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Summary, in English
Conclusion
The results from the optimization with GA shows that there is no noticeable
difference between optimizing for arithmetic and geometric mean of the resolution.
The idea behind using the geometric mean is that it would lend smaller
importance to outlier values. Both settings found about the same range of values
for VBend, VTweak and VExt, with comparable standard deviations. When
optimizing for the new resolution measure and taking either the geometric or
arithmetic mean of the resolution between the energies, the other type of mean
is also displayed in table 4. When optimizing for the arithmetic mean, the same
result, calculated as a geometric mean can be compared to the case where we
actually optimized for the geometric mean. The result shows that there is no
difference in the quality of solutions between the two. In both cases the GA
found solutions with better resolution values than the manually found solution.
The GA found quite similar values for VExt, but more varying values for VBend
and VTweak. This is because there is a trade off between high values for VBend
and low values for VTweak. This is easy to understand because both parameters
tend to shrink the image on the detector. So a higher VBend can be compensated
for with a lower VTweak to give a similar resolution value. Although for different
energies, this trade off can be seen in figure 18.
The result for the pattern search algorithm were, as expected, very sensitive
to the initial starting point. In the four cases the pattern search did not find
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parameter values that were better than the ones found by the GA. The pattern
search is probably still useful if an informed guess is made for the start values
instead of choosing random ones. It could for example be used to find an even
better optimum near some experimentally found value. This test was however
done to compare the performance when searching for a global optimum. Since
the GA starts with a random population, so should the pattern search start at
random point so a comparison can be made.
The results from the optimization with GA shows that there is no noticeable
difference between optimizing for arithmetic and geometric mean of the resolution.
The idea behind using the geometric mean is that it would lend smaller
importance to outlier values. Both settings found about the same range of values
for VBend, VTweak and VExt, with comparable standard deviations. When
optimizing for the new resolution measure and taking either the geometric or
arithmetic mean of the resolution between the energies, the other type of mean
is also displayed in table 4. When optimizing for the arithmetic mean, the same
result, calculated as a geometric mean can be compared to the case where we
actually optimized for the geometric mean. The result shows that there is no
difference in the quality of solutions between the two. In both cases the GA
found solutions with better resolution values than the manually found solution.
The GA found quite similar values for VExt, but more varying values for VBend
and VTweak. This is because there is a trade off between high values for VBend
and low values for VTweak. This is easy to understand because both parameters
tend to shrink the image on the detector. So a higher VBend can be compensated
for with a lower VTweak to give a similar resolution value. Although for different
energies, this trade off can be seen in figure 18.
The result for the pattern search algorithm were, as expected, very sensitive
to the initial starting point. In the four cases the pattern search did not find
31
parameter values that were better than the ones found by the GA. The pattern
search is probably still useful if an informed guess is made for the start values
instead of choosing random ones. It could for example be used to find an even
better optimum near some experimentally found value. This test was however
done to compare the performance when searching for a global optimum. Since
the GA starts with a random population, so should the pattern search start at
random point so a comparison can be made.
Department/s
Publishing year
2011
Language
English
Full text
Document type
Student publication for Bachelor's degree
Topic
- Physics and Astronomy
Supervisor
- Erik Månsson