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\begin{document}

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



\author[1]{Mohamed Abdellahi Amar }%
\author[2]{Walid Khaznaji }%
\affil[1]{CRISTAL-GRIFT Laboratory}%
\affil[2]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\begin{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.%
\end{abstract}%



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