This paper presents the main characteristics of the evolutionary optimization code named EOS, Evolutionary Optimization at Sapienza, and its successful application to challenging, real-world space trajectory optimization problems. EOS is a global optimization algorithm for constrained and unconstrained problems of real-valued variables. It implements a number of improvements to the well-known Differential Evolution (DE) algorithm, namely, a self-adaptation of the control parameters, an epidemic mechanism, a clustering technique, an $\varepsilon$-constrained method to deal with nonlinear constraints, and a synchronous island-model to handle multiple populations in parallel. The results reported prove that EOSis capable of achieving increased performance compared to state-of-the-art single-population self-adaptive DE algorithms when applied to high-dimensional or highly-constrained space trajectory optimization problems.