An application and Parallel Tabu Search Algorithm for Solving the PTSP Under the OpenMP-MPI Environment

Abstract

This paper reviews some real-world problems modeling as Probabilistic Traveling Salesman Problem (PTSP), by presenting the important results found in the literature. It illustrates the usefulness of the inclusion of probabilistic elements in deterministic models. We propose a new modeling of the PTSP by the deviations of the routing of a robot in order to avoid obstacles which are not foreseen in its path. The Probabilistic Traveling Salesman Problem(PTSP) is a variation of the classic Traveling Salesman Problem (TSP) where each node i is present with probability pi. The solution for the PTSP consists in finding an a priori tour that visits all the cities that minimizes the expected length of the tour. From the litterateur the PTSP is NP-Complete, therefore the execution time is a prime factor in its resolution. In the last of his paper we present a new parallel Tabu search heuristic for solving PTSP by using the Open MPI environment.