ETD Collection

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  • Item
    Simulated annealing driven pattern search algorithms for global optimization
    (2008-08-06T09:45:48Z) Gabere, Musa Nur
    This dissertation is concerned with the unconstrained global optimization of nonlinear problems. These problems are not easy to solve because of the multiplicity of local and global minima. In this dissertation, we first study the pattern search method for local optimization. We study the pattern search method numerically and provide a modification to it. In particular, we design a new pattern search method for local optimization. The new pattern search improves the efficiency and reliability of the original pattern search method. We then designed two simulated annealing algorithms for global optimization based on the basic features of pattern search. The new methods are therefore hybrid. The first hybrid method is the hybrid of simulated annealing and pattern search. This method is denoted by MSA. The second hybrid method is a combination of MSA and the multi-level single linkage method. This method is denoted by SAPS. The performance of MSA and SAPS are reported through extensive experiments on 50 test problems. Results indicate that the new hybrids are efficient and reliable.
  • Item
    An osteological documentation of hybrid wildebeest and its bearing on black wildebeest (Connochaetes Gnou) evolution
    (2008-05-14T12:24:04Z) De Klerk, Bonita
    ABSTRACT Wildebeest are part of the sub family Alcelaphinae and the genus Connochaetes. There are two extant species of wildebeest namely Connochaetes gnou (black wildebeest) and Connochaetes taurinus (blue wildebeest). From fossil evidence, it is thought that co-generic blue and black wildebeest diverged ca. 1Ma. Historically, geographic ranges of these two species have overlapped, but different social behaviour and habitat preference prevented sexual interaction. It has been proposed that reproductive isolation between C. taurinus and C. gnou may have disappeared due to artificial management. This has caused mate choice to change in the absence of species-specific mates, resulting in hybridisation. Most documented cases of hybridisation have occurred from dispersing blue wildebeest bulls introgressing into black herds however, the opposite has been observed. Genetic studies on a population where the blue males have introgressed with black females, show that the blue wildebeest populations are “pure” and that the black wildebeest populations are receiving an influx of blue alleles. In this research, 14 skeletons of modern hybrid Connochaetes taurinus and Connochaetes gnou, from more than one post-hybridisation generation from the Spioenkop reserve, were morphologically as well as metrically compared with a sample of ten modern “pure” blue and 15 black wildebeest. This project showed that univariate, bivariate statistical analyses of selected measurements of the skeletons were successful in identifying all of the Spioenkop individuals as hybrids. Morphologically, the hybrids exhibit a general increase in body size, and have unusual horns. The auditory bullae of the Spioenkop specimens are highly deformed, as are some axes. There is unusual bone growth on most of the post crania, morphological differences are observed on the distal ends of the metapodials, and the radius and ulna are fused in many specimens.
  • Item
    Some Population Set-Based Methods for Unconstrained Global Optimization
    (2006-11-16T08:40:11Z) Kaelo, Professor
    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, efcient, reliable and derivative-free global optimization methods for solving such problems are needed. In this thesis, we focus on improving the efciency 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 ve new versions of de. In the 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 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 ve new versions of crs2. The rst version modies the point generation scheme of crs2 by introducing a local mutation technique. In the second and third modications, 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 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 ve new versions of the real coded genetic algorithm (ga) with arithmetic crossover. In the 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 fth versions are based on the probabilistic adaptation of crossover rules. The efciency and reliability of the new methods are evaluated through numerical experiments using a large test suite of both simple and difcult problems from the literature. Results indicate that the new hybrids are much better than their original counterparts both in reliability and efciency. 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.