In this book, a Genetic Algorithm (GA) is hybridized with the local search called Quadratic Approximation (QA) that helps in finding the minima of a quadratic surface passing through three different arbitrary points in the search space. The designed hybrid GA is proposed to solve both unconstrained and unconstrained optimization problems. Initially, a qualitative combination of GA operators is being investigated to solve unconstrained optimization problems and is testified through some typical unconstrained benchmark functions. The proposed algorithm is used to solve some real world problems those are free of constraints. Later, the unconstrained algorithm is developed to handle constraints and its efficiency and efficacy is verified through some constrained typical benchmark function. Further, it is applied to some constrained real world problems. Towards the end, an efficient retrievable GA is proposed to solve to the Japanese number game called "Sudoku Puzzle" with a higher success rate.