PARALLEL GENETIC ALGORITHMS AND THE SCIENCE OF ASTEROSEISMOLOGY

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PARALLEL GENETIC ALGORITHMS AND THE SCIENCE OF
ASTEROSEISMOLOGY

• A Review of the Doctoral Dissertation Research of
  Dr. Travis Metcalfe

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Outline

• Introduction
• The Science of Asteroseismology
• The Genetic Algorithm
• Parallel Computing
• Conclusion

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Introduction

• Astronomers observe the universe and gather
  information about it. They then fit this
  information into mathematical models. The
  process of fitting involves adjusting the many
  parameters of the model. When they have a good
  fit, they use the parameter settings to tell them
  something about the object or phenomenon they are
  studying. The author uses a parallel genetic
  algorithm to solve this problem of optimization.

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• The Goal of the Research
• To Further the Understanding of the Composition
  and Characteristics of White Dwarves
• More Generally, Since White Dwarves are the
  Endpoint for all but the most massive stars, this
  research can lead to a better understanding of
  stellar evolution

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Source
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Traditional Technique

• Make an initial guess for parameter values
• Use some iterative technique to improve upon the
  initial guesses.

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Adjustable Input Parameters

• Mass
• Temperature
• H and He layer masses
• Convective Efficiency
• Core composition

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Problem with this technique

• Results often depend on the initial guess
• The initial guess is inherently subjective, often
  the result of intuition or past experience

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The Genetic Algorithm

• A genetic algorithm provides a more systematic
  approach to optimizing the results
• The genetic algorithm used was PIKAIA
• PIKAIA is a general purpose function
  optimization genetic algorithm
• Public domain software
• Fortran-77

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Outline

• Introduction
• The Science of Asteroseismology
• The Genetic Algorithm
• Parallel Computing
• Conclusion

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• White dwarves which show a regular variation in
  light intensity are known as pulsating white
  dwarves
• Using photometric techniques, this variation in
  intensity can be very accurately measured with
  such instruments as the Whole Earth Telescope
  (WET)

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• The pulsation is the result of seismic activity
  within the white dwarf
• Just as seismological information can be used to
  study the internal nature of the earth,
  seismological data, as expressed in varying
  stellar luminosity, can be used to determine the
  characteristics of these pulsating white dwarves.

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Observed Light Curve for the White Dwarf GD 358.
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Outline

• Introduction
• The Science of Asteroseismology
• The Genetic Algorithm
• Parallel Computing
• Conclusion

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Initial Conditions

• Population size 1000 ( in later work this was
  reduced to 128).
• No rationale was given for how the initial
  population value was chosen, or why it was
  changed.
• For each member of the initial population,
  parameter values are randomly set

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Duration

• Until the difference between the average fitness
  and the best fitness in the population were less
  than 1.
• In later work, he used a constant 200 generations.

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Fitness Measurement

• The model is then run using these initial values
• Fitness is based on the root-mean-square
  differences between the observed and calculated
  pulsation periods

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Fitness Measurement

• The fitness value is converted to a survival
  probability by normalizing with respect to the
  most fit member
• The next generation is chosen randomly. This
  random selection is weighted, based on each
  members survivability ratio

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Crossover

• Numerical encoding
• Each of the initial parameter values are
  concatenated into one long string
• A single point crossover technique is used. The
  position along the string is picked randomly

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Mutation

• Mutation is achieved by randomly selecting a
  number in the string and changing it to a new,
  randomly chosen value

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Illustration

• Consider two members, each with two parameters.
• M1 has X2.573 and Y 4.457.
• M2 has parameter values X3.547 and Y2.332.
• After encoding, M125734457 and M235472332

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Illustration

• The crossover point is randomly chosen, and the
  string segments swapped

M1 25734457 ? 25734332 M2 35472332 ?
35472457
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Illustration

• Mutating M1 involves picking a random spot along
  the string, and changing that value

M1 25734332 ? 25784332
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Illustration

• The strings would then be parsed back into
  parameter values. For M1, this would be

M1 X 2.578 Y4.332 Modified from 1
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Crossover and Mutation Rate

• The cross over rate 65
• The mutation rate 0.3.
• In later work, the author increased the crossover
  rate to 85 and varied the mutation rate from
  0.1 to 16.6, depending on the variation between
  the mean fitness value, and the best fitness value

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Elitism

• The most fit solution was passed unaltered the
  next generation

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Rationale

• The idea behind the relatively low crossover and
  mutation rate is to prevent removing promising
  solutions from each generation too rapidly

