Ant Systems

This article describes Ant Systems a meta heuristic based on an ant foraging metaphor The presentation of Ant Systems has been somewhat generalized by adding a Queen process in charge of co ordinating classi cal Ant processes so that recent Ant Systems can be naturally included while remaining close to the metaphor To illustrate how Ant Systems are practically implemented a number of applications to the quadratic assignment problem are reviewed A model of real ants The metaphor on which Ant Systems are based can be illustrated by obser vations of ants of the species Linepithema humile An ant colony nest is isolated and a food source is provided which is accessible by a bridge composed of two branches of the same length Although the ants are totally free to choose the left or the right branch of the bridge it is rapidly observed that almost all ants use a given branch even if there is no reason to prefer the left or the right one This phenomenon is explained by the fact that ants deposit a chemical substance while traveling They are able to detect this substance with their antennae This substance carries informations and is called a pheromone A real ant is modeled as a probabilistic process In the absence of pheromone the ant explores the surrounding area in a totally randommanner If a pheromone trail is present the ant follows the pheromone trail with a high probability If two pheromone trails cross each other the ant follows the trail with the larger amount of pheromone with a higher probability Since the ant deposits ad ditional pheromone when traveling the foraging process evolves with positive feedback Moreover pheromones evaporate meaning that a trail that is not used gradually disappears amplifying the positive feedback e ect The observation has been repeated with a bridge whose branches have dif ferent lengths Applying the same probabilistic behavior model it can be deduced that the ants will rapidly choose the shorter branch and this is in fact observed The phenomenon is explained as follows at the beginning when no pheromone is present the ants choose the left or the right branch with equal probability Since the ants which chose the shorter branch arrive earlier at the food and come back to the nest earlier the pheromone quantity on the shorter branch grows faster So the ants are able to nd the shortest path between nest and food even if each ant has an extremely limited view of the surrounding area Inspired by this natural optimization process Colorni Dorigo and Maniezzo design a new meta heuristic that can be applied to combinatorial optimization problems The basic idea is to consider arti cial ant processes that repeatedly build solutions to the optimization problem Each process builds a solution with the help of a common memory that can be read and modi ed by any arti cial ant The common memory plays the role of trails in the real model However when translated into a combinatorial optimization process the simpli ed foraging process presented above is generally not able to create e cient heuristic methods and this historical model must be extended to cover recent and e cient applications inspired by ant colonies Indeed a simple pos itive feedback mechanism is di cult to tune correctly and often leads to degen erate situations When the feedback is too strong the only existing trail is that of the rst ant which built a solution and when it is too weak the trails are uniformly distributed in the whole search space In the rst situation all ants use the same path and in the second the the ants just perform a random walk The model is extended by considering an ant colony composed of di erenti ated ants such as workers soldiers or sexual individuals Each of these special ized individual is assigned a di erent task The most important individual of the colony is the queen which has the ability to create new ants and to choose the type of the created ants Therefore the queen co ordinates the whole colony and has also a strategic role Inclusion of an intelligent queen helps in the design of e cient algorithms since search strategies can be included within the arti cial ant system while remaining close to the ant metaphor Arti cial Ant Systems Since the introduction of Ant Systems the algorithms based on the ant metaphor have evolved Instead of reviewing successive evolutions of these al gorithms a general Ant System model developed from the real ant model is presented This general model is properly called the Ant System meta heuristic and is de ned by a set of principles or a methodology that allows the develop ment of heuristics for a wide range of combinatorial optimization problems Arti cial ant systems are derived from the real ant model by making three analogies Real ants corresponds to processes in charge of building solutions to the combinatorial problem considered these processes are often referred as Arti cial ants or simply Ant processes The pheromone trails corresponds to a common memory that is updated each time a new solution is built more precisely the memory records a value associated with each component of a solution The queen corresponds to a central process in charge of activating and co ordinating arti cial ants and of managing the common memory A meta heuristic based on ant behavior can be described by a set of pro cesses that collaborate through a common memory The rst set of processes corresponding to the ants built solutions in a probabilistic way with proba bilities depending on information stored in memory All these arti cial Ant processes are activated and co ordinated by a Queen process that also manages the common memory Very schematically an ant system can be speci ed by two di erent processes