Geodesic
On sequential traversal of sets
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 487-504

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The problem of sequential traversal of megapolises with precedence conditions is investigated; this problem is oriented to mechanical engineering — CNC metal cutting machines. There is the following setting singularity: the terminal component of additive criterion contains the dependence on the starting point. This singularity leads to the fact that the natural solution procedure based on dynamic programming must be applied individually for every starting point. The investigation goal consists in the construction of an optimizing algorithm for determining a complex including a route (a variant of megapolis numbering), a trajectory, and a starting point. The proposed algorithm realizes an idea of directed enumeration of starting points. This algorithm is realized as a program for PC; computations for model examples are made.
Keywords: route optimization, dynamic programming, start point optimization. 
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     author = {A. G. Chentsov and P. A. Chentsov},
     title = {On sequential traversal of sets},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {487--504},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a9/}
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A. G. Chentsov; P. A. Chentsov. On sequential traversal of sets. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 487-504. http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a9/