The gray code optimization (GCO) algorithm is a deterministic global optimization algorithm based on integer representation. It utilizes the adjacency property of Gray code representation. By controlling the number of bits flipped, it searches through the space effciently. A further development of the GCO algorithm is conducted in this research to avoid getting stuck in local minima. To further improve the performance, and take the advantage of cheaper but more powerful CPUs, a parallel computation paradigm using MPI is implemented. Analysis of the mechanism of the GCO algorithm indicated that it can be modeled by mixture gaussian. This led to a new stochastic evolutionary global optimization algorithm based on mixture of gaussians and real numbers. The EM algorithm is used to acquire the parameters of each Gaussian component. With a mathematic model in hand, a lot of theoretical questions, such as convergence property, convergence rate, and the benefits of using the mixture model could be investigated. The relationship between the proposed algorithms and other evolutionary algorithms including genetic algorithms, evolutionary programming and evolutionary strategy will be studied. To combine the merits of different evolutionary algorithms, a uniform global optimizer based on parallel computing was proposed to solve a broad range of problems. The proposed algorithms are general global optimization methods. They have a broad range of applications in engineering and science. The applications in molecular conformation search, curve fitting, and spectral analysis are reported in this report.

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