An effective particle swarm optimization algorithm embedded in sa to solve the traveling salesman problem

The heuristic methods have been widely developed for solution of complicated optimization methods. Recently hybrid methods that are based on combination of different approaches have shown more potential in this regard. This paper also introduces a new method by embedding the idea of particle swarm (PS) intelligence into the well-known method of simulated annealing (SA). This way SA has been capable to search a subspace of the search space by means of an individual particle; therefore the annealing process can start from lower temperatures and use shorter Markov chains for each particle, leading to faster solutions. The results obtained with the proposed method show its potential in achieving both accuracy and speed in small and medium size problems, compared to many advanced methods.