By Eric Bonabeau And Guy Théraulaz
S M A R T S
by Eric Bonabeau and Guy Théraulaz
Y
JAMES GAR
Copyright 2000 Scientific American, Inc.
Using ants and other social insects as models, computer scientists have
created software agents that cooperate to solve complex problems, such
as the rerouting of traffic in a busy telecom network
nsects that live in colonies—ants,
bees, wasps, termites—have long
fascinated everyone from naturalists
Ito artists. Maurice Maeterlinck, the
Belgian poet, once wrote, “What is it that governs here? What is it that
issues orders, foresees the future, elaborates plans and preserves equi-
librium?” These, indeed, are puzzling questions.
Each insect in a colony seems to have its own agenda, and yet the
group as a whole appears to be highly organized. Apparently the seamless
integration of all individual activities does not require any supervision. In
fact, scientists who study the behavior of social insects have found that
Swarm Smarts
Scientific American
March 2000 73
Copyright 2000 Scientific American, Inc.
cooperation at the colony level is largely self-organized: in
numerous situations the coordination arises from interac-
NEST
FOOD
tions among individuals. Although these interactions might
be simple (one ant merely following the trail left by another),
together they can solve difficult problems (finding the short-
est route among countless possible paths to a food source).
PHEROMONE
TRAIL
This collective behavior that emerges from a group of social
insects has been dubbed “swarm intelligence.”
Y
AN CHRISTIE
Recently a growing community of researchers has been de-
BR
vising new ways of applying swarm intelligence to diverse
tasks. The foraging of ants has led to a novel method for
PHEROMONE TRAILS enable
rerouting network traffic in busy telecommunications sys-
ants to forage efficiently. Two
tems. The cooperative interaction of ants working to trans-
ants leave the nest at the same
a
port a large food item may lead to more effective algorithms
time (top), each taking a differ-
FOOD SOURCES
for robots. The way in which insects cluster their colony’s
ent path and marking it with
ANTS
pheromone. The ant that took
dead and sort their larvae can aid in analyzing banking data.
the shorter path returns first
And the division of labor among honeybees could help
(bottom). Because this trail is
streamline assembly lines in factories.
NEST
now marked with twice as much
pheromone, it will attract oth-
Virtual Foraging
er ants more than the longer
route will.
b
One of the early studies of swarm intelligence investigated
the foraging behavior of ants. Jean-Louis Deneubourg of
the Free University of Brussels and his colleagues showed that
the ant “highways” often seen in nature (and in people’s
DIFFERENT FOOD SOURCES are raided
kitchens) result from individual ants exuding pheromone, a
sequentially because of pheromone
chemical substance, that attracts other ants. Deneubourg, a pi-
evaporation. In this computer simula-
oneer in the field, also demonstrated that this process of laying
PHEROMONE
tion, three identical sources of food are
a trail of pheromone that others can follow was a good strategy
located at unequal distances from a
for finding the shortest path between a nest and a food source.
nest. After foraging randomly (a), the
In experiments with the Argentine ant Linepithema humile,
ants begin to raid the food sources
c
Deneubourg constructed a bridge with two branches, one
that are closest (b, c). As those supplies
dwindle, the concentration of phero-
twice as long as the other, that separated a nest from a food
ab
mone along their trails decreases
source. Within just a few minutes the colony usually selected
edia L
through evaporation (d). The ants will
the shorter branch. Deneubourg found that the ants lay and
MIT M
then exploit the farther source.
follow trails of pheromone as they forage. The first ants re-
turning to the nest from the food source are those that have
taken the shorter path in both directions, from the nest to the
CH RESNICK
food and back. Because this route is the first to be doubly
B
marked with pheromone, nestmates are attracted to it.
d
TESY OF MIT
If, however, the shorter branch is presented to the colony af-
OUR
,
C
ter the longer branch, the ants will not take it because the
OGO
L
longer branch has already been marked with pheromone. But
TAR
computer scientists can overcome this problem in an artificial
system by introducing pheromone decay: when the chemical
evaporates quickly, longer paths will have trouble maintain-
TION DONE IN S
A
ing stable pheromone trails. The software ants can then select
SIMUL
a shorter branch even if it is discovered belatedly. This proper-
ty is highly desirable in that it prevents the system from con-
verging on mediocre solutions. (In L. humile, the pheromone
concentrations do decay but at a very slow rate.)
