Geodesic
Optimizing multi-inserts in routing problems with constraints
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 4, pp. 513-530

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We consider a problem of sequential traversal of megalopolises (nonempty finite sets) with travel cost functions depending on the set of pending tasks and precedence constraints. Its formulation is aimed at engineering problems in fission power generation connected with minimizing the exposure of staff to radiation and in machine engineering (routing of a CNC sheet cutting machine's tool). This discrete optimization problem is assumed to be sufficiently large-scale to necessitate the use of heuristics. We consider a procedure of local improvement for heuristics through a successive application of optimizing multi-inserts-finite disjoint sets of inserts. Each insert is assumed to be optimized by means of a broadly understood dynamic programming procedure. We show that in an “additive” routing problem of this kind (with precedence constraints and complex travel cost functions) the result's improvements are also aggregated additively. The proposed construction admits a parallel implementation for multiprocessor systems; in this case, the inserts are distributed to computational nodes and formed in an independent way.
Keywords: dynamic programming, multi-inserts, parallel algorithm. 
@article{VUU_2018_28_4_a5,
     author = {A. G. Chentsov and A. M. Grigor'ev},
     title = {Optimizing multi-inserts in routing problems with constraints},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {513--530},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2018_28_4_a5/}
}
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A. G. Chentsov; A. M. Grigor'ev. Optimizing multi-inserts in routing problems with constraints. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 4, pp. 513-530. http://geodesic.mathdoc.fr/item/VUU_2018_28_4_a5/