Computing closely matching upper and lower bounds on textile nesting problems |
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Affiliation: | 1. Faculty of Chemistry, Adam Mickiewicz University, Poznan, Poland;2. Department of Chemical Engineering, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain;3. Poznan Science and Technology Park, Adam Mickiewicz University Foundation, Poznan, Poland |
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Abstract: | We consider an industrial cutting problem in textile manufacturing and report on algorithms 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). |
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