NETWORK TRAFFIC can be
In a computer simulation of pheromone evaporation [see il-
rerouted on the fly with soft-
lustration at left], researchers presented identical food sources
ware agents that mimic ants.
A transmission that needs to
to an artificial colony at different distances from the nest. At
travel from A to B must go
first the virtual ants explored their environment randomly.
through a number of inter-
A
Y
AN CHRISTIE
Then they established trails that connected all of the food
mediate nodes.If a portion of
BR
sources to the nest. Next they maintained only the trails of the
the shortest path (orange)
sources closest to the nest, leading to the exploitation of those
between the two locations is congested, the system must redirect
supplies. With the depletion of that food, the software ants
the transmission through an alternative (green). Software agents
began to raid the farther sources.
can perform this rerouting automatically in a manner that is simi-
Extending this ant model, Marco Dorigo, a computer scien-
lar to how ants raid different food sources (illustration above). In
tist at the Free University of Brussells, and his colleagues have
the analogy, a congested path is like a depleted food source.
devised a way to solve the famous “traveling salesman prob-
74
Scientific American
March 2000
Swarm Smarts
Copyright 2000 Scientific American, Inc.
T r a v e l i n g S a l e s A n t s
ants as its pheromone evaporated.
Another problem occurs when a short
route contains a very long link that initial-
ly is less likely to be used. But Dorigo has
shown that even though the connection
In the traveling salesman problem,a
ous times, the artificial ants are indeed
might be a slow starter, once it has been
person must find the shortest route by
able to obtain progressively shorter tours,
selected it will quickly become reinforced
which to visit a given number of cities,
such as that shown in the bottom illustra-
more than other, competing links.
each exactly once.The classic problem is
tion below.
It is important to note that this ant-
devilishly difficult: for just 15 cities [see top
Nevertheless, a difficulty arises when
based method is effective for finding
illustration below] there are billions of
many routes happen to use a link that, as
short routes but not necessarily the short-
route possibilities.
it turns out, is not part of a short tour. (In
est one. Nevertheless, such near-optimal
Recently researchers have begun to ex-
fact, such a link might belong to many,
solutions are often more than adequate,
periment with antlike agents to derive a
many long routes.) Dorigo discovered
particularly because obtaining the best
solution.The approach relies on the artifi-
that although this popular link might bias
route can require an unwieldy amount of
cial ants laying and following the equiva-
the search for several iterations, a better
computation. In fact, determining the ex-
lent of pheromone trails [see illustrations
connection will eventually replace it.This
act solution quickly becomes intractable
on opposite page].
optimization is a consequence of the sub-
as the number of cities increases.
Envision a colony of such ants, each in-
tle interplay between reinforcement and
In addition,Dorigo’s system has one ad-
dependently hopping from city to city, fa-
evaporation, which ensures that only the
vantage:its inherent flexibility.Because the
voring nearby locations but otherwise
better links survive. Specifically, at some
artificial ants are continuously exploring
traveling randomly. After completing a
point an alternative connection that is
different paths,the pheromone trails pro-
tour of all the cities, an ant goes back to
part of a short route would be selected by
vide backup plans.So,whenever one of the
the links it used and deposits pheromone.
chance and would become reinforced
links breaks down (bad weather between
The amount of the chemical is inversely
more than the popular link, which would
Houston and Atlanta, for instance), a pool
proportional to the overall length of the
then lose its attractiveness to the artificial
of alternatives already exists. —E.B. and G.T.
tour: the shorter the distance, the more
pheromone each of the links receives.
SEATTLE
Thus, after all the ants have completed
their tours and spread their pheromone,
the links that belonged to the highest
BOSTON
number of short tours will be richest with
SALT LAKE
CITY
the chemical. Because the pheromone
evaporates, links in long routes will even-
SAN
NEW YORK
FRANCISCO
LAS
tually contain significantly less of the sub-
VEGAS
INDIANAPOLIS
stance than those in short tours will.
OKLAHOMA
The colony of artificial ants is then re-
LOS
CITY
ANGELES
ATLANTA
leased to travel over the cities again, but
PHOENIX
this time they are guided by the earlier
SAN DIEGO
ALBUQUERQUE
pheromone trails (high-concentration
links are favored) as well as by the inter-
city distances (nearby locations have pri-
ority), which the ants can obtain by con-
HOUSTON
MIAMI
sulting a table storing those numbers. In
general, the two criteria—pheromone
strength and intercity distance—are
weighted roughly equally.
