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A Hybrid Genetic—GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem

Author

Listed:
  • Yannis Marinakis

    (Technical University of Crete)

  • Athanasios Migdalas

    (Technical University of Crete)

  • Panos M. Pardalos

    (University of Florida)

Abstract

Hybridization techniques are very effective for the solution of combinatorial optimization problems. This paper presents a genetic algorithm based on Expanding Neighborhood Search technique (Marinakis, Migdalas, and Pardalos, Computational Optimization and Applications, 2004) for the solution of the traveling salesman problem: The initial population of the algorithm is created not entirely at random but rather using a modified version of the Greedy Randomized Adaptive Search Procedure. Farther more a stopping criterion based on Lagrangean Relaxation is proposed. The combination of these different techniques produces high quality solutions. The proposed algorithm was tested on numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the algorithms of the DIMACS Implementation Challenge are also presented.

Suggested Citation

  • Yannis Marinakis & Athanasios Migdalas & Panos M. Pardalos, 2005. "A Hybrid Genetic—GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 311-326, December.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:4:d:10.1007_s10878-005-4921-7
    DOI: 10.1007/s10878-005-4921-7
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    References listed on IDEAS

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    1. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1992. "New Insertion and Postoptimization Procedures for the Traveling Salesman Problem," Operations Research, INFORMS, vol. 40(6), pages 1086-1094, December.
    2. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    3. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    4. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    5. Jon Jouis Bentley, 1992. "Fast Algorithms for Geometric Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 4(4), pages 387-411, November.
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    Cited by:

    1. Shuli Hu & Huan Liu & Xiaoli Wu & Ruizhi Li & Junping Zhou & Jianan Wang, 2019. "A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. Kyriakakis, Nikolaos A. & Marinaki, Magdalene & Matsatsinis, Nikolaos & Marinakis, Yannis, 2022. "A cumulative unmanned aerial vehicle routing problem approach for humanitarian coverage path planning," European Journal of Operational Research, Elsevier, vol. 300(3), pages 992-1004.

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