Ant Colony Optimization: Routing

TEMPLATE: ADRIAN WILKE
Ant Colony Optimization

University of Paderborn
Bio-Inspired Networking Seminar
January 18, 2011
Adrian Wilke

Talk focus: Routing

Ant Colony Optimization - Adrian Wilke January 18, 2011 2

History: Double bridge experiments
[Goss et al., 1989]

r = ratio of long to short branch


History: Double bridge experiments
[Deneubourg et al., 1990]

Analogy
Students on
a campus:
The more a
point is passed,
the more the
vegetation is
trampled.


From real behaviour to artificial systems

• Stigmergy: Indirect • Possible fields?
communication through Optimization problems,
modifications in environment routing
[Caro and Dorigo, 1998]
• Routing: Direct data flow
• Where to store pheromone from source to destination
in distributed systems? (Shortest path)

• Evaporation? (Pheromone • Congestion?
decreases over time) (Too much load)


Introductory example
Positive feedback

(a) (b) (c) (d)
Exploring Pheromone Additional Shortest
trail node path


Ant System
[Dorigo et al., 1996]

“A new general-purpose heuristic algorithm [...]
to solve different optimization problems”

Covered topics

• Path selection: Choice of the next node
• Updating pheromone
• Ant System algorithm


Ant System: Transition probability
Path selection

??


Choice of the next node

 α β
[τij (t)] ·[νij ]

 α β if j ∈ alloweda
a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise




 α β

a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise


τij (t) is the intensity of trail on edge (i, j) at time t.



 α β

a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise


dij is the euclidean distance i − j between two nodes i and j.
1
νij = dij
is called the visibility. Smaller distance → higher visibility.



 α β

a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise


1
νij = dij
α is the weight of the trail (Simulation: α = 1).
β is the weight of the visibility (Simulation: β = 5).



 α β

a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise


1
νij = dij
a
Denominator of fraction ensures that pij (t) = 1.
j∈N



 α β

a
pij (t) = [τiy (t)] ·[νiy ] (1)
 y ∈alloweda
0 otherwise


1
νij = dij
a
Denominator of fraction ensures that pij (t) = 1.
j∈N

tabua is the tabu list of nodes, which were alredy visited by the ath ant.
alloweda N − tabua is the list of nodes, which were not visited by the ath ant.



α β
... = α β
α=1
[τiy (t)] ·[νiy ]
y ∈alloweda
β=5

Greedy:

??



α β
... = α β
α=1
[τiy (t)] ·[νiy ]
y ∈alloweda
β=5

Greedy:

??
(Image source: [Dorigo et al., 1996])


Ant System
Updating pheromone

S S
?
? S

D D D


Ant System
Updating pheromone

Q
a La if ath ant uses edge (i, j) in its tour
∆τij = (2)
0 otherwise
Q is a constant, “its inﬂuence was found to be negligible.”
La is the length of the tour of the ath ant.


Ant System
Updating pheromone

Q
∆τij = (2)
0 otherwise

m
a
∆τij = ∆τij (3)
a=1


Ant System
Updating pheromone

Q
∆τij = (2)
0 otherwise

m
a
∆τij = ∆τij (3)
a=1

τij (t + n) = ρ · τij (t) + ∆τij (4)
ρ ρ < 1 is a constant , which represents the evaporation of trail.


Ant System
Algorithm: All together

Require: NCMAX
NC ← 0 and t ← 0 and s ← 1
∆τij ← 0
τij (t) ← c
shortestTour ← ∞

for all ants a = 1 to m do
tabua (s) = choose start node
end for


Ant System

Require: NCMAX
NC ← 0 and t ← 0 and s ← 1
∆τij ← 0
τij (t) ← c

tabua (s) = choose start node
end for

repeat { // Each cycle

repeat
s ←s +1
a
move a to next node j by pij (t)
insert node j in tabua (s)
end for
until s = n


Ant System

Require: NCMAX for all ants a = 1 to m do
NC ← 0 and t ← 0 and s ← 1 compute length La of tabua
∆τij ← 0 shortestTour ← update(tabua , La )
τij (t) ← c end for
for all edges (i, j) and all ants a = 1 to m do
for all ants a = 1 to m do compute ∆τij a
tabua (s) = choose start node compute ∆τij
end for end for

repeat { // Each cycle for all edges (i, j) do
compute τij (t + n)
repeat ∆τij ← 0
s ←s +1 end for
a
move a to next node j by pij (t)
insert node j in tabua (s)
end for
until s = n


Ant System

Require: NCMAX for all ants a = 1 to m do
NC ← 0 and t ← 0 and s ← 1 compute length La of tabua
∆τij ← 0 shortestTour ← update(tabua , La )
τij (t) ← c end for
for all edges (i, j) and all ants a = 1 to m do
for all ants a = 1 to m do compute ∆τij a
tabua (s) = choose start node compute ∆τij
end for end for

repeat { // Each cycle for all edges (i, j) do
compute τij (t + n)
repeat ∆τij ← 0
s ←s +1 end for
a
move a to next node j by pij (t) NC ← NC + 1 and t ← t + n
insert node j in tabua (s) move a to tabua (1) and clear tabua (2 . . . n)
end for
until s = n } until NC < NCMAX and no stagnation
return shortestTour


Ant System
Some results

• Oliver30 problem
(30 nodes TSP)
• Columns: basic
heuristic and
improvements
• Entries: Solutions

• Ant System outperformed 2-opt
But: Longer computational time
• Best-known solution in less than 400 cycles,
100 cycles for values under 430
• As effective or better than some general-purpose heuristics


From Ant System to AntNet

Ant System AntNet
• Focus: General-purpose • Focus: Internet Protocol
heuristic with irregular topology
• Global data structure • Routing table


AntNet: Data structures
[Caro and Dorigo, 1998]

Routing table Traffic model Queues
destinations destinations low priority
mean
neighbours

variance - data packets
time - forward ants

high priority
probabilistic
traffic distribution
desirability backward ants

node identifiers s k x
elapsed time 0 5 8 x


AntNet
Algorithm in short

• At time intervals: Forward ant is launched to a destination
Choice of destination: Data ﬂow to possible targets
• Next node on a tour is chosen by
the routing table entries and queue lengths of neighbours
• At nodes on path, forward ant memorizes
the current node ID and the time from source node
• At a destination the forward ant is destroyed and a
backward ant is launched
• Backward ants use the known paths back and
update the routing table entries and
the trafﬁc model on path nodes


From AntNet to Mobile ad hoc networks

AntNet
• Introduced: Routing tables
• Approach works for IP

• What about dynamic networks
with leaving nodes

From AntNet to Mobile ad hoc networks

AntNet MANETs
• Introduced: Routing tables • Mobile ad hoc networks
• Approach works for IP • Restriction:
Limited bandwidth
• No central component,
no ﬁxed infractructure
• Dynamic structure:
Nodes are joining
and leaving
→ Paths can
become useless

• What about dynamic networks
with leaving nodes

AntHocNet
[Di Caro et al., 2005]

An approach for MANETs

• Hybrid approach:
• Reactive path setup phase

• Proactive maintenance

• Also of interest:

• Pheromone updates


AntHocNet
Reactive path setup

• Node s wants to reach d • Same generation: only best
• Unicast, if pheromone • First hop different:
available. Else: broadcast Acceptance factor 0.9


AntHocNet
Pheromone updates

Pheromone calculated by backward ants
using a known Path P

Mathematical Informal
î î i
Tmac = α · Tmac + (1 − α) · tmac Time to send a packet form a
node i (Running average)
î i î
Ti+1 = (Qmac + 1) · Tmac Time for packets in queue (+1)
ˆ n−1 ˆ i
TP = i=1 Ti+1 Time for whole path
ˆ
T i +h·T
i
τd = d 2 hop Consider unloaded conditions
i i
Tnd = γ · Tnd + i
(1 − γ) · τd Final routing table entry
(Running average)


AntHocNet
Proactive probing & exploration

• No broadcast:
• Probe of path

• Broadcast:
• Improve paths
• Path variations


AntHocNet
Proactive maintenance

HelloMessages Link failures
• Every 1 sec: HelloMessage • Neighbors which lost best
(Just senders address) path: Also broadcast
• Received HelloMessage LinkFailureNotification
→ Add in routing table Failed transmission
Link failures • Broadcast PathRepairAnt
• 2 HelloMessages missing: (like reactive forward ant)
• Remove from routing table • But: Max. 2 broadcasts
• Broadcast
LinkFailureNotification
• LinkFailureNotification: List
of destinations to which best
path lost & new best delay


AntHocNet
Proactive maintenance

HelloMessages Link failures
• Every 1 sec: HelloMessage • Neighbors which lost best
(Just senders address) path: Also broadcast
• Received HelloMessage LinkFailureNotification
→ Add in routing table Failed transmission
Link failures • Broadcast PathRepairAnt
• 2 HelloMessages missing: (like reactive forward ant)
• Remove from routing table • But: Max. 2 broadcasts
• Broadcast
LinkFailureNotification Task for you:
• LinkFailureNotification: List • Count the broadcasts
of destinations to which best on this page!
path lost & new best delay


From AntHocNet to HOPNET

AntHocNet HOPNET
• Reactive path setup phase • Hybrid approach
• Proactive maintenance • Avoid overhead and
• Results: Better than AODVa achieve scalability
except for overhead • Idea: Use Zones

• Inside zones:
Proactively maintained

• Between zones:
Reactive part, on demand

a
AODV: Ad-hoc on-demand distance vector routing,
“reference algorithm in area”

HOPNET: Routing tables
[Wang et al., 2009]

Intrazone routing table Interzone routing table

• Inside zones • Between zones
• Proactively maintained • Reactive part, on demand
• Size: Nodes in zone × • Used, if destination not in
Node degree (neighbours) Intrazone routing table
Pheromone Destination
Visited times Sequence number
Hops Between node and Path
nodes in zone Expire
Sequence number
Incremented each time
f./b.-ants are generated

HOPNET example

S wants to send data to T.
(Reworked example from paper)


HOPNET example

T not in zone.
S sends external forward ant to pheripheral nodes.


HOPNET example

D sends external forward ant to K and M,
the other ants are destroyed.


HOPNET example

M sends external forward ant to pheripheral nodes,
except of S and A.


HOPNET example

T is in intrazone routing tables.
Two paths were found.
A backward ant is launched.

HOPNET: Pheromone updates I
Source update algorithm

Internal forward ants update pheromone during movement

vs
Vs Vi Vj vi
vl

ϕ(vi , vs ) = ϕ(vi , vs ) +
T (vs , vi ) + w (vi , vj )

constant
Pheromone(neighbor , source)+ =
time(vs , vi ) + timeOnLink

ϕ(vl , vs ) = ϕ(vl , vs ) · (1 − E ), ∀ l = i


HOPNET: Pheromone updates II
Updates by backward ants

Backward ants update pheromone

vD
vb VS Vk Vb VD
vl

ϕ(vb , vD ) = ϕ(vb , vD ) +
T (vS , vD ) − T (vS , vk )

ϕ(vl , vD ) = ϕ(vl , vD ) · (1 − E ), ∀ l = b


HOPNET
Results: Overhead and Scalability


Summary

Overview
• History: Double bridge experiments
• Ant System: First approach
• AntNet: Wired IP networks
• AntHocNet: First MANET approach
• HOPNET: MANET with zones

To take away
• Stigmergy: Indirect communication through
modiﬁcations in environment
• Routing table for pheromone
• Proactive and reactive parts


Thank you for your attention

1

1
Source: http://xkcd.com/638/, Found: http://www.idsia.ch/˜gianni/

References I

[Bonabeau et al., 1999] Bonabeau, E., Dorigo, M., and Theraulz, G. (1999).
Swarm Intelligence.
Oxford University Prress.
[Caro and Dorigo, 1998] Caro, G. D. and Dorigo, M. (1998).
AntNet: Distributed Stigmergetic Control for Communications Networks.
Journal of Artiﬁcial Intelligence Research, 9:317–365.
[Deneubourg et al., 1990] Deneubourg, J.-L., Aron, S., Goss, S., and Pasteels, J. M. (1990).
The Self-Organizing Exploratory Pattern of the Argentine Ant.
Journal of lnsect Behavior, 3(2).
[Di Caro et al., 2005] Di Caro, G., Ducatelle, F., and Gambardella, L. M. (2005).
AntHocNet: an adaptive nature-inspired algorithm for routing in mobile ad hoc networks.
European Transactions on Telecommunications, 16(5):443–455.
[Dorigo et al., 1996] Dorigo, M., Maniezzo, V., and Colorni, A. (1996).
Ant system: optimization by a colony of cooperating agents.
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 26(1):29–41.
[Dorigo and Stutzle, 2004] Dorigo, M. and Stutzle, T. (2004).
¨ ¨
Ant Colony Optimization.
MIT press.


References II

[Dressler and Akan, 2010] Dressler, F. and Akan, O. B. (2010).
A survey on bio-inspired networking.
Computer Networks, 54(6):881–900.
[Goss et al., 1989] Goss, S., Aron, S., Deneubourg, J. L., and Pasteels, J. M. (1989).
Self-organized Shortcuts in the Argentine Ant.
Naturwissenschaften, 76:579–581.
[Wang et al., 2009] Wang, J., Osagie, E., Thulasiraman, P., and Thulasiram, R. K. (2009).
HOPNET: A hybrid ant colony optimization routing algorithm for mobile ad hoc network.
Ad Hoc Networks, 7(4):690–705.


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