Towards Multilevel Ant Colony Optimisation for the Euclidean Symmetric Traveling Salesman Problem

Ant Colony Optimization ACO metaheuristic is one of the best known examples of swarm intelligence systems in which researchers study the foraging behavior of bees, ants and other social insects in order to solve combinatorial optimization problems. In this paper, a multilevel Ant Colony Optimization MLV-ACO for solving the traveling salesman problem is proposed, by using a multilevel process operating in a coarse-to-fine strategy. This strategy involves recursive coarsening to create a hierarchy of increasingly smaller and coarser versions of the original problem. The heart of the approach is grouping the variables that are part of the problem into clusters, which is repeated until the size of the smallest cluster falls below a specified reduction threshold. Subsequently, a solution for the problem at the coarsest level is generated, and then successively projected back onto each of the intermediate levels in reverse order. The solution at each level is improved using the ACO metaheuristic before moving to the parent level. The proposed solution has been tested both in circular and randomized environments, and outperform single level counterparts.