This dissertation is concerned with the unconstrained global optimization of nonlinear problems. Theseudproblems are not easy to solve because of the multiplicity of local and global minima. In this dissertation,udwe first study the pattern search method for local optimization. We study the pattern search methodudnumerically and provide a modification to it. In particular, we design a new pattern search method forudlocal optimization. The new pattern search improves the efficiency and reliability of the original patternudsearch method. We then designed two simulated annealing algorithms for global optimization based onudthe basic features of pattern search. The new methods are therefore hybrid. The first hybrid method is theudhybrid of simulated annealing and pattern search. This method is denoted by MSA. The second hybridudmethod is a combination of MSA and the multi-level single linkage method. This method is denotedudby SAPS. The performance of MSA and SAPS are reported through extensive experiments on 50 testudproblems. Results indicate that the new hybrids are efficient and reliable.
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