ant colony optimization-1

8/13/2019 Ant Colony Optimization-1

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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_problem


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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/Pheromone


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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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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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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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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.pdf


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THANKS

ant colony optimization-1

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