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An Overview of Swarm
Intelligence and Ant ColonyOptimization Heuristics
Philipp A. Djang Ph.D.
Army Research Labs
"Go to the ant, thou sluggard; consider her ways, and be wise:Which having no guide, overseer, or ruler,
Provideth her meat in the summer,and gathereth her food in the harvest"
(Proverbs vi 6-8)
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Overview
Swarm Intelligence
Ant Colony Algorithm
Solving a Traveling SalespersonProblem
Other Examples
References
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Swarm Intelligence Swarm Intelligence (SI) is the property of a
system whereby the collective behaviors of(unsophisticated) agents interacting locallywith their environment cause coherentfunctional global patterns to emerge.
SI provides a basis with which it is possible toexplore collective (or distributed) problemsolving without centralized control or theprovision of a global model.
Leverage the power of complex adaptivesystems to solve difficult non-linear stochasticproblems
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Swarm Intelligence
Characteristics of a swarm:
Distributed, no central control or data
source; Limited communication
No (explicit) model of the environment;
Perception of environment (sensing) Ability to react to environment changes.
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Swarm Intelligence
Social interactions (locally sharedknowledge) provides the basis for
unguided problem solving The efficiency of the effort is related to
but not dependent upon the degree or
connectedness of the network and thenumber of interacting agents
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Swarm Intelligence
Robust exemplars of problem-solving inNature Survival in stochastic hostile environment
Social interaction creates complexbehaviors
Behaviors modified by dynamicenvironment.
Emergent behavior observed in: Bacteria, immune system, ants, birds
And other social animals
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Ants Swarm Intelligence
Example Franks observed Lasius Nigerants,
regulation of 1 degree Celsius range;
forming bridges;
raiding specific areas for food; building and protecting nest;
sorting brood and food items;
cooperating in carrying large items;
emigration of a colony;
finding shortest route from nest to food source; preferentially exploiting the richest food source available.
Without Any Central Leadership or Control
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Ant Colony Optimization:
Introduction First proposed by M. Dorigo, 1992
Heuristic optimization method inspired by
biological systems Multi-agent approach for solving difficult
combinatorial optimization problems
Traveling Salesman, vehicle routing, sequential
ordering, graph coloring, routing incommunications networks
Has become new and fruitful research area
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Ant Colony Algorithms Algorithm was inspired by observation
of real ant colonies.
Ants are essentially blind, deaf and
dumb. Ants are social creatures behavior
directed to survival of colony
Q: how can ants find the short path tofood sources?
Ants deposit pheromoneson groundthat form a trail. The trail attracts otherants.
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Ant Colony Algorithms
Ant behavior is a kind of stochasticdistributed optimization behavior.
Although one ant is capable of buildinga solution, it is the behavior of anensemble of ants that exhibits theshortest path behavior.
The behavior is induced by indirectcommunication (pheromone paths)without central control.
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Ant Colony Algorithms Ants do not know the global structure of
the problem - discoverthe network
Limited ability to sense localenvironment - can only see adjacentnodes of immediate neighborhood.
Each ant chooses an action based onvariableprobability
random choice
pheromone mediated
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Ant Colony Algorithms
Each ant collects information aboutlocal environment; acts concurrently
and independentlyNo direct communication: stigmergy
paradigm governs information exchange
Incremental constructive approach tobuilding solutions
High quality solutions emerge via globalcooperation.
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Stigmergy
Indirect communication via interactionwith environment [Gass, 59, Wilson,75] Sematonic stigmergy
action of agent directly related to problemsolving and affects behavior of other agents.
Sign-based stigmergy action of agent affects environment not directly
related to problem solving activity.
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Species lay pheromone trails traveling fromnest, to nest or possibly in both directions.
Pheromones evaporate. Pheromones accumulate with multiple ants
using path.
Pheromone Trails
Foodsource
Nest
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Pheromone Trails Example
D
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A
B
d=0.5
d=0.5
d=1.0
d=1.0
15ants
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A
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30 ants
15
ants15
ants
15ants
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ants
T =
0
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H
D
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A
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30 ants
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ants20
ants
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ants
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ants
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ants
T =
1
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Ant Colony Algorithms Pheromone mediated following
behavior induces the emergence ofshortest paths.
Probability of choosing a branch of apath at a certain time depends on thetotal amount of pheromone on thebranch.
The choice is proportional to thenumber of ants that have used thebranches.
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Ant Colony Algorithms
Let um and lm be the number of ants thathave used the upper and lower
branches. The probability Pu(m) with which the
(m+1)th ant chooses the upper branch
is:
)()(
)()(
klku
kuP
mm
mm
hh
h
u
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Traveling Salesperson Problem
Famous NP-Hard Optimization Problem
Given a fully connected, symmetric
G(V,E) with known edge costs, find theminimum cost tour.
Artificial ants move from vertex to vertex
to order to find the minimum cost tourusing only pheromone mediated trails.
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Traveling Salesperson Problem
The three main ideas that this antcolony algorithm has adopted from real
ant colonies are: The ants have a probabilistic preference
for paths with high pheromone value
Shorter paths tend to have a higher rate of
growth in pheromone value It uses an indirect communication system
through pheromone in edges
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Traveling Salesperson Problem
Ants select the next vertex based on aweighted probability function based on twofactors: The number of edges and the associated cost The trail (pheromone) left behind by other ant
agents.