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Repetition

• The paper states Repeating this procedure many
  times with different random number seeds helps to
  ensure that the minimum found is truly global
• It does not elaborate on how many Many times is,
  though

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Repetition

• In a later paper, he uses 5 repetitions
• This result was obtained in the following way

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• Values were put in for the model, and pulsation
  periods generated.
• The genetic algorithm attempted to find the
  original parameters based on the output of the
  model
• This was done 20 times, and the results were as
  follows

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Results (second paper)

• First Order Solution

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• The genetic algorithm found the exact result 9/20
  times, and was close enough on four other
  occasions for the correct result to be determined
  by the addition of some other iterative
  technique, for a total of 65 accuracy.

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• If the GA was rerun, and the best result
  selected, the accuracy increased to 88
• After 5 runs, the accuracy was over 99
• Because no correct answer was found after 200
  iterations, the number of generations was reduced
  to 200

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Output Curve
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Outline

• Introduction
• The Science of Asteroseismology
• The Genetic Algorithm
• Parallel Computing
• Conclusion

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• Problem Division
• Part one running the numerical model using a
  large number of different initial parameters.
• Part two determining fitness, selecting the next
  generation, and performing crossover/mutation

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Master-Slave Paradigm

• Part one running the model with a given set of
  parameters was performed by the slave nodes
• Part two fitness evaluation, selection/crossover
  /mutation was performed by the master node

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PVM

• PVM was used as the message passing library

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Execution

• The master machine generates a job pool of
  parameter values that it passes to the slave
  machines.
• The slave machines in turn run the model and
  return the results to the master.
• If there are more parameter sets available, the
  node is given another job.

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Execution

• The master calculates variance.
• Determines fitness.
• After the models have been run for a given
  generation, the master determines the members of
  the next generation and runs the
  crossover/mutation methods on the appropriate
  portion of the new population.
• As the new parameters are created, they are sent
  to the workstations.

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The Network

• The Cluster is composed of one master computer
  and 64 slave nodes
• The cluster of computers is divided into three
  subnets
• Each subnet is connected to the master serially,
  using coaxial cable and a 10base-2 (thin
  Ethernet) system

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Darwin

• Pentium-II 333 MHz system with 128 MB RAM
• Two 8.4 GB hard disks.
• Three NE-2000 compatible network cards, one for
  each of the segments

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Darwin
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Nodes

• Motherboard
• Processor
• Single 32 MB RAM chip
• NE-2000 compatible network card
• No Hard drive!

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Nodes

• Half of the nodes contain Pentium-II 300 MHz
  processors, while the other half are AMD K6-II
  450 MHz chips

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The Cluster
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Conclusion

• Based on initial results, the use of genetic
  algorithms appears to be a promising method for
  minimizing the residual difference between
  observational data and the WilsonDevinney model

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Conclusion

• It is also a wonderful example of how parallel
  computing, open source software and clusters of
  workstations can have a profound impact on the
  course of research.

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PIKAIA Namesake
Pikaia Gracilens, a little worm-like beast that
crawled in the mud of a long gone seafloor of the
Cambrian era, 530 million years ago. While not
particularly impressive in the tooth and claw
department, Pikaia is believed to be the founder
of the phylum Chordata, whose subsequent
evolution had consequences still very much felt
today by the rest of the ecosystem
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References

• Metcalfe, T. S. (1999), Genetic-Algorithm Based
  Light-Curve Optimization Applied to Observations
  of the W Ursae Majoris Star Bh Cassiopeiae, The
  Astronomical Journal, Vol. 117, No. 5, pp.
  2503-2510
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• Metcalfe, T. S., R. E. Nather, and D. E. Winget
  (2000), Genetic-Algorithm-Based
  Asteroseismological Analysis of the DBV White
  Dwarf GD 358, The Astrophysical Journal, Vol.
  545, No. 2, pp. 974-981
•  
• Metcalfe, T. S. (2000), The Asteroseismology
  Metacomputer, Baltic Astronomy, Vol. 9, pp.
  479-483

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References

• Authors Web page
• http//www.whitedwarf.org
• Wilson-Devinney
• http//cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?1
  971ApJ...166..605W
• PIKAIA Web Page
• http//www.hao.ucar.edu/public/research/si/pikaia/
  pikaia.html

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References

• Image Sources
• All images were taken from http//www.whitedwarf.
  org
• Except
• H-R Diagram
• http//www.astunit.com/tutorials/stellar.htm
• Pikaia Gracilens PIKAIA Website