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Hybrid Metaheuristics for Packing Problems

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Hybrid Metaheuristics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 114))

Three variants of the two dimensional packing problem are considered, where the items to be packed are (a) rectangles with fixed widths and heights, (b) rectangles with adjustable widths and heights, or (c) irregular shapes. All problems are solved by hybrid metaheuristics that combine local search and mathematical programming techniques of linear, nonlinear and/or dynamic programming. Basic ideas of these algorithms are explained on a unified basis, together with some computational results. It appears to indicate that mathematical programming is a vital tool for enhancing metaheuristic algorithms.

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References

  1. Adamowicz M, Albano A (1976) Nesting two-dimensional shapes in rectangular modules, Computer-Aided Design 8:27-33

    Article  Google Scholar 

  2. Agarwal PK, Guibas LJ, Har-Peled S, Rabinovitch A, Sharir M (2000) Penetration depth of two convex polytopes in 3D, Nordic Journal of Computing 7:227–240

    MATH  MathSciNet  Google Scholar 

  3. Albano A, Sapuppo G (1980) Optimal allocation of two-dimensional irregular shapes using heuristic search methods, IEEE Transactions on Systems, Man and Cybernetics 10:242–248

    Article  Google Scholar 

  4. Art Jr. RC (1966) An approach to the two-dimensional irregular cutting stock problem, Technical Report 36-Y08, IBM Cambridge Science Center

    Google Scholar 

  5. Babu AR, Babu NR (2001) A genetic approach for nesting of 2-D parts in 2-D sheets using genetic and heuristic algorithms, Computer-Aided Design 33:879–891

    Article  Google Scholar 

  6. Baker BS, Coffman Jr. EG, Rivest RL (1980) Orthogonal packing in two dimensions, SIAM Journal on Computing 9:846–855

    Article  MATH  MathSciNet  Google Scholar 

  7. Beltrán JD, Calderón JE, Cabrera RJ, Pérez JAM, Moreno-Vega JM (2004) GRASP/VNS hybrid for the strip packing problem, In: Proceedings of the First International Workshop on Hybrid Meta-heuristics (HM04), 79–90

    Google Scholar 

  8. Bennell JA (1998) Incorporating problem specific knowledge into a local search framework for the irregular shape packing problem, Ph.D. thesis, European Business Management School, University of Wales, Swansea

    Google Scholar 

  9. Bennell JA, Dowsland KA (1999) A tabu thresholding implementation for the irregular stock cutting problem, International Journal of Production Research 37:4259–4275

    Article  MATH  Google Scholar 

  10. Bennell JA, Dowsland KA (2001) Hybridising tabu search with optimisation techniques for irregular stock cutting, Management Science 47:1160–1172

    Article  Google Scholar 

  11. Bennell JA, Dowsland KA, Dowsland WB (2001) The irregular cutting-stock problem—a new procedure for deriving the no-fit polygon, Computers & Operations Research 28:271–287

    Article  Google Scholar 

  12. Bertsekas DP (1999) Nonlinear Programming (2nd edition), Athena Scientific.

    Google Scholar 

  13. Błażewicz J, Hawryluk P, Walkowiak R (1993) Using a tabu search for solving the two-dimensional irregular cutting problem, Annals of Operations Research 41:313–325

    Article  MATH  Google Scholar 

  14. Burke E, Hellier R, Kendall G, Whitwell G (2006) A new bottom-left-fill heuristic algorithm for the two-dimensional irregular packing problem, Operations Research 54:587–601

    Article  MATH  MathSciNet  Google Scholar 

  15. Burke EK, Kendall G, Whitwell G (2004) A new placement heuristic for the orthogonal stock-cutting problem, Operations Research 52: 655–671

    Article  MATH  Google Scholar 

  16. Chang YC, Chang YW, Wu GM, Wu SW (2000) B*-trees: a new representation for non-slicing floorplans, In: Proceedings of the 37th Design Automation Conference, 458–463

    Google Scholar 

  17. Chu CCN, Young EFY (2004) Nonrectangular shaping and sizing of soft modules for floorplan-design improvement, IEEE Transactions Computer Aided Design of Integrated Circuits and Systems 23:71–79

    Article  Google Scholar 

  18. Coffman Jr. EG, Garey MR, Johnson DS, Tarjan RE (1980) Performance bounds for level-oriented two-dimensional packing algorithms, SIAM Journal on Computing 9:801–826

    MathSciNet  Google Scholar 

  19. Dobkin D, Hershberger J, Kirkpatrick D, Suri S (1993) Computing the intersection-depth of polyhedra, Algorithmica 9:518–533

