Skip to main content
Log in

Choosing optimal road trajectory with random work cost in different areas

  • Control in Social Economic Systems, Medicine, and Biology
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider the road construction optimization problem in deterministic and stochastic settings. We show a mathematical model of the road construction process that takes into account varying work costs in different areas. We propose an algorithm for this problem based on dynamical programming, scenario scheme, and the branch-and-bound method. We illustrate our constructions with an example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kall, P. and Wallace, S.W., Stochastic Programming, Chichester: Wiley, 1994.

    MATH  Google Scholar 

  2. Rogozhkin, V.M. and Dvizov, D.A., Choosing an Optimal Way to Build Magistral Constructions, Interstroimekh-2005: Tr. mezhd. nauchn.-tekh. konf. (Proc. Intl. Sci.-Tech. Conf.), Tyumen, 2005, pp. 97–99.

  3. Dvizov, D.A., Choosing an Optimal Way to Build Magistral Constructions, Mater. XI mezhd. nauchn.-prakticheskoi konf. molodykh uchenykh i studentov Volzhskogo (Proc. XI Intl. Sci.-Pract. Conf. of Young Scientists and Students in Volzhskii), Volgograd, 2006, pp. 4–5.

  4. Dvizov, D.A., Solving the Optimal Trajectory Selection Problem for Building Magistral Constructions with Dynamic Programming, Interstroimekh-2006: Mater. mezhd. nauchn.-tekh. konf. (Proc. Intl. Sci.-Tech. Conf.), Moscow, 2006, pp. 326–328.

  5. Boiko, A.V., On Choosing the Optimal Route for a Magistral Pipeline with Dynamic Programming, in Neft’ i gaz i ikh produkty (Oil, Gas, and Their Products), Moscow, 1971.

  6. Kibzun, A.I. and Malyshev, V.V., Analiz i sintez vysokotochnogo upravleniya letatel’nymi apparatami (Analysis and Synthesis of High-Precision Control for Flying Vehicles), Moscow: Mashinostroenie, 1987.

    Google Scholar 

  7. Kibzun, A.I. and Kan, Yu.S., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Stochastic Programming Problems with Probabilistic Criteria), Moscow: Fizmatlit, 2009.

    MATH  Google Scholar 

  8. Venttsel’, E.S., Elementy dinamicheskogo programmirovaniya (Elements of Dynamic Programming), Moscow: Nauka, 1964.

    Google Scholar 

  9. Christofides, N., Graph Theory. An Algorithmic Approach, New York: Academic, 1975. Translated under the title Teoriya grafov. Algoritmicheskii podkhod, Moscow: Mir, 1978.

    MATH  Google Scholar 

  10. Dijkstra, E.W., A Note on Two Problems in Connexion with Graphs, in Numerische Mathematik 1, 1959, pp. 269–271.

  11. Zhitenev, A.I., Finding Solutions in Optimal Routing Problem for a Pipeline Route with a Weighted Graph, Vestn. Voronezh. Gos. Techn. Univ., 2009, vol. 5, no. 2, pp. 108–111.

    Google Scholar 

  12. Bellman, R., Dynamic Programming, Princeton: Princeton Univ. Press, 1957. Translated under the title Dinamicheskoe programmirovanie, Moscow: Inostrannaya Literatura, 1960.

    MATH  Google Scholar 

  13. Land, A.H. and Doig, A.G., An Automatic Method of Solving Discrete Programming Problems, Econometrica, 1960, vol. 28, pp. 497–520.

    Article  MathSciNet  MATH  Google Scholar 

  14. Little, J.D.C., Murty, K.G., and Sweeney, D.W., An Algorithm for the Traveling Salesman Problem, Oper. Res., 1963, vol. 11, pp. 972–989.

    Article  MATH  Google Scholar 

  15. Malyshev, V.V., Konspekt lektsii po teorii optimal’nykh sistem (Lecture Notes on Optimal Systems Theory), Moscow: Mosk. Aviats. Inst., 1974.

    Google Scholar 

  16. Bertsekas, D.P. and Shreve, S.E., Stochastic Optimal Control: The Discrete Time Case, New York: Academic, 1978. Translated ubder the title Stokhasticheskoe optimal’noe upravlenie, Moscow: Nauka, 1985.

    MATH  Google Scholar 

  17. Kibzun, A.I., Stokhasticheskoe upravlenie dinamicheskimi sistemami (Stochastic Control for Dynamical Systems), Moscow: Mosk. Aviats. Inst., 1991.

    MATH  Google Scholar 

  18. Construction norms and rules. Automobile roads, SNiP 3.06.03-85.

  19. Construction norms and rules. Automobile roads, SNiP 2.05.02-85*.

  20. Reference of Cost Values for Certain Types of Capital Building (Similar Objects), Russian Ministry of Regional Development, Moscow, 2009 (www.minregion.ru).

  21. Information Technologies in Construction,” 2010, October, no. 10 (113).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.I. Kibzun, O.M. Khromova, 2012, published in Avtomatika i Telemekhanika, 2012, No. 7, pp. 89–108.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kibzun, A.I., Khromova, O.M. Choosing optimal road trajectory with random work cost in different areas. Autom Remote Control 73, 1181–1194 (2012). https://doi.org/10.1134/S0005117912070089

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117912070089

Keywords

Navigation