View source for Ant colony optimization algorithms

== Introduction ==

[[Ant colony optimization algorithms|Ant colony optimization (ACO)]] are a set of [[Computational Intelligence|computational intelligence]] techniques inspired by the behavior of real ant colonies. These algorithms are used to solve discrete optimization problems, such as the [[Travelling Salesman Problem|travelling salesman problem]], [[Vehicle Routing Problem|vehicle routing problem]], and [[Quadratic Assignment Problem|quadratic assignment problem]]. ACO algorithms are part of the larger field of [[Swarm Intelligence|swarm intelligence]], which studies collective behaviors in decentralized systems.

[[Image:Detail-76455.jpg|thumb|center|A close-up view of ants working together to transport food.|class=only_on_mobile]]
[[Image:Detail-76456.jpg|thumb|center|A close-up view of ants working together to transport food.|class=only_on_desktop]]

== Theoretical Background ==

ACO algorithms are based on the concept of [[Stigmergy|stigmergy]], a form of indirect communication through the environment. In nature, ants deposit a chemical substance called [[Pheromone|pheromone]] on their paths, which influences the behavior of other ants. This pheromone trail is a form of positive feedback: the more ants follow a path, the stronger the pheromone trail becomes, attracting more ants to that path. This behavior allows ant colonies to find the shortest paths between their nest and food sources.

== Algorithm Description ==

The basic ACO algorithm works as follows:

# A set of artificial ants is placed on the nodes of a graph representing the problem to be solved.
# Each ant builds a solution to the problem by moving from node to node along the edges of the graph.
# The decision to move from one node to another is made stochastically, based on the amount of pheromone on the edges and a heuristic information related to the problem.
# Once all ants have built their solutions, they deposit a quantity of pheromone on the edges they traversed, with the amount of pheromone being inversely proportional to the quality of the solution.
# The pheromone on the edges evaporates over time, which is a form of negative feedback.

This process is repeated until a termination condition is met, such as a maximum number of iterations or a satisfactory solution has been found.

== Variants of ACO Algorithms ==

There are several variants of the basic ACO algorithm, each with its own characteristics and suitable for different types of problems. These include:

# [[Ant System|Ant System (AS)]]: This is the original ACO algorithm, proposed by Marco Dorigo in his Ph.D. thesis in 1992.
# [[Ant Colony System|Ant Colony System (ACS)]]: This variant introduces a local pheromone update rule, which accelerates the convergence of the algorithm.
# [[Max-Min Ant System|Max-Min Ant System (MMAS)]]: This variant introduces a maximum and minimum limit for the pheromone trail, preventing the algorithm from converging too quickly to a suboptimal solution.
# [[Rank-Based Ant System|Rank-Based Ant System (RAS)]]: In this variant, only the best solutions contribute to the pheromone update, which reduces the influence of poor solutions.
# [[Continuous Ant Colony Optimization|Continuous Ant Colony Optimization (CACO)]]: This variant extends the ACO framework to continuous optimization problems.

== Applications ==

ACO algorithms have been successfully applied to a wide range of optimization problems, including:

# [[Routing in telecommunication networks|Routing in telecommunication networks]]: ACO algorithms can be used to find the shortest paths for data packets in a network.
# [[Vehicle routing problem|Vehicle routing]]: ACO algorithms can be used to determine the optimal routes for a fleet of vehicles delivering goods to a set of customers.
# [[Scheduling problems|Scheduling]]: ACO algorithms can be used to schedule tasks in a manufacturing process or in a computer system.
# [[Protein folding problem|Protein folding]]: ACO algorithms can be used to predict the three-dimensional structure of a protein based on its amino acid sequence.

== See Also ==

[[Swarm Intelligence]]
[[Particle Swarm Optimization]]
[[Genetic Algorithms]]
[[Evolutionary Computation]]
[[Metaheuristic]]

== References ==

[[Category:Computational Intelligence]]
[[Category:Optimization Algorithms]]
[[Category:Swarm Intelligence]]