A Hybrid Symbiotic Organisms Search Algorithm with Variable Neighbourhood Search for Solving Symmetric and Asymmetric Traveling Salesman Problem

Combinatorial optimization has been frequently used to solve both problems in science, engineering, and commercial applications. One combinatorial problems in the field of transportation is to find a shortest travel route that can be taken from the initial point of departure to point of destination, as well as minimizing travel costs and travel time. When the distance from one (initial) node to another (destination) node is the same with the distance to travel back from destination to initial, this problems known to the Traveling Salesman Problem (TSP), otherwise it call as an Asymmetric Traveling Salesman Problem (ATSP). The most recent optimization techniques is Symbiotic Organisms Search (SOS). This paper discuss how to hybrid the SOS algorithm with variable neighborhoods search (SOS-VNS) that can be applied to solve the ATSP problem. The proposed mechanism to add the variable neighborhoods search as a local search is to generate the better initial solution and then we modify the phase of parasites with adapting mechanism of mutation. After modification, the performance of the algorithm SOS-VNS is evaluated with several data sets and then the results is compared with the best known solution and some algorithm such PSO algorithm and SOS original algorithm. The SOS-VNS algorithm shows better results based on convergence, divergence and computing time.