Advanced Computational Modelingof Social Systems

Lars-Erik Cederman and Luc GirardinCenter for Comparative and International Studies (CIS)

Swiss Federal Institute of Technology Zurich (ETH)http://www.icr.ethz.ch/teaching/compmodels

Artificial life andartificial intelligence

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Today’s agenda

• Complex Adaptive Systems• Artificial intelligence• Artificial life• Genetic algorithms

– Foundation– Genetic operators

• GeneIPD

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Complexity theory

A model of the Internet

The Santa Fe Institute

“Boids”

Complex adaptive systems exhibit properties that emerge from local interactions among many heterogeneous agents mutually constituting their own environment

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Complex Adaptive Systems

A CAS is a network exhibiting aggregate properties that emerge from primarily local interaction among many, typically heterogeneous agents mutually constituting their own environment.

Emergent properties Large numbers of diverse agents Local and/or selective interaction Adaptation through selection Endogenous, non-parametric environment

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What is the mind?

• Marionettes (ancient Greeks)• Hydraulics (Descartes)• Pulleys and gears (Industrial Revolution)• Telephone switchboard (1930’s)• Boolean logic (1940’s)• Digital computer (1960’s)• Hologram (1970’s)• Neural networks (1980’s - ?)

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Bottom-up vs top-down approach

Intelligence Lifemodel this

model these

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Definition of life

• No universally agreed definition of life.• Typical features

– Self-organization– Emergence– Autonomy– Growth– Development– Reproduction– Adaptation– Responsiveness– Evolution – Metabolism

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Artificial life

• “By the middle of this century, mankind has acquired the power to extinguish life on Earth.”

• “By the middle of next century, it will be able to create it. Of the two it is hard to say which places the largest responsibility on our shoulders”

Chris Langton

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Artificial life

• Theoretical biology• Artifactual (man-made), not unreal• Bottom up, not top down• Synthesis, not analysis• Leverages emergence• “The ‘artificial’ in Artificial Life refers to the

component parts, not the emergent processes. If the component parts are implemented correctly, the processes they support are genuine—every bit as genuine as the natural processes they imitate.” (Langton)

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Boids

• Craig Reynolds (1987) work on flocking behavior

• Virtual birds with basic flight capability• 3 rules

– (i) collision avoidance – avoid collisions with nearby flock-mates

– (ii) velocity matching – attempt to match velocity with nearby flock-mates.

– (iii) flock centering – attempt to stay close to nearby flock-mates

• Each boid is a basic unit that “sees” only its nearby flock-mates and “flies” according to the 3 rules.

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Boids (cont.)

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Boids (cont.)

• Result: boids flocked and flew as a cohesive group. When obstacles appeared in their way they spontaneously split into 2 subgroups, without central guidance, and rejoined after clearing obstruction.

• Illustrate basic principles of Alife systems – Large number of simple elemental units– Units interacting with nearby neighbors with no

central controller– High-level emergent phenomena from low level

interactions

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Novelty

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Genetic algorithms

• Genetic algorithms (GA’s) are an optimization technique

• GA’s are based on Darwin’s theory of evolution

• Genetic algorithms combine search algorithms with the genetics of nature.  

• Invented by John Holland in mid 70’s

Charles Darwin 1809-1882

John Holland

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Biological terminology

• Cell nucleus contain the genetic information

• Genetic information is stored in the chromosomes

• The chromosome is divided in parts: genes

• The different settings of the genes for one property is called: allele

• Every gene has an unique position on the chromosome: locus

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Reproduction

• During sexual reproduction, crossover occurs

• This recombination of chromosomes become the new individual

• Hence genetic information is shared between the parents in order to create new offspring

• During reproduction “errors” occur: mutation

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Natural selection

• The Origin of Species: “Preservation of favourable variations and rejection of unfavourable variations.”

• There are more individuals born than can survive, so there is a continuous struggle for life.

• Individuals with an advantage have a greater chance to survive: survival of the fittest.

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How does it works?

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Why genetic algorithms?

• If nature can do it, why can’t computers?

• Power of evolution to solve optimization problems

• Particularly well suited for hard problems where little is known about the underlying search space

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Selection

• Main idea: better individuals get higher chance

• Roulette-wheel sampling gives more fit individuals better chance:

A C

1/6 = 17%

3/6 = 50%

B

2/6 = 33%

f(A) = 3

f(B) = 1

f(C) = 2

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1-point crossover

• Sexual reproduction is performed by mixing genes from the parents

• With a certain probability, we cross over some couples.

