The present paper focuses on the determination of optimum layouts for linear arrays of heaving Wave Energy Converters (WECs) in front of a vertical wall. Optimum layouts maximize the annual averaged absorbed energy at a given marine site and satisfy spatial constraints. For achieving this goal, we developed an efficient optimization numerical framework, where a genetic algorithm solver is appropriately coupled with a frequency-domain hydrodynamic model, while, furthermore, a numerical wave model is utilized to determine the local wave climate conditions at the site of interest. The context is applied for an array of five semi-immersed, oblate spheroidal heaving WECs deployed at five near-shore sites of mild wave environments in the Aegean Sea, Greece. For each site, different optimization cases are solved, facilitating the investigation of different aspects of the examined problem. The largest annual energy absorption ability is observed for optimum layouts, characterized by the placement of the array close to the wall and the formation of clusters of closely-positioned WECs near the wall edges. Compared to arrays employed at sites in south-eastern Aegean, optimally-arranged arrays at central Aegean locations showed reduced energy absorption ability due to milder local wave conditions and/or the existence of quite limited water depths.