ETD Collection

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    An efficient algorithm for nonlinear integer programming
    (2011-11-02) Moepya, Stephen Obakeng
    Abstract This dissertation is concerned with discrete global optimization of nonlinear problems. These problems are constrained and unconstrained and are not easily solvable since there exists multiplicity of local and global minima. In this dissertation, we study the current methods for solving such problems and highlight their ine ciencies. We introduce a new local search procedure. We study the rapidly-exploring random tree (RRT) method, found mostly in the research area of robotics. We then design two global optimization algorithms based on RRT. RRT has never been used in the eld of global optimization. We exploit its attractive properties to develop two new algorithms for solving the discrete nonlinear optimization problems. The rst method is called RRT-Optimizer and is denoted as RRTOpt. RRTOpt is then modi ed to include probabilistic elements within the RRT. We have denoted this method by RRTOptv1. Results are generated for both methods and numerical comparisons are made with a number of recent methods.
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    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.