Robert Jackson Marks II2 Applications: Warfare & Game Theory Aviation Weekly, Sept 29, 2003.

Robert Jackson Marks II 2

Applications: Warfare & Game Theory

Aviation Weekly , Sept 29, 2003


Applications: Business““Swarm Intelligence: A Whole New Way to Swarm Intelligence: A Whole New Way to

Think About Business”Think About Business”

Harvard Business Review, May 2002Harvard Business Review, May 2002

Using swarm intelligence optimization, Using swarm intelligence optimization, Southwest Airlines slashed freight transfer Southwest Airlines slashed freight transfer

rates by as much as 80%.rates by as much as 80%.

““Similar research into the behavior of Similar research into the behavior of social insects has helped … Unilever, social insects has helped … Unilever,

McGraw Hill, and Capital One, to develop McGraw Hill, and Capital One, to develop more efficient ways to schedule factory more efficient ways to schedule factory

equipment, divide tasks among workers, equipment, divide tasks among workers, organize people , and even plot strategy.”organize people , and even plot strategy.”


Applications: Telecommunications

Scientific American, March 2000Scientific American, March 2000

“Several companies are [using swarm intelligence] for handling the

traffic on their networks. France Télécom and British

Telecommunications have taken an early lead in applying antbased

routing methods to their systems… The ultimate application,

though, may be on the Internet, where traffic is particularly

unpredictable.”


Applications: OptimizationApplications: Optimization

Particle Swarm: An Particle Swarm: An (enormously effective!) (enormously effective!)

multi- agent multi- agent optimization optimization

algorithm based on the algorithm based on the biomimetics of bird biomimetics of bird

flight.flight.


Application: FictionApplication: Fiction


Boundary Marking: The Problem

• Solve the equationSolve the equation f f ((xx)) = c = c

f f (( .. )) is a function,is a function, c c is a given constant, and is a given constant, and xx is a vector. is a vector.

• Assumption: Assumption: There are a number of solutions.There are a number of solutions.

(The problem is(The problem is ill-posedill-posed.).)


Solve for contourSolve for contourf(f(xx) = c) = c

x1

x2

Edge Island

In 59 Dimensions Details Notes


What is Swarm Intelligence?What is Swarm Intelligence?Simple Rules for Multiple Agents.Simple Rules for Multiple Agents.

Randy’s RulesRandy’s Rules–Drive FastDrive Fast

–Turn LeftTurn Left


Another rule…Another rule…

– Drive FastDrive Fast– Turn LeftTurn Left– Don’t hit stuffDon’t hit stuff

• Emergent BehaviorEmergent Behavior– Competition- Winning!Competition- Winning!


Gnat Swarm: One Simple Rule

Steady State

In

Out


The Dumb Termite Clearing Wood

RULES• Run around randomly until you bump

into a piece of wood.• Pick it up.• Run around randomly until you bump

into a piece of wood.• Put it down.• Repeat forever.Q: What does this do? MOVIE


The Dumb Termite Clearing Wood

• Run around randomly until you bump into a piece of wood.

• Pick it up.• Run around randomly until you bump

into a piece of wood.• Put it down.• Repeat forever.Q: What does this do?

MOVIE


Ant Clustering

Ants cluster

their dead to clean

their nest.


Termite Wood Moving


Another Termite Simulation with a Velocity Bias

Click


Worm Search: Looking for Your Lost Pet Turtle Under a Lamppost

Tradeoffs:Tradeoffs:• Easier to look Easier to look

under lamppost under lamppost • Want to look Want to look

uniformly in uniformly in around the area.around the area.

Pareto Optimization Pareto Optimization (Efficient Frontier)(Efficient Frontier)

Agent Rule:

1. Diminishing Radius Momentum – if the visible

radius decreases, the momentum is increased.

2. Don’t tred on me.

Emergent Behavior: A parameter to tune between the optimization criteria.


Q: What does a pile of sand have to do with a swarm?

