We used the particle swarm optimization algorithm, an evolutionary computational technique, to design metal nanoparticle arrays that produce broadband plasmonic field enhancement over the entire visible spectral range. The resulting structures turn out to be aperiodic and feature dense Fourier spectra with many closely packed particle clusters. We conclude that broadband field-enhancement effects in nanoplasmonics can be achieved by engineering aperiodic arrays with a large number of spatial frequencies that provide the necessary interplay between long-range diffractive interactions at multiple length scales and near-field quasi-static coupling within small nanoparticle clusters.