Two simplified solar water heating models were used to simulate the yearly solar fraction of systems using two strategies to control collector fluid flow: on-off and proportional control. Since the on-off control depends on the flow rate of the collector fluid, while the proportional control depends on the temperature of the fluid exiting the collector, a genetic algorithm was used to optimize the parameters that control fluid flow, i.e. the values of collector flow rate and collector fluid temperature that maximize the solar fraction using both on-off and proportional control schemes, respectively. Simulated results showed that for very low collector areas, the on-off control scheme is more effective, but for medium to high areas (comprising the range of usable collector areas), the proportional control scheme is more effective. It was found that the solar fraction of systems using proportional control may exceed the solar fraction of systems using on-off control by more than 50 %. Moreover, it was also found that for the proportional control scheme, the solar fraction always increases with increasing storage volume, but for the on-off scheme, especially for medium to high collector areas, the solar fraction generally remains constant or even decreases slightly with increasing storage volume.