Marco Dorigo of the Free University of
Brussels and his colleagues have imple-
mented this ant-based system in software.
Of course, the methodology assumes that
the favored links, when taken together, will
lead to an overall short route.Dorigo has
found that after repeating the process
(tour completion followed by pheromone
reinforcement and evaporation) numer-
Y
AN CHRISTIE
BR
Swarm Smarts
Scientific American
March 2000 75
Copyright 2000 Scientific American, Inc.
lem” [see box on preceding page]. The problem calls for find-
cally static, or nonvarying, antlike agents can also cope with
ing the shortest route that goes through a given number of
glitches and dynamic environments—for example, a factory
cities exactly once. This test is appealing because it is easy to
where a machine breaks down. By maintaining pheromone
formulate and yet extremely difficult to solve. It is “NP-com-
trails and continuously exploring new paths, the ants ser-
plete”: the solution requires a number of computational steps
endipitously set up a backup plan and thus are prepared to re-
that grows faster than the number of cities raised to any finite
spond to changes in their environment. This property, which
power (NP stands for nondeterministic polynomial). For such
may explain the ecological success of real ants, is crucial for
problems, people usually try to find an answer that is good
many applications.
enough but not necessarily the best (that is, a route that is suf-
Consider the dynamic unpredictability of a telephone net-
ficiently short but perhaps not the shortest). Dorigo has shown
work. A phone call from A to B generally has to go through a
that he can obtain near-optimal routes by using artificial ants
number of intermediate nodes, or switching stations, requir-
that are tweaked so that the concentration of pheromone they
ing a mechanism to tell the call where it should hop next to
deposit varies with the overall distances they have traveled.
establish the A-to-B connection. Obviously the algorithm for
Similar approaches have been successful in a number of
this process should avoid congested areas to minimize delays,
other optimization tasks. For instance, artificial ants provide
and backup routes become especially valuable when condi-
the best solution to the classic quadratic assignment problem,
tions change dramatically. Bad weather at an airport or a
in which the manufacture of a number of goods must be as-
phone-in competition on TV will lead to transient local surges
signed to different factories so as to minimize the total dis-
of network traffic, requiring on-the-fly rerouting of calls
tance over which the items need to be transported between fa-
through less busy parts of the system.
cilities. In a related application, David Gregg of Unilever in
To handle such conditions, Ruud Schoonderwoerd and
the U.K. and Vincent Darley of Bios Group in Santa Fe,
Janet Bruten of Hewlett-Packard’s research laboratories in
N.M., report that they have developed an ant-based method
Bristol, England, and Owen Holland of the University of the
for decreasing the time it takes to perform a given amount of
West of England have invented a routing technique in which
work in a large Unilever plant. The system must efficiently
antlike agents deposit bits of information, or “virtual
schedule various storage tanks, chemical mixers, packing lines
pheromone,” at the network nodes to reinforce paths through
and other equipment.
uncongested areas. Meanwhile an evaporation mechanism
In addition to solving optimization problems that are basi-
adjusts the node information to disfavor paths that go
through busy areas.
Specifically, each node keeps a routing table that tells phone
calls where to go next depending on their destinations.
Antlike agents continually adjust the table entries, or scores,
to reflect the current network conditions. If an agent experi-
C o o p e r a t i v e T r a n s p o r t
i n A n t s a n d R o b o t s
In some ant species,nestmates are recruited to help when a
single ant cannot retrieve a large prey.Then, during an initial
period that can last up to several minutes, the ants change their
positions and alignments around the object until they are able
to move the prey toward their nest.
Using mechanical robots, C. Ronald Kube and Hong Zhang of
the University of Alberta have reproduced this behavior. The
es
tur
ic
inden P
ANTS WORK TOGETHER to fold a large leaf (left). Such team-
M
T
work has inspired scientists to program robots without the
use of complex software. In an experiment at the University
of Alberta (below), the robots must push an illuminated cir-
MARK MOFFET
cular box toward a light. Even though each robot (right) does
not communicate with the others and acts independently by
following a small set of simple instructions, together the
group is able to accomplish its goal.
