorithm approach to compaction, bin packing, and nesting problems. Tech. Rep. 940702, Case Center for Computer-Aided Engineering and Manufacturing, Michigan State University (1994)Google Scholar
  20. 20.
    L. Hu-yao, H. Yuan-jun, NFP-based nesting algorithm for irregular shapes, in Symposium on Applied Computing, pp. 963–967. ACM Press, New York, NY, USA (2006). doi: 10.1145/1141277.1141507
  21. 21.
    S. Jiang, Y.S. Ong, J. Zhang, L. Feng, Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans. Cybern. 44(12), 2391–2404 (2014). doi: 10.1109/TCYB.2014.2307319 CrossRefGoogle Scholar
  22. 22.
    S. Kukkonen, J. Lampinen, GDE3: the third evolution step of generalized differential evolution, in IEEE Congress on Evolutionary Computation, pp. 443–450. IEEE (2005). doi: 10.1109/CEC.2005.1554717
  23. 23.
    A.C. Kumari, K. Srinivas, M. Gupta, Software module clustering using a hyper-heuristic based multi-objective genetic algorithm, in IEEE 3rd International Advance Computing Conference (IACC), pp. 813–818 (2013)Google Scholar
  24. 24.
    Y.L. Li, Z.H. Zhan, Y.J. Gong, W.N. Chen, J. Zhang, Y. Li, Differential evolution with an evolution path: a deep evolutionary algorithm. IEEE Trans. Cybern. 45(9), 1798–1810 (2015). doi: 10.1109/TCYB.2014.2360752 CrossRefGoogle Scholar
  25. 25.
    A. Lodi, S. Martello, M. Monaci, Two-dimensional packing problems: a survey. Eur. J. Oper. Res. 141(2), 241–252 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    E. López-Camacho, An evolutionary framework for producing hyper-heuristics for solving the 2D irregular bin packing problem. Ph.D. thesis, Tecnológico de Monterrey (2012)Google Scholar
  27. 27.
    E. López-Camacho, G. Ochoa, H. Terashima-Marín, E.K. Burke, An effective heuristic for the two-dimensional irregular bin packing problem. Ann. Oper. Res. 206(1), 241–264 (2013). doi: 10.1007/s10479-013-1341-4 MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    E. López-Camacho, H. Terashima-Marín, G. Ochoa, S.E. Conant-Pablos, Understanding the structure of bin packing problems through principal component analysis. Int. J. Prod. Econ. Special Issue on Cutting and Packing. pp. 488–499 (2013). doi: 10.1016/j.ijpe.2013.04.041
  29. 29.
    E. López-Camacho, H. Terashima-Marín, P. Ross, Defining a problem-state representation with data mining within a hyper-heuristic model which solves 2D irregular bin packing problems. Adv. Artif. Intell. IBERAMIA Lect. Notes Comput. Sci. 6433, 204–213 (2010). doi: 10.1007/978-3-642-16952-6_21 Google Scholar
  30. 30.
    E. López-Camacho, H. Terashima-Marin, P. Ross, G. Ochoa, A unified hyper-heuristic framework for solving bin packing problems. Expert Syst. Appl. 41(15), 6876–6889 (2014). doi: 10.1016/j.eswa.2014.04.043 CrossRefGoogle Scholar
  31. 31.
    M. Maashi, E. Özcan, G. Kendall, A multi-objective hyper-heuristic based on choice function. Expert Syst. Appl. 41(9), 4475–4493 (2014). doi: 10.1016/j.eswa.2013.12.050 CrossRefGoogle Scholar
  32. 32.
    A. Martinez-Sykora, R. Alvarez-Valdes, J.A. Bennell, R. Ruiz, J.M. Tamarit, Matheuristics for the irregular bin packing problem with free rotations. Eur. J. Oper. Soc. 258(2), 440–455 (2017)MathSciNetCrossRefGoogle Scholar
  33. 33.
    H. Okano, A scanline-based algorithm for the 2D free-form bin packing problem. J. Oper. Res. Soc. Jpn. 45(2), 145–161 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    G.L. Pappa, G. Ochoa, M. Hyde, A.A. Freitas, J. Woodward, J. Swan, Contrasting meta-learning and hyper-heuristic research: the role of evolutionary algorithms. Genet. Program. Evol. Mach. 15(1), 3–35 (2014). doi: 10.1007/s10710-013-9186-9 CrossRefGoogle Scholar
  35. 35.
