In order to investigate the origins of the Universe, it is necessary to carry out full sky surveys of the temperature and polarisation of the Cosmic Microwave Background (CMB) radiation, the remnant of the Big Bang. Missions such as COBE and Planck have previously mapped the CMB temperature, however in order to further constrain evolutionary and inflationary models, it is necessary to measure the polarisation of the CMB with greater accuracy and sensitivity than before. Missions undertaking such observations require large arrays of feed horn antennas to feed the detector arrays. Corrugated horns provide the best performance, however owing to the large number required (circa 5000 in the case of the proposed COrE+ mission), such horns are prohibitive in terms of thermal, mechanical and cost limitations. In this paper we consider the optimisation of an alternative smooth-walled piecewise conical profiled horn, using the mode-matching technique alongside a genetic algorithm. The technique is optimised to return a suitable design using efficient modelling software and standard desktop computing power. A design is presented showing a directional beam pattern and low levels of return loss, cross-polar power and sidelobes, as required by future CMB missions. This design is manufactured and the measured results compared with simulation, showing excellent agreement and meeting the required performance criteria. The optimisation process described here is robust and can be applied to many other applications where specific performance characteristics are required, with the user simply defining the beam requirements.