Adaptive Ant Colony Optimization with node clustering applied to the Travelling Salesman Problem

This article presents the Ant Colony Optimization algorithm to solve the Travelling Salesman Problem. The pro-posed algorithm implements three novel techniques to enhance the overall performance, lower the execution time and reduce the negative effects particularly connected with ACO-based methods such as falling into a local optimum and issues with settings of control parameters for different instances. These techniques include (a) the node clustering concept where transition nodes are organised in a set of clusters, (b) adaptive pheromone evapo-ration controlled dynamically based on the information entropy and (c) the formulation of the new termination condition based on the diversity of solutions in population. To verify the effectiveness of the proposed principles, a number of experiments were conducted using 30 benchmark instances (ranging from 51 to 2,392 nodes with various nodes topologies) taken from the well-known TSPLIB benchmarks and the results are compared with sev-eral state-of-the-art ACO-based methods; the proposed algorithm outperforms these rival methods in most cases. The impact of the novel techniques on the behaviour of the algorithm is thoroughly analysed and discussed in respect to the overall performance, execution time and convergence.