The Prize Collecting Traveling Salesman Problem (PCTSP) can be associated to a salesman who collects a prize in each city visited and pays a penalty for each city not visited, with travel costs among the cities. The objective is to minimize the sum of the travel costs and penalties, including in the tour enough number of cities that allow collecting a minimum prize. This paper contributes with the development of a hybrid metaheuristic to PCTSP, based on GRASP and search methods in variable neighborhood (VNS/VND) to solve PCTSP approximately. In order to validate the obtained solutions, we proposed a mathematical formulation to be solved by a commercial solver to find the best solution to the problem, being this solver applied to small problems. Computational results demonstrate the efficiency of the proposed method, as much in relation to the quality of the obtained final solution as in relation to the time of execution.
Traveling salesman problem; metaheuristic; GRASP; VNS; VND
