International Journal of Industrial Engineering Computations 7 (2016) 245–256 Contents lists available at GrowingScience International Journal of Industrial Engineering Computations homepage: www.GrowingScience.com/ijiec A population-based algorithm for the multi travelling salesman problem Rubén Iván Bolaños a , Eliana M. Toro O b and Mauricio Granada E a* a Department of Electrical Engineering, Universidad Tecnológica de Pereira, Colombia b Department of Industrial Engineering, Universidad Tecnológica de Pereira, Colombia C H R O N I C L E A B S T R A C T Article history: Received July 22 2015 Received in Revised Format Septmber17 2015 Accepted October 14 2015 Available online October 15 2015 This paper presents the implementation of an efficient modified genetic algorithm for solving the multi-traveling salesman problem (mTSP). The main characteristics of the method are the construction of an initial population of high quality and the implementation of several local search operators which are important in the efficient and effective exploration of promising regions of the solution space. Due to the combinatorial complexity of mTSP, the proposed methodology is especially applicable for real-world problems. The proposed algorithm was tested on a set of six benchmark instances, which have from 76 and 1002 cities to be visited. In all cases, the best known solution was improved. The results are also compared with other existing solutions procedure in the literature. © 2016 Growing Science Ltd. All rights reserved Keywords: Combinatorial optimization Multi-traveling salesman problem Population-based algorithm Local search operators 1. Introduction The mTSP problem can be viewed from the perspective of two well-known problems: i) as a generalization of the Travelling Salesman Problem (TSP), where a set of routes is assigned to m salesmen who all start from and return to a home city, and ii) as a special case of the vehicle routing problem (VRP), in which customers are considered unitary demands and every travelling salesman only visits a predetermined number of cities. Thus, the mTSP can also be utilized for solving several types of VRPs and all formulations and solution approaches for the VRP are valid for the mTSP. Although the VRP and TSP have been widely discussed in the literature, the research on the mTSP is limited. Moreover, few papers in the literature address the mTSP through efficient population-based algorithms. The main motivation for formulating a population methodology lies in the ease of integration with multi-objective strategies, which allow introducing practical aspects, such as profit, fuel consumption and environmental impact, among others. Therefore, it becomes relevant to develop and implement an effective and robust optimization methodology based on population. * Corresponding author. E-mail: magra@utp.edu.co (M. Granada E) © 2016 Growing Science Ltd. All rights reserved. doi: 10.5267/j.ijiec.2015.10.005