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A Lagrangian heuristic for the Prize CollectingTravelling Salesman Problem

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  • M. Dell'Amico
  • F. Maffioli
  • A. Sciomachen

Abstract

In this paper, we consider the Prize Collecting Travelling Salesman Problem (PCTSP),which is a variant of the Travelling Salesman Problem (TSP), where a tour visiting eachnode at most once in a given graph has to be computed such that a prize is associated witheach node and a penalty has to be paid for every unvisited node: moreover, a knapsackconstraint guarantees that a sufficiently large prize is collected. We develop a Lagrangianheuristic and obtain an upper bound in the form of a feasible solution starting from a lowerbound to the problem recently proposed in the literature. We evaluate these bounds utilizingboth randomly generated instances and real ones with very satisfactory results. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • M. Dell'Amico & F. Maffioli & A. Sciomachen, 1998. "A Lagrangian heuristic for the Prize CollectingTravelling Salesman Problem," Annals of Operations Research, Springer, vol. 81(0), pages 289-306, June.
    • Handle: RePEc:spr:annopr:v:81:y:1998:i:0:p:289-306:10.1023/a:1018961208614
    DOI: 10.1023/A:1018961208614
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    Cited by:

    1. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    2. Álvarez-Miranda, Eduardo & Luipersbeck, Martin & Sinnl, Markus, 2018. "Gotta (efficiently) catch them all: Pokémon GO meets Orienteering Problems," European Journal of Operational Research, Elsevier, vol. 265(2), pages 779-794.
    3. L Tang & X Wang, 2008. "An iterated local search heuristic for the capacitated prize-collecting travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 590-599, May.

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