Swarm Intelligence Ant-based Algorithms Reference Various research - - PowerPoint PPT Presentation

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Swarm Intelligence Ant-based Algorithms Reference Various research - - PowerPoint PPT Presentation

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Swarm Intelligence Ant-based Algorithms Reference Various research papers & online material Ant Algorithms 1 Swarm Intelligence Originated from the study of colonies, swarms of social organism Studies of the social behaviour of

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Ant Algorithms 1

Swarm Intelligence

Ant-based Algorithms Reference Various research papers & online material

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Ant Algorithms

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Swarm Intelligence

Originated from the study of colonies, swarms of social organism

Studies of the social behaviour of organisms (individuals) in swarms lead to the design of very efficient algorithms

the foraging behaviour of ants resulted in ant colony optimization algorithms

simulation studies of the graceful, but unpredictable, choreography of bird flocks results in Particle swarm optimization

A very young field in computer science, with much potential

..lots of possibilities to discover!

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Ant Algorithms

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Ant System

Swarm Intelligence Algorithm

Based on real life animal swarms/groups

Exhibit efficient ways to solve problems

Ant System

Developed by Marco Dorigo, 1991

Modeled after real life ant colonies, based on results of experiment by Goss

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Ant Algorithms

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Ant-based algorithms

 Ant-based systems are a population-based stochastic search

methods.

 Sound familiar- it is similar to genetic algorithms

 There is a population of ants, with each ant finding a solution

and then communicating with the other ants, how?

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Ant Algorithms

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Ants!!

 Biological Inspiration  Trail between nest and food  Communicate via pheromone

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Ant Algorithms

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Real Ant Optimization

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Ant Algorithms

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Real Ant Optimization

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Ant Algorithms

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Real Ant Optimization

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Ant Algorithms

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Real Ant Optimization

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Ant Algorithms

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Ant System

Experiment by Goss et al ’89

Ants started at nest

Food placed some distance away

Paths of different length between nest and food

Ants found shortest path!

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Ant Algorithms

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Ant System

When ants travel they mark their path with substance called pheromone

Attracts other ants

When an ant reaches a fork in its path the direction it follows is based

  • n amount of pheromone it detects

Decision probabilistically made

This causes positive feedback situation (i.e. Choosing a path increases the probability it will be chosen)

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Ant Algorithms

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Ant algorithms

We need to explore the search space, rather than simply mapping a route

  • Ants should be allowed to explore paths and follow the best paths with

some probability in proportion to the intensity of the pheromone on a given edge/trail.

If the ants simply follow the path with the highest amount of pheromone on it, our search will quickly likely settle on a very sub-

  • ptimal solution
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Ant Algorithms

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Ant algorithms

  • The probability of an ant following a certain route is a function
  • f both the pheromone intensity, and of what the ant can see.
  • Furthermore, the pheromone trail must not build unbounded,

hence evaporation is needed.

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Ant Algorithms

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Ant System

Group of ants start at home/nest

An initial amount of pheromone already placed on edges

Travel on edges

Edges contain pheromone amount

Visit nodes

Probability of Selecting next node

Based on distance between nodes and pheromone amount

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Ant Algorithms

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Ant System

Ants travel from node to node until end

 decision based on transition probability (called state transition)

Once all ants finished

 Solutions compared  Pheromone evaporation applied to all edges  Pheromone increased along each edge of best/each ant’s path

 Original ant system: at each iteration, the pheromone values are

updated by all the ants that have build a solution in the iteration itself.

