This dissertation presents the studies of microwave image reconstructions that are approached based on the time-domain technique (finite difference time domain, FDTD) and several optimization methods for a 2-D homogeneous dielectric cylinder. The dielectric cylinder is located in free space, or buried in half-space media, or embedded in a three-layered material medium, respectively. For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering several optimization methods are utilized to determine the shape, location and the permittivity of the cylindrical scatterer with arbitrary cross section. The subgirdding technique is implemented for the FDTD code in order to model the shape of the cylinder more smoothly. In order to describe an unknown cylinder with arbitrary cross section more effectively during the course of searching, the closed cubic-spline expansion is adopted to represent the scatterer contour instead of the frequently used trigonometric series. The former is still used in the forward scattering part. In order to explore the unknown dielectric cylinder in different environments, an electromagnetic pulse can be conducted to illuminate the cylinder, for which the scattered E fields can then be measured. The inverse problem is then resolved by an optimization approach. The idea is to perform the image reconstruction by utilization of some optimization scheme to minimize the discrepancy between the measured and calculated scattered field data. Three optimization schemes are tested and employed to search the parameter space to determine the shape, location and permittivity of the dielectric cylinder. They are the modified particle swarm optimization (MPSO), the dynamic differential evolution (DDE) and the non-uniform steady state genetic algorithm (NU-SSGA). The suitability and efficiency of applying the above methods for microwave imaging of a 2D dielectric cylinder are examined in this dissertation. Numerical results show that even when the initial guesses are far away from the exact one, good reconstruction can be obtained by all these optimization methods. However, the DDE and MPSO outperform the NU-SSGA regarding the reconstruction accuracy and the convergent speed in terms of the number of the objective function calls.