We designed the optics supporting structure (OSS) of a 3.8 m segmented mirror telescope by applying genetic algorithm optimization. The telescope is the first segmented mirror telescope in Japan whose primary mirror consists of 18 petal shaped segment mirrors. The whole mirror is supported by 54 actuators (3 actuators per each segment). In order to realize light-weight and stiff telescope structure, we have adopted full truss structure as OSS of the telescope. We optimized its design by a newly developed software program incorporating genetic algorithm. The program automatically generates new OSS design step-by-step by optimizing the OSS parameters for realizing both light-weight structure and homologous deformation of the mirror surface supