Robert Jackson Marks II2 Applications: Warfare & Game Theory Aviation Weekly, Sept 29, 2003.
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Transcript of 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
Robert Jackson Marks II 3
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.”
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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.”
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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.
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Application: FictionApplication: Fiction
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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.).)
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Solve for contourSolve for contourf(f(xx) = c) = c
x1
x2
Edge Island
In 59 Dimensions Details Notes
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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
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Another rule…Another rule…
– Drive FastDrive Fast– Turn LeftTurn Left– Don’t hit stuffDon’t hit stuff
• Emergent BehaviorEmergent Behavior– Competition- Winning!Competition- Winning!
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Gnat Swarm: One Simple Rule
Steady State
In
Out
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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
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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
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Ant Clustering
Ants cluster
their dead to clean
their nest.
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Termite Wood Moving
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Another Termite Simulation with a Velocity Bias
Click
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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.
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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
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Bullies & Dweebs• Evasion – Pursuit
Click
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• 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.
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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
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-1800
-900
0
900
1800
0 3 6 9 12 15 18 21 24 27Time [sec]
rpm
trajectoryresponse
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0
1
2
3
4
5
0 3 6 9 12 15 18 21 24 27Time [sec]
Tu
rn
trajectoryresponse
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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”
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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
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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
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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
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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
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Disjunctive vs. Conjunctive Inferencing:
Plasticity & Robustness
Dynamic Adaptivity
Cognitive Parallels
Reasoning In Complex Situations
Under Finite Computational Resources
Tractability
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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
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