In this paper, an efficient optimization algorithm for solving the inverse problem of a two-dimensional lossless homogeneous dielectric object is investigated. A lossless homogeneous dielectric cylinder of unknown permittivity scatters the incident wave in free space and the scattered fields are recorded. Based on the boundary condition and the incident field, a set of nonlinear surface integral equation is derived. The imaging problem is reformulated into optimization problem and the steady-state genetic algorithm is employed to reconstruct the shape and the dielectric constant of the object. Numerical results show that the permittivity of the cylinders can be successfully reconstructed even when the permittivity is fairly large. The effect of random noise on imaging reconstruction is also investigated.