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IE 607 Heuristic Optimization
Ant Colony Optimization
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Double Bridge Experiment
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Behavior of Real Ants
Real Ants Find the Shortest Path to Food Resource
Pheromone Is Laid by Ants along the Trail
Pheromone Evaporates over Time
Pheromone Intensity Increases with Number of Ants
Using Trail
Good Paths Are Reinforced And Bad Paths Gradually
Disappear
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ACO
Meta-Heuristic Optimization Method
Inspired by Real Ants
First published by Marco Dorigo (1992) as his dissertation
Is currently greatly expanding in applications and interest,
mainly centered in Europe
Positive & Negative Feedback
Constructive Greedy Heuristic
Population-based Method
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Application
TSP QAP VRP Telecommunication Network Scheduling Graph Coloring Water Distribution Network etc
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Methodology
ACO Algorithm
Set all parameters and initialize the pheromone trails
Loop
Sub-Loop
Construct solutions based on the state transition rule
Apply the online pheromone update rule
Continue until all ants have been generated
Apply Local Search
Evaluate all solutions and record the best solution so far
Apply the offline pheromone update rule
Continue until the stopping criterion is reached
ACO
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Methodology
Each ant represents a complete solution Online updating is performed each time after an ant
constructed a solution: more chance to exploration Local search is applied after all ants construct
solutions Offline updating is employed after the local search:
allow good ants to contribute
Overview of ACO Algorithm
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Methodology
: Pheromone trail of combination (i,j)
: Local heuristic of combination (i,j)
: Transition probability of combination (i,j)
: Relative importance of pheromone trail
: Relative importance of local heuristic
: Determines the relative importance of exploitation versus exploration
: Trail persistence
Parameters of ACO Algorithm
ij
ij
ijP
0q
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Ant System (AS) – the earliest version of ACO
State Transition Probability
Pheromone Update Rule
Ulilil
ijijijP
)()(
)()(
NA
k
kij
oldij
newij
1
,Qkij
ij
kij d
Q k
kij L
Qor
Methodology
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ASelite
ASrank
eij
NA
k
kij
oldij
newij
1
eij
e
r
rij
oldij
newij
1
1
eeij L
Qe
rrij L
Qre )(
Methodology
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Ant-Q & Ant Colony System (ACS)
Local Updating
(Online Updating)
Global Updating
(Offline Updating)
V
vilil
Ul])()[(maxarg
0
0
Ulilil
ivivivP
)()(
)()(
0)1( oldij
newij
eij
oldij
newij )1(
Exploitation
Exploration
Methodology
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Max-Min Ant System (MMAS)
ANTS
eij
oldij
newij maxmin ij
Ulilil
ijijijP ])1([
)1(
)1(0 LBL
LBL
avg
kkij
NA
k
kij
oldij
newij
1
Methodology
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Website & Books
http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html Bonabeau E., M. Dorigo & T. Theraulaz (1999).
From Natural to Artificial Swarm Intelligence. New York: Oxford University Press.
Corne D., M. Dorigo & F. Glover, Editors (1999). New Ideas in Optimisation. McGraw-Hill .