Ant colony optimization

HISTORY introduced by Marco Dorigo (MILAN,ITALY) in his doctoral thesis in 1992 Using to solve traveling salesman problem(TSP).traveling salesman problem

INTRODUCTION Ants (blind) go through the food while laying down pheromone trailspheromone 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) J k (i): :set of cities that have not yet been visited by ant k in city i P k (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. tract_2443.pdfhttp://astro2005.abstractsnet.com/pdfs/abs tract_2443.pdf

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