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Swarm Intelligence for
Optimisation Problems
ACAT 2002 Moscow
Bruce Denby
LISIF, Paris, France
[email protected]
Sylvie Le Hégarat
CETP, Vélizy, France
[email protected]
Introduction
• In 1959 entomologist Pierre-Paul Grassé
showed that the behaviour of certain species of
mound-building termites could be explained by
a set of simple rules
termite mound:
Nest Building Algorithm: Bellicositermes Natalensis
•
•
•
•
Make masticated pulp balls and carry them about
Drop them on raised, open areas when possible
Sniff out existing piles and stick yours on top
If tower gets too high:
– Go elsewhere if no other pile
in sniffing distance
– Else, attach ball in direction
of nearest neighbouring pile
 Result : complex termite nest structures
Swarm Intelligence
• Scientists have found similar behaviours in other
social insects as well: bees, wasps, ants…
Honeybee ‘Figure 8’
Waggle Dance
- Waggle axis codes
direction w/resp to sun
- Length and intensity
of waggle codes
distance to nectar source
Swarm Intelligence
• Since the early 1990’s, a significant amount of
work has been done using social insect-inspired
algorithms to solve both ‘toy’ and ‘real’
problems
• There are yearly international conferences on
swarm intelligence of various types - e.g.
ANTS'2002 - From Ant Colonies to Artificial
Ants: Third International Workshop on Ant
Algorithms, Brussels, 11-14 Sept. 2002
Swarm Intelligence
• Applications: TSP, quadratic assignment, graph
colouring, optimisation, network routing, cluster
finding, job scheduling, search engines, load
balancing, etc.
• Much of the work was performed using variants
of Ant Colony Optimisation (ACO)
• ACO researchers: Schoonderwoerd, Holland,
Dorigo, di Caro, Bonabeau, Théraulauz,
Deneuborg, etc. ...
Ant Colony Optimisation
• The most straightforward analogy of ACO is in
‘routing’ problems
• While searching for food, ants deposit trails of
pheromones which attract other ants
Ant Colony Optimisation
• Shorter paths to food are traversed more quickly
and have a better chance of being reinforced by
other ants before the volatile pheromones
evaporate
• Using pheromones and random search procedures
the colony thus rapidly finds the shortest paths to
food
• Illustrative Example: ACO for Routing in a
Satellite Network (E. Sigel, B. Denby, S. Le Hégarat,
to appear in Annals of Telecommunications, 2002)
ACO Routing for a Satellite Network
• di Caro, Dorigo, and others
showed that ACO gives good
performance for routing in
large scale telecom and
computer networks
• We adapted the ‘Dorigo’ algorithm to routing in
a network of 72 LEO satellites
• ACO was found to give performance superior
to a ‘standard’ routing algorithm, SPF
The Satellite Network Model
• 72 LEO satellites in 9 orbits of radius 1603 km
• 50 o equatorial inclination; min. elevation 17.5 o
• Orbital period 118.5 minutes; satellite footprint 5100
km diameter
• Each satellite has 155 Mbits/s up & downlink
transceivers and four 155.5 Mbits/s bi-directional
intersatellite links (ISL) to communicate with 2 nearest
inter- and intra-orbit neighbors.
• Earth's surface (Mercator projection) divided in 12 
24 grid with a single gateway handling all the traffic of
the cell
The Traffic Model
12
10
8
traffic
(% of the 6
whole day
traffic) 4
voice
2
0
0
5
10
15
time (h)
20
25
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
data
0
5
10
15
time (h)
20
Temporal dependence of voice and data traffic expressed
as a percentage versus time of day over 24 hours.
25
Traffic Levels for Gateways: Projection 2005
60
30
latitude
(deg rees)
0
-30
-60
-90
-180
-120
-60
0
60
120
180
longitude (degrees)
Grey scale: 1: 0.41 call/s, 2: 1.62 call/s, 3: 4.06 call/s, 4: 8.12 call/s,
5: 24.1 call/s, 6: 48.4 call/s, 7: 60.6 call/s, 8 = 80.7 calls/s.
Communication Establishment Probabilities
destination 
North
America
Europe
Asia
South
America
Africa
Oceania
North America
85 (74)
4 (18)
4 (2)
3 (2)
2 (2)
2 (2)
Europe
4 (24)
85 (68)
4 (2)
3 (2)
3 (2)
1 (2)
Asia
5 (24)
5 (18)
83 (52)
1 (2)
2 (2)
4 (2)
South America
7 (24)
7 (18)
2 (2)
81 (52)
2 (2)
1 (2)
Africa
5 (24)
7 (18)
4 (2)
2 (2)
81 (52)
1 (2)
Oceania
5 (24)
2 (18)
7 (2)
1 (2)
1 (2)
84 (52)
source
Values for voice (data) as a function of geographic
location of source and destination nodes. Percentages
sum to 100% left to right.
Simulation Scenarios
I
II
III
traffic
model
system
voice lo ad
(Gbit s/s)
low
2.24
data
sessions
per hour
per
gateway
50000
normal
2.24
intermed.
IV
V
packets % of 10
per data aug mented
session
data
sessions
VI
VII
system
data lo ad
(Gbit s/s)
system
total load
(Gbit s/s)
2000
-
1.08
3.32
100000
2000
-
2.15
4.39
2.24
100000
3000
-
3.23
5.47
high
2.24
100000
4000
-
4.30
6.54
packet
-
100000
4000
-
4.30
4.34
bursty I
2.24
100000
2000
10
2.15
4.39
bursty II
2.24
100000
2000
50
2.15
4.39
bursty III
2.24
100000
2000
75
2.15
4.39
Baseline Ant Routing Algorithm
• Once every 100 ms, each satellite node emits an
ant with a random destination.
• The ant follows the routing tables to the
destination, except for a 1% ‘exploration’
probability, waiting in queues and memorising
trip times en route.
• When the destination is reached, it follows the
same path back, jumping all queues, and updating
routing tables along the way.
Ant Routing
Algorithm:
Conceptual
T
Ts, Ti, Tj
T
Pjdn d;nNj
Tj d d
Ts
P
T
P
{T}
{T}
s
k
{T}
Pjdk(Tj-Td, Tjd)
(Tj-Td)
j
KEY:
i
d
P
Ts, Ti
T
P
Ts, Ti, Tj, Tk
: sd ant
: update
{Tj d d}: mean jd trip time table
{Pjdn d; nNj}: node j routing table
for destination d, neighborhood Nj
Ant Routing Table Update
Algorithm
• First calculate r = min{T/(<T>); 1} where T is
the current ant trip time and <T> is the mean
time for the path in question
• Next, modify the probability of the link that is
part of the ant's path according to
Pant ISL = Pant ISL + (1-r)(1- Pant ISL)
• and decrement the other three ISL's as
PISL(i) = PISL(i) - (1-r) PISL(i)
Improvements to Baseline ACO
• Two generic improvements to 'baseline' ACO
are cited in the literature:
 Replacing r by a so-called 'squashed' value rs (s
here was chosen to be 0.2).
 Using the 'fuzzy' routing technique of the ant
packets for normal data packets as well.
• Results presented are 'squashed'/'fuzzy' ACO
• Improvement with ‘fuzzy’ routing is not
without cost, as it leads to increased packet
fragmentation
Geographic distribution of packet delays
60
30
latitude
(deg rees)
packet
delays
(ms)
0
-30
-60
-90
-180
-120
-60
0
60
120
180
longitude (degrees)
Values for 'normal' traffic &'baseline' ACO, midnight at int’l dateline.
Dijkstra Algorithm for Comparison
• Dijkstra finds the absolute shortest path
according to some cost function involving
propagation delays and queue lengths.
• It assumes global, instantaneous knowledge and
is not realisable.
• Our version of Dijkstra ignored queue lengths
and thus corresponds to a true absolute minimum
(though unrealisable) delay, i.e., propagation
delay only.
SPF Algorithm for Comparison
• Each satellite sends a list of its queue lengths to
every node in the network once per second.
• The receiving node then updates its routing table
based on this delayed information, using Dijkstra
shortest path with a cost function
cost = tpropagation + 0.6tqueue + 0.4<t>queue
• The SPF update rate chosen gives an average
routing bandwidth of about 408 kbits/s, i.e.,
roughly twice that of ACO (230.4 kbits/s).
90th
percentile
packet
delays
(s)
SPF
ANT
DIJKSTRA
a) 'low'
time (s)
90th
percentile
packet
delays
(s)
c)
'intermediate'
time (s)
b) 'normal'
time (s)
d) 'high'
time (s)
90th
percentile
packet
delays
(s)
e) 'packet'
SPF
ANT
DIJKSTRA
f) 'bursty I'
time (s)
time (s)
90th
percentile
packet
delays
(s)
g) 'bursty II'
time (s)
h) 'bursty III'
time (s)
Main Results
• ACO satellite network routing gives near
optimal packet delay distributions
• ACO mean packet delays tens to hundreds of
milliseconds lower than link state alg. SPF over
a wide range of traffic conditions
• Additional routing bandwidth introduced by
ACO is 230.4 kbits/s, negligible compared to the
system load of several Gbits/s, and about half
that of SPF in these simulations (408 kbits/s)
‘Nature-Inspired’ Algorithms
• A number of other modern optimisation and/or
computing techniques are modelled upon
natural phenomena:
• Simulated Annealing / Annealing of crystalline
structures
• Genetic/Evolutionary Algorithms / Evolution
in living systems
• Neural Networks / Animal nervous systems
• Agent-based systems / Social interactions
Simulated Annealing
• Analogy between thermodynamic behaviour
of solids and large combinatorial optimisation
problems
• A heated solid melts and particles take
random configurations; then, the temperature
is slowly decreased to let them arrange
themselves in a state of minimal energy
• If temperature is decreased too quickly, the
solid freezes into a meta-stable state rather
than into the ground state.