A: 1. Simple RulesA: 1. Simple Rules2. Pareto Statistics2. Pareto Statistics

(Power Law)(Power Law)EarthquakesEarthquakes

IncomeIncomeCitationCitation

Size of warsSize of warsSize of citiesSize of cities

Dweeb MassacresDweeb Massacres


Bullies & Dweebs• Evasion – Pursuit

Click


• Based on intuition and judgment• No need for a mathematical model• Relatively simple, fast and adaptive

• Less sensitive to system fluctuations• Can implement design objectives,

difficult to express mathematically, in linguistic or descriptive rules.


CELN MN SN ZE SP MP LP

LN LN LN LN LN MN SN SNMN LN LN LN MN SN ZE ZESN LN LN MN SN ZE ZE SP

E ZE LN MN SN ZE SP MP LPSP SN ZE ZE SP MP LP LPMP ZE ZE SP MP LP LP LPLP SP SP MP LP LP LP LP

Antecedents Consequent


-1800

-900

0

900

1800

0 3 6 9 12 15 18 21 24 27Time [sec]

rpm

trajectoryresponse


0

1

2

3

4

5

0 3 6 9 12 15 18 21 24 27Time [sec]

Tu

rn

trajectoryresponse


Combinatorial Rule Explosion

• For the trajectory example given– 2 antecedents– 7 rules each– 72 rules

• In general– A antecedents– R rules each– RA rules = exponential growth– e.g. 10 antecedents, 10 rules = 10 billion rules per

consequent

“The curse of dimensionality”


Dweeb Control• Antecedents for Dweeb control

– Nearest bully x – Nearest bully y– Nearest Dweeb tracked by Bully x – Nearest Dweeb tracked by Bully y– Nearest Dweeb x– Nearest Dweeb y– Distance from ceiling– Distance from floor– Distance from right wall– Distance from left wall

• Consequents– Dweeb’s x & y– Dweeb’s twiddlex & twiddley


10 antecedents, 3 rules per =310

rules

4 consequents

= 236,196 rules

Dweeb Control• Antecedents for Dweeb control

– Nearest bully x – Nearest bully y– Nearest Dweeb tracked by Bully x – Nearest Dweeb tracked by Bully y– Nearest Dweeb x– Nearest Dweeb y– Distance from ceiling– Distance from floor– Distance from right wall– Distance from left wall

• Consequents– Dweeb’s x & y– Dweeb’s twiddlex & twiddley


Dweeb Control: How we Think• Antecedents for Dweeb control

– Nearest bully x Dweeb x – Nearest bully y Dweeb y – Nearest Dweeb tracked by Bully x Dweeb x – Nearest Dweeb tracked by Bully y Dweeb y – Nearest Dweeb x Dweeb x – Nearest Dweeb y Dweeb x – Distance from ceiling Dweeb y – Distance from floor Dweeb y – Distance from right wall Dweeb x – Distance from left wall Dweeb x

• 30 rules for x and y, not 118,098


Combs & Andrews

(ABC…) R (AR)+(BR)+(CR)+…

Conjunctive inference: Disjunctive inference:

1. RA rules per consequent 1. RA rules per consequent

2. Brittle 2. Plastic

3. Expert Unmanageable 3. Expert Manageable


Disjunctive vs. Conjunctive Inferencing:

Plasticity & Robustness

Dynamic Adaptivity

Cognitive Parallels

Reasoning In Complex Situations

Under Finite Computational Resources

Tractability


Multi-Agent Criteria: Uncover Multi-Agent Criteria: Uncover important search area.important search area.

• Antecedents:1. Distance from

Unexplored Area2. Location of Newly

Discovered area3. Distance of Nearest

Agent4. Radius

Diminishment

• Consequents:

Velocity Components

1. In direction of new discovery

2. In direction of unexplored area

3. Away from nearby agents

4. In direction of diminished radius

Robert Jackson Marks II2 Applications: Warfare & Game Theory Aviation Weekly, Sept 29, 2003.

Documents

Transcript of Robert Jackson Marks II2 Applications: Warfare & Game Theory Aviation Weekly, Sept 29, 2003.