Horn-loaded loudspeakers increase the efficiency and control the spatial distribution of sound radiated from the horn mouth. They are often used as components in cinema sound systems where it is desired that the sound be broadcast onto the audience uniformly at all frequencies, improving the listening experience. The sound distribution, or beamwidth, is related to the shape of the horn and can be predicted by numerical methods, such as the boundary-element or source-superposition method, however the cost of evaluating the objective function is high. To overcome this a surrogate optimization method called Efficient Global Optimization (EGO) was used with a spline-based parameterization to find the shape of the horn that gives a frequency-independent beamwidth, thus giving a high quality listening experience.