Simulated Annealing
• Modelled using a Boltzmann distribution with a
‘temperature’ parameter, T :
where Ei is the energy of the system in state i, kB
the Boltzmann constant and Z(T) a normalisation
factor
• Transition i  j accepted if ∆Uij = Ei-Ej < 0, or, if
∆Uij > 0, with probability
Simulated Annealing
• At high T almost all modifications accepted,
while at low T only small jumps accepted.
• Simulated annealing is a stochastic relaxation
algorithm which in theory enables to reach
global optimality
• Applications: as optimisation of NP-hard
problems, integrated circuit routing, image
processing
Genetic/ Evolutionary Algorithms
• Each individual is a point in solution space
• Population made to evolve by applying operators
for crossover ( inherited traits), mutation (new
behaviours), and selection (survival of the fittest)
• Key Issues:
–
–
–
–
–
Genome: how are individuals coded?
How is the initial population determined?
How is the ‘fitness function’ defined?
How are crossover and mutation implemented?
What is the selection mechanism (top 5?, best only?)
Genetic/Evolutionary Algorithms
• These types of strategies have been applied to
everything imaginable, but most often ‘academic’
problems: knapsack problem, graph problems, set
covering, noisy function evaluation
• The high computational complexity makes ‘realworld’ applications difficult for the moment
• Some (M. Sipper, D. Mange, U. Tangen...)
propose evolutionary hardware (FPGA…) to help
overcome this problem
Neural Networks
• Feed forward networks are good for pattern
recognition and are used in a wide variety of
applications from particle physics to finance
• Recurrent (feedback) networks have been used
with success in industrial control applications
Agent-Based Computing
• « An autonomous agent is a system situated
within and a part of an environment that senses
that environment and acts on it, over time, in
pursuit of its own agenda and so as to effect
what it senses in the future. »
Stan Franklin and Art Graesser
Institute for Intelligent Systems
University of Memphis
Common properties that make agents
different from conventional programs
from : « A gentle introduction to agents and their applications »,
by Michael Weiss, MITEL Corp.
• Agents are autonomous, that is they act on behalf
of the user
• Agents contain some level of intelligence, from
fixed rules to learning engines that allow them to
adapt to changes in the environment
• Agents don't only act reactively, but sometimes
also proactively
Properties of agents, cont’d.
• Agents have social ability, that is they
communicate with the user, the system, and
other agents as required
• Agents may also co-operate with other agents
to carry out more complex tasks than they
themselves can handle
• Agents may move from one system to another
to access remote resources or even to meet
other agents
Reactive Agents
• Reactive agents do not have internal symbolic
models, but react to the current state of the
environment
• They are simple and interact with others in
simple ways
• Complex patterns of behaviour can emerge
from these interactions
• Benefits: robustness, fast response time
• Challenges: how to debug them?
Mobile Agents
• Can migrate from one machine to another
• Execute in platform-independent environment
• Advantages:
– Reduced communication cost
– Asynchronous computing
• Applications:
– Distributed information retrieval
– Telecommunication network routing
We may conclude that ‘ants’ are
reactive, mobile, multi-agent
systems
Careful, ‘agent’ doesn’t mean the same thing to all people!!
Why ‘Nature-inspired’ Algorithms?
• They work
• We might not otherwise have thought them up
• The underlying physical model acts as a guide
and gives us the confidence to try them
• The introduction of randomness clearly plays a
role in simulated annealing and in several
aspects of genetic algorithms (initial state,
mutations, crossover…)
Why - Distributed Computing?
• The distributed nature of the algorithm is a factor
in neural networks (distributed information
storage) and agent-based models (distributed
problem solving)
– Grassé postulated that the termites’ depositing
pheromones amounted to leaving environmental
markers which could be combined with those of other
agents to obtain more ‘global’ information
– This he called ‘stigmergy’ (cf. stigma: mark)
Why - Emergent Property?
• The complex final states of swarm systems
recall the attractor states found in cellular
automata and recurrent neural network systems
• Some would say that swarm intelligence is an
emergent property of multi-agent systems in the
same way that an avalanche is an emergent
property of a pile of individual snowflakes
Why - Self Organisation?
• Self-organisation is an important aspect of
agent-based systems
– In simulated annealing and genetic algorithms,
an ‘omniscient’ judge accepts or rejects
subsequent steps
– In ACO, shorter paths are automatically
selected since faster ants refresh the
pheromones more quickly
Conclusions
• We’ve visited several ‘Nature-inspired’
algorithms
• What’s new here are the ACO-like ones
• Is ‘Agent-Based Computing’ poised to become
the ‘Neural Networks’ of the 2000’s?
• Will Ants help find the Higgs?
Conclusions
• ACO adapts well to network-like structures
- those with inherent distributed computing
- while ACO simulations take forever (like
genetic alg.)
• One could imagine applications in
– Online control (machines, networks, etc.)
– Anything resembling image processing
– Iterative data analysis tasks - track
reconstruction, clustering - where some
optimisation takes place