Swarm Intelligence for Optimisation Problems

ACAT 2002 Moscow

Bruce Denby

LISIF, Paris, France

denby@ieee.org

Sylvie Le Hégarat

CETP, Vélizy, France

mascle@cetp.ipsl.fr

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

0 5 10 15 20 25time (h)

12

10

8

6

4

2

0

traffic(% of thewhole day

traffic)

0 5 10 15 20 25time (h)

5.55

4.54

3.53

2.52

1.51

0.5

Temporal dependence of voice and data traffic expressed as a percentage versus time of day over 24 hours.

voice data

The Traffic Model

longitude (degrees)-180 -120 -60 0 60 120 180

60

30

0

-30

-60

-90

latitude(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.

Traffic Levels for Gateways: Projection 2005

destination

source

NorthAmerica

Europe Asia SouthAmerica

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)

Values for voice (data) as a function of geographic location of source and destination nodes. Percentages sum to 100% left to right.

Communication Establishment Probabilities

Simulation ScenariosI II III IV V VI VII

trafficmodel

systemvoice load(Gbits/s)

datasessionsper hour

pergateway

packetsper datasession

% of 10augmented

datasessions

systemdata load(Gbits/s)

systemtotal load(Gbits/s)

low 2.24 50000 2000 - 1.08 3.32

normal 2.24 100000 2000 - 2.15 4.39

intermed. 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.

s d

s d

s d

s d

s d

s d

s d

P

T d

P

T s

P

T k

P

T i s d

Pjdn d;nNj

Tj d d j

Pjdk(Tj-Td, Tjd)

(Tj-Td)Ts

Ts, Ti

Ts, Ti, Tj

Ts, Ti, Tj, Tk

{T}

{T}

{T}

Ant RoutingAlgorithm:Conceptual

: sd ant

{Tj d d}: mean jd trip time table

{Pjdn d; nNj}: node j routing table

for destination d, neighborhood Nj

KEY:

: update

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

packetdelays(ms)

longitude (degrees)-180 -120 -60 0 60 120 180

60

30

0

-30

-60

-90

latitude(degrees)

Values for 'normal' traffic &'baseline' ACO, midnight at int’l dateline.

Geographic distribution of packet delays

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 + 0.6tqueue + 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).

time (s)time (s)

90th percentile

packet delays

(s)

b) 'normal'a) 'low'

time (s)time (s)

90th percentile

packet delays

(s)

d) 'high'c) 'intermediate'

SPFANTDIJKSTRA

time (s)time (s)

90th percentile

packet delays

(s)

f) 'bursty I'e) 'packet'

time (s)time (s)

90th percentile

packet delays

(s)

h) 'bursty III'g) 'bursty II'

SPFANTDIJKSTRA

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 ‘real-world’ 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