In this thesis, the basic principles and concepts of single and multi-objective Genetic Algorithms (GA) are reviewed. Two algorithms, one for single objective and the other for multi-objective problems, which are believed to be more efficient are described in details. The algorithms are coded with MATLAB and applied on several test functions. The results are compared with the existing solutions in literatures and shows promising results. Obtained pareto-fronts are exactly similar to the true pareto-fronts with a good spread of solution throughout the optimal region. Constraint handling techniques are studied and applied in the two algorithms. Constrained benchmarks are optimized and the outcomes show the ability of algorithm in maintaining solutions in the entire pareto-optimal region. In the end, a hybrid method based on the combination of the two algorithms is introduced and the performance is discussed. It is concluded that no significant strength is observed within the approach and more research is required on this topic. For further investigation on the performance of the proposed techniques, implementation on real-world engineering applications are recommended.