ant colony algorithm

Ant colony optimization algorithm

PRESENTED BY:BHARAT SHARMA 13001502002MTIC(2nd year)

Ant Colony Optimization (ACO)

Overview

“Ant Colony Optimization (ACO) studies artificial systems that take inspiration from the behavior of real ant colonies and which are used to solve discrete

optimization problems.”

Ant Colony Optimization (ACO)

Ant Colony Optimization (ACO)

A C O

• Ant Colony Optimization is another family of optimization algorithms inspired by pheromone-based strategies of ant foraging.

• ACO algorithms were originally conceived to find the shortest route in travelling salesman problems.

• In ACO several ants travel across the edges that connect the nodes of the graph while depositing virtual pheromones.

• PHEROMONES : a chemical substance secreted externally by some animals(especially insects) that influence the physiology or behavior of other animals(insects) of same species.

Ant Colony Optimization (ACO)

A C O

• Ants that travel on the shortest path will be able to make more return trips and deposit more pheromones in a given amount of time.

• Consequently, that path will attract more ants in a positive feedback loop.

• ACO assumes that virtual pheromones evaporates ,thus reducing the probability that long paths are selected.

• Pheromone evaporation has also 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.

Ant Colony Optimization (ACO)

Ant Colony OptimizationThe Ant System (AS)

Ant Colony Optimization (ACO)

• Almost blind.

• Incapable of achieving complex tasks alone.

• Rely on the phenomena of swarm intelligence for survival.

• Capable of establishing shortest-route paths from their colony to feeding sources and back.

• Use stigmergic communication via pheromone trails.

Ants….

Ant Colony Optimization (ACO)

• Follow existing pheromone trails with high probability.

• What emerges is a form of autocatalytic behavior: the more ants follow a trail, the more attractive that trail becomes for being followed.

• The process is thus characterized by a positive feedback loop, where the probability of a discrete path choice increases with the number of times the same path was chosen before.

Ants ,contd.

Ant Colony Optimization (ACO)

Ants ,contd.It is well known that the primary means for ants to form and maintain the line is a pheromone trail. Ants deposit a certain amount of pheromone while walking, and each ant probabilistically prefers to follow a direction ,rich in pheromone.

ℙ (𝐶 )<ℙ (𝐵 )<ℙ ( 𝐴 )

ℙ (𝐴)

ℙ (𝐵)

ℙ (𝐶 )

Ant Colony Optimization (ACO)

E

D

CH

B

A

(b)

30 ants

30 ants

15 ants

15 ants15 ants

15 ants

t = 0

d = 0.5

d = 0.5

d = 1

d = 1

E

D

CH

B

A

(a)

E

D

CH

B

A

(c)

30 ants

30 ants

20 ants

20 ants10 ants

10 ants

t = 1

τ = 30

τ = 30

τ = 15

τ = 15

Initial state:no ants

Ant Colony Optimization (ACO)

Pheromone trailsShortest path around an obstacle

This elementary behavior of real ants can be used to explain how they can find the shortest path that reconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path.

Ants are moving on a straight line that connects a food source to their nest.

Let us consider the following scenario:

Ant Colony Optimization (ACO)

Pheromone trailsShortest path around an obstacle

This elementary behavior of real ants can be used to explain how they can find the shortest path that reconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path.

An obstacle appears on the path.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path around an obstacle

This elementary behavior of real ants can be used to explain how they can find the shortest path that reconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path.

Those ants which are just in front of the obstacle cannot continue to follow the pheromone trail and therefore they have to choose between turning right or left. In this situation we can expect half the ants to choose to turn right and the other half to turn left.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path around an obstacle

This elementary behavior of real ants can be used to explain how they can find the shortest path that reconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path.

