Ant colony optimization

HISTORY

• introduced by Marco Dorigo (MILAN,ITALY) in his doctoral thesis in 1992

• Using to solve traveling salesman problem(TSP).

INTRODUCTION

• Ants (blind) go through the food while laying down pheromone trails

• Shortest path is discovered via pheromone trails– each ant moves at random (first)– pheromone is deposited on path– Shorter path, more pheromone rails (positive

feedback sys)– ants follow the intense pheromone trails

introduction

Algorithm parameters

attractiveness

Trails (pheromones)

evaporation

ACO

ALGORITHM

• Each ant located at city i hops to a city j selected among the cities that have not yet been visited according 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 the amount of pheromone trail on edge (i,j)

• Jk(i): :set of cities that have not yet been visited by ant k in city i

• Pk(i,j): Probability that ant k in city i will go to city j

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 ant deposits pheromone on the complete tour by a quantity which is calculated by the

following formula:

Formal Ant Cycle

Trail UpdateConstruction

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

Advantages & Disadvantages

• Can be used in dynamic applications (adapts to changes such as new distances, etc.)

• Has been applied to a wide variety of applications

• As with GAs, good choice for constrained discrete problems (not a gradient-based algorithm)

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

Advantages & Disadvantages

• Tradeoffs in evaluating convergence:– In NP-hard problems, need high-quality solutions quickly – focus

is on quality of solutions– In dynamic network routing problems, need solutions for

changing conditions – focus is on effective evaluation of alternative 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

Advantages & Disadvantages

• Compared to GAs (Genetic Algorithms):– retains memory of entire colony instead of

previous generation only– less affected by poor initial solutions (due to

combination of random path selection and colony memory)

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/abstract_2443.pdf

THANKS