In this chapter, four optimization methods genetic algorithm, particle swarm optimization, hill climbing and simulated annealing are implemented and compared in the missing data problem. These methods are tested on two sets of data and these are mechanical system and artificial taster. For the mechanical system case, the results obtained demonstrate that genetic algorithms, particle swarm optimization and simulated annealing give comparable results even though simulated annealing is the best of the four. Furthermore, it is observed that it is much easier to estimate one missing variables when compared to estimating two or three missing variables. Steepest descent method is found to perform worse than the three methods. This is because steepest descent method is a local optimization procedure and the missing data problem requires the identification of global optimal points. In general, genetic algorithm is found to the most computationally efficient followed very closely by simulated annealing and then steepest descent method. Simulated annealing is found to be the most computationally expensive method and this is mainly due to its Monte Carlo simulation nature, which is generally computationally expensive. For the artificial taster method, genetic algorithms and particle swarm optimization are found to give similar results followed closely by simulated annealing. Steepest descent method is found to perform the worst. This is mainly due to the fact that the missing data estimation problem is a problem that requires a global optimization method and, therefore, global methods GA, PSO and SA perform better than local methods such steepest gradient...