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Heuristics for Large Strip Packing Problems with Guillotine Patterns: An Empirical Study

  • Christine L. Mumford-Valenzuela
  • Janis Vick
  • Pearl Y. Wang
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

In this paper, we undertake an empirical study which examines the effectiveness of eight simple strip packing heuristics on data sets of different sizes with various characteristics and known optima. We restrict this initial study to techniques that produce guillotine patterns (also known as slicing floor plans) which are important industrially. Our chosen heuristics are simple to code, have very fast execution times, and provide a good starting point for our research. In particular, we examine the performance of the eight heuristics as the problems become larger, and demonstrate the effectiveness of a preprocessing routine that rotates some of the rectangles by 90 degrees before the heuristics are applied. We compare the heuristic results to those obtained by using a good genetic algorithm (GA) that also produces guillotine patterns. Our findings suggest that the GA is better on problems of up to about 200 rectangles, but thereafter certain of the heuristics become increasingly effective as the problem size becomes larger, producing better results much more quickly than the GA.

Keywords

Strip packing Heuristics Genetic algorithm. 

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Bibliography

  1. B. S. Baker and J. S. Schwarz. Shelf algorithms for two-dimensional packing problems. SIAM Journal of Computing, 12 (3): 508–525, August 1983.MathSciNetzbMATHCrossRefGoogle Scholar
  2. D. J. Cavicchio. Adaptive Search Using Simulated Evolution. PhD thesis, University of Michigan, Ann Arbor, 1970.Google Scholar
  3. E. G. Coffman Jr., M. R. Garey, and D. S. Johnson. Approximation algorithms for bin packing — an updated survey. In G. Ausiello, N. Lucertini, and P. Serafini, editors, Algorithm Design for Computer Systems Design, pages 49–106. Springer-Verlag, Vienna, 1984.Google Scholar
  4. E. G. Coffman Jr., M. R. Garey, D. S. Johnson, and R. E. Tarjan. Performance bounds for level-oriented two-dimensional packing algorithms. SIAM Journal of Computing, 9: 808–826, 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  5. E. G. Coffman Jr. and P. W. Shor. Packings in two dimensions: Asymptotic average-case analysis of algorithms. Algorithmica, 9: 253–277, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  6. I. Golan. Performance bounds for orthogonal oriented two-dimensional pack- ing algorithms. SIAM Journal of Computing, 10 (3): 571–581, August 1981.MathSciNetzbMATHCrossRefGoogle Scholar
  7. E. Hopper and B. C. H. Turton. An empirical investigation of meta-heuristic and heuristic algorithms for a 2d packing problem. European Journal of Operational Research, 128: 34–57, 2001.zbMATHCrossRefGoogle Scholar
  8. S. M. Hwang, C. Y. Kao, and J. T. Horng. On solving rectangle bin packing problems using genetic algorithms. In Proceedings of the 1994 IEEE International Conference on Systems, Man and Cybernetics, pages 1583–1590, 1994.Google Scholar
  9. S. Jakobs. On genetic algorithms for the packing of polygons. European Journal of Operational Research, 88: 165–181, 1996.zbMATHCrossRefGoogle Scholar
  10. R. M. Karp, M. Luby, and A. Marchetti-Spaccamela. Probabilistic analysis of multi-dimensional bin-packing problems. In Proceedings of the 16th ACM Symposium on the Theory of Computing, pages 289–298, 1984.Google Scholar
  11. B. Kröger. Guillotineable bin packing: A genetic approach. European Journal of Operational Research, 84: 645–661, 1995.zbMATHCrossRefGoogle Scholar
  12. D. Liu and H. Teng. An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research, 112: 413–420, 1999.zbMATHCrossRefGoogle Scholar
  13. I. M. Oliver, D. J. Smith, and J. R. C. Holland. A study of permutation crossover operators on the travelling salesman problem. In Genetic Algorithms and their Applications: Proceedings of the Second International Conference on Genetic Algorithms, pages 224–230, 1987.Google Scholar
  14. D.D.K. Sleator. A 2.5 times optimal algorithm for packing in two dimensions. Information Procesing Letters, 10 (1): 37–40, February 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  15. C. L. Valenzuela and P. Y. Wang. A Genetic Algorithm for VLSI Floorplanning. In Parallel Problem Solving from Nature — PPSN VI, Lecture Notes in Computer Science 1917, pages 671–680, 2000.Google Scholar
  16. C. L. Valenzuela and P. Y. Wang. Data set generation for rectangular placement problems. European Journal of Operational Research, 134 (2): 150–163, 2001.Google Scholar
  17. C. L. Valenzuela and P. Y. Wang. VLSI Placement and Area Optimization Using a Genetic Algorithm to Breed Normalized Postfix Expressions. IEEE Transactions on Evolutionary Computation, 6 (4): 390–401, 2002.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Christine L. Mumford-Valenzuela
    • 1
  • Janis Vick
    • 2
  • Pearl Y. Wang
    • 2
  1. 1.Department of Computer ScienceCardiff UniversityWalesUK
  2. 2.Department of Computer ScienceGeorge Mason UniversityFairfaxUSA

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