ant colony optimization overview

8/2/2019 Ant Colony Optimization Overview

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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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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

E

H C

A

B

d=0.5

d=0.5

d=1.0

d=1.0

15ants

E

D

H C

A

B

30 ants

15

ants15

ants

15ants

30

ants

T =

0

E

H

D

C

A

B

30 ants

10

ants20

ants

20

ants

10

ants

30

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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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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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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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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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/

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