• Choose a random point on the two parents• Split parents at this crossover point• Create children by exchanging tails

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Mutation

• Occurs at the isolated gene level within a chromosome

• Can result in changes, both positive and negative, in the fitness of an individual

• When positive, can help increase individual’s chance of being selected to be a parent of next generation

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A standard genetic algorithm

1. Start with a randomly generated population of n chromosomes (genotypes)

2. Calculate the fitness developed by each chromosomes in the population

3. Repeat the following steps until n offspring have been created:a) Select a pair of parent chromosomes from the current population,

the probability of selection being an increasing function of fitness

b) Crossover the pair, with probability pc (crossover rate), at one or two randomly chosen points, to produce two new offspring

c) Mutate the offspring at each locus with probability pm (mutation rate), and place the resulting chromosomes in the new population

4. Replace the current population with the new population

5. Go to step 2 (next generation)

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Iterated Prisoner’s Dilemma

• Cohen, Riolo, and Axelrod. 1999. “The Emergence of Social Organization in the Prisoner's Dilemma” (SFI Working Paper 99-01-002)http://www.santafe.edu/research/publications/wpabstract/199901002

• In The Evolution of Cooperation, Robert Axelrod (1984) created a computer tournament of IPD– cooperation sometimes emerges– Tit For Tat a particularly effective strategy

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Prisoner’s Dilemma Game

Column: C D

C 3,3 0,5Row:

D 5,0 1,1

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One-Step Memory Strategies

C

D

C

D

p

q

Memory:C

D

Strategy = (i, p, q)i = prob. of

cooperating at t = 0

p = prob. of cooperating if opponent cooperated

q = prob. of cooperating if opponent defected

t-1 t

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The Four Strategies

Name i p q

ALLC 1 1 1

TFT 1 1 0

ATFT 0 0 1

ALJD 0 0 0

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TFT meets ALLD

t0 1 2 3 4

Row(TFT)

Column(ALLD)

i=1

i=0

p=1; q=0

0

5

1 1

1 1 1

1

= 8

= 3+ + +

+ + +

D

C

D

C

D

D

D

D

D

D

p=0; q=0

CumulatedPayoff

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Payoffs for 4x4 strategies

Own strategy

Other‘s strategyALLC TFT ATFT ALLD

pay/move

sum

pay/move

sum

pay/move

sum

pay/move

sum

ALLC 333312

333312

00000

00000

TFT 333312

333312

01539

01113

ATFT 555520

51039

13138

10001

ALLD 555520

51118

155516

11114

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Genetic encoding for IPD model

• For each of the possible historical cases – encode a move.

C D D C D C D D D C C D D C C C D C

DD D C D C D D C C C C C C C D C C

Player 1

Player 2

History

Sliding window (memory depth =

3)

Future

C

D

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Genetic encoding for IPD (cont.)

Initialphantom

move

Second phantom

move

Two-rounds memory

D C D C D C D C D C D C D C D C DC C

C

C

C

C

D

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 01 1

D

D

D

D

D

D

Memory depth = 2

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GeneIPD

• Do cooperation emerge in a spatial world?

• Do defection emerge in a soup?• Is this always the case?• How does the crossover and

mutation rates affect the simulation?

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Definition of life

• What is life? Is “artificial” life possible?• Webster dictionary

– 1a. The quality that distinguishes a vital and functional being from a dead body or purely chemical matter.

– 1b. The state of a material complex or individual characterized by the capacity to perform certain functional activities including metabolism, growth and reproduction

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Life versus Intelligence

• Life is…Islands of information that

persist and reproduce.

• Intelligence is…The use of information to persist

and reproduce.

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Alternative Crossover Operators

• Performance with 1-point crossover depends on the order that variables occur in the representation– More likely to keep together genes that are

near each other– Can never keep together genes from opposite

ends of string– This is known as Positional Bias– Can be exploited if we know about the

structure of our problem, but this is not usually the case

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n-point crossover

• Choose n random crossover points• Split along those points• Glue parts, alternating between parents• Generalization of 1 point (still some

positional bias)

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Uniform crossover

• Assign 'heads' to one parent, 'tails' to the other• Flip a coin for each gene of the first child• Make an inverse copy of the gene for the

second child• Inheritance is independent of position

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Genetic encoding for IPD (cont.)

• 1 move remembered:If CC (case 1), then CIf CD (case 2), then DIf DC (case 3), then CIf DD (case 4), then D

• Can be encoded as the string “CDCD” or “1010”

• For two possible moves remembered ->16 (4 x 4) possibilities (16 bits string)

• For three possible moves remembered ->64 (4 x 4 x 4) possibilities (64 bits string)

Tit-For-Tat

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Genetic encoding for IPD (cont.)

• But this is not enough, as the strategy requires results from previous games

• Extra genes to encode hypothetical moves:1 move memory: 4 + 1 = 5 bits2 moves memory: 16 + 3 =19 bits3 moves memory: 64 + 7 = 71 bits

• Number of potential strategies for 3 moves history is in the order of 1021