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Exact and approximate methods for the score-constrained packing problem

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  • Hawa, Asyl L.
  • Lewis, Rhyd
  • Thompson, Jonathan M.

Abstract

This paper investigates a packing problem related to the one-dimensional bin packing problem in which the order and orientation of items influences the feasibility of a solution. We give an exact polynomial-time algorithm for the Constrained Ordering Problem, explaining how it can be used to find a feasible packing of items in a single bin. We then introduce an evolutionary algorithm for the multi-bin version of the problem, which incorporates the exact algorithm along with a local search procedure and three recombination operators. The mechanisms and results produced by each of the recombination operators are compared, and we discuss the circumstances in which each approach proves most advantageous.

Suggested Citation

  • Hawa, Asyl L. & Lewis, Rhyd & Thompson, Jonathan M., 2022. "Exact and approximate methods for the score-constrained packing problem," European Journal of Operational Research, Elsevier, vol. 302(3), pages 847-859.
    • Handle: RePEc:eee:ejores:v:302:y:2022:i:3:p:847-859
    DOI: 10.1016/j.ejor.2022.01.028
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    References listed on IDEAS

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    1. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    2. Bennell, J.A. & Cabo, M. & Martínez-Sykora, A., 2018. "A beam search approach to solve the convex irregular bin packing problem with guillotine guts," European Journal of Operational Research, Elsevier, vol. 270(1), pages 89-102.
    3. Yaodong Cui & Xiang Song & Yan Chen & Yi-Ping Cui, 2017. "New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 269-280, March.
    4. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    5. Enrico Malaguti & Michele Monaci & Paolo Toth, 2008. "A Metaheuristic Approach for the Vertex Coloring Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 302-316, May.
    6. Belov, G. & Scheithauer, G., 2002. "A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths," European Journal of Operational Research, Elsevier, vol. 141(2), pages 274-294, September.
    7. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 1999. "Approximation algorithms for the oriented two-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 112(1), pages 158-166, January.
    8. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    9. Kai Helge Becker & Gautam Appa, 2015. "A heuristic for the Minimum Score Separation Problem, a combinatorial problem associated with the cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(8), pages 1297-1311, August.
    10. C Goulimis, 2004. "Minimum score separation—an open combinatorial problem associated with the cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1367-1368, December.
    11. Karen Rocha Coelho & Adriana Cristina Cherri & Edméa Cassia Baptista & Charbel José Chiappetta Jabbour & Edilaine Martins Soler, 2017. "Sustainable operations: The cutting stock problem with usable leftovers from a sustainable perspective," Post-Print hal-02000703, HAL.
    12. Chunyang Zhou & Chongfeng Wu & Yun Feng, 2009. "An exact algorithm for the type-constrained and variable sized bin packing problem," Annals of Operations Research, Springer, vol. 172(1), pages 193-202, November.
    13. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
    14. Karen Aardal & Stan Hoesel & Arie Koster & Carlo Mannino & Antonio Sassano, 2007. "Models and solution techniques for frequency assignment problems," Annals of Operations Research, Springer, vol. 153(1), pages 79-129, September.
    15. J Levine & F Ducatelle, 2004. "Ant colony optimization and local search for bin packing and cutting stock problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 705-716, July.
    16. Lewis, R. & Song, X. & Dowsland, K. & Thompson, J., 2011. "An investigation into two bin packing problems with ordering and orientation implications," European Journal of Operational Research, Elsevier, vol. 213(1), pages 52-65, August.
    17. Kenmochi, Mitsutoshi & Imamichi, Takashi & Nonobe, Koji & Yagiura, Mutsunori & Nagamochi, Hiroshi, 2009. "Exact algorithms for the two-dimensional strip packing problem with and without rotations," European Journal of Operational Research, Elsevier, vol. 198(1), pages 73-83, October.
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