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In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Artificial ants stand for multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used.^[2] Combinations of artificial ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing.

As an example, ant colony optimization^[3] is a class of optimization algorithms modeled on the actions of an ant colony.^[4] Artificial 'ants' (e.g. simulation agents) locate optimal solutions by moving through a parameter space representing all possible solutions. Real ants lay down pheromones directing each other to resources while exploring their environment. The simulated 'ants' similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions.^[5] One variation on this approach is the bees algorithm, which is more analogous to the foraging patterns of the honey bee, another social insect.

This algorithm is a member of the ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations. Initially proposed by Marco Dorigo in 1992 in his PhD thesis,^[6][7] the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food. The original idea has since diversified to solve a wider class of numerical problems, and as a result, several problems have emerged, drawing on various aspects of the behavior of ants. From a broader perspective, ACO performs a model-based search^[8] and shares some similarities with estimation of distribution algorithms.

Overview

In the natural world, ants of some species (initially) wander randomly, and 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).^[9]

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. A short path, by comparison, gets marched over more frequently, and thus the pheromone density becomes higher on shorter paths than longer ones. Pheromone evaporation also has the advantage of avoiding the convergence to a locally optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend to be excessively attractive to the following ones. In that case, the exploration of the solution space would be constrained. The influence of pheromone evaporation in real ant systems is unclear, but it is very important in artificial systems.^[10]

The overall result is that when one ant finds a good (i.e., short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads to many ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with "simulated ants" walking around the graph representing the problem to solve.

Ambient networks of intelligent objects

New concepts are required since “intelligence” is no longer centralized but can be found throughout all minuscule objects. Anthropocentric concepts have been known to lead to the production of IT systems in which data processing, control units and calculating forces are centralized. These centralized units have continually increased their performance and can be compared to the human brain. The model of the brain has become the ultimate vision of computers. Ambient networks of intelligent objects and, sooner or later, a new generation of information systems that are even more diffused and based on nanotechnology, will profoundly change this concept. Small devices that can be compared to insects do not dispose of a high intelligence on their own. Indeed, their intelligence can be classed as fairly limited. It is, for example, impossible to integrate a high performance calculator with the power to solve any kind of mathematical problem into a biochip that is implanted into the human body or integrated in an intelligent tag which is designed to trace commercial articles. However, once those objects are interconnected they dispose of a form of intelligence that can be compared to a colony of ants or bees. In the case of certain problems, this type of intelligence can be superior to the reasoning of a centralized system similar to the brain.^[11]

Nature offers several examples of how minuscule organisms, if they all follow the same basic rule, can create a form of collective intelligence on the macroscopic level. Colonies of social insects perfectly illustrate this model which greatly differs from human societies. This model is based on the co-operation of independent units with simple and unpredictable behavior.^[12] They move through their surrounding area to carry out certain tasks and only possess a very limited amount of information to do so. A colony of ants, for example, represents numerous qualities that can also be applied to a network of ambient objects. Colonies of ants have a very high capacity to adapt themselves to changes in the environment as well as an enormous strength in dealing with situations where one individual fails to carry out a given task. This kind of flexibility would also be very useful for mobile networks of objects which are perpetually developing. Parcels of information that move from a computer to a digital object behave in the same way as ants would do. They move through the network and pass from one knot to the next with the objective of arriving at their final destination as quickly as possible.^[13]

Artificial pheromone system

Pheromone-based communication is one of the most effective ways of communication which is widely observed in nature. Pheromone is used by social insects such as bees, ants and termites; both for inter-agent and agent-swarm communications. Due to its feasibility, artificial pheromones have been adopted in multi-robot and swarm robotic systems. Pheromone-based communication was implemented by different means such as chemical ^[14][15][16] or physical (RFID tags,^[17] light,^{[18][19][20][21]} sound^[22]) ways. However, those implementations were not able to replicate all the aspects of pheromones as seen in nature.

