Geodesic
About routing in the sheet cutting
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 25-39

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The solution of the problem of tool routing in CNC sheet cutting machines is considered. It is assumed that the initial problem formulation is complicated by different restrictions. It is required to construct a solution of this routing problem that respects the constraints and minimizes the additive criterion, including the costs of (external) displacements and “internal” related to cutting parts on a closed contour works. Compliance of the constraints is supposed to be provided through a special assignment of cost functions, i.e. (in fact) due to the formation of penalties for the restriction violation. The procedure based on widely understood dynamic programming is the main way of problem solving in this paper. The program of problem solving on a multi-core PC is constructed. The presentation of this algorithm is the main goal of this paper.
Keywords: routing problem; precedence conditions; engineering constraints. 
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     author = {A. A. Petunin and A. G. Chentsov and P. A. Chentsov},
     title = {About routing in the sheet cutting},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a2/}
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A. A. Petunin; A. G. Chentsov; P. A. Chentsov. About routing in the sheet cutting. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 25-39. http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a2/