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An Ant Colony Optimization
Approach to the BorderPenetration Model
Philipp A. Djang Ph.D.
ARL/SLAD/IEPDDecember 12, 2002
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Overview
Introduction to Ant Colony Algorithms
An Application to Border Penetration
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Introduction
First proposed by M. Dorigo, 1992
Heuristic optimization method inspired
by biological systemsMulti-agent approach for solving difficult
combinatorial optimization problems
Traveling Salesman, vehicle routing,sequential ordering, graph coloring, routing
in communications networks
Has become new and fruitful research
area
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Ant Colony AlgorithmsAlgorithm was inspired by observation
of real ant colonies.
Ants are essentially blind, deaf and
dumb.Ants are social creaturesbehavior
directed to survival of colony
Q: how can ants find the short path tofood sources?
Ants depositpheromoneson groundthat form a trail. The trail attracts otherants.
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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 umand lmbe the number of ants that
have used the upper and lower
branches. The probability Pu(m) with which the
(m+1)thant chooses the upper branch
is:
)()(
)()(
klku
kuP
mm
mmhh
h
u
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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) andis termed stigmergy.
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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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Ant Colony AlgorithmsAnts do not know the global structure of
the problem - discoverthe network
Limited ability to sense local
environment - can only see adjacent
nodes of immediate neighborhood.
Each ant chooses an action based on
variableprobability
random choice
pheromone mediated
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Algorithm: Overview
Initialize ants: pick start and goal nodes For each ant do:
Move: Select a node in local neighborhood
Randomly choose a node
pheromone mediated (greedy)
Communicate: deposit scent trail
If goal node is found, increase pheromoneweights of path
Check Time-to-Live: ant dies if time is
exceeded.
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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 transition
policy
Artificial ants:Discrete state transitions
Pheromones based on solution quality
Pheromone laying is problem dependent
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Border Penetration Problem
An application of an Ant ColonyOptimization Algorithm
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Border Penetration ProblemA group of terrorists must travel from
destination city in Canada to a targetcity in the US.
A fixed number of locations and routesthat link the locations are given.
For each route, a difficulty rating and
risk rating are assigned. The problem is to find the shortest path
given the risk and difficulty of eachroute.
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Border Penetration Problem
However, this is a stochastic problem.From any location, the agent selects thenext location and a fair die is rolled.
If the value of the die is less than thedifficulty rating, the agent waits oneturn, otherwise the agent proceeds.
If the value of the die is less than therisk rating, the agent lives, otherwise,the agent dies.
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Border Penetration Problem
Formally, the problem can constructed as:
Given a Graph G with Nodes (N) and a set ofedges (E). G is incompletely connected.
Let i,j N, a set of NodesAnd i* = start node and j* = end node
Let xij=1 if the edge between node i and j areselected in the optimal route.
Let Dijrepresent an estimate of the difficultyfor edge i->j and ijbe realized value
Let Rij represent an estimate of the risk for
edge i->j and ijbe realized value
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Border Penetration Problem The problem is to find the minimum
route path subject to difficulty and risk
constraints
ij ijij ijij
ij ijij ijij
j iji
rx
dx
xMin
z
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Border Penetration Problem
An ant colony optimization algorithmwas developed to address thisstochastic problem.
A software simulation system wasimplemented to visualize thepenetration of the border.
And illustrate how the system discoversdifferent routes and eventually finds thebest routes.
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Border Penetration ProblemAnts have a limited time to live and are
removed when
The risk policy forces death
Time to live (simulation steps) is exceededDead ants are replaced at the next time
step
Ants select nodes stochastically:
With probabilityp, a random node isselected
With probability 1-p, the pheromone trail
will influence the selection of a node.
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Border Penetration Problem
Better routes are stored in artificialpheromone memory and used to bias theselection of future nodes
The selection probability for an edge changesas better routes are discovered.
The simulation allows the user to select any
start and end node; ants discover the graphand construct paths from the start to the endnode.
The simulation records descriptive statistical
behaviors of the ant colony.
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A Screen Shot
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Future WorkDevelop a blue agent system to protect
against red agent penetration.
Blue agent adjusts the risk factor of the
edges subject to resource constraints.
Blue agent decisions will be based on
reflexive control concepts
Interaction between red and blue agents
may give yield co-evolutionary
strategy development
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Conclusion The ant colony algorithm is can be
generalized to other problems.
For example, if the ants can be
considered and mobile (disposable)unattended ground sensors, the
algorithm could be used to guide them
to find interesting objects. The algorithm could also be used to
assist with intelligent movement of
tactical vehicles