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An efficient constructive heuristic for the rectangular packing problem with rotations.

Xusheng Zhao1,2, Yunqing Rao1,2, Peng Qi1,2

  • 1School of Mechanical Science & Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China.

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Summary
This summary is machine-generated.

This study introduces an efficient algorithm for the rectangular packing problem, optimizing item placement with rotations. The algorithm achieves a O(nlogn) time complexity for constructive packing and demonstrates good performance on benchmark problems.

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Area of Science:

  • Operations Research
  • Computer Science
  • Industrial Engineering

Background:

  • The rectangular packing problem is crucial in industry, but efficient implementation is less studied than positioning techniques.
  • Existing research primarily focuses on rectangle positioning, leaving efficient packing procedures underexplored.

Purpose of the Study:

  • To propose an efficient constructive algorithm for the rectangular packing problem that includes item rotations.
  • To enhance packing efficiency through a novel preprocessing step and a categorized gap placement strategy.

Main Methods:

  • A preprocess procedure utilizing four data structures for efficient item selection.
  • A placement procedure categorizing skyline gaps into three types for optimized item insertion.
  • A packing improvement phase employing random perturbation for sequence and orientation optimization.

Main Results:

  • The constructive packing phase achieves a time complexity of O(nlogn).
  • The algorithm demonstrates efficiency across small-scale to extra-large-scale stochastic problems.
  • The proposed method shows good performance on established benchmark instances (C21, N13, NT, Babu, CX).

Conclusions:

  • The developed algorithm offers an efficient solution for the rectangular packing problem with rotations.
  • The preprocessing and placement strategies contribute to improved packing efficiency.
  • The algorithm's performance is validated through extensive testing on various problem scales and benchmarks.