In this paper, we introduce a new evolutionary optimization algorithm based on Tukey's symmetric lambda distribution. Tukey distribution is defined by 3 parameters, the shape parameter, the scale parameter, and the location parameter or average value. Various other distributions can be approximated by changing the shape parameter, and as a result can encompass a large class of probability distributions. In addition, Because of these attributes, an Evolutionary Programming (EP) algorithm with Tukey mutation operator may perform well in a large class of optimization problems. Various schemes in implementation of EP with Tukey distribution are discussed, and the resulting algorithms are applied to selected test functions and antenna design problems.