Swarm Smarts
Copyright 2000 Scientific American, Inc.
ences a long delay because it went through a highly congested
Worldcom has been investigating artificial ants not only for
portion of the network, it will add just a tiny amount of
managing the company’s telephone network but also for oth-
“pheromone” to the table entries that would send calls to that
er tasks such as customer billing. The ultimate application,
overloaded area. In mathematical terms, the scores for the
though, may be on the Internet, where traffic is particularly
corresponding nodes would be increased just slightly. On the
unpredictable.
other hand, if the agent went quickly from one node to anoth-
To handle the demanding conditions of the Net, Dorigo
er, it would reinforce the use of that path by leaving a lot of
and his colleague Gianni Di Caro of the Free University of
“pheromone”—that is, by increasing the appropriate scores
Brussells have increased the sophistication of the ant agents by
substantially. The calculations are such that even though a
taking into account several other factors, including the overall
busy path may by definition have many agents traveling on it,
time it takes information to get from its origin to its destina-
their cumulative “pheromone” will be less than that of an un-
tion. (The approach for phone networks considers just the
congested path with fewer agents.
time it takes to go from one node to another, and the traffic in
The system removes obsolete solutions by applying a math-
the reverse direction is assumed to be the same.) Simulation
ematical form of evaporation: all of the table entries are de-
results indicate that Dorigo and Di Caro’s system outperforms
creased regularly by a small amount. This process and the
all other routing methods in terms of both maximizing
way in which the antlike agents increase the scores are de-
throughput and minimizing delays. In fact, extensive tests sug-
signed to work in tandem so that busy routes experience more
gest that the ant-based method is superior to Open Shortest
evaporation than reinforcement, whereas uncongested routes
Path First, the protocol that the Internet currently uses, in
undergo just the opposite.
which nodes must continually inform one another of the sta-
Any balance between evaporation and reinforcement can
tus of the links to which they are connected.
be disrupted easily. When a previously good route becomes
congested, agents that follow it are delayed, and evaporation
A Swarm of Applications
overcomes reinforcement. Soon the route is abandoned, and
the agents discover (or rediscover) alternatives and exploit
them. The benefits are twofold: when phone calls are rerouted
Other behaviors of social insects have inspired a variety
of research efforts. Computer scientists are studying in-
through the better parts of a network, the process not only al-
sect swarms to devise different techniques for controlling a
lows the calls to get through expeditiously but also enables
group of robots. One application being investigated is coop-
the congested areas to recover from the overload.
erative transport [see box below]. Using such approaches, en-
Several companies are exploring this approach for handling
gineers could design relatively simple and cheap robots that
the traffic on their networks. France Télécom and British
would work together to perform increasingly sophisticated
Telecommunications have taken an early lead in applying ant-
tasks. In another project, a model that was initially intro-
based routing methods to their systems. In the U.S., MCI
duced to explain how ants cluster their dead and sort their
task for their robotic army was to push a box
tions and alignments. Even temporary setbacks
toward a goal, and each individual was pro-
are evident, as when the box is moved in a di-
T
A
grammed with very simple instructions: find
rection away from the goal.The robots make
the box, make contact with it, position yourself
continual adjustments when they lose contact
Y OF ALBER
so that the box is between you and the goal,
with the box, when they block one another or
then push the box toward the goal.
when the box rotates. Eventually the robots,
Y
,
UNIVERSIT
Although the robots were intentionally pro-
despite their limited capabilities, are successful
OR
T
A
grammed very crudely, the similarity between
in delivering the box to the goal.
ABOR
their behavior and that of a swarm of ants is
Obviously, individuals trying to push an ob-
CH L
striking. (The videotaped experiments can be
ject can find far more efficient ways to work to-
viewed at http://www.cs.ualberta.ca/~kube/
gether. But because of the extreme simplicity
TICS RESEAR
on the World Wide Web.) At first, the robots
of this ant-based approach
OBO
—for one thing, the
R
move randomly, trying to find the box. After lo-
robots do not need to communicate with one
cating it they begin pushing, but if they are un-
another—it is promising for miniaturization
successful in moving it they change their posi-
and low-cost applications.
—E.B. and G.T.
Y
,
OR
T
A
ABOR
T
A
CH L
Y OF ALBER
TICS RESEAR
OBO
R
UNIVERSIT
Swarm Smarts
Scientific American
March 2000 77
Copyright 2000 Scientific American, Inc.
