Post on 04-Jun-2018
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Ant colony optimization
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HISTORY
introduced by Marco Dorigo
(MILAN,ITALY)in his doctoral thesis in
1992
Using to solve traveling salesman
problem(TSP).
http://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problem8/13/2019 Ant Colony Optimization-1
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INTRODUCTION
Ants (blind) go through the food whilelaying down pheromonetrails
Shortest path is discovered via pheromone
trails each ant moves at random (first)
pheromone is deposited on path
Shorter path, more pheromone rails (positivefeedback sys)
ants follow the intense pheromone trails
http://en.wikipedia.org/wiki/Pheromonehttp://en.wikipedia.org/wiki/Pheromone8/13/2019 Ant Colony Optimization-1
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introduction
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Algorithm parameters
attractiveness
Trails (pheromones)
evaporation
ACO
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ALGORITHM
Each ant located at city i hops to a city j selectedamong the cities that have not yet been visitedaccording to the probability.
d(i,j):attractiveness, d(i,j)is the function
which is chosen to the inverse of the cost. t(i,j) :the trail level t(i,j) of the move, indicating theamount of pheromone trail on edge (i,j)
Jk(i): :set of cities that have not yet been visited byant k in city i
Pk(i,j): Probability that ant k in city i will go to city j
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ALGORITHM Once a tour has been completed (i.e. each city has been visited exactly once by
the ant) pheromone evaporation the edges are calculated and then each antdeposits pheromone on the complete tour by a quantity which is calculated by the
following formula:
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Formal Ant Cycle
Trail UpdateConstruction
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Formal Ant Cycle
1. {Initialization} Initialize tij and hij, "(ij).
2. {Construction}For each ant k (currently in state i) do
repeat choose in probability the state to move into.
append the chosen move to the k-th ant's set tabuk.
until ant k has completed its solution.
end for
3. {Trail update}
For each ant move (ij ) do compute Dtij update the trail matrix.
end for
4. {Terminating condition} If not(end test) go to step 2
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Advantages & Disadvantages
Can be used in dynamic applications (adapts to
changes such as new distances, etc.)
Has been applied to a wide variety ofapplications
As with GAs, good choice for constraineddiscrete problems (not a gradient-based
algorithm)
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Advantages & Disadvantages
Theoretical analysis is difficult:
Due to sequences of random decisions (not
independent)
Probability distribution changes by iteration
Research is experimental rather than
theoretical
Convergence is guaranteed, but time to
convergence uncertain
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Advantages & Disadvantages
Tradeoffs in evaluating convergence: In NP-hard problems, need high-quality solutions quicklyfocus
is on quality of solutions
In dynamic network routing problems, need solutions forchanging conditionsfocus is on effective evaluation ofalternative paths
Coding is somewhat complicated, not straightforward Pheromone trail additions/deletions, global updates and local
updates Large number of different ACO algorithms to exploit different
problem characteristics
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Advantages & Disadvantages
Compared to GAs (Genetic Algorithms):
retains memory of entire colony instead of
previous generation only
less affected by poor initial solutions (due tocombination of random path selection and
colony memory)
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Appliaction in IMRT
The main use of Ant Colony Optimization
in IMRT is in Beam Angle Optimization
(BAO) part.
Ex. ACO is implemented for BAO by
Yonjie.Le.
http://astro2005.abstractsnet.com/pdfs/abs
tract_2443.pdf
http://astro2005.abstractsnet.com/pdfs/abstract_2443.pdfhttp://astro2005.abstractsnet.com/pdfs/abstract_2443.pdfhttp://astro2005.abstractsnet.com/pdfs/abstract_2443.pdfhttp://astro2005.abstractsnet.com/pdfs/abstract_2443.pdf8/13/2019 Ant Colony Optimization-1
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THANKS