Those ants which choose, by chance, the shorterpath around the obstacle will more rapidly reconstitute the interrupted pheromone trailcompared to those which choose the longer path. Thus, the shorter path will receive a greater amount of pheromone per time unit and in turn a larger number of ants will choose the shorter path.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path around an obstacle

This elementary behavior of real ants can be used to explain how they can find the shortest path that reconnects a broken line after the sudden appearance of an unexpected obstacle has interrupted the initial path.

Shortest path is being obtained.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Let us describe the algorithm:

A small amount of ants travel randomly around the nest.

N

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

One of the ants find food source.

SN

Pheromone trailsShortest path from the nest to the food source

When ant finds food, it returns to the nest while laying down pheromones trail.

SN

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

When other ants find a pheromone trail, they are likely not to keep travelling at random, but to instead follow the trail.

SN

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

If an ant eventually find food by following a pheromone trail, it returning to the nest while reinforcing the trail with more pheromones.

SN

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Due to their stochastic behavior, some ants are not following the pheromone trails, and thus uncover more possible paths.

SN

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Over time, however, the pheromones trails starts to evaporate, thus reducing its attractive strength.

SN

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Ant Colony Optimization (ACO)

Pheromone trailsShortest path from the nest to the food source

Shortest path is being obtained.

SN

Ants are able, without using any spatial Information, to identify a sudden appearance of a food source around their nest, and to find the shortest available path to it.

Ant Colony Optimization (ACO)

• Let us consider the algorithm more formally. The number of ants M is usually equal to the number of nodes N in the graph.

• A small amount of virtual pheromones is deposited on all edges of the beginning of the search.

• The probability that ant k chooses the edge from node i to node j.

Where = amount of virtual pheromones on that edge .

= visibility of the node computed as the inverse of the edge length .

constant a & b weight the importance of the two factors.

Formal ANT Algorithm

Ant Colony Optimization (ACO)

• If a = 0, ants choose solely on the basis of shortest distance .

• Conversely if b = 0, ants choose solely on the basis of the pheromones amount.

• The divider in the fraction sums up the pheromones and visibility values for the edges H that are available at the node where the ants sits as long as they belong to the set of the nodes that the ants k has not yet visited .

• as soon as the ant visits a node , this is deleted from the list .

• Once all the ants have completed a tour of the graph, each ant k retraces its own path and deposits an amount of pheromones on the travelled edges according to

• where = total length of the path found by ant k.• Q is a constant , which is set to be the length of the shortest path

estimated with a simple heuristic method.

=

Formal ANT Algorithm , contd.

Ant Colony Optimization (ACO)

• The amount of pheromones on each edge after all M ants have retraced their own paths is equal to

• Before starting all ants again in a search for the shortest path, pheromone levels evaporate according to

• Where 0 ≤ ρ ≥ 1 is the coefficient of pheromone evaporation.

• This concludes one iteration of the algorithm. This process is repeated for several

Hundred iterations until satisfactory short path has been found.

∆ =

= (1 - ρ) ∆

Formal ANT Algorithm , contd.

Ant Colony Optimization (ACO)

• Positive Feedback accounts for rapid discovery of good solutions.

• Virtual ants discover and maintain several short paths in addition to the best one because of the probabilistic edge choice.

• Distributed computation avoids premature convergence.

• The greedy heuristic helps find acceptable solution in the early solution in the early stages of the search process.

• The collective interaction of a population of agents.

Some inherent advantages

Ant Colony Optimization (ACO)

• Slower convergence than other Heuristics.

• Performed poorly for TSP problems larger than 75 cities.

• No centralized processor to guide the AS towards good solutions

Disadvantages in Ant Systems

Ant Colony Optimization (ACO)

• ACO is a recently proposed meta-heuristic approach for solving hard combinatorial optimization problems.

• Artificial ants implement a randomized construction heuristic which makes probabilistic decisions.

• The cumulated search experience is taken into account by the adaptation of the pheromone trail.

• ACO Shows great performance with the “ill-structured” problems like network routing.

• In ACO Local search is extremely important to obtain good results.

Conclusions

Ant Colony Optimization (ACO)

Questions, Comments?

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