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A Grouping Genetic Algorithm For The Multiple Traveling Salesperson Problem

Author

Listed:
  • EVELYN C. BROWN

    (Department of Engineering, East Carolina University, 225 Slay Building, Greenville, NC 27858, USA)

  • CLIFF T. RAGSDALE

    (Department of Business Information Technology, Virginia Tech, 1007 Pamplin Hall, Blacksburg, VA 24061, USA)

  • ARTHUR E. CARTER

    (College of Information Science and Technology, Radford University, P.O. Box 6933, Radford, VA, 24142, USA)

Abstract

The multiple traveling salesperson problem (MTSP) involves schedulingm > 1salespersons to visit a set ofn > mlocations. Thus, thenlocations must be divided intomgroups and arranged so that each salesperson has an ordered set of cities to visit. The grouping genetic algorithm (GGA) is a type of genetic algorithm (GA) designed particularly for grouping problems. It has been successfully applied to a variety of grouping problems. This paper focuses on the application of a GGA to solve the MTSP. Our GGA introduces a new chromosome representation to indicate which salesperson is assigned to each tour and the ordering of the cities within each tour. We compare our method to standard GAs that employ either the one-chromosome or two-chromosome representation for MTSP. This research demonstrates that our GGA with its new chromosome representation is capable of solving a variety of MTSP problems from the literature and can outperform the traditional encodings of previously published GA methods.

Suggested Citation

  • Evelyn C. Brown & Cliff T. Ragsdale & Arthur E. Carter, 2007. "A Grouping Genetic Algorithm For The Multiple Traveling Salesperson Problem," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 333-347.
    • Handle: RePEc:wsi:ijitdm:v:06:y:2007:i:02:n:s0219622007002447
    DOI: 10.1142/S0219622007002447
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    Cited by:

    1. Tamás Kalmár-Nagy & Giovanni Giardini & Bendegúz Dezső Bak, 2017. "The Multiagent Planning Problem," Complexity, Hindawi, vol. 2017, pages 1-12, February.
    2. He, Pengfei & Hao, Jin-Kao, 2023. "Memetic search for the minmax multiple traveling salesman problem with single and multiple depots," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1055-1070.
    3. Johannes Inführ & Günther Raidl, 2016. "A memetic algorithm for the virtual network mapping problem," Journal of Heuristics, Springer, vol. 22(4), pages 475-505, August.
    4. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.

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