A GRASP with restarts heuristic for the Steiner traveling salesman problem

Given a set of nodes and the distances between them, the traveling salesman problem (TSP) consists in finding the shortest route that visits each node exactly once and returns to the first. The Steiner traveling salesman problem (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by a shortest route, eventually visiting some nodes and edges more than once. In this paper, we extend some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2-opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path-relinking and restarts are reported. In addition, a set of test instances and best known solutions is made available for benchmarking purposes.