Fig. 1

A graphic representation of the generalized traveling salesman problem (GTSP) solved with an ant-based heuristic called reinforcing Ant Colony System (RACS) is illustrated. The first picture shows an ant starting from the nest to find food, going once through each cluster and returning to the nest; all the ways are initialized with the same \(\tau _{0}\) pheromone quantity; after several iterations performed by each ant from the nest, the solution is visible. The second picture shows a solution of generalized traveling salesman problem (GTSP) represented by the largest pheromone trail (thick lines); the pheromone is evaporating on all the other trails (gray lines)