This article is cited in 2 papers

MATHEMATICS

Optimizing multi-inserts in routing problems with constraints

A. G. Chentsov^ab, A. M. Grigor'ev<sup>a

a</sup> Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
^b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: 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.

UDC: 519.6

MSC: 49L20, 90C39

Received: 17.09.2018

DOI: 10.20537/vm180406

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