Multi-fidelity global design optimization including parallelization potential

The DIRECT global optimization algorithm is a relatively new space partitioning algorithm designed to determine the globally optimal design within a designated design space. This dissertation examines the applicability of the DIRECT algorithm to two classes of design problems: unimodal functions where small amplitude, high frequency fluctuations in the objective function make optimization difficult; and multimodal functions where multiple local optima are formed by the underlying physics of the problem (as opposed to minor fluctuations in the analysis code). DIRECT is compared with two other multistart local optimization techniques on two polynomial test problems and one engineering conceptual design problem.; Three modifications to the DIRECT algorithm are proposed to increase the effectiveness of the algorithm. The DIRECT-BP algorithm is presented which alters the way DIRECT searches the neighborhood of the current best point as optimization progresses. The algorithm reprioritizes which points to analyze at each iteration. This is to encourage analysis of points that surround the best point but that are farther away than the points selected by the DIRECT algorithm. This increases the robustness of the DIRECT search and provides more information on the characteristics of the neighborhood of the point selected as the global optimum.; A multifidelity version of the DIRECT algorithm is proposed to reduce the cost of optimization using DIRECT. By augmenting expensive high-fidelity analysis with cheap low-fidelity analysis, the optimization can be performed with fewer high-fidelity analyses. Two correction schemes are examined using high- and low-fidelity results at one point to correct the low-fidelity result at a nearby point. This corrected value is then used in place of a high-fidelity analysis by the DIRECT algorithm. In this way the number of high-fidelity analyses required is reduced and the optimization became less expensive.; Finally the DIRECT algorithm is parallelized to allow its implementation on multiple processors. Two master-slave implementations are proposed using an arbitrary number of processors to speed the analysis of points for the optimization. The two methods are compared on a heterogeneous collection of processors with special attention to computational and algorithmic efficiency.