Post on 04-Jun-2018
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Ant Colony Optimization
Preparedby:Akshay Raturi, Chitransh Shrivastava, Vishal Dhangar
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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
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Natural behavior of an antForaging modes
Wander mode
Search mode
Return mode Attracted mode
Trace mode
Carry mode
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Natural behavior of ant
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Ant Colony Optimization
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/Algorithm8/13/2019 Final Ant Colony
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Ant Colony Optimization
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/Random8/13/2019 Final Ant Colony
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Ant Colony Optimization
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_feedback8/13/2019 Final Ant Colony
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Ant Colony Optimization
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Ant Colony Optimization
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.
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Ant Colony Optimization
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.
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Ant Colony Optimization
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.
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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
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General ACO
Ants work concurrently and independently Collective interaction via indirect
communication leads to good solutions
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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.
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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
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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.
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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.
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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
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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
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THANK YOU