Dynamic programming and solvability of bottleneck routing problem with resource constraints

被引：4
|
作者：
Chentsov, A. G. [1 ,2 ]
Chentsov, A. A. [1 ]
机构：
[1] Russian Acad Sci, NN Krasovskii Inst Math & Mech, Ural Branch, ul S Kovalevskoi 16, Ekaterinburg 620219, Russia
[2] Ural Fed Univ, ul Mira 19, Ekaterinburg 620002, Russia
来源：
VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI | 2022年 / 32卷 / 04期
关键词：
dynamic programming; route; precedence conditions; TRAVELING SALESMAN PROBLEM;
D O I：
10.35634/vm220406
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The article deals with the problem of admissible routing for a system of cycles each of which contains exterior permutation and works connected with megalopolises (non-empty finite sets) visiting. In the initial setting, a resource constraint is given; this constraint should be fulfilled for every cycle under permutation. The solvability conditions in this problem are connected with the extremum of the auxil-iary bottleneck routing problem without above-mentioned constraint, in which the apparatus of widely understood dynamic programming (DP) is used. A particular case of the setting is the known bottleneck courier problem which can be used (in particular) for routing a vehicle (airplane or helicopter) aiming to realize the given shipping system with a limited fuel reserve on each flight. An algorithm implemented on a personal computer is constructed.
引用
收藏
页码：569 / 592
页数：24
相关论文
共 50 条
  • [1] Generalized a bottleneck routing problem: dynamic programming and the start point optimization
    Chentsov, Alexei A.
    Chentsov, Alexander G.
    Sesekin, Alexander N.
    [J]. IFAC PAPERSONLINE, 2018, 51 (32): : 373 - 377
  • [2] Dynamic programming in the routing problem with constraints and costs depending on a list of tasks
    A. G. Chentsov
    A. A. Chentsov
    [J]. Doklady Mathematics, 2013, 88 : 637 - 640
  • [3] Dynamic programming in the routing problem with constraints and costs depending on a list of tasks
    Chentsov, A. G.
    Chentsov, A. A.
    [J]. DOKLADY MATHEMATICS, 2013, 88 (03) : 637 - 640
  • [4] A multiphase dynamic programming algorithm for the shortest path problem with resource constraints
    Himmich, Ilyas
    El Hallaoui, Issmail
    Soumis, Francois
    [J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2024, 315 (02) : 470 - 483
  • [5] Extremal bottleneck routing problem with constraints in the form of precedence conditions
    A. A. Chentsov
    A. G. Chentsov
    [J]. Proceedings of the Steklov Institute of Mathematics, 2008, 263 : 23 - 36
  • [6] Extremal Bottleneck Routing Problem with Constraints in the Form of Precedence Conditions
    Chentsov, A. A.
    Chentsov, A. G.
    [J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2008, 263 (Suppl 2) : S23 - S36
  • [7] Extremal bottleneck routing problem with constraints in the form of precedence conditions
    Chentsov, A. A.
    Chentsov, A. G.
    [J]. TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2008, 14 (02): : 129 - 142
  • [8] On a bottleneck routing problem
    Sesekin, A. N.
    Chentsov, A. A.
    Chentsov, A. G.
    [J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2011, 272 : 165 - 185
  • [9] On a bottleneck routing problem
    A. N. Sesekin
    A. A. Chentsov
    A. G. Chentsov
    [J]. Proceedings of the Steklov Institute of Mathematics, 2011, 272 : 165 - 185
  • [10] Scaling the Dynamic Resource Routing Problem
    Schmoll, Sebastian
    Friedl, Sabrina
    Schubert, Matthias
    [J]. SSTD '19 - PROCEEDINGS OF THE 16TH INTERNATIONAL SYMPOSIUM ON SPATIAL AND TEMPORAL DATABASES, 2019, : 80 - 89
12345