# Ant colony optimization

Overview[ edit ] In the natural world, ants of some species initially wander randomlyand upon finding food return to their colony while laying down pheromone trails. If other ants find such a path, they are likely not to keep travelling at random, but instead to follow the trail, returning and reinforcing it if they eventually find food see Ant communication. Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, the more time the pheromones have to evaporate.

We consider its application to the traveling salesman problem TSP. In the TSP a set of locations e.

The problem consists of finding a closed tour of minimal length that visits each city once and only once. To apply ACO to the TSP, we consider the graph defined by associating the set of cities with the set of vertices of the graph.

This graph is called construction graph. Since in the TSP it is possible to move from any given city to any other city, the construction graph is fully connected and the number of vertices is equal to the number of cities.

We set the lengths of the edges between the vertices to be proportional to the distances between the cities represented by these vertices and we associate pheromone values and heuristic values with the edges of the graph.

Pheromone values are modified at runtime and represent the cumulated experience of the ant colony, while heuristic values are problem dependent values that, in the case of the TSP, are set to be the inverse of the lengths of the edges. The ants construct the solutions as follows.

Each ant starts from a randomly selected city vertex of the construction graph. Then, at each construction step it moves along the edges of the graph. Each ant keeps a memory of its path, and in subsequent steps it chooses among the edges that do not lead to vertices that it has already visited.

An ant has constructed a solution once it has visited all the vertices of the graph. At each construction step, an ant probabilistically chooses the edge to follow among those that lead to yet unvisited vertices.

The probabilistic rule is biased by pheromone values and heuristic information: Once all the ants have completed their tour, the pheromone on the edges is updated.

Each of the pheromone values is initially decreased by a certain percentage. Each edge then receives an amount of additional pheromone proportional to the quality of the solutions to which it belongs there is one solution per ant.

This procedure is repeatedly applied until a termination criterion is satisfied. Pheromone values are used and updated by the ACO algorithm during the search.

The ants move from vertex to vertex along the edges of the construction graph exploiting information provided by the pheromone values and in this way incrementally building a solution.

Additionally, the ants deposit a certain amount of pheromone on the components, that is, either on the vertices or on the edges that they traverse. Subsequent ants utilize the pheromone information as a guide towards more promising regions of the search space. The ACO metaheuristic is: This construct is repeated until a termination criterion is met.

Typical criteria are a maximum number of iterations or a maximum CPU time. In most applications of ACO to NP-hard problems however, the three algorithmic components undergo a loop that consists in i the construction of solutions by all ants, ii the optional improvement of these solution via the use of a local search algorithm, and iii the update of the pheromones.

These three components are now explained in more details. The exact rules for the probabilistic choice of solution components vary across different ACO variants. The best known rule is the one of ant system AS Dorigo et al. DaemonActions Once solutions have been constructed, and before updating the pheromone values, often some problem specific actions may be required.

The most used daemon action consists in the application of local search to the constructed solutions: UpdatePheromones The aim of the pheromone update is to increase the pheromone values associated with good solutions, and to decrease those that are associated with bad ones.

Pheromone evaporation implements a useful form of forgetting, favoring the exploration of new areas in the search space. A well-known example is the AS-update rule, that is, the update rule of ant system Dorigo et al. Although this increases the speed with which good solutions are found, it also increases the probability of premature convergence.

Here we briefly overview, in the historical order in which they were introduced, the three most successful ones: In order to illustrate the differences between them clearly, we use the example of the traveling salesman problem.

Its main characteristic is that the pheromone values are updated by all the ants that have completed the tour.

## Book subject areas

When constructing the solutions, the ants in AS traverse the construction graph and make a probabilistic decision at each vertex. Ant colony system The first major improvement over the original ant system to be proposed was ant colony system ACSintroduced by Dorigo and Gambardella The first important difference between ACS and AS is the form of the decision rule used by the ants during the construction process.Ant Colony Optimization (ACO) is the best example of how studies aimed at understanding and modeling the behavior of ants and other social insects can provide inspiration for the development of computational algorithms for the solution of difficult mathematical problems.

The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant regardbouddhiste.com: \$ The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant behavior.

Introduction Main ACO AlgorithmsApplications of ACO Advantages and DisadvantagesSummaryReferences Outline 1 Introduction Ant Colony Optimization Meta-heuristic Optimization.

Ant colony optimization is a technique for optimization that was introduced in the early ’s. The inspiring source of ant colony optimization is the foraging behavior of real ant colonies.