An Ant System Algorithm for the Vehicle Routing Problem with Backhauls

The ant system is a metaheuristic developed for the solution of hard combinatorial optimization problems. It was first proposed by Colorni et al. [4] and Dorigo [6]. The method was inspired by the observation of the behaviour of real life ant colonies, in particular the way in which real ants find the shortest path between food sources and their nest. While walking ants deposit a substance called pheromone on to the ground which forms a pheromone trail. Ants can detect the pheromone and choose their way according to the level of the pheromone trail. The greater the concentration of pheromone on the ground the higher the probability that an ant will choose that path. Where there is a shorter path from a food source to the nest, ants will reach the end of the path in a quicker time compared to ants on a longer path. This means that the trail will build up at a faster rate on the shorter path which in turn causes more ants to choose the shorter path which also causes a greater level of pheromone. In time all ants will have the tendency to choose the shorter path.