# Ant Colony Optimization

Topics: Ant colony optimization, Ant, Travelling salesman problem Pages: 7 (1415 words) Published: August 1, 2013
Ant Colony Optimization

EDWIN WONG PHILLIP SUMMERS ROSALYN KU PATRICK XIE PIC 10C SPRING 2011

Swarm Intelligence
Swarms
Swarm of bees Ant colony as swarm of ants Flock of birds as swarm of birds Traffic as swarm of cars Immune system as swarm of cells and molecules ...

Swarm Intelligence/Agent Based Modeling
Model complex behavior using simple agents

Swarm Intelligence
Digital Crumbs a la Hansel and Gretel
Idea: stigmergy is a mechanism of communication by modifying the environment Example Take some dirt in your mouth Moisten it with pheromones Walk in the direction of the strongest pheromone concentration Drop what you are carrying where the smell is the strongest

Ant Colony Optimization uses artificial stigmergy

Swarm Intelligence
Ant Colony Optimization
Marco Dorigo (1991) – PhD thesis

Technique for solving problems which can be expressed as finding good paths through graphs Each ant tries to find a route between its nest and a food source

Swarm Intelligence
The behavior of each ant in nature
Wander randomly at first, laying down a pheromone trail If food is found, return to the nest laying down a pheromone trail If pheromone is found, with some increased probability follow the pheromone trail Once back at the nest, go out again in search of food

However, pheromones evaporate over time, such that unless they are reinforced by more ants, the pheromones will disappear.

Ant Colony Optimization
1. The first ant wanders randomly until it finds the food

source (F), then it returns to the nest (N), laying a pheromone trail

Ant Colony Optimization
2.

3.

Other ants follow one of the paths at random, also laying pheromone trails. Since the ants on the shortest path lay pheromone trails faster, this path gets reinforced with more pheromone, making it more appealing to future ants. The ants become increasingly likely to follow the shortest path since it is constantly reinforced with a larger amount of pheromones. The pheromone trails of the longer paths evaporate.

Ant Colony Optimization
Paradigm for optimization problems that can be expressed as finding short paths in a graph Goal To design technical systems for optimization, and NOT to design an accurate model of nature

Ant Colony Optimization
Nature Natural habitat Nest and food Ants Visibility Pheromones Foraging behavior Computer Science Graph (nodes and edges) Nodes in the graph: start and destination Agents, our artificial ants The reciprocal of distance, η Artificial pheromones ,τ Random walk through graph (guided by pheromones)

Ant Colony Optimization
Scheme:
Construct ant solutions Define attractiveness τ, based on experience from previous solutions Define specific visibility function, η, for a given problem (e.g. distance)

Ant walk
Initialize ants and nodes (states) Choose next edge probabilistically according to the attractiveness and visibility

Each ant maintains a tabu list of infeasible transitions for that iteration Update attractiveness of an edge according to the number of ants that pass through

Ant Colony Optimization
Pheromone update

Parameter is called evaporation rate Pheromones = long-term memory of an ant colony ρ small ρ large low evaporation high evaporation slow adaptation fast adaptation

Note: rules are probabilistic, so mistakes can be made! “new pheromone” or Δτ usually contains the base attractiveness constant Q and a factor that you want to optimize (e.g. ) Q/length of tour

General Ant Colony Pseudo Code
Initialize the base attractiveness, τ, and visibility, η, for each edge; for i < IterationMax do: for each ant do: choose probabilistically (based on previous equation) the next state to move into;

add that move to the tabu list for each ant; repeat until each ant completed a solution; end; for each ant that completed a solution do: update attractiveness τ for each edge that the ant traversed; end; if (local best solution better than global solution) save...

References: Dorigo M, Stützle T. Ant Colony Optimization. MIT Press; 2004 Vittorio Maniezzo, Luca Maria Gambarde, Fabio de Luigi. http://www.cs.unibo.it/bison/publications/ACO.pdf Monash University CSE 460 lecture notes http://www.csse.monash.edu.au/~berndm/CSE460/Lectu res/cse460-9.pdf “Ant colonies for the traveling salesman problem” http://www.idsia.ch/~luca/acs-bio97.pdf