 Daemon activities can be run (like local search)

Redo until termination criteria met

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Ant Algorithms

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Ant System

Set parameters, initialize pheromone trails SCHEDULE_ACTIVITIES ConstructAntSolutions DaemonActions {optional} UpdatePheromones END_SCHEDULE_ACTIVITIES

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Ant Algorithms

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Requirements

 Problem being solved must be in graphical format

 Since algorithm is based on path finding behavior  Not always apparent

 Must be finite (must have a start and end)

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Ant Algorithms

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Algorithm

 While ( termination not satisfied )

 create ants  Starting point depends on problem constraints  Initial pheromone is > 0, but very small  Find solutions  Pheromone update  Daemon activities {optional}

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Ant Algorithms

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Algorithm

While ( termination not satisfied )

 create ants  Find solutions

 Transition probability:

 Pheromone update  Daemon activities {optional}

            

nodes allowed

1 ) ( 1 ) ( ) (

j ij ij ij ij i

d t d t t P j

   

 

Quantity of pheromone Heuristic distance α,β constants

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Ant Algorithms

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   

) , (

) ( ) 1 ( ) 1 (

j i edge used that Colony k k ij ij

L Q t t   

Algorithm

 While ( termination not satisfied )

 create ants  Find solutions  Pheromone update  Daemon activities {optional}

Evaporation rate Pheromone laid by each ant that uses edge (i,j)

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Ant Algorithms

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Algorithm

 While ( termination not satisfied )

 create ants  Find solutions  Pheromone evaporation  Daemon activities {optional}

 Usually, a local search algorithm is employed here  May also appear after “Find solutions” stage

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Ant Algorithms

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Ant System

State Transition

Pheromone Evaporation

Pheromone Update

Where,

            

nodes allowed

1 ) ( 1 ) ( ) (

j ij ij ij ij i

d t d t t P j

   

 

) ( ) ( n t n t

ij ij ij

       

            

  • therwise

far so best f Q n t

evaluation ij

, ) _ _ ( ) ( 

parameters defined user , deposit to pheromone

  • f

quantity constant t coefficien n evaporatio j to i node from travel y to probabilit j and i nodes between distance j to i nodes from edge

  • n

pheromone

  • f

quantity           Q p d

ij ij ij

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Ant Algorithms

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Problems

 Ant System tends to converge quickly

This means that its exploitation of the best solution found is too high, it should be exploring solution space more

 Pheromone evaporation/update rule (better rule may exist)

what is the evaporation rate?

 Led to extensions of the ant system

 MAX-MIN Ant system  Ant colony system  Foot-Stepping  Others (will not be discussed)

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Ant Algorithms

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Ant Colony System

Most popular/interesting contribution of ACS is

introduction of a local pheromone update in addition to the pheromone update performed at the end of the construction process (known as offline pheromone update)

Local pheromone update is performed by all ants after each construction step

Each ant applies it only to the last edge traversed: where is the pheromone decay coefficient

฀  ij  (1). ij  . 0

฀   (0,1)

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Ant Algorithms

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Ant Colony System (ACS)

 Pseudo-random proportional rule

 Best is chosen with probability q  Otherwise use regular Edge Selection rule

 Local pheromone update

 Amount of pheromone is reduced as ants use the edge   Minimum pheromone limit

 Pheromone update done only by best ant

) 1 (          

ij ij

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Ant Algorithms

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Max-Min Ant System (MMAS)

 Only best ant add pheromone  Max and Min pheromone limits  Initially all pheromone is Max  System restart when approaching stagnation

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Ant Algorithms

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ACO Meta-heuristic

Set parameters, initialize pheromone trails SCHEDULE_ACTIVITIES ConstructAntSolutions DaemonActions {optional} UpdatePheromones END_SCHEDULE_ACTIVITIES

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Ant Algorithms

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ACO for TSP

 Input: set of cities given, and distance between each

city is known

 Goal: Find the shortest tour that allows each city to

visited exactly once.

 ACO algorithm

set parameters, initiliaze pheromone trails while termination condition not met do ConstructAntSolution ApplyLocal search (optional) UpdatePheromones EndWhile

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Ant Algorithms

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ACO-TSP (Diagrams by A. Runka, Brock)

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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ACO-TSP

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Ant Algorithms

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Ant Algorithms - Applications

  • Marco Dorigo, who did the seminal work on ant algorithms,

maintains a WWW page devoted to this subject

  • http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html

Check this site further information about ant algorithms, tutorial, software, applications and main publications.