Skip to main content
Springer Nature Link
Log in

A Preprocessing That Combines Heuristic and Surrogate Constraint Analysis to Fix Variables in TSP

  • Conference paper
MICAI 2004: Advances in Artificial Intelligence (MICAI 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2972))

Included in the following conference series:

Abstract

A preprocessing procedure that uses a local guided search defined in terms of a neighborhood structure to get a feasible solution (UB) and the Osorio and Glover [18], [20] exploiting of surrogate constraints and constraint pairing is applied to the traveling salesman problem. The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the linear relaxation of the problem. The objective function is made a constraint less or equal than a feasible solution (UB). The surrogate constraint is paired with this constraint to obtain a combined equation where negative variables are replaced by complemented variables and the resulting constraint is used to fix variables to zero or one before solving the problem.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Garey, M., Johnson, D.: Computers and Intractability, Computers and Intractability. W.H. Freeman, San Francisco (1979)

    Google Scholar 

  2. Gass, S. (ed.): Encyclopedia of Operations Research and Management Sciences. Kluwer Academic Publishers, New York (1997)

    Google Scholar 

  3. Glover, F.: Flows in Arborescences. Management Science 17, 568–586 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  4. Glover, F.: Surrogate Constraints. Operations Research 16, 741–749 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  5. Glover, F.: Surrogate Constraint Duality in Mathematical Programming. Operations Research 23, 434–451 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  6. Glover, F., Sherali, H., Lee, Y.: Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming. Computational Optimization and Applications 8, 151–172 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Greenberg, H., Pierskalla, W.: Surrogate Mathematical Programs. Operations Research 18, 924–939 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  8. Granot, F., Hammer, P.L.: On the use of boolean functions in 0-1 linear programming. Methods of Operations Research, 154–184 (1971)

    Google Scholar 

  9. Hammer, P., Padberg, M., Peled, U.: Constraint Pairing in Integer Programming. INFOR 13, 68–81 (1975)

    MATH  MathSciNet  Google Scholar 

  10. Hooker, J.N.: Logic-based methods for optimization. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874, pp. 336–349. Springer, Heidelberg (1994)

    Google Scholar 

  11. Hooker, J.N.: A Framework for combining solution methods. Carnegie Mellon University, Pittsburgh (2003) (working paper)

    Google Scholar 

  12. Hooker, J.N., Osorio, M.A.: Mixed Logical/Linear Programming. Discrete Applied Mathematics 96-97, 395–442 (1999)

    Article  MathSciNet  Google Scholar 

  13. Jeroslow, R.E., Lowe, J.K.: Modeling with integer variables. Mathematical Programming Studies 22, 167–184 (1984)

    MATH  MathSciNet  Google Scholar 

  14. Johnson, D.S.: Local Optimization and the Traveling Salesman Problem. In: Proceedings of the 17th International Colloquium on Automata, Languages and Programming, pp. 446–461. Springer, Berlin (1990)

    Chapter  Google Scholar 

  15. Johnson, D.S., McGeoch, L.A.: The Traveling Salesman Problem: A Case Study in Local Optimization. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley and Sons, Ltd., Chichester (1997)

    Google Scholar 

  16. Johnson, D.S., Gutin, G., McGeoch, L.A., Yeo, A., Zhang, W., Zverovich, A.: Experimental Analysis of Heuristics for the ATSP. In: Gutin, G., Punnen, A. (eds.) The Traveling Salesman Problem and its Variations, pp. 445–487. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  17. Karwan, M.H., Rardin, R.L.: Some relationships between Lagrangean and surrogate duality in integer programming. Mathematical Programming 17, 230–334 (1979)

    Article  MathSciNet  Google Scholar 

  18. Osorio, M.A., Glover, F., Hammer, P.: Cutting and Surrogate Constraint Analysis for Improved Multidimensional Knapsack Solutions. Annals of Operations Research 117, 71–93 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Osorio, M.A., Glover, F.: Hard Problem Generation for MKP. In: Proceedings of the XI CLAIO. Concepción, Chile (2002)

    Google Scholar 

  20. Osorio, M.A., Glover, F.: Exploiting Surrogate Constraint Analysis for Fixing Variables in both bounds for Multidimensional Knapsack Problems. In: Chávez, E., Favela, J., Mej´ıa, M., Oliart, A. (eds.) Proceedings of the Fourth Mexican International Conference on Computer Science, pp. 263–267. IEEE Computer Society, New Jersey (2003)

    Chapter  Google Scholar 

  21. Salkin, M.: Integer Programming. Adisson-Wesley Publishing Company, New York (1975)

    MATH  Google Scholar 

  22. Tucker, A.: On Directed Graphs and Integer Programs, IBM Mathematical Research Projecft Technical Report, Princeton University (1960)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Universidad Autónoma de Puebla, 72560, Puebla, México

    M. Lama & D. Pinto

Authors
  1. M. Lama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Pinto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, Tecnológico de Monterrey, Campus Estado de México, Carretera al lago de Guadalupe, Km 3.5, Atizapán, 52926, Mexico

    Raúl Monroy

  2. Instituto de Investigaciones Electricas, Reforma # 113, Col. Palmira, 62490, Morelos, Cuernavaca, Mexico

    Gustavo Arroyo-Figueroa

  3. Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro No. 1, 72840, Puebla, México

    Luis Enrique Sucar

  4. Centro de Investigación en Computación – IPN, Av. Juan de Dios Batíz, esquina con Miguel Othón de Mendizábal, Ciudad de México, 07738, México

    Humberto Sossa

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lama, M., Pinto, D. (2004). A Preprocessing That Combines Heuristic and Surrogate Constraint Analysis to Fix Variables in TSP. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds) MICAI 2004: Advances in Artificial Intelligence. MICAI 2004. Lecture Notes in Computer Science(), vol 2972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24694-7_75

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24694-7_75

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21459-5

  • Online ISBN: 978-3-540-24694-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics