Presentation by David M.S. Rodrigues on a novel algorithm for Ant Colony System that includes a negative pheromone that acts as a non-entry signal for unrewarding paths in the Travelling Salesman Problem (TSP)

1. 2nd
Order
Swarm
Intelligence
Vitorino
Ramos,
David
Rodrigues+,
and
Jorge
Louçã
HAIS
2013,
Salamanca
September
11-­‐13,
2013
hHp://goo.gl/OXc0Oh
+
The
Open
University,
UK
–
david.rodrigues@open.ac.uk

2. Outline
• Present
an
algorithm
that
is
an
extension
to
Ant
Colony
System
• Use
of
non-­‐entry
signal
via
a
negaSve
pheromone.
• Use
of
2
pheromones
improves
quality
of
results

3. Ant
Colony
OpSmisaSon
• ProbabilisSc
technique
• Searching
for
OpSmal
Path
in
the
graph
(Based
on
the
behaviour
of
ants
seeking
a
path
between
colony
and
source
of
food)
• Mata-­‐heurisSc
opSmisaSon

4. ACO
Concept
• Ants
navigate
from
nest
to
food
source.
Blindly!
• Shortest
path
is
discovered
via
pheromone
trails
deposited
by
other
ants.
• Each
ant
moves
stochasScally
• Pheromone
is
deposited
on
path
• More
pheromone
implies
higher
probability
of
path
being
followed.

5. ACO
IllustraSon

6. TSP
Problem
• A
Salesman
must
visit
N
ciSes,
passing
through
each
city
only
once,
and
returning
to
the
start
city.
• The
cost
of
the
transportaSon
between
all
ciSes
is
known
• The
ObjecSve
is
to
choose
the
order
of
the
tour
so
the
total
cost
is
minimum.

7. History
• Ant
System
developed
by
Marco
Dorigo
(1992,
PhD
thesis)
• Max-­‐Min
Ant
System
by
Hoos
and
Stützle
(1996)
• Ant
Colony
by
Gambardella,
Dorigo
(1997)

8. Biology
Findings
of
non-­‐entry
singals
• Pharaoh's
ants
(Monomorium
pharaonis)
deposit
a
pheromone
as
a
'no
entry'
signal
to
mark
unrewarding
foraging
paths.
[Robinson,
2005,
2007;
Grüter
2012]

9. 2nd
Order
Swarm
Intelligence
• Double
Pheromone
Model
on
top
of
tradiSonal
ACS.
– TradiSonal
posiSve
reinforcement
pheromone
– Use
of
NegaSve
Pheromone
• Marker
for
forbidden
paths
• Forbidden
paths
are
obtained
from
the
worse
ant
tour
of
each
iteraSon
• This
Blockade
isn’t
permanent
as
the
pheromone
evaporates.

10. State
TransiSon
Rule

11. State
TransiSon
Rule

12. Global
UpdaSng
Rule

13. Local
UpdaSng
Rule

14. 2nd
Order
Reasoning

15. 2nd
Order
Response
Maps

16. 2nd
Order
AS
Results

17. Influence
of
NegaSve
Pheromone

18. kroA100.tsp
with
negaSve
pheromone
performs
beHter

19. NegaSve
Pheromone
Also
is
important
for
bigger
problems.

20. NegaSve
pheromone
can’t
dominate
the
pheromone
maps.

21. Take
Home
Message
• From
Biology
Findings:
use
of
negaSve
pheromone
as
non-­‐entry
signal
• New
algorithm
based
on
ACS
with
minimal
changes
to
tradiSonal
algorithm
• BeHer
results
(faster
convergence
to
good
results/
faster
• ApplicaSon
to
Dynamical
problems
for
faster
tracking
of
the
soluSons.