Designing multiband antennas with low volume becomes of practical interest for mobile telecommunications. This paper presents the designs of five small dual band patch antennas for GSM 1800 (1710-1880MHz) and Bluetooth (2400-2483.5MHz) applications using a genetic algorithm combined with MoM (Method of Moments). A substrate with dielectric constant 3.2 and height 8mm is used for the first two dual band designs. The height is reduced thanks to the optimization process to 6mm in the third design by inserting a shorting pin to the fragmented patch antenna. Further the height is reduced to 4mm in the by inserting two shorting pins. In the final design with three shorting pins, the height is only 3mm. The patch dimensions are similar to that of the conventional rectangular patch for the center frequency of the lowest frequency band but with the advantage of having dual-band operation at the desired bands. Genetic algorithm optimization is used to optimize the patch geometry, feed position and shorting positions. HFSS is used to carry out simulations. The antenna thickness is reduced from 8mm to 3mm by incorporating shorting pins which position is optimized by the genetic algorithm.