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The Black and White Traveling Salesman Problem

Author

Listed:
  • Gianpaolo Ghiani

    (Centre de recherche sur les transports, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Quebec, Canada H3C 3J7 and Dipartimento di Ingegneria dell’Innovazione, Università di Lecce, Via per Arnesano, 73100 Lecce, Italy)

  • Gilbert Laporte

    (Centre de recherche sur les transports, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Quebec, Canada H3C 3J7 and HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Quebec, Canada H3T 2A7)

  • Frédéric Semet

    (LAMIH, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont-Houy, 59311 Valenciennes Cedex 9, France)

Abstract

The black and white traveling salesman problem (BWTSP) is defined on a graph G whose vertex set is partitioned into black and white vertices. The aim is to design a shortest Hamiltonian tour on G subject to cardinality and length constraints: both the number of white vertices as well as the length of the tour between two consecutive black vertices are bounded above. The BWTSP has applications in airline scheduling and in telecommunications. This paper proposes an integer linear formulation for the undirected BWTSP, as well as several classes of valid inequalities. An exact branch-and-cut algorithm is then developed. Extensive tests show that it can solve exactly instances involving up to 100 vertices. The algorithm can also be applied directly to solve unit demand vehicle routing problems of similar sizes.

Suggested Citation

  • Gianpaolo Ghiani & Gilbert Laporte & Frédéric Semet, 2006. "The Black and White Traveling Salesman Problem," Operations Research, INFORMS, vol. 54(2), pages 366-378, April.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:2:p:366-378
    DOI: 10.1287/opre.1050.0218
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    References listed on IDEAS

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    Cited by:

    1. Gopalan, Ram, 2014. "The Aircraft Maintenance Base Location Problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 634-642.
    2. Khalid Mekamcha & Mehdi Souier & Hakim Nadhir Bessenouci & Mohammed Bennekrouf, 2021. "Two metaheuristics approaches for solving the traveling salesman problem: an Algerian waste collection case," Operational Research, Springer, vol. 21(3), pages 1641-1661, September.
    3. Li, Xiangyong & Lin, Shaochong & Tian, Peng & Aneja, Y.P., 2017. "Models and column generation approach for the resource-constrained minimum cost path problem with relays," Omega, Elsevier, vol. 66(PA), pages 79-90.
    4. Gerardo Berbeglia & Gilles Pesant & Louis-Martin Rousseau, 2012. "Feasibility of the Pickup and Delivery Problem with Fixed Partial Routes: A Complexity Analysis," Transportation Science, INFORMS, vol. 46(3), pages 359-373, August.
    5. Gouveia, Luis & Leitner, Markus & Ruthmair, Mario, 2017. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 908-928.

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