F r o m C e m e t e r i e s t o D a t a b a s e s
In some ant species,such as Messor
a particular person would repay a loan.
sancta, workers pile up their colony’s
If, for example, a mortgage applicant be-
dead to clean their nests.The illustration
longed to a group dominated by de-
at the right shows the dynamics of such
faulters, that person might not be a
cemetery organization. If the corpses are
good credit risk.
randomly distributed at the beginning
Because clusters are generally visual-
of the experiment, the workers will form
ized best in two dimensions (higher di-
clusters within a few hours.
mensions make the data difficult for hu-
Jean-Louis Deneubourg of the Free
mans to interpret), Lumer and Faieta
University of Brussels and his colleagues
represent each customer as a point in a
have proposed a simple explanation:
plane. So each client is like a brood item,
small groups of items grow by attracting
and software ants can move the clients
workers to deposit more items, and this
around, picking them up and depositing
positive feedback leads to the formation
them according to the surrounding
of larger and larger bunches. Scientists,
items.The distance between two cus-
however, still do not know the exact de-
tomers indicates how similar they are.
tails of the individual behavior that im-
For the single attribute of age, for in-
plements the feedback mechanism.
stance, shorter distances depict smaller
Another phenomenon can be ex-
age differences.The artificial ants make
plained in a similar way.The workers of
their sorting decisions by considering all
the ant Leptothorax unifasciatus sort the
the different customer characteristics si-
colony’s brood systematically. Eggs and
multaneously. And depending on the
microlarvae are placed at the center of an
bank’s objectives, the software could
area, the largest larvae at the periphery,
mathematically weigh some of the at-
and pupae and prepupae in between.
tributes more heavily than others.
One explanation of this behavior is that
Through this kind of analysis, one clus-
ants pick up and drop items according
ter might contain people who are about
to the number of similar surrounding ob-
20 years old and single,most of them liv-
jects. For example, if an ant finds a large
ing with their parents and whose most
larva surrounded by eggs, it will most
popular banking service is interest
likely pick up the larval “misfit.”And that
checking. Another grouping may consist
ant will probably deposit its load in a re-
of people who are about 57, female,
gion containing other large larvae.
married or widowed, and homeowners
By studying such brood sorting, Erik
with no mortgage.
Lumer of University College London and
Of course, banks and insurance com-
Baldo Faieta of Interval Research in Palo
panies have already used similar types
Alto, Calif., have developed a method for
of cluster analyses. But the ant-based ap-
exploring a large database. Imagine that
proach enables the data to be visualized
a bank wants to determine which of its
easily, and it boasts one intriguing fea-
customers is most likely to repay a loan.
ture: the number of clusters emerges au-
AZ
The problem is that many of the cus-
tomatically from the data, whereas con-
UL
A
tomers have never borrowed money
ventional methods usually assume a
THÉR
from any financial institution.
predefined number of groups into
But the bank has a large database of
which the data are then fit.Thus, antlike
U AND GUY
customer profiles with attributes such as
sorting has been effective in discovering
age, gender, marital status, residential
interesting commonalities that might
ERIC BONABEA
status, banking services used by the cus-
otherwise have re-
tomer and so on. If the bank had a way
mained hidden.
WORKER ANTS cluster their dead to clean their nest. At the out-
set of this experiment, 1,500 corpses are located randomly (top).
to visualize clusters of people with simi-
—E.B. and G.T.
After 26 hours, the workers have formed three piles (bottom).
lar characteristics, loan officers might be
This behavior and the way in which ants sort their larvae has led
able to predict more accurately whether
to a new type of computer program for analyzing banking data.
78
Scientific American
March 2000
Swarm Smarts
Copyright 2000 Scientific American, Inc.
B u s y a s a B e e
larvae has become the basis of a new approach for analyzing
financial data [see box at left]. And research investigating the
flexible way in which honeybees assign tasks could lead to a
more efficient method for scheduling jobs in a factory [see
box at right].
HANS PFLETSCHINGER Peter Arnold, Inc.
Additional examples abound. Applying knowledge of how
In a honeybee colony,individuals
wasps construct their nests, Dan Petrovich of the Air Force In-
specialize in certain tasks,depend-
stitute of Technology in Dayton, Ohio, has designed a swarm
ing on their age.Older bees,for ex-
of tiny mobile satellites that would assemble themselves into a
ample,tend to be the foragers for
larger, predefined structure. H. Van Dyke Parunak of the En-
the hive.But the allocation of tasks is
vironmental Research Institute of Michigan in Ann Arbor is
not rigid:when food is scarce,
deploying a variety of insectlike software agents to solve man-
ufacturing problems
younger nurse bees will forage,too.
