Transformation operators based grey wolf optimizer for travelling salesman problem

Abstract

In the field of swarm intelligence, the Grey Wolf Optimizer (GWO) is a popular algorithm based on leadership hierarchy. Primarily, GWO was proposed to solve continuous optimization problem. However, in recent years, GWO has been extensively explored to deal with a wide variety of real world problem regardless the nature of problem. GWO has received a lot of attention from researchers because of its advantages over other swarm intelligence approaches and its simplicity. The classical GWO is redesigned in this paper by incorporating the swap, shift and symmetry transformation operators to solve permutation-coded travelling salesman problem (TSP), and it is named as transformation operator based grey wolf optimizer (TO-GWO). In TO-GWO, each wolf represents a possible solution of TSP and using swap, shift and symmetry operators wolves interact with leader wolves in order to obtain optimal solution for TSP. In order to improve the proposed algorithm’s local search capability when solving discrete problems, 2-opt algorithm have also been adapted. The TO-GWO is implemented in MATLAB environment. In this study, the TO-GWO is tested over 50 TSP instances. Also, the results of proposed algorithm are compared with 12 state-of-the-art algorithms for TSP instances with various numbers of cities in order to evaluate its performance. For the majority of the TSP instances used in the experiment, the TO-GWO significantly outperforms other algorithms in terms of quality of solutions and efficiency.