    Article  MATH  MathSciNet  Google Scholar 

  20. Dréo J, Pétrowski JDA, Siarry P, Taillard E (2006) Metaheuristics for Hard Optimization, Springer.

    Google Scholar 

  21. Dyckhoff H (1990) A typology of cutting and packing problems, European Journal of Operational Research 44:145–159

    Article  MATH  MathSciNet  Google Scholar 

  22. Egeblad J, Nielsen BK, Odgaard A (2007) Fast neighborhood search for two- and three-dimensional nesting problems, European Journal of Operational Research 183:1249–1266

    Article  MATH  MathSciNet  Google Scholar 

  23. Glover F (1995) Tabu thresholding: Improved search by nonmonotonic trajectories, ORSA Journal on Computing 7:426–442

    MATH  Google Scholar 

  24. Glover FW, Kochenberge GA (eds) (2003) Handbook of Metaheuristics, Springer.

    Google Scholar 

  25. Gomes AM, Oliveira JF (2002) A 2-exchange heuristic for nesting problems, European Journal of Operational Research 141:359–370

    Article  MATH  MathSciNet  Google Scholar 

  26. Gomes AM, Oliveira JF (2006) Solving irregular strip packing problems by hybridising simulated annealing and linear programming, European Journal of Operational Research 171:811–829

    Article  MATH  Google Scholar 

  27. Guo PN, Takahashi T, Cheng CK, Yoshimura T (2001) Floorplanning using a tree representation, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 20:281–289

    Article  Google Scholar 

  28. Heckmann R, Lengauer T (1995) A simulated annealing approach to the nesting problem in the textile manufacturing industry, Annals of Operations Research 57:103–133

    Article  MATH  Google Scholar 

  29. Hopper E, Turton BCH (2001) An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem, European Journal of Operational Research 128:34–57

    Article  MATH  Google Scholar 

  30. Ibaraki T, Nakamura K (2006) Packing problems with soft rectangles, In: Almeida F, Blesa Aguilera MJ, Blum C, Vega JMM, Pérez MP, Roli A, Sampels M (eds) Hybrid Metaheuristics, Springer Lecture Notes on Computer Science 4030:13–27

    Google Scholar 

  31. Imahori S, Yagiura M, Ibaraki T (2003) Local search algorithms for the rectangle packing problem with general spatial costs, Mathematical Programming 97:543–569

    Article  MATH  MathSciNet  Google Scholar 

  32. Imahori S, Yagiura M, Ibaraki T (2005) Improved local search algorithms for the rectangle packing problem with general spatial costs, European Journal of Operational Research 167:48–67

    Article  MATH  MathSciNet  Google Scholar 

  33. Imahori S, Yagiura M, Ibaraki T (2005) Variable neighborhood search for the rectangle packing problem, In: Proceedings of the 6th Metaheuristics International Conference (MIC05), 532–537

    Google Scholar 

  34. Imamichi T, Yagiura M, Nagamochi H (2006) An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem, Technical Report 2007-009, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, February, 2007 (available at http://www.amp.i.kyoto-u.ac.jp/tecrep/); A short version is available in: Proceedings of the Third International Symposium on Scheduling (ISS06), 132–137

  35. Itoga H, Kodama C, Fujiyoshi K (2005) A graph based soft module handling in floorplan, IEICE Transactions Fundamentals E88-A:3390–3397

    Google Scholar 

  36. Johnson DS (1990) Local optimization and the traveling salesman problem, In: Peterson MS (ed) Automata, Languages and Programming, Lecture Notes in Computer Science 443:446–461

    Article  Google Scholar 

  37. Kenyon C, Rémila E (2000) A near-optimal solution to a two-dimensional cutting stock problem, Mathematics of Operations Research 25:645–656

    Article  MATH  MathSciNet  Google Scholar 

  38. Kim YJ, Lin MC, Manocha D (2004) Incremental penetration depth estimation between convex polytopes using dual-space expansion, IEEE Transactions on Visualization and Computer Graphics 10:152–163

    Article  Google Scholar 

  39. Konno H, Kuno T (1995) Multiplicative programming problems, In: Horst R, Pardalos PM (eds) Handbook of Global Optimization, Kluwer Academic Publishers, 369–406

    Google Scholar 

  40. Kurebe Y, Miwa H, Ibaraki T (2007) Weighted module placement based on rectangle packing, 4th ESICUP meeting (EURO Special Interest Group on Cutting and Packing).

