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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.

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  • 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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    7. 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.
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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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