New heuristic and interactive approaches to 2D rectangular strip packing

  • Authors:

  • N. Lesh;J. Marks;A. McMahon;M. Mitzenmacher

  • Affiliations:

  • Mitsubishi Electric Research Laboratories, Cambridge, MA;Mitsubishi Electric Research Laboratories, Cambridge, MA;University of Miami, Florida;Harvard University, Cambridge, MA

  • Venue:
  • Journal of Experimental Algorithmics (JEA)
  • Year:
  • 2005

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Abstract

In this paper, we consider the two-dimensional rectangular strip packing problem. A standard simple heuristic, Bottom-Left-Decreasing (BLD), has been shown to perform quite well in practice. We introduce and demonstrate the effectiveness of BLD*, a stochastic search variation of BLD. While BLD places the rectangles in decreasing order of height, width, area, and perimeter, BLD* successively tries random orderings, chosen from a distribution determined by their Kendall-tau distance from one of these fixed orderings. Our experiments on benchmark problems show that BLD* produces significantly better packings than BLD after only 1 min of computation. Furthermore, we also show that BLD* outperforms recently reported metaheuristics. Furthermore, we observe that people seem able to reason about packing problems extremely well. We incorporate our new algorithms in an interactive system that combines the advantages of computer speed and human reasoning. Using the interactive system, we are able to quickly produce significantly better solutions than BLD* by itself.