Browse Theses

This dissertation research addresses several issues in global optimization by developing complexity analysis for random search algorithms, by constructing new algorithms and by applying existing algorithms in engineering design. Markov chain theory is used to develop models that can be used to analyze random search algorithms. Complexity analysis is set forth for several random search algorithms, including a combination of Pure Adaptive Search (PAS) and Pure Random Search (PRS) in a single algorithm. A probability of accepting non-improving points as is typically done in Simulated Annealing type algorithms is added to the analysis. An exact expression for an upper bound for the expected number of iterations to convergence is derived, and for special cases an exact expression is derived for the expected number of iterations to find the optimum. Numerical results are obtained for an algorithm called Hesitant Adaptive Search (HAS), by performing simulations for the algorithm. The results are compared with theoretical predictions. The Improving Hit-and-Run algorithm is also modeled and analyzed using Markov chains. A new algorithm, called the Hybrid Algorithm, is set forth and tested on several global optimization test problems. The hybrid algorithm is motivated by the complexity results that were derived for the random search algorithms. The algorithm combines interval methods and random search methods in a single algorithm. Finally the random search algorithm, Improving Hit-and-Run, is applied in engineering design to optimally design composite aircraft fuselage structures.