A parallel hybrid heuristic based on Karp's partitioning for PTSP on multi-core processors

Abstract

This paper provides a new parallel hybrid-heuristic by using the Open MPI environment for solving the Probabilistic Traveling Salesman Problem (PTSP). It is a variation of the classic Traveling Salesman Problem (TSP) where each node is present with probability. The PTSP models many real-world applications: in wireless sensor network as TSP based mobility protocol, based on K-means clustering, also in the internet of things terrestrial ubiquitous sensor networks using public unmanned aerial vehicles. Nowadays these applications give many data, so the solving very large-size PTSPs give an asymptotic analysis of the PTSP by implementing the algorithm of Karp's partitioning which consists in subdividing the square, in sub-squares. So we transform the resolution of a large size problem to the resolution of sub-problems which can be near optimal solved. This application can be grid field and this different sub-problem would be processed in parallel by different nodes since they are totally independent. In each sub-square a method of resolution is used.