Function optimization (constrained and unconstrained) is a process of finding the optimal point for the given problem. As the research is being carried out and new problem areas are being investigated, global optimization problems are getting more and more complex. The research presented in this dissertation is about to build a new accelerated function optimization technique based on evolutionary algorithm (EA). EAs have low convergence rate due to their evolutionary nature. The acceleration of evolutionary algorithm in the function optimization is achieved by incorporating gene excitation. In General, the distribution of the initial population into the search space effects the evolutionary algorithm performance. Concept of opposition based populations is employed to distribute the chromosomes more effectively. Image Segmentation is a significant and successful way for many real world applications like segmenting lung from CT scanned images. Segmentation is the process of finding optimal segments within an image. The main objective of this thesis is to make a new entirely automatic system that segments the lungs from the CT scanned images. To achieve this objective, a completely automatic un-supervised scheme is developed to segment lungs. The methodology utilizes a fuzzy histogram based image filtering technique to remove the noise, which preserves the image details for low as well as highly corrupted images. Peaks and Valley are found in bimodal group of images using Genetic Algorithm (GA). GAs are used for function optimization process and hence determining the global optimal solutions. The optimal and dynamic grey level is find out by using GA. Finding optimal clustering within a dataset is an important data mining task. Clustering and segmentations are somewhat related optimization problems of finding optimal grouping in the provided set of points. Clustering of datasets has been achieved by using an entirely automatic un-supervised approach. The employed technique optimizes multi- objective as compared to optimize single objective for clustering. Relative cloning is performed to adopt the individuals according to their fitness, which improves the algorithm performance.