Ant colony optimization is a metaheuristic algorithm that is inspired by the behavior of real ant colonies. Real ants deposit pheromone on paths between their nest and food sources, and other ants are more likely to follow paths with higher pheromone densities, allowing the colony to find the shortest path over time without centralized control. The algorithm models this behavior to solve optimization problems, with artificial ants probabilistically building solutions and adjusting pheromone levels to bias toward better solutions. The presentation discusses how ant colony optimization works and its components, including probabilistic solution construction, pheromone updating, and evaporation. It then provides an example application of using ant colony optimization for adaptive routing in communication networks.

1. Ant Colony Optimization
For Adaptive Routing
Presented by
Thushara Urumbil
December 7th 2012

2. What we will see today

3. Swarm Intelligence
@Peter Scoones/Getty Images
@Peter Scoones/Getty Images

4. Swarm Intelligence
 Collective effort
 Group of homogeneous members
 Simple interaction methodology
 Self organization
 Distributed problem solving by
dynamically constituting a natural
model

5. Intelligent Ants !!

6. Scientific approach
 Double Bridge Experiment by Jean-
Louis Deneubourg [BDG93]
He concluded that ants chooses the shortest path

7. How do these Blind Deaf Dumb
insects do this ?
 Ants starts to walk random
 They form pheromone trail
 Ants choosing shortest path return home
depositing more pheromone on shorter
path
 Followers choose path with higher
pheromone density
 Pheromone evaporation occurs on less
used path
 Shortest path emerges !!

8. Mathematical modeling of
Ants’ "technique"
The probability of ant choosing the short
branch
𝑃𝑖𝑠(𝑡) =
(𝑡𝑠+ɸ𝑖𝑠(𝑡) 𝜶
(𝑡𝑠+ɸ𝑖𝑠(𝑡) 𝜶+ (𝑡𝑠+ɸ𝑖𝑙(𝑡) 𝜶
𝑡𝑠- Time to travel the shortest branch
ɸ𝑖𝑎- function of pheromone used until
time t where a ∈(s,l)
𝜶 –Derived from Monte Carlo simulations
and the best suited value was 2 [DS04]

9. Moving onto Artificial ants
 Makes use of graphical modeling
Experimental model with 2 nodes

10. Building blocks ..
 The long branch is r times longer than
the short one
 Time is discrete(1,2,3..)
 At each time step ant moves one step
in constant speed
 Ant add one unit of pheromone in one
unit of time in one edge
 Ant starts moving on the graph
probabilistically

11. More on probability
 Pis(t) – Probability for an ant at node i to
choose shortest path at time t
𝑃𝑖𝑠(𝑡) =
(ɸ𝑖𝑠(𝑡) 𝜶
[ɸ𝑖𝑠 𝑡 ] 𝜶+[ɸ𝑖𝑙 𝑡 ] 𝜶
 Pil(t) - Probability for an ant at node i to
choose longest path at time t
𝑃𝑖𝑙(𝑡) =
(ɸ𝑖𝑙(𝑡) 𝜶
[ɸ𝑖𝑠 𝑡 ] 𝜶+[ɸ𝑖𝑙 𝑡 ] 𝜶

12. Maths contd..
Consider mi(t) be the number of ants on node
i at time t
mi(t)= Pjs(t-1)mj(t-1)+𝑃j𝑙(t-r)mj(t-r)
 The pheromone trail on the short branch is
ɸis(t)= ɸis(t-1)+ Pis(t-1) mi(t-1)+ Pj𝑠(t-1) mi(t-1)
 The pheromone trail on the long branch is
ɸi𝑙(t)= ɸi𝑙(t-1)+ Pi𝑙(t-1) mi(t-1)+ Pj𝑙(t-r) m𝑗(t-r)

13. Ant Colony Optimization
Algorithm
 Ant Colony optimization algorithm is developed on the basis of
Deneubourg’s double bridge experiment.
 Designed to work on more complex multinode graphs/networks.
 G = (V , E) where V is the set of vertices (nodes) and E is the
undirected edges connecting the vertices
 When a minimum cost path between source and destination
needs to be done, the modeling is based on the nest and food
source solution from real ants.

14. Properties of ant k
 Ant k explores the network graph G = (V, E) results in optimal
solution s* ∈ S*
 All the ants has a stored memory 𝑀 𝑘 about the path. Ants uses
this memory for computing heuristic values ή for building the
feasible solution and evaluating.
 Ant uses the stored memory 𝑀 𝑘 to retrace the path it has
already traveled
 The start state is 𝑋 𝑠
𝑘 and the termination state is 𝑒 𝑘
 when 𝑒 𝑘 is not satisfied ant moves form state Xr = < Xr−1,i > to
a state < Xr , j > where j is a neighboring node
 The neighboring node j is determined based on the
probabilistic decision rule which is a combination of ant’s
private memory, local pheromone trail and the problem
constraints.
 Once the ants reached destination it is able to retrace the path
back to source.

15. Components of ACO
Probabilistic forward ants and
solution construction
◦ Ants when travelling from source to
destination is in forward motion.
◦ The movement in forward mode is
determined probabilistically and it is
biased by the pheromone intensity of the
preceding ants.
◦ Local information stored on the node is
read by the ant and used in a stochastic
way to decide which node to move to
next

16. Components of ACO
Deterministic backward ants and
pheromone update
◦ After reaching the destination node, the ant
switches from the forward mode to the backward
mode and then retraces step by step the same path
backward to the source node
◦ An explicit local memory is assigned to ants which
will allow it to retrace the path it traveled.
◦ If ant ‘k’ is in the backward mode through edge (i,j),
it changes the pheromone value as
τij = τij + Δ τk

17. Components of ACO
 Pheromone updates based on solution
quality
o Ants which have detected a shorter path deposit
pheromone earlier than ants traveling on a longer
path
oBy making Δ τk to be a function of the path length,
shorter the path will have more amount of
pheromone deposited(biasing future ants to take
shorter paths)
oBy the end of the forward mode ants will be capable
of calculating the best cost path. This result will bias
the quantity of pheromone update during backward
mode. This approach will help in acquiring a faster
best solution

18. Components of ACO
Pheromone evaporation
◦ The pheromone evaporation which happens
naturally in ant colonies is implemented by a
set of pheromone evaporation rules
◦ If there is a better route found then the effect
on the pheromone already deposited on the
existing paths will decay in time
◦ This mechanism, by favoring the forgetting
of errors or of poor choices done in the past,
provides scope for continuous improvement
of the ‘‘learned’’ problem structure

19. ACO Meta-heuristics
Step 1
• Pheromone Information
Step 2
• Solution Construction
Step 3
• Pheromone Update
Step 4
• Stopping Criterion

23. Antnet
 Major challenges of an effective
routing in a communication network
are
 Distributed property:
 Non-deterministic and fluctuating with
time
 Conflicting performance evaluation
criteria
 Balancing reliability and quality

24. Antnet Algorithm
 Data structures

25. Antnet Algorithm: Network
routing

27. Implementation of Antnet
using OMNeT

28. OMNet network module layout

29. Experimental setup of
OMNeT++

30. Structure of NED

32. Questions ?
Thank you
Ok..Class listen !!
This problem might seem
trivial to you , but believe me ,
there are inferior species
existing who still thinks
it’s a hard problem

33. Bibliography
 [BDG93] R. Beckers,J. L. Deneubourg,and S. Goss. Modulation of trail laying in
the ant lasius niger (hymenoptera: Formicidae) and its role in the collective
selection of a food source. Journal of InsectBehavior,1993.
 [CBTT92] Robert F. Cohen,G. Di Battista,R. Tamassia,and Ioannis G. Tollis.A
framework for dynamic graph drawing. CONGRESSUS NUMERANTIUM,42:149--
160,1992.
 [CD97] Gianni Di Caro and Marco Dorigo. Antnet: A mobile agents approach to
adaptive routing. Technical report,1997.
 [CD98] Gianni Di Caro and Marco Dorigo. Antnet: Distributed stigmergetic control
for communications networks. Journal of Artificial Intelligence Research,1998.
 [Com12] OMNeT++ Community. 2001-2012. www.omnetpp.org/.
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Optimization and Swarm Intelligence 4th International Workshop,ANTS
2004,Brussels,Belgium,September 5-8,2004,Proceeding. Springer,2004.

34. Bibliography
 [DS04] Marco Dorigo and Thomas Stützle. Ant Colony Optimization. Bradford
Company,Scituate,MA,USA,2004.
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exploratory pattern of the argentine ant. Journal of Insect Behavior.
 [JLDP90] S. Goss J.-L. Deneubourg,S. Aron and J. M. Pasteels. The
selforganizing exploratory pattern of the argentine ant. Journal of Insect
Behavior,3:159â168,1990.

35. Bibliography
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