Topological variable neighborhood search

The design of the novel metaheuristic method, called Topological Variable Neighborhood Search, is presented and its theoretical properties are elaborated. The proposed metaheuristic method is implemented, applied to several well-known NP-hard problems on graphs (metric dimension problem, roman domination problem and maximum betweeness problem) and compared with the relevant optimization methods for these problems. The obtained experimental results clearly show that the proposed method achieves a significant improvement for the investigated problems and outperforms other methods that participated in the comparison (number of successfully solved problems is increased by 11.5%, 3% and 31.8%, respectively). In particular, it was shown that the Topological Variable Neighborhood Search is consistently better than the classical Variable Neighborhood Search.