Swarm Intelligence for Optimisation Problems ACAT 2002 Moscow

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Swarm Intelligence for Optimisation
ProblemsACAT 2002 Moscow

• Bruce Denby
• LISIF, Paris, France
• denby_at_ieee.org

Sylvie Le Hégarat CETP, Vélizy,
France mascle_at_cetp.ipsl.fr
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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

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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

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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

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Swarm Intelligence

• Since the early 1990s, 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

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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. ...

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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

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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)

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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

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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

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The Traffic Model
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Temporal dependence of voice and data traffic
expressed as a percentage versus time of day
over 24 hours.
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Traffic Levels for Gateways Projection 2005
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.
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Communication Establishment Probabilities
Values for voice (data) as a function of
geographic location of source and destination
nodes. Percentages sum to 100 left to right.
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Simulation Scenarios
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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.

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Ant Routing Algorithm Conceptual
Ts, Ti, Tj, Tk
KEY
s?d ant
T
Tj ?d ?d mean j?d trip time table
Pjdn ?d n?Nj node j routing table
for destination d, neighborhood Nj
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Ant Routing Table Update Algorithm

• First calculate r minT/(ltTgt) 1 where T is
  the current ant trip time and ltTgt 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)

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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

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Geographic distribution of packet delays
Values for 'normal' traffic 'baseline' ACO,
midnight at intl dateline.
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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.

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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?lttgtqueue
• 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).

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SPF ANT DIJKSTRA
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SPF ANT DIJKSTRA
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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)

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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

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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.

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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 lt 0,
  or, if ?Uij gt 0, with probability

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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

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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?)

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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

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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

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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

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Common properties that make agents different from
conventional programsfrom  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

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Properties of agents, contd.

• 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

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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?

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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

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We may conclude that ants are reactive, mobile,
multi-agent systems
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Careful, agent doesnt mean the same thing to
all people!!
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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)

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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)

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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

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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

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Conclusions

• Weve visited several Nature-inspired
  algorithms
• Whats new here are the ACO-like ones
• Is Agent-Based Computing poised to become the
  Neural Networks of the 2000s?
• Will Ants help find the Higgs?

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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