High efficiency, compactness, light weight and low return loss are of high importance in antennas, especially in space applications. In this contribution a modified nondominated sorting genetic algorithm (NSGA-II) is applied to the design of Horn antennas for discrete lens applications to achieve a Pareto-optimal solution. Horn design is aimed not only towards higher possible efficiency but also towards large band and compactness. (C) 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE 21:174-181, 2011.