Abstract
The problem of routing movements in a finite system of sets is considered. The problem is constrained by precedence conditions and by necessity of executing several (internal) jobs on the sets. The cost of execution of these jobs is summed up with the cost of performing (external) movements from set to set. The contents of the paper correspond to the presentation made by the author at the Conference on Control of Dynamical Systems (IPM RAS, Moscow, 2009)
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References
M. R. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir, Moscow, 1978).
I. I. Melamed, S. I. Sergeev, and I. Kh. Sigal, “Travelling Salesman Problem”, Avtom. Telemekh., No. 9 (1989).
R. Bellman, “Application of Dynamic Programming to the Travelling Salesman Problem”, in Kiberneticheskii Sbornik, Vol. 9 (Mir, Moscow, 1964), Vol. 9 [in Russian].
M. Held and R. M. Karp, “Application of Dynamic Programming to Ordering Problems”, in Kiberneticheskii Sbornik, Vol. 9 (Mir, Moscow, 1964) [in Russian].
L. N. Korotaeva, A. N. Sesekin, and A. G. Chentsov, “On a Modification of Dynamic Programming Method in Problems of Successive Approach”, Zh. Vychisl. Mat. Mat. Fiz. 29(8), (1989).
L. N. Korotaeva, E. M. Nazarov, and A. G. Chentsov, “On an Assignment Problem”, in Zh. Vychisl. Mat. Mat. Fiz. 33(4) (1993).
L. N. Korotaeva and A. G. Chentsov, “On a Generalization of Travelling Salesman Problem to ” Bottlenecks”,” Zh. Vychisl. Mat. Mat. Fiz. 35(7) (1995).
A. A. Chentsov and A. G. Chentsov, “Solving the Routing Optimization Problem Using the Dynamic Programming Method”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 3, (1999) [Comp. Syst. Sci. 38 (3), 409–420 (1999)].
A. A. Chentsov and A. G. Chentsov, “Reduction of Route Optimization Problems,” Avtom. Telemekh. 61b(10), (2000) [Automat. Remote Control 61b (10), 1708–1722(2000)].
A. A. Chentsov and A. G. Chentsov, “On Solution of the Problem of Successive Round of Sets by the “Non-closed” Travelling Salesman Problem”, Avtom. Telemekh. 69(11), (2002) [Automat. Remote Control 63 (11), 1832–1845(2002)].
A. G. Chentsov, Extremal Problems of Routing and Tasks Allocation: Theoretical Problems (Izhevsk-Moscow, 2008) [in Russian].
J. Little, K. Murty, D. Sweeny, et al., “An Algorithm for the Travelling Salesman Problem” Econ.-Mat. Metody 1(1), (1965).
I. Kh. Sigal and A. P. Ivanova, Introduction to Applied Discrete Programming (Fizmatlit, Moscow, 2007) [in Russian].
S. I. Sergeev, “Hybrid Control Systems and the Dynamic Traveling Salesman Problem”, Avtom. Telemekh. 69(1), (2008) [Automat. Remote Control 69 (1), 42–51 (2008)].
A. N. Sesekin, O. L. Tashlykov, S. E. Shcheklein, et al., “Application of the Dynamic Programming Method for Optimization of Trajectories of Movement of Workers in Radiation-Dangerous Zones to Minimize radiation”, Izv. Vuzov. Yadernaya Energetika, No. 2 (2006).
A. N. Sesekin, A. A. Chentsov, and A. G. Chentsov, “A Generalized Courier Problem with the Cost Function Depending on the List of Tasks”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 2, (2010) [Comp. Syst. Sci. 49 (2), (2010)].
A. N. Sesekin, O. L. Tashlykov, A. G. Chentsov, et al., “Development of Optimal Algorithms of Withdrawal of NPS with the Use of Mathematical Simulation Methods” Izv. Vuzov. Yadernaya Energetika, No. 2 (2009).
K. Kuratovsky and A. Mostovsky, The Theory of Sets (Mir, Moscow, 1970) [in Russian].
T. Cormen, C. Leiserson, and R. Rivest, Algorithms: Design and Analysis (MTsNMO, Moscow, 2002) [in Russian].
A. A. Chentsov and A. G. Chentsov, “Dynamic Programming Method in the Generalized Courier Problem”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 3, (2008) [Comp. Syst. Sci. 47 (3), 455–463 (2008)].
A. G. Chentsov, “On Optimal Routing under Condition of Constraints”, Dokl. Akad. Nauk 423(3) (2008).
A. A. Chentsov, A. G. Chentsov, and P. A. Chentsov, “Extremal Routing Problems with Internal Losses”, Tr. Instituta Matematiki i Mekhaniki 14(3) (2008).
N. N. Krasovskii, Game-Theoretic Problems of Motions Rendezvous (Nauka, Moscow, 1970) [in Russian].
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].
A. A. Chentsov and A. G. Chentsov, “On Implementation of the Dynamic Programming Method in the Generalized Courier Problem”, Tr. Instituta Matematiki i Mekhaniki 13(3) (2007).
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Original Russian Text © A.G. Chentsov, 2010, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2010, No. 3, pp. 52–66.
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Chentsov, A.G. Dynamic programming method in extremal constrained routing problems. J. Comput. Syst. Sci. Int. 49, 392–405 (2010). https://doi.org/10.1134/S1064230710030081
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DOI: https://doi.org/10.1134/S1064230710030081