Circular arrays of log-periodic (LP) antennas are designed for broadband applications. A sophisticated electromagnetic simulation environment involving integral equations and fast solvers is developed to analyze the LP arrays both accurately and efficienuy. The resulting matrix equation obtained by the discretization of the electric field integral equation is solved iteratively via the multilevel fast multipole algorithm (MLFMA). Genetic algorithms interacting with MLFMA is employed to optimize the excitations of the array elements to increase the frequency independence and also to add the beam-steering ability to the arrays.