Student Number : 0214677F -
PhD thesis -
School of Camputational and Applied Mathematics -
Faculty of Science / Many real-life problems are formulated as global optimization problems with continuous variables.
These problems are in most cases nonsmooth, nonconvex and often simulation based,
making gradient based methods impossible to be used to solve them. Therefore, ef#2;cient, reliable
and derivative-free global optimization methods for solving such problems are needed.
In this thesis, we focus on improving the ef#2;ciency and reliability of some global optimization
methods. In particular, we concentrate on improving some population set-based methods
for unconstrained global optimization, mainly through hybridization. Hybridization has widely
been recognized to be one of the most attractive areas of unconstrained global optimization.
Experiments have shown that through hybridization, new methods that inherit the strength of
the original elements but not their weakness can be formed. We suggest a number of new hybridized
population set-based methods based on differential evolution (de), controlled random
search (crs2) and real coded genetic algorithm (ga).
We propose #2;ve new versions of de. In the #2;rst version, we introduce a localization, called
random localization, in the mutation phase of de. In the second version, we propose a localization
in the acceptance phase of de. In the third version, we form a de hybrid algorithm by
probabilistically combining the point generation scheme of crs2 with that of de in the de algorithm.
The fourth and #2;fth versions are also de hybrids. These versions hybridize the mutation
of de with the point generation rule of the electromagnetism-like (em) algorithm. We also propose
#2;ve new versions of crs2. The #2;rst version modi#2;es the point generation scheme of crs2
by introducing a local mutation technique. In the second and third modi#2;cations, we probabilistically
combine the point generation scheme of crs2 with the linear interpolation scheme of a
trust-region based method. The fourth version is a crs hybrid that probabilistically combines the
quadratic interpolation scheme with the linear interpolation scheme in crs2. In the #2;fth version, we form a crs2 hybrid algorithm by probabilistically combining the point generation scheme
of crs2 with that of de in the crs2 algorithm. Finally, we propose #2;ve new versions of the real
coded genetic algorithm (ga) with arithmetic crossover. In the #2;rst version of ga, we introduce a
local technique. We propose, in the second version, an integrated crossover rule that generates
two children at a time using two different crossover rules. We introduce a local technique in
the second version to obtain the third version. The fourth and #2;fth versions are based on the
probabilistic adaptation of crossover rules.
The ef#2;ciency and reliability of the new methods are evaluated through numerical experiments
using a large test suite of both simple and dif#2;cult problems from the literature. Results
indicate that the new hybrids are much better than their original counterparts both in reliability
and ef#2;ciency. Therefore, the new hybrids proposed in this study offer an alternative to many
currently available stochastic algorithms for solving global optimization problems in which the
gradient information is not readily available.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/1771 |
| Date | 16 November 2006 |
| Creators | Kaelo, Professor |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 233308 bytes, 160418 bytes, 225019 bytes, 408929 bytes, 143873 bytes, 573882 bytes, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf, application/pdf |
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