Each agent modifies the environment in twodifferent ways :
Local trail updating: As the ant moves betweencities it updates the amount of pheromone on theedge
Global trail updating: When all ants havecompleted a tour the ant that found the shortestroute updates the edges in its path
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Traveling Salesperson Problem
Local Updating is used to avoid verystrong pheromone edges and hence
increase exploration (and hopefullyavoid locally optimal solutions).
The Global Updating function gives the
shortest path higher reinforcement byincreasing the amount of pheromone onthe edges of the shortest path.
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Empirical Results
Compared Ant Colony Algorithm tostandard algorithms and meta-heuristic
algorithms on Oliver 30 a 30 city TSP Standard: 2-Opt, Lin-Kernighan,
Meta-Heuristics: Tabu Search andSimulated Annealing
Conducted 10 replications of eachalgorithm and provided averaged results
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Comparison to Standard
Algorithms Examined Solution
Quality not speed;
in general, standardalgorithms weresignificantly faster.
Best ACO solution -
420
2-Opt L-K
NearNeighbor
437 421
Far Insert 421 420
Near Insert 492 420
Space Fill 431 421
Sweep 426 421
Random 663 421
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Comparison to Meta-Heuristic
Algorithms Meta-Heuristics are algorithms that can be
applied to a variety of problems with a minimumof customization.
Comparing ACO to other Meta-heuristicsprovides a fair market comparison (vice TSPspecific algorithms).
Best Mean Std Dev
ACO 420 420.4 1.3
Tabu 420 420.6 1.5
SA 422 459.8 25.1
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Other Application Areas
Scheduling : Scheduling is awidespread problem of practical
importance. Paul Forsyth & Anthony Wren,
University of Leeds Computer Science
department developed a bus driverscheduling application using ant colonyconcepts.
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Other Application Areas Telecommunication Networks : Network
routingrefers to the activity of creating,maintaining and using routing tables (one foreach node in the network) to determinewhere to direct an incoming data stream sothat it can continue its travel through thenetwork.
In telecommunications, this is an extremelydifficult problem because of the constantchanges in network traffic load. The AntColony algorithm provides adaptiveadvantages that can adjust to traffic load.
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Other Application Areas
Vehicle Routing Problem: The VRP issimilar to the TSP, but is complicated by
multiple vehicles, vehicle capacity, pick-up and drop off points (which candictate vehicle packing and scheduling).
Bernd Mullenheimer, Richard Hartl andChristine Strauss developed an AntColony algorithm for solving the VRP
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Ant Colony Algorithms: Summary
Ant Colony Algorithms mimic Real Ants
Colony of cooperating individuals
Simulated Pheromone Trail and Stigmergy
Shortest path searching with local moves
Stochastic and myopic state transitionpolicy
Artificial ants:Discrete state transitions
Pheromones based on solution quality
Pheromone laying is problem dependent
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Interesting Reading
Alexandrov D., Kochetov Y. Behavior of the Ant ColonyAlgorithm for the Set Covering Problem, Proc. of Symposium.on Operations. Research., Springer Verlag, 2000
On the MAX/MIN Ant system, Thomas Sttzle, 2001.
Hybrid Ant System for the Sequential Ordering Problems, LucaGambardella, 2002.
Parallelization Strategies for Ant Colony Optimization byThomas Sttzle. In Proceedings of PPSN-V, Amsterdam,Springer Verlag, LNCS 1998
Improvements on the Ant System: Introducing the MAX-MIN Ant
System by Thomas Sttzle. Proceedings of Artificial Neural Netsand Genetic Algorithms 1997
The Ant System Applied to the Quadratic Assignment Problemby Maniezzo, Colorni and Dorigo. Tech. Rep. IRIDIA/94-28,Universit Libre de Bruxelles 1994
http://aida.intellektik.informatik.th-darmstadt.de/~tom/tsp.htmlhttp://www.idsia.ch/~luca/has-sop.htmlhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/PPSN-V.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzftp://iridia.ulb.ac.be/pub/dorigo/tec.reps/TR.03-ANT-QAP.ps.gzftp://iridia.ulb.ac.be/pub/dorigo/tec.reps/TR.03-ANT-QAP.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/ICANNGA97.ps.gzhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/publications/PPSN-V.ps.gzhttp://www.idsia.ch/~luca/has-sop.htmlhttp://aida.intellektik.informatik.th-darmstadt.de/~tom/tsp.html -
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Interesting Reading
Dorigo, M., Maniezzo, V., Colorni, A., The AntSystem: Optimization by a Colony of CooperatingAgents, IEEE Transactions on Systems, Man andCybernetics-Part B, v26,n1, 1996
Rafael S. Parpinelli and Heitor S. Lopes and Alex A.Freitas, An Ant Colony Based System for DataMining: Applications to Medical Data, Proceedings ofthe Genetic and Evolutionary ComputationConference ({GECCO}-2001)
Nicolas Monmarch, Mohamed Slimane, GillesVenturini,AntClass: discovery of clusters in numericdata by an hybridization of an ant colony with thekmeans algorithm, 1999
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On-Line Resources
http://www.swarm.org/
http://www.swarm-bots.org/
http://dsp.jpl.nasa.gov/members/payman/swarm/
http://www.engr.iupui.edu/~shi/pso.html
http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html
http://www.cs.technion.ac.il/~wagner/
http://ants.gsfc.nasa.gov/