Routing under constraints: Problem of visit to megalopolises

Ченцов, А. Г.; Chentsov, P. A.

doi:10.1134/s0005117916110060

Cited by 17 publications

(29 citation statements)

References 8 publications

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“…To solve the problems of the form (2.6), one can use the broadly understood DP in the spirit of [7][8][9][10][11]13]; here, we consider these procedures in their algorithmic form (see [11,16]).…”

Section: Problem Statementmentioning

confidence: 99%

“…In terms of I (3.1), let us introduce the family [16]) a recurrence procedure for constructing C 1 , . .…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…The way of solving this problem is described, in particular, in [16]; in the same paper, there are also constructed the feasible task set families C, C 1 , . .…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…, C N similar to those mentioned in the beginning of the section. Based on that (in [16]), state space layers…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…Coming back to the problem (2.8), note that the aforementioned algorithm (which admits a natural analogy with [16]) must be modified: the layers v 1 , . .…”

Section: Algorithm For Optimization Of Starting Pointmentioning

confidence: 99%

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Optimizing the Starting Point in a Precedence Constrained Routing Problem With Complicated Travel Cost Functions

Ченцов

Grigoryev

2018

UMJ

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We study the optimization of the initial state, route (a permutation of indices), and track in an extremal problem connected with visiting a finite system of megalopolises subject to precedence constraints where the travel cost functions may depend on the set of (pending) tasks. This problem statement is exemplified by the task to dismantle a system of radiating elements in case of emergency, such as the Chernobyl or Fukushima nuclear disasters. We propose a solution based on a parallel algorithm, which was implemented on the Uran supercomputer. It consists of a two-stage procedure: stage one determines the value (extremum) function over the set of all possible initial states and finds its minimum and also the point where it is achieved. This point is viewed as a base of the optimal process, which is constructed at stage two. Thus, optimization of the starting point for the route through megalopolises, connected with conducting certain internal tasks there, is an important element of the solution. To this end, we employ the apparatus of the broadly understood dynamic programming with elements of parallel structure during the construction of Bellman function layers.

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Section: Problem Statementmentioning

confidence: 99%

“…In terms of I (3.1), let us introduce the family [16]) a recurrence procedure for constructing C 1 , . .…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…The way of solving this problem is described, in particular, in [16]; in the same paper, there are also constructed the feasible task set families C, C 1 , . .…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…, C N similar to those mentioned in the beginning of the section. Based on that (in [16]), state space layers…”

Section: Dynamic Programming In Starting Point Optimization Problemmentioning

confidence: 99%

“…Coming back to the problem (2.8), note that the aforementioned algorithm (which admits a natural analogy with [16]) must be modified: the layers v 1 , . .…”

Section: Algorithm For Optimization Of Starting Pointmentioning

confidence: 99%

See 3 more Smart Citations