Chapter

Algorithms — ESA '96

Volume 1136 of the series Lecture Notes in Computer Science pp 392-405

Date:

Computing upper and lower bounds on textile nesting problems

  • Ralf HeckmannAffiliated withInstitute for Algorithms and Scientific Computing, German National Research Center for Information Technology (GMD)
  • , Thomas LengauerAffiliated withInstitute for Algorithms and Scientific Computing, German National Research Center for Information Technology (GMD)Department of Computer Science, University of Bonn

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Abstract

We consider an industrial cutting problem in textile manufacturing and report on heuristics for computing cutting images and lower bounds on waste for this problem. For the upper bounds we use greedy strategies based on hodographs and global optimization based on simulated annealing. For the lower bounds we use branch-and-bound methods for computing optimal solutions of placement subproblems that determine the performance of the overall subproblem. The upper bounds are computed in less than an hour on a common-day workstation and are competitive in quality with results obtained by human nesters. The lower bounds take a few hours to compute and are within 0.4% of the upper bound for certain types of clothing (e.g., for pants).