an ant colony optimization

8/22/2019 An Ant Colony Optimization

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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 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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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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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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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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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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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

an ant colony optimization

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