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A Lagrangian heuristic for the Prize CollectingTravelling Salesman Problem

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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.

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Dell'Amico, M., Maffioli, F. & Sciomachen, A. A Lagrangian heuristic for the Prize CollectingTravelling Salesman Problem. Annals of Operations Research 81, 289–306 (1998). https://doi.org/10.1023/A:1018961208614

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