Final Ant Colony

8/13/2019 Final Ant Colony

1/23

Ant Colony Optimization

Preparedby:Akshay Raturi, Chitransh Shrivastava, Vishal Dhangar


2/23

Swarm intelligence

Collective system capable of accomplishing difficulttasks in dynamic and varied environments without anyexternal guidance or control and with no centralcoordination

Achieving a collective performance which could notnormally be achieved by an individual acting alone

Constituting a natural model particularly suited to

distributed problem solving


3/23


4/23


5/23


6/23

Natural behavior of an antForaging modes

Wander mode

Search mode

Return mode Attracted mode

Trace mode

Carry mode


7/23

Natural behavior of ant


8/23


Applications: The ant colony optimizationalgorithm(ACO)is a probabilistic

technique for solving computational problems which can be reduced to

finding good paths through graphs.
http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Graph_%28mathematics%29http://en.wikipedia.org/wiki/Graph_%28mathematics%29http://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Algorithm


9/23


Overview:

In the real world, ants (initially) wander randomly, and upon finding food

return to their colony while laying down pheromonetrails. If other ants

find such a path, they are likely not to keep travelling at random, but to

instead follow the trail, returning and reinforcing it if they eventually find

food. 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 faster, and thus thepheromone density remains high as it is laid on the path as fast as it can

evaporate. Pheromone evaporation has also the advantage of avoiding

the convergence to a locally optimal solution.
http://en.wikipedia.org/wiki/Randomhttp://en.wikipedia.org/wiki/Pheromonehttp://en.wikipedia.org/wiki/Pheromonehttp://en.wikipedia.org/wiki/Random


10/23


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.

Thus, 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 positivefeedbackeventually leads all the 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.
http://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Positive_feedback


11/23

http://en.wikipedia.org/wiki/File:Aco_branches.svg


12/23


The original idea comes from observing the

exploitation of food resources among ants, in which

ants individually limited cognitive abilities have

collectively been able to find the shortest path

between a food source and the nest.1. The first ant finds the food source (F), via any way (a), then

returns to the nest (N), leaving behind a trail pheromone (b)

2. Ants indiscriminately follow four possible ways, but the

strengthening of the runway makes it more attractive as the

shortest route.

3. Ants take the shortest route, long portions of other ways

lose their trail pheromones.


13/23


In a series of experiments on a colony of ants with a choicebetween two unequal length paths leading to a source of food,biologists have observed that ants tended to use the shortestroute. A model explaining this behaviour is as follows:1. An ant (called "blitz") runs more or less at random around the

colony;

2. If it discovers a food source, it returns more or less directly to thenest, leaving in its path a trail of pheromone;

3. These pheromones are attractive, nearby ants will be inclined tofollow, more or less directly, the track;

4. Returning to the colony, these ants will strengthen the route;

5. If two routes are possible to reach the same food source, the

shorter one will be, in the same time, traveled by more ants thanthe long route will;

6. The short route will be increasingly enhanced, and thereforebecome more attractive;

7. The long route will eventually disappear, pheromones are volatile;

8. Eventually, all the ants have determined and therefore "chosen"the shortest route.


14/23


Theoretically, if the quantity of pheromone

remained the same over time on all edges,

no route would be chosen. However,

because of feedback, a slight variation onan edge will be amplified and thus allow

the choice of an edge. The algorithm will

move from an unstable state in which noedge is stronger than another, to a stable

state where the route is composed of the

strongest edges.


15/23

General ACO

A stochastic construction procedure Probabilistically build a solution

Iteratively adding solution components to partial

solutions- Heuristic information

- Pheromone trail

Reinforcement Learning reminiscence

Modify the problem representation at each

iteration


16/23

General ACO

Ants work concurrently and independently Collective interaction via indirect

communication leads to good solutions


17/23

Some inherent advantages

Positive Feedback accounts for rapid discoveryof good solutions

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 ofagents.


18/23

Disadvantages in Ant Systems

Slower convergence than other Heuristics Performed poorly for TSP problems larger

than 75 cities.

No centralized processor to guide the AStowards good solutions


19/23

Travelling Salesman Problem (TSP)

TSP PROBLEM : Given N cities, and a distance function d betweencities, find a tour that:

1. Goes through every city once and only once

2. Minimizes the total distance.

Problem is NP-hard

Classical combinatorial

optimization problem to

test.


20/23

ACO for the Traveling Salesman Problem

The TSP is a very important problem in the context ofAnt Colony Optimization because it is the problem to

which the original AS was first applied, and it has later

often been used as a benchmark to test a new idea

and algorithmic variants.

The TSP was chosen for many reasons:

It is a problem to which the ant colony metaphor

It is one of the most studied NP-hard problems in the combinatorial optimization

it is very easily to explain. So that the algorithm behavior is not obscured by

too many technicalities.


21/23

Ant Systems (AS)

Ant Systems for TSP

Graph (N,E): where N = cities/nodes, E = edges

= the tour cost from city i to city j (edge weight)

Ant move from one city i to the next j with some transition probability.

ijd

A

D

C

B


22/23

Ant Systems Algorithm for TSP

Initialize

Place each ant in a randomly chosen city

Choose NextCity(For Each Ant)

more cities

to visit

For Each Ant

Return to the initial cities

Update pheromone level using the tour cost for each ant

Print Best tour

yes

No

Stopping

criteria

yes

No


23/23

THANK YOU

Final Ant Colony

Documents