Strategies and Rubrics for Teaching Chaos and Complex Systems Theories as Elaborating, Self-Organizing, and Fractionating Evolutionary Systems

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Strategies and Rubrics for Teaching Chaos and
Complex Systems Theories as Elaborating,
Self-Organizing, and Fractionating Evolutionary
Systems
Fichter, Lynn S., Pyle, E.J., and Whitmeyer,
S.J., 2010, Journal of Geoscience Education (in
press)
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Elaborating Evolutionary Mechanisms
The General Evolutionary Algorithm
1. Differentiate
The units of selection and the information
carriers are different in each kind of system but
the algorithm is the same . . .
2. Select
3. Amplify
Repeat
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Elaborating Evolution
Word Evolv
Genetic Algorithms
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Elaborating Evolution
A genetic algorithm (GA) is a search technique
used to find exact or approximate solutions to a
problem.
In biological evolution the solution is
measured as a fitness function, how well adapted
the organism is to its environment.
Natural selection works on the organisms,
eliminating those that are less fit, while
allowing the more fit to live, and reproduce.
For example . . .
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General Evolutionary Algorithm in Biology
Differentiate
Select
Amplify
Repeat
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Elaborating Evolution
WordEvolv is a genetic algorithm that
demonstrates how efficient natural selection is.
The procedure is . . .
Create a fitness function. For example, the
phrase, What is this phrase. This is known as
the target string.
Then 1. Generate at random 20 strings of letters
and spaces of the same length as the target
string.
2. Pass the 20 strings through a selection
filter, comparing each of the strings with the
target string. Keep the one string closest to
the target, discard (select out) all the other
strings.
3. Reproduce the one surviving string 20 times,
but mutate each at random (i.e. change one letter
in each string from the initial).
4. Repeat process.
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Elaborating Evolution
John Muir Trail
Can we evolve via natural selection (i.e. a
genetic algorithm) an electronic ant that can
learn to run a maze?
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The John Muir Trail
The Trail
The trail itself is a series of black squares on
a 32x32 white toroidal (ie, wraparound) grid.
Each black square is numbered sequentially, from
1, directly next to the starting square, to 89,
the ending square. The ant's task is to follow
this trail and move across each square in
sequence That is, it does not get a score of 89
for waltzing across the board from square 0
directly to square 89. It must first visit each
square in turn.
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The John Muir Trail
Random Approach
UCLA experiment the power, or lack thereof, of a
random search.

• 1 billion strings of genetic code were generated
  at random.

• The best was only able to get to square 81 on the
  trail.

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The John Muir Trail
Evolutionary Approach
Generate a series of electronic ants each with
a genetic code created at random.
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The John Muir Trail
The Ant gene consists of 512 bits of information,
a series of 1's and 0's. The genetic makeup is
changed each generation at some low frequency
either by cross overtwo individuals exchange
part of their string of genesor by mutationone
gene has its bit flipped from 1 to 0 or vice
versa.
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The John Muir Trail
The ants are simple state machines which can move
along the trail and sense their immediate
surroundings.

• The ant stands on a single square and can face
  north, south, east, or west.

• It is capable of sensing the state of the square
  directly in front of it.

• In each time step, the ant must take one of four
  actions. It may turn left, turn right, move
  forward one step, or stand still.

• The ant's score is the value of the highest
  square it was able to reach when a fixed amount
  of time has passed.

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Learning to Run the John Muir Trail
1. The first generation of ants was given
totally random genotypesthey were strings of
ones and zeros selected by chance.
2. A population of 64 K, or 65,536, of these
"random" ants was created.
3. In this first generation, it was common for
ants not to move at all, or to move haphazardly,
or to continue stubbornly in a single direction.
4. After each ant was scored, the top 1 was
selected for reproduction in the next generation
and copied to compose a full population
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Learning to Run the John Muir Trail
5. During reproduction.

• Mutate a small percent of the new ants at a low
  rate

• Conduct crossovers at a certain small rate.

REPEAT
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The John Muir Trail
Typical Run of an Ant Experiment as run by
Patrick Brennan note that an ant capable of
running nearly the entire trail evolved in less
than 200 generations.
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Examples of the General Evolutionary Algorithm In
Practice
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Ramps, Anti-Ramps and the Red Queen
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Danny Hillis, 1991, 'Co-evolving Parasites
Improve Simulated Evolution as an Optimization
Procedure'
Ramps is a genetic algorithm evolving to reach a
fitness peak at solving a mathematical problem -
the ability to sort a random number list.
Fitness is measured by the shortest number of
steps evolved to solve the various problems
present in the environment.
Antiramps is a genetic algorithm evolving to
reach a fitness peak at creating test cases the
Ramps can not solve well with the strategies
evolved to date. That is, the most fit Antiramps
are those which resist being sorted easily or
well.
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The Prisoners Dilemma and Evolution of
Cooperation