Using projected light was presented in an 2007 IEEE paper by Garnier, Simon, et al. as an experimental setup to study pheromone-based communication with micro autonomous robots.^[23] Another study presented a system in which pheromones were implemented via a horizontal LCD screen on which the robots moved, with the robots having downward facing light sensors to register the patterns beneath them.^[24][25]

Algorithm and formula

In the ant colony optimization algorithms, an artificial ant is a simple computational agent that searches for good solutions to a given optimization problem. To apply an ant colony algorithm, the optimization problem needs to be converted into the problem of finding the shortest path on a weighted graph. In the first step of each iteration, each ant stochastically constructs a solution, i.e. the order in which the edges in the graph should be followed. In the second step, the paths found by the different ants are compared. The last step consists of updating the pheromone levels on each edge.

procedure ACO_MetaHeuristic is
    while not terminated do
        generateSolutions()
        daemonActions()
        pheromoneUpdate()
    repeat
end procedure

Edge selection

Each ant needs to construct a solution to move through the graph. To select the next edge in its tour, an ant will consider the length of each edge available from its current position, as well as the corresponding pheromone level. At each step of the algorithm, each ant moves from a state ${\displaystyle x}$ to state ${\displaystyle y}$, corresponding to a more complete intermediate solution. Thus, each ant ${\displaystyle k}$ computes a set ${\displaystyle A_{k}(x)}$ of feasible expansions to its current state in each iteration, and moves to one of these in probability. For ant ${\displaystyle k}$, the probability ${\displaystyle p_{xy}^{k}}$ of moving from state ${\displaystyle x}$ to state ${\displaystyle y}$ depends on the combination of two values, the attractiveness ${\displaystyle \eta _{xy}}$ of the move, as computed by some heuristic indicating the a priori desirability of that move and the trail level ${\displaystyle \tau _{xy}}$ of the move, indicating how proficient it has been in the past to make that particular move. The trail level represents a posteriori indication of the desirability of that move.

In general, the ${\displaystyle k}$th ant moves from state ${\displaystyle x}$ to state ${\displaystyle y}$ with probability

${\displaystyle p_{xy}^{k}={\frac {(\tau _{xy}^{\alpha })(\eta _{xy}^{\beta })}{\sum _{z\in \mathrm {allowed} _{y}}(\tau _{xz}^{\alpha })(\eta _{xz}^{\beta })}}}$

where ${\displaystyle \tau _{xy}}$ is the amount of pheromone deposited for transition from state ${\displaystyle x}$ to ${\displaystyle y}$, 0 ≤ ${\displaystyle \alpha }$ is a parameter to control the influence of ${\displaystyle \tau _{xy}}$, ${\displaystyle \eta _{xy}}$ is the desirability of state transition ${\displaystyle xy}$ (a priori knowledge, typically ${\displaystyle 1/d_{xy}}$, where ${\displaystyle d}$ is the distance) and ${\displaystyle \beta }$ ≥ 1 is a parameter to control the influence of ${\displaystyle \eta _{xy}}$. ${\displaystyle \tau _{xz}}$ and ${\displaystyle \eta _{xz}}$ represent the trail level and attractiveness for the other possible state transitions.

Pheromone update

Trails are usually updated when all ants have completed their solution, increasing or decreasing the level of trails corresponding to moves that were part of "good" or "bad" solutions, respectively. An example of a global pheromone updating rule is

${\displaystyle \tau _{xy}\leftarrow (1-\rho )\tau _{xy}+\sum _{k}^{m}\Delta \tau _{xy}^{k}}$

where ${\displaystyle \tau _{xy}}$ is the amount of pheromone deposited for a state transition ${\displaystyle xy}$, ${\displaystyle \rho }$ is the pheromone evaporation coefficient, ${\displaystyle m}$ is the number of ants and ${\displaystyle \Delta \tau _{xy}^{k}}$ is the amount of pheromone deposited by ${\displaystyle k}$th ant, typically given for a TSP problem (with moves corresponding to arcs of the graph) by

Zdroj:https://en.wikipedia.org?pojem=Ant_colony_optimization_algorithms
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