Discrete Grey Wolf Optimizer for symmetric travelling salesman problem

Grey Wolf Optimizer (GWO) is a recently developed population-based metaheuristic algorithm which imitates the behaviour of grey wolves for survival. Initially, GWO was proposed to solve continuous optimization problems where it performed well. In recent years, numerous versions of GWO are available in the literature and GWO has been widely used to solve engineering problems. This paper presents a novel discrete GWO algorithm (D-GWO) to solve complex discrete travelling salesman problem (TSP). The 2-opt algorithm is incorporated into it to improve the performance of the proposed algorithm. To inspect the performance of D-GWO, the results of the proposed algorithm are compared with well-known metaheuristic algorithms such as Bat Algorithm(BA), Discrete Firefly Algorithm, Imperialist Competitive Algorithm and some other classical algorithms over several known TSP instances. In order to obtain unbiased and rigorous comparison, descriptive statistics such as mean and standard deviation are used as well as statistical tests such as Friedman test and Holm's test are also conducted. The D-GWO is implemented in MATLAB environment. The computational result carried out in this study has shown that D-GWO outperforms significantly over other alternative algorithms.