—for example, scheduling a complex net-
work of suppliers to a factory. Paul B. Kantor of Rutgers Uni-
Using such a biological system as
versity has developed a swarm-intelligence approach for find-
a model, we have worked with
orbis
C
ing information over the World Wide Web and in other large
Michael Campos of Northwestern
networks. Web surfers looking for interesting sites can, if they
University to devise a technique for
SOUDERS
belong to a “colony” of users, access information in the form
A.
scheduling paint booths in a truck
UL
of digital pheromones (essentially, ratings) left by fellow mem-
P
A
factory. In the facility the booths
bers in previous searches.
must paint trucks coming out of an
HONEYBEES (top) perform
Indeed, the potential of swarm intelligence is enormous. It
tasks based on the hive’s
offers an alternative way of designing systems that have tra-
assembly line, and each booth is
needs. By studying the
ditionally required centralized control and extensive prepro-
like an artificial bee specializing in
way in which these jobs
gramming. It instead boasts autonomy and self-sufficiency,
one color.The booths can change
are assigned, scientists
relying on direct or indirect interactions among simple indi-
their colors if needed, but doing so
hope to develop better
vidual agents. Such operations could lead to systems that can
is time-consuming and costly.
ways to program the
adapt quickly to rapidly fluctuating conditions.
equipment in an auto-
Because scientists have yet to
But the field is in its infancy. Because researchers lack a de-
mated factory (bottom).
understand exactly how honey-
tailed understanding of the inner workings of insect swarms,
identifying the rules by which individuals in those swarms in-
bees regulate their division of labor, we made the following as-
teract has been a huge challenge, and without such informa-
sumption: an individual performs the tasks for which it is spe-
tion computer scientists have had trouble developing the ap-
cialized unless it perceives an important need to perform an-
propriate software. In addition, although swarm-intelligence
other function.Thus, a booth with red paint will continue to
approaches have been effective at performing a number of
handle orders of that color unless an urgent job requires a
optimization and control tasks, the systems developed have
white truck and the other booths, particularly those specializ-
been inherently reactive and lack the necessary overview to
ing in white, have much longer queues.
solve problems that require in-depth reasoning techniques.
Furthermore, one criticism of the field is that the use of au-
Although this basic rule sounds simplistic,in practice it is very
tonomous insectlike agents will lead to unpredictable behav-
effective.In fact,a honeybeelike system enables the paint booths
ior in the computers they inhabit. This characteristic may ac-
to determine their own schedules with higher efficiency—specif-
tually turn out to be a strength, though, in that it could allow
ically,fewer color changes—than a centralized computer can
such systems to adapt to solve new, unforeseen problems—a
provide. And the method is adept at responding to changes in
flexibility that traditional software typically lacks.
consumer demand.If the number of trucks that need to be paint-
Many futurists predict that chips will soon be embedded
ed blue surges unexpectedly,other booths can quickly forgo
into thousands of mundane objects, from envelopes to trash
their specialty colors to accommodate the unassigned vehicles.
cans to heads of lettuce. Enabling all these pieces of silicon to
communicate with one another in a meaningful way will re-
Furthermore,the system copes easily with glitches.When a paint
quire novel approaches. As high-technology author Kevin
booth breaks down,other stations compensate swiftly by imme-
Kelly puts it, “Dumb parts, properly connected into a swarm,
diately divvying up the additional load.
—E.B. and G.T.
yield smart results.” The trick, of course, is in the proper con-
nection of all the parts.
SA
The Authors
Further Information
ERIC BONABEAU and GUY THÉRAULAZ study the behaviors of social insects and
Swarm Intelligence: From Natural to Arti-
their application in the design of complex systems. Bonabeau is chief scientist at Euro-
ficial Systems. Eric Bonabeau, Marco Dorigo
Bios in Paris. He received a Ph.D. in theoretical physics and advanced degrees in com-
and Guy Théraulaz. Oxford University Press,
puter science and applied mathematics from the University of Paris XI (Paris-Sud).
1999.
Théraulaz is a research associate at the Laboratory of Ethology and Animal Psychology
For more information on ant-based optimiza-
of CNRS at Paul Sabatier University in Toulouse, France. He received a Ph.D. in neuro-
tion, see iridia.ulb.ac.be/dorigo/ACO/ACO.html
science and ethology from the University of Provence.
on the World Wide Web.
Swarm Smarts
Scientific American
March 2000 79
Copyright 2000 Scientific American, Inc.
