Novel global optimization techniques with applications and image processing system with theoretical and computational analysis

This research introduces innovative global optimization methodologies with a focus on deterministic filled function techniques, extending their theoretical foundations and practical applications, particularly in engineering. Recognizing the limitations of conventional local optimization methods—especially in navigating complex, multimodal landscapes—this work develops novel auxiliary functions capable of systematically escaping local minima and progressing toward global optima. These new filled functions are designed to address critical shortcomings in existing methods, such as sensitivity to tuning parameters and the numerical instability caused by exponential and logarithmic expressions. The thesis begins by formulating the global optimization problem, outlining the classification of solution strategies into stochastic, heuristic, and deterministic frameworks. Emphasis is placed on deterministic methods, particularly filled function-based approaches, due to their structured nature and reproducibility. A key contribution of this work is the construction of a parameter-free, numerically stable filled functions that eliminates the need for delicate tuning and avoids computational issues common in earlier methods. This approach is theoretically validated and benchmarked across standard test functions, demonstrating superior performance in terms of convergence speed and robustness. Beyond theoretical development, the filled function methodology is extended to tackle real-world optimization problems. A significant application "The Facility Layout Problem (FLP)" are explored in depth. For FLP, the proposed technique is adapted to handle the combinatorial complexity inherent in layout design, offering efficient solutions that outperform existing methods in accuracy and computational cost. Further, the scope of this study is expanded into the domain of image processing through offering the smoothing technique used in non-smoothed algorithms. Recognizing that many image processing tasks, such as denoising and segmentation, inherently involve non-smooth objective functions, this thesis we use a smoothing-based total variation model. This model is analytically constructed to maintain fidelity to original image structures while effectively suppressing noise. The proposed method is benchmarked on several standard images and compared with widely used denoising algorithms with non-smoothed norm function showing notable improvements in image clarity and feature preservation. Through extensive experimentation and rigorous theoretical support, this dissertation establishes a versatile and powerful optimization framework that not only enhances the reliability of global searches in mathematical models but also brings significant advancements to real-world applications in engineering and image analysis. The proposed filled function approaches, with its adaptability and computational stability, contribute a robust tool for researchers and practitioners seeking optimal solutions in complex, high-dimensional problem spaces.