Abstract
Consideration was given to the problem of constrained routing including visits to a finite system of megalopolises and at that execution of one or another internal job. The costs of displacements and executed jobs may depend on the list of the not yet completed tasks. A variant of the method of dynamic programming doing without construction of the entire array of values of the Bellman function was proposed. Some variants of the heuristic algorithms were discussed. Possible applications may be related, in particular, with the problems of reducing irradiance of the personnel of the nuclear power plants and sheet article cutting on the numerically controlled machine tools.
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Korobkin, V.V., Sesekin, A.N., Tashlykov, O.L., and Chentsov, A.G., Metody marshrutizatsii i ikh prilozheniya v zadachakh povysheniya bezopasnosti i effektivnosti ekspluatatsii atomnykh stantsii (Methods of Routing and Their Applications to Problems of Increasing Safety and Efficiency of Nuclear Power Plants), Kalyaev, I.A., Ed., Moscow: Novye Tekhnologii, 2012.
Tashlykov, O.L., Remont oborudovaniya atomnykh stantsii: uch. pos. dlya vuzov (Repair of Nuclear Power Station Equipment. Univ. Textbook), Shcheklein, S.E., Ed., Yekaterinburg: Ural. Gos. Tekhn. Univ.-UPI, 2003.
Petunin, A.A., On Some Strategies of Forming the Tool Route at Developing the Control Programs for the Thermal Cutting Machines, Vestn. Ufim. Gos. Aviats. Tekh. Univ., Ser. Upravlen., Vychisl. Mat. Inform., 2009, vol. 13, no. 2(35), pp. 280–286.
Bellman, R., Dynamic Programming Treatment of the Travelling Salesman Problem, J. ACM (JACM), 1962, vol. 9, no. 1, pp. 61–63. Translated under the title Primenenie dinamicheskogo programmirovaniya k zadache o kommivoyazhere, in Kiberneticheskii Sbornik (Cybernetical Series), Moscow: Mir, 1964, vol. 9, pp. 219–228.
Held, M. and Karp, R., A Dynamic Programming Approach to Sequencing Problems, J. SIAM, 1962, no. 10, no. 1, pp. 196–210. Translated under the title Primenenie dinamicheskogo programmirovaniya k zadacham uporyadocheniya, in Kiberneticheskii Sbornik (Cybernetical Series), Moscow: Mir, 1964, vol. 9, pp. 202–218.
Little, J.D., Murty, K.G., Sweeney, D.W., and Karel, C., An Algorithm for the Traveling Salesman Problem, Oper. Res., 1963, no. 11(6), pp. 972–989. Translated under the title Algoritm dlya resheniya zadachi o kommivoyazhere, Ekon. Mat. Metod., 1965, vol. 1, vol. 1, pp. 90–107.
Chentsov, A.G., Ekstremal’nye zadachi marshrutizatsii i raspredeleniya zadanii: voprosy teorii (Extremal Problems of Routing and Allocation of Tasks: Questions of Theory), Moskva-Izhevsk: Regulyarnaya i Khaoticheskaya Dinamika, 2008.
Chentsov, A.G., On Routing Complexes of Jobs, Vestn. Udmurd. Gos. Univ., Mat. Mekh. Comput. Sci., 2013, no. 1, pp. 59–82.
Chentsov, A.A., Chentsov, A.G., and Chentsov, P.A., Dynamic Programming in Extremal Problems of Routing: General Theory and Elements of Parallel Structure, in Tr. VI Mezhd. konf. “Parallel’nye vychisleniya i zadachi upravleniya” (Proc. VI Int. Conf. “Parallel Computations and Control Problems” (PACO’2012)), Moscow, 2012, vol. 2, pp. 183–198.
Chentsov, A.G. and Chentsov, P.A., Dynamic Programming in One Nonstationary Problem of Routing, Izv. Inst. Mat. Informatics Udmurd. Gos. Univ., 2012, no. 1, pp. 151–154.
Chentsov, A.G. and Chentsov, P.A., Routing of Displacements with Constraints and Nonstationary Cost Functions, Nauchn.-Tekhn. Vedomosti S.-Peterburg. Gos. Politekh. Univ., Ser. Inform. Telekomm. Upravlen., 2012, no. 4(152), pp. 88–93.
Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., Traveling Salesman Problem. I. Theoretical Issues, Autom. Remote Control, 1989, vol. 50, no. 9, part 1, pp. 1147–1173.
Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., Traveling Salesman Problem. II. Exact Methods, Autom. Remote Control, 1989, vol. 50, no. 10, part 1, pp. 1303–1324.
Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., Traveling Salesman Problem. III. Approximate Algorithms, Autom. Remote Control, 1989, vol. 50, no. 11, part 1, pp. 1459–1479.
Plotinskii, Yu.M., Generalized Delivery Problem, Autom. Remote Control, 1973, vol. 34, no. 6, part 2, pp. 946–949.
Melamed, I.I. and Plotinskii, Yu.M., Heuristic Algorithm for Solving the Generalized Delivery Problem, Autom. Remote Control, 1979, vol. 40, no. 12, part 2, pp. 1845–1849.
Warga, J., Optimal Control of Differential and Functional Equations, New York: Academic, 1972. Translated under the title Optimal’noe upravlenie differentsial’nymi i funktsional’nymi uravneniyami, Moscow: Nauka, 1979.
Cormen, T.H., Leizerson, C.E., and Rivest, R.L., Introduction to Algorithms, Cambridge: MIT Press, 1990. Translated under the title Algoritmy. Postroenie i analiz, Moscow: Mosk. Tsentr Nepreryvn. Mat. Obrazov., 1999.
Chentsov, A.G. and Chentsov, P.A., On One Nonstationary Problem of Routing under Constraints, Model. Anal. Inf. Sist., 2012, vol. 19, no. 4, pp. 5–24.
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Original Russian Text © A.G. Chentsov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 4, pp. 170–190.
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Chentsov, A.G. Problem of successive megalopolis traversal with the precedence conditions. Autom Remote Control 75, 728–744 (2014). https://doi.org/10.1134/S0005117914040122
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DOI: https://doi.org/10.1134/S0005117914040122