Energy extraction from ocean waves and conversion to electrical energy is a promising form of renewable energy, yet achieving economic viability of wave energy converters (WECs) has proven challenging. In this article, the design of a heaving cylinder WEC will be explored. The optimal plant (i.e. draft and radius) design space with respect to the design's optimal control (i.e. power take-off trajectory) for maximum energy production is characterized. Irregular waves based on the Bretschneider wave spectrum are considered. The optimization problem was solved using a pseudospectral method, a direct optimal control approach that can incorporate practical design constraints, such as power flow, actuation force, and slamming. The results provide early-stage guidelines for WEC design. Results show the resonance frequency required for optimal energy production with a regular wave is quite different than the resonance frequency found for irregular waves; specifically, it is much higher.