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Embedding learning capability in Lagrangean relaxation: An application to the travelling salesman problem

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  • Zamani, Reza
  • Lau, Sim Kim

Abstract

This paper presents an effective procedure that finds lower bounds for the travelling salesman problem based on the 1-tree using a learning-based Lagrangian relaxation technique. The procedure can dynamically alter its step-size depending upon its previous iterations. Along with having the capability of expansion-contraction, the procedure performs a learning process in which Lagrange multipliers are influenced by a weighted cost function of their neighbouring nodes. In analogy with simulated annealing paradigm, here a learning process is equivalent to escaping local optimality via exploiting the structure of the problem. Computational results conducted on Euclidean benchmarks from the TSPLIB library show that the procedure is very effective.

Suggested Citation

  • Zamani, Reza & Lau, Sim Kim, 2010. "Embedding learning capability in Lagrangean relaxation: An application to the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 201(1), pages 82-88, February.
  • Handle: RePEc:eee:ejores:v:201:y:2010:i:1:p:82-88
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    References listed on IDEAS

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    1. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    2. Volgenant, Ton & Jonker, Roy, 1982. "A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation," European Journal of Operational Research, Elsevier, vol. 9(1), pages 83-89, January.
    3. Baker, Barrie M. & Sheasby, Janice, 1999. "Accelerating the convergence of subgradient optimisation," European Journal of Operational Research, Elsevier, vol. 117(1), pages 136-144, August.
    4. Lorena, Luiz Antonio N. & Goncalves Narciso, Marcelo, 2002. "Using logical surrogate information in Lagrangean relaxation: An application to symmetric traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 138(3), pages 473-483, May.
    5. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
    6. P M E Shutler, 2003. "A priority list based heuristic for the job shop problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 571-584, June.
    7. Ravi, R. & Sinha, Amitabh, 2008. "Approximating k-cuts using network strength as a Lagrangean relaxation," European Journal of Operational Research, Elsevier, vol. 186(1), pages 77-90, April.
    8. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
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    Cited by:

    1. Zamani, Reza, 2013. "A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 229(2), pages 552-559.

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