Evolutionary Optimization Methods for Accelerator Design
In partial fulfillment of the requirements for the degree of Doctor
of Philosophy from Michigan State University.
AbstractMany problems from the fields of accelerator physics and beam theory can be
formulated as optimization problems and, as such, solved using optimization methods.
Despite growing efficiency of the optimization methods, the adoption of modern
optimization techniques in these fields is rather limited. Evolutionary Algorithms
(EAs) form a relatively new and actively developed optimization methods family.
They possess many attractive features such as: ease of the implementation, modest
requirements on the objective function, a good tolerance to noise, robustness, and
the ability to perform a global search efficiently which make them the tool of choice
for many design and optimization problems. In this work we study the application of
EAs to problems from accelerator physics and beam theory.
We review the most commonly used methods of unconstrained optimization and
describe the GATool, evolutionary algorithm and the software package, used in this
work, in detail. Then we use a set of test problems to assess its performance in
terms of computational resources, quality of the obtained result, and the tradeoff
between them. We justify the choice of GATool as a heuristic method to generate
cutoff values for the COSY-GO rigorous global optimization package for the COSY
Infinity scientific computing package. We design the model of their mutual interaction
and demonstrate that the quality of the result obtained by GATool increases as the
information about the search domain is refined, which supports the usefulness of this
model. We discuss GATool's performance on the problems suffering from static and
dynamic noise and study useful strategies of GATool parameter tuning for these and
other difficult problems.
We review the challenges of constrained optimization with EAs and methods commonly
used to overcome them. We describe REPA, a new constrained optimization
method based on repairing, in exquisite detail, including the properties of its two
repairing techniques: REFIND and REPROPT. We assess REPROPT's performance
on the standard constrained optimization test problems for EA with a variety of
different configurations and suggest optimal default parameter values based on the
results. Then we study the performance of the REPA method on the same set of test
problems and compare the obtained results with those of several commonly used constrained
optimization methods with EA. Based on the obtained results, particularly
on the outstanding performance of REPA on test problem that presents significant
difficulty for other reviewed EAs, we conclude that the proposed method is useful
and competitive. We discuss REPA parameter tuning for difficult problems and critically
review some of the problems from the de-facto standard test problem set for
the constrained optimization with EA.
In order to demonstrate the practical usefulness of the developed method, we
study several different problems of accelerator design and demonstrate how they can
be solved or solved faster with EAs. These problems include a simple accelerator
design problem (design a quadrupole triplet to be stigmatically imaging, find all
possible solutions), a complex real-life accelerator design problem (an optimization of
the front end section for the future neutrino factory), and a problem of the normal
form defect function optimization which is used to rigorously estimate the stability of
the beam dynamics in circular accelerators. The positive results we obtained suggest
that the application of EAs to problems from accelerator theory can be very beneficial
and has large potential. The developed optimization scenarios and tools can be used
to approach similar problems.
A. Poklonskiy (2009)
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