Skip to main content
Log in

Optimizing Insertions in a Constraint Routing Problem with Complicated Cost Functions

  • SYSTEMS ANALYSIS AND OPERATIONS RESEARCH
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

An iterative method for solving routing problems subject to constraints and possible dependence of the cost functions on the list of tasks that have not been accomplished is considered. Such statements occur in some problems of nuclear power engineering and in developing optimizing programs for sheet cutting on programmable numerically controlled machines (in the first case, the dependence on the list of tasks can occur due to sequential dismantling of radiation sources, and in the second case it can be due to taking into account technological constraints using penalties). It is assumed that the problems under examination are large, which calls for the use of heuristic methods. The approach proposed in the paper makes it possible to design an iterative procedure based on optimizing insertions that use widely interpreted dynamic programming. The proposed algorithm is implemented on a multicore personal computer.

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.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. I. I. Melamed, S. I. Sergeev, and I. Kh. Sigal, “The traveling salesman problem. Theory questions,” Avtom. Telemekh., No. 9, 3–34 (1989).

  2. I. I. Melamed, S. I. Sergeev, and I. Kh. Sigal, “The traveling salesman problem. Exact algorithms,” Avtom. Telemekh., No. 10, 3–29 (1989).

  3. I. I. Melamed, S. I. Sergeev, and I. Kh. Sigal, “The traveling salesman problem. Approximate algorithms,” Avtom. Telemekh., No. 11, 3–26 (1989).

  4. G. Gutin and A. Punnen, The Traveling Salesman Problem and its Variations (Springer, Berlin, 2002).

    MATH  Google Scholar 

  5. A. G. Chentsov, Extreme Tasks of Routing and Distribution of Tasks: Theory Questions (Regulyar. Khaot. Dinamika, Izhevsk, Moscow, 2008) [in Russian].

    Google Scholar 

  6. A. A. Chentsov and A. G. Chentsov, “Problem of successive megalopolis traversal,” Vestn. Tambov. Univ., Ser. Estestv. Tekh. Nauki. 19, 154–175 (2014).

    Google Scholar 

  7. A. A. Petunin, A. G. Chentsov, and P. A. Chentsov, “Local dynamic programming incuts in routing problems with restrictions,” Vestn. UdGU, Mat. Mekh. Komp. Nauki, No. 2, 56–75 (2014).

    MATH  Google Scholar 

  8. A. G. Chentsov, “Problem of successive megalopolis traversal with the precedence conditions,” Autom. Remote Control 75, 728 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. G. Chentsov, “The Bellmann insertions in the route problem with constraints and complicated cost functions,” Vestn. UdGU. Mat. Mekh. Komp. Nauki, No. 4, 122–141 (2014).

    Google Scholar 

  10. A. A. Petunin, “About some strategies of the programming of tool route by developing of control programs for thermal cutting machines,” Vestn. UGATU, Ser. Upravl., Vychisl. Tekh. Inform. 13, 280–286 (2009).

    Google Scholar 

  11. R. Dewil, P. Vansteenwegen, and D. Cattrysse, “Construction heuristics for generating tool paths for laser cutters,” Int. J. Prod. Res. (in press). https://doi.org/10.1080/00207543.2014

  12. A. A. Petunin, A. G. Chentsov, and P. A. Chentsov, “To the question about instrument routing in the automated machines of the sheet cutting,” Nauch.-Tekh. Vedom. SPbGPU. Inform. Telekommun. Upravl., No. 2 (169), 103–111 (2013).

  13. J. Hoeft and U. S. Palekar, “Heuristics for the plate-cutting traveling salesman problem,” IIE Trans. 29, 719–731 (1997).

    Google Scholar 

  14. A. A. Petunin, “Tool route optimization for sheet cutting machines,” in Proceedings of the 13th International Conference on Computer Sciences and Informational Technologies CSIT’2011, Ufa, 2011, Vol. 1, pp. 179–182.

  15. R. Dewil, P. Vansteenwegen, and D. Cattrysse, “Cutting path optimization using tabu search,” Key Eng. Mater. 473, 739–748 (2011).

    Article  Google Scholar 

  16. G. G. Wang and S. Q. Xie, “Optimal process planning for a combined punch-and-laser cutting machine using ant colony optimization,” Int. J. Prod. Res. 43, 2195–2216 (2005).

    Article  Google Scholar 

  17. M.-K. Lee and K.-B. Kwon, “Cutting path optimization in CNC cutting processes using a two-step genetic algorithm,” Int. J. Prod. Res. 44, 5307–5326 (2006).

    Article  MATH  Google Scholar 

  18. Y. Jing and C. Zhige, “An optimized algorithm of numerical cutting-path control in garment manufacturing,” Adv. Mater. Res. 796, 454–457 (2013).

    Article  Google Scholar 

  19. N. D. Ganelina and V. D. Frolovskii, “On constructing the shortest circuits on a set of line segments,” Sib. Zh. Vychisl. Mat. 9, 201–212 (2006).

    Google Scholar 

  20. M. A. Verkhoturov and P. Yu. Tarasenko, “Mathematical support of the optimization problem of the cutting tool path with a flat figure cut on the basis of chain cutting,” Vestn. UGATU, Upravl., VTiIT 10, 123–130 (2008).

    Google Scholar 

  21. K. Kuratowski and A. Mostowski, Set Theory: Studies in Logic and The Foundations of Mathematics (PWN, North-Holland, Warsaw, Amsterdam, 1976).

  22. T. Cormen, Ch. Leiserson, and R. Rivest, Introduction to Algorithms (MIT Press, Cambridge, MA, 2009; MTsNMO, Moscow, 2002).

  23. A. G. Chentsov, “To question of routing of works complexes,” Vestn. UdGU, Mat. Mekh. Komp’yut. Nauki, No. 1, 59–82 (2013).

    Google Scholar 

  24. A. G. Chentsov and A. A. Chentsov, “Dynamic programming of the problems of routing with constraints and costs depending on the list of jobs,” Dokl. Math. 88, 637 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  25. A. A. Chentsov, A. G. Chentsov, and P. A. Chentsov, “Elements of dynamic programming in extreme routing problems,” Probl. Upravl., No. 5, 12–21 (2013).

  26. A. A. Petunin, A. G. Chentsov, and P. A. Chentsov, “On one optimization model and algorithm for solving the problem of tool routing for CNC sheet cutting machines,” in Proceedings of the 2nd International Conference on Informational Technologies and Systems ITiS – 2013 (Chelyab. Gos. Univ., Chelyabinsk, 2013), pp. 55–61.

  27. A. A. Petunin, A. A. Chentsov, A. G. Chentsov, and P. A. Chentsov, “Elements of dynamic programming in local improvement constructions for heuristic solutions of routing problems with constraints,” Autom. Remote Control 78, 666 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  28. A. G. Chentsov and P. A. Chentsov, “Routing under constraints: problem of visit to megalopolises,” Autom. Remote Control 77, 1957 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  29. A. G. Chentsov, “The Bellmann insertions in route problems with constraints and complicated cost functions. II,” Vestn. UdGU. Mat. Mekh. Komp’yut. Nauki 26, 565–578 (2016).

    MATH  Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research, project no. 17-08-01385.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. A. Petunin, A. G. Chentsov or P. A. Chentsov.

Additional information

Translated by A. Klimontovich

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petunin, A.A., Chentsov, A.G. & Chentsov, P.A. Optimizing Insertions in a Constraint Routing Problem with Complicated Cost Functions. J. Comput. Syst. Sci. Int. 58, 113–125 (2019). https://doi.org/10.1134/S106423071901012X

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106423071901012X

Navigation