Abstract:

The multiple traveling salesman problem aims to minimize the total cost of m tours while visiting each city only once form sellers who start a tour from a single depot and finish the tour at the same depot. In the open multiple traveling salesman problem, m sellers complete the tour in the city they last visited without returning to the depot. The aim of the problem is to minimize the total travelled distance formed by m sellers. This problem is encountered in the logistics sector, especially in cargo transportation. In this study, a solution is proposed to solve by using open source softwares. First, the cities to be visited by m sellers are determined by the K-Medoids Clustering Algorithm which is an unsupervised machine learning algorithm, and then the routes are formed with the Nearest Neighborhood Algorithm. The performance of the proposed method was tested on datasets with different clustering characteristics such as clustered, random and a hydrid random-clustered dataset from the literature. Its performance was compared with the optimal solutions taken from the Gurobi commercial solver. The results indicate that the proposed method is reasonably successful; however, it exhibits different behaviors on datasets with distinct characteristics.

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