In this paper we consider the Prize Collecting Travelling Salesman Problem (PCTSP), that is a variant of the Travelling Salesman Problem (TSP) where a tour visiting each node at most once in a given graph has to be computed, such that a prize is associated with each node and a penalty has to be paid for every unvisited node; moreover, a knapsack constraint guarantees that a sufficiently large prize is collected. We develop a Lagrangean heuristic and obtain an upper bound in the form of a feasible solution starting from a lower bound to the problem recently proposed in the literature. We evaluate these bounds utilizing both randomly generated instances and real ones with very satisfactory results.
A Lagrangean Heuristic for Prize Collecting Travelling Salesman Problem / Dell'Amico, Mauro; F., Maffioli; A., Sciomachen. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - STAMPA. - 81:(1998), pp. 289-305.