# 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
Outline

   Introduction
   The Science of Asteroseismology
   The Genetic Algorithm
   Parallel Computing
   Conclusion
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.
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
* Source
Traditional Technique

   Make an initial “guess” for parameter
values

   Use some iterative technique to improve
upon the initial guesses.
Adjustable Input Parameters

   Mass
   Temperature
   H and He layer masses
   Convective Efficiency
   Core composition
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
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
Outline

   Introduction
   The Science of Asteroseismology
   The Genetic Algorithm
   Parallel Computing
   Conclusion
   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)
   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.
Observed Light Curve for the White
Dwarf GD 358.
Outline

   Introduction
   The Science of Asteroseismology
   The Genetic Algorithm
   Parallel Computing
   Conclusion
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
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.
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
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 member’s survivability ratio
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
Mutation

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

   Consider two members, each with two
parameters.
   M1 has X=2.573 and Y= 4.457.
   M2 has parameter values X=3.547 and
Y=2.332.
   After encoding, M1=25734457 and
M2=35472332
Illustration
   The crossover point is randomly chosen, and the
string segments swapped

M1    25734|457  25734332
M2    35472|332  35472457
Illustration
   Mutating M1 involves picking a random spot
along the string, and changing that value:

M1      257|3|4332  25784332
Illustration*
   The strings would then be parsed back into
parameter values. For M1, this would be:

M1      X= 2.578 Y=4.332

* Modified from [1]
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
Elitism

   The most fit solution was passed
unaltered the next generation
Rationale

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

   In a later paper, he uses 5 repetitions

   This result was obtained in the following
way…
   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…
Results (second paper)

   First Order Solution…
Generation
Run    Teff    M/Ms    log(MHE/M*)   rms
Found
1     26,800   0.560      -5.70      0.67      245
2     25,000   0.600      -5.96      0.00      159
3     24,800   0.605      -5.96      0.52      145
4     25,000   0.600      -5.96      0.00      68
5     22,500   0.660      -6.33      1.11      97
6     25,000   0.600      -5.96      0.00      142
7     25,000   0.600      -5.96      0.00      97
8     25,000   0.600      -5.96      0.00      194
9     25,200   0.595      -5.91      0.42      116
10    26,100   0.575      -5.80      0.54      87
11    23,900   0.625      -6.12      0.79      79
12    25,000   0.600      -5.96      0.00      165
13    26,100   0.575      -5.80      0.54      92
14    25,000   0.600      -5.96      0.00      95
15    24,800   0.605      -5.96      0.52      42
16    26,600   0.565      -5.70      0.72      246
17    24,800   0.605      -5.96      0.52      180
18    25,000   0.600      -5.96      0.00      62
19    24,100   0.620      -6.07      0.76      228
20    25,000   0.600      -5.96      0.00      167
   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.
   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
Output Curve
Outline

   Introduction
   The Science of Asteroseismology
   The Genetic Algorithm
   Parallel Computing
   Conclusion
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
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
PVM

   PVM was used as the message passing
library
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.
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.
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
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
Darwin
Nodes

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

   Half of the nodes contain Pentium-II 300
MHz processors, while the other half are
AMD K6-II 450 MHz chips
The Cluster
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 Wilson—Devinney model
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.
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”
References
1.   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

2.   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

3.   Metcalfe, T. S. (2000), The Asteroseismology Metacomputer, Baltic
Astronomy, Vol. 9, pp. 479-483
References
Author’s Web page:
http://www.whitedwarf.org

Wilson-Devinney:
http://cdsads.u-strasbg.fr/cgi-bin/nph-
bib_query?1971ApJ...166..605W

PIKAIA Web Page:
http://www.hao.ucar.edu/public/research/si/pikaia
/pikaia.html
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

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