    A.F. Rafique, Multiobjective hyper heuristic scheme for system design and optimization. In: 9TH International Conference on Mathematical Problems in Engineering, Aerospace and Scince, ICNPAA 2012, pp. 764–769 (2012). doi: 10.1063/1.4765574
  36. 36.
    Z. Ren, H. Jiang, J. Xuan, Y. Hu, Z. Luo, New insights into diversification of hyper-heuristics. IEEE Trans. Cybern. 44(10), 1747–1761 (2014). doi: 10.1109/TCYB.2013.2294185 CrossRefGoogle Scholar
  37. 37.
    P. Ross, Hyper-heuristics. In: E.K. Burke, G. Kendall (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques: Second Edition, pp. 611–638. Springer, New York (2014). doi: 10.1007/978-1-4614-6940-7_20
  38. 38.
    N.R. Sabar, M. Ayob, G. Kendall, R. Qu, A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems. IEEE Trans. Cybern. 45(2), 217–228 (2015). doi: 10.1109/TCYB.2014.2323936 CrossRefGoogle Scholar
  39. 39.
    K. Sim, E. Hart, B. Paechter, A lifelong learning hyper-heuristic method for bin packing. Evol. Comput. 23(1), 37–67 (2015)CrossRefGoogle Scholar
  40. 40.
    H. Terashima-Marín, P. Ross, C.J. Farías-Zárate, E. López-Camacho, M. Valenzuela-Rendón, Generalized hyper-heuristics for solving 2D regular and irregular packing problems. Ann. Oper. Res. 179(1), 369–392 (2010). doi: 10.1007/s10479-008-0475-2 MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    D.A. Van Veldhuizen, G.B. Lamont, Multiobjective evolutionary algorithm test suites, in Proceedings of the 1999 ACM symposium on Applied computing, pp. 351–357. ACM (1999). doi: 10.1145/298151.298382
  42. 42.
    J. Vázquez Rodríguez, S. Petrovic, A. Salhi, An investigation of hyper-heuristic search spaces, in IEEE Congress on Evolutionary Computation, pp. 3776–3783 (2007). doi: 10.1109/CEC.2007.4424962
  43. 43.
    J.A. Vázquez-Rodríguez, S. Petrovic, A mixture experiments multi-objective hyper-heuristic. J. Oper. Res. Soc. 64(11), 1664–1675 (2013). doi: 10.1057/jors.2012.125 CrossRefGoogle Scholar
  44. 44.
    N. Veerapen, D. Landa-Silva, X. Gandibleux, Hyper-heuristic as component of a multi-objective metaheuristic, in Proceedings of the Doctoral Symposium Engineering Stochastic Local Search Algorithms, no. TR/IRIDIA/2009-024 in IRIDIA, pp. 51–55 (2009)Google Scholar
  45. 45.
    G. Wäscher, H. Hausner, H. Schumann, An improved typology of cutting and packing problems. Eur. J. Oper. Res. Special Issue on Cutting, Packing and Related Problems 183(3), 1109–1130 (2007)zbMATHGoogle Scholar
  46. 46.
    H. Xia, J. Zhuang, D. Yu, Combining crowding estimation in objective and decision space with multiple selection and search strategies for multi-objective evolutionary optimization. IEEE Trans. Cybern. 44(3), 378–393 (2014). doi: 10.1109/TCYB.2013.2256418 CrossRefGoogle Scholar
  47. 47.
    E. Zitzler, S. Knzli, Indicator-based selection on multiobjective search. PPSN Lect. Notes Comput. Sci. 3242(1), 832–842 (2004)CrossRefGoogle Scholar
  48. 48.
    E. Zitzler, M. Laumanns, L. Thiele, SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization, in Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems. Proceedings of the EUROGEN2001 Conference, Athens, Greece, September 19-21, 2001, pp. 95–100 (2002)Google Scholar
  49. 49.
    E. Zitzler, L. Thiele, Multiobjective optimization using evolutionary algorithms: acomparative case study, Lecture Notes in Computer Science, vol. 1498, chap. 29, pp. 292–301. Springer Berlin Heidelberg (1998). doi: 10.1007/BFb0056872
  50. 50.
    E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999). doi: 10.1109/4235.797969 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Electronics, División de IngenieríasUniversidad de Guanajuato Campus Irapuato-SalamancaSalamancaMexico
  2. 2.School of Engineering and SciencesTecnológico de MonterreyMonterreyMexico

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