Swarm Intelligence

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Swarm Intelligence

• So far we have formulated problems based on an
  "Evolutionary behaviour" metaphor
• i.e.

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Swarm Intelligence

• Now we will use a "social insect behaviour"
  metaphor .

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Swarm Intelligence

• Objective
• the design of adaptive, decentralised, flexible
  artificial problem solving systems inspired by
  the behaviour of social insects
• e.g
• termites
• bees
• and ants

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Swarm Intelligence

• two important characteristics of insect
  societies
• self-organisation
• stigmergy
• self-organisation
• global structures emerge from the interaction of
  simple lower level components.
• eg
• global structure the identification of a food
  source close to the nest.
• lower level components the seemingly random
  movement of insects around the landscape.

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Swarm Intelligence

• two important characteristics of insect
  societies
• self-organisation
• stigmergy
• stigmergy
• mechanisms exploited by social insects to
  coordinate and control their activity via
  indirect interactions.
• eg
• a termite does not direct the building of a nest
  but is guided by it

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Swarm Intelligence

• Social insect behaviours include
• foraging
• division of labour
• clustering and sorting
• building
• co-operation and transport
• problem solving algorithms can be based on each
  of these

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Swarm Intelligence

• Problem formulation
• Graphs
• nodes and edges
• directed and undirected
• eg Travelling salesman problem (TSP) as a
  symmetric directed graph.
• Four cities (A,B,C D), the distance from A to B
  is the same as for B to A etc

A
B
D
C
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Swarm Intelligence

• The map colouring problem as an undirected graph
• For the six mainland states and territories of
  Australia

NSW
NT
Q
WA
V
SA
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Swarm Intelligence

• The basic ANT algorithm for the TSP problem
• How can an ant' solve the problem?
• place an ant at a randomly selected city.
• create a tour' by visiting other cities.
• ants remember' which cities they still have to
  visit.
• evaluate the length of the tour and identify
  the shortest .
• and finally, there are a lot of ants!

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Swarm Intelligence

• the issue becomes, how does an ant determine
  which city to visit next?
• we determine which city has the greatest
  probability of being selected.
• to do this the foraging metaphor is used, more
  particularly the pheromone trail
• the search is directed by a pheromone and a
  visibility matrix.
• the pheronome matrix has an entry for each path
  and reflects the amount of pheronome deposited
  by ants as they use the path.
• the visibility matrix is the inverse of the
  distance matrix

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Swarm Intelligence

• For the cities that form the basis of tutorial 4
  the distance matrix would be

so the visibility matrix is the inverse of this
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Swarm Intelligence

• The probability that city j will be visited next
  by an ant, currently at city i is

is the entry in the pheronome matrix for the path
between city i and city j.
is the entry in the visibility matrix for the
path between city i and city j.
a and ß are two parameters ( 0) that control the
relative importance of each matrix
summation of all still to be visited
J is the set of cities still to be visited by the
ant.
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Swarm Intelligence

• Note the visibility matrix is constant during
  the search, whereas the pheronome matrix is
  constantly updated to reflect the usage of a path
  and the evaporation of the chemical.

• The algorithm
• initialise pheronome matrix.
• create visibility matrix
• place each ant, a, randomly at a city
• for each ant create the set J
• let T be the shortest tour(path) found and L
  the length
• let tmax be the maximum number of iterations
• For t 1 to t tmax
• apply pheronome decay
• For each ant, a
• Build a tour Ta(t), applying the following
  (cities -1) times.
• Choose next city j by applying.

End For For each ant compute La(t) of the tour
Ta(t) If an improved tour is found, update T and
L Update the pheronome matrix
End For
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Swarm Intelligence

• Sample application areas
• eg routing in telecommunication networks

• Not all nodes are directly connected.
• Objective is maximise network performance and
  minimise cost (eg performance costs such as
  delay, throughput, call rejection).
• Dynamic in nature.

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Swarm Intelligence