    Google Scholar 

  41. Li Z, Milenkovic V (1995) Compaction and separation algorithms for non-convex polygons and their applications, European Journal of Operational Research 84:539–561

    Article  MATH  Google Scholar 

  42. Lodi A, Martello S, Monaci M (2002) Two-dimensional packing problems: A survey, European Journal of Operational Research 141:241–252

    Article  MATH  MathSciNet  Google Scholar 

  43. Lodi A, Martello S, Vigo D (1999) Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems, INFORMS Journal on Computing 11:345–357

    Article  MATH  MathSciNet  Google Scholar 

  44. Milenkovic VJ (1998) Rotational polygon overlap minimization and compaction, Computational Geometry 10:305–318

    Article  MATH  MathSciNet  Google Scholar 

  45. Murata H, Fujiyoshi K, Nakatake S, Kajitani Y (1996) VLSI module placement based on rectangle-packing by the sequence-pair, IEEE Transactions on Computer Aided Design 15:1518–1524

    Article  Google Scholar 

  46. Murata H, Kuh ES (1998) Sequence-pair based placement method for hard/soft/preplaced modules, In: Proceedings of International Symposium on Physical Design, 167–172

    Google Scholar 

  47. Nagamochi H (2005) Packing soft rectangles, International Journal of Foundations of Computer Science 17:1165–1178

    Article  MathSciNet  Google Scholar 

  48. Nakatake S, Fujiyoshi K, Murata H, Kajitani Y (1998) Module packing based on the BSG-structure and IC layout applications, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 17:519–530

    Article  Google Scholar 

  49. Nesterov Y, Nemirovskii A (1994) Interior Point Polynomial Algorithms in Convex Programming, SIAM Pub.

    Google Scholar 

  50. Okano H (2002) A scanline-based algorithm for the 2D free-form bin packing problem, Journal of the Operations Research Society of Japan 45:145–161

    MATH  MathSciNet  Google Scholar 

  51. Oliveira JF, Ferreira JS (1993) Algorithms for nesting problems, In: Vidal RVV (ed) Applied Simulated Annealing. Lecture Notes in Economics and Mathematical Systems 396, Springer-Verlag, 255–274

    Google Scholar 

  52. Oliveira JF, Gomes AM, Ferreira JS (2000) TOPOS—a new constructive algorithm for nesting problems, OR Spektrum 22:263–284

    Article  MATH  MathSciNet  Google Scholar 

  53. Preas BT, van Cleemput WM (1979) Placement algorithms for arbitrarily shaped blocks, In: Proceedings of the ACM/IEEE Design Automation Conference, 474–480

    Google Scholar 

  54. Ramkumar GD (1996) An algorithm to compute the Minkowski sum outer-face of two simple polygons, In: Proceedings of the Twelfth Annual Symposium on Computational Geometry (SCG96), 234–241

    Google Scholar 

  55. Stoyan YG, Novozhilova MV, Kartashov AV (1996) Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem, European Journal of Operational Research 92:193–210

    Article  MATH  Google Scholar 

  56. Takahashi T (1996) An algorithm for finding a maximum-weight decreasing sequence in a permutation, motivated by rectangle packing problem (in Japanese), Technical Report of IEICE VLD96-30, 31–35

    Google Scholar 

  57. Tang X, Tian R, Wong DF (2001) Fast evaluation of sequence pair in block placement by longest common subsequence computation, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 20:1406–1413

    Article  Google Scholar 

  58. Umetani S, Yagiura M, Imamichi T, Imahori S, Nonobe K, Ibaraki T (2006) A guided local search algorithm based on a fast neighborhood search for the irregular strip packing problem, In: Proceedings of the Third International Symposium on Scheduling (ISS06), 126–131

    Google Scholar 

  59. Wäscher G, Haußner H, Schumann H (2007) An improved typology of cutting and packing problems, European Journal of Operational Research 183:1109–1130

    Article  MATH  Google Scholar 

  60. Young FY, Chu CCN, Luk WL, Wong YC (2001) Handling soft modules in general nonslicing floorplan using Lagrangean relaxation, IEEE Transactions on Computer-Aided Design of Integrated Circuit and Systems 20: 687–692

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan

    Shinji Imahori

  3. Graduate School of Information Science, Nagoya University, Nagoya, Japan

    Mutsunori Yagiura

Authors
  1. Toshihide Ibaraki
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  2. Shinji Imahori
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  3. Mutsunori Yagiura
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Editor information

Editors and Affiliations

  1. Dept. Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Jordi Girona 1-3 Omega 112, E-08034, Barcelona, Spain

    Christian Blum

  2. Dept. Llenguatges i Sistemes Informátics, Universitat Politècnica de Catalunya, Jordi Girona 1-3 Omega 213, E-08034, Barcelona, Spain

    Maria José Blesa Aguilera

  3. Università di Bologna, Via Venezia 52, I-47023, Cesena, Italy

    Andrea Roli

  4. Université Libre de Bruxelles, Avenue Franklin Roosevelt 50, B-1050, Brussels, Belgium

    Michael Sampels

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Ibaraki, T., Imahori, S., Yagiura, M. (2008). Hybrid Metaheuristics for Packing Problems. In: Blum, C., Aguilera, M.J.B., Roli, A., Sampels, M. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78295-7_7

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  • DOI: https://doi.org/10.1007/978-3-540-78295-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78294-0

  • Online ISBN: 978-3-540-78295-7

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