Mostafa Mohammadi - Master of science in in industrial engineering ،Mazandaran University of Science and Technology
Golman Rahmanifar - Master of science in in industrial engineering ،Mazandaran University of Science and Technology
Ghasem Kaveh Garna - Master of Science in in industrial engineering ،Islamic Azad University of Noor

The Multiple Travelling Salesman Problems (MTSP) are one of the main scopes of discontinuous optimization problems and is the extension of the well-known travelling salesman problem.The (MTSP) can in general be defined as follows: Given a set of nodes (cities), let there be m salesmen located at a single depot node. The remaining nodes that are to be visited are called intermediate nodes. Then, the MTSP consists of finding tours for all my salesmen, who all start and end at the depot, such that each intermediate node is visited exactly once and the total cost of visiting all nodes is minimized.The purpose of this paper is following a set of paths for the salesman with the aim of balancing the workload between them. So that number of nodes don't consider predetermined interval for each salesman. But visit time of each node for each salesman follows oriented position learning effect function that depends on the skill of each salesman, and these nodes are determined according to the seller's acquisition skills using a number of repetitions. to the best of our knowledge, this paper presents the first study that brings learning effect in the distribution and in order to achieve optimum quality and local escape answer using a meta-heuristic algorithms. In this study, a Meta heuristic algorithm, called Fire Fly Algorithm (FA), has been presented for solving the MTSP.

Multiple Travelling Salesman Problems (MTSP), optimization, Fire Fly Algorithm (FA)، learning effect