Fixture is a device used in manufacturing industry to immobilize and localize workpieces. A fixturing system consists of clamps and locators for localization accuracy and force closure conditions. Fixture layout is the primary task of fixture design and consists of the determination of the position of clamps and locaters. The fixture layout influences the work piece deformation during the machining process. Hence the optimization of fixture layout with minimization as quality function which reduces the work piece deformation and it is the main objective of this work. Discrete Fixture Layout Optimization Method (DFLOM), Continuous Fixture Layout Optimization Method (CFLOM) and Integrated Fixture Layout Optimization Method (IFLOM) are used to compare the deformation of the workpiece. The finite element method is used to calculate workpiece deformation using MATLAB. The Impulse and Harmonic analysis was carried out on the workpiece for three different fixture layout optimization methods. Genetic Algorithm, Particle swarm Algorithm and Simulated Annealing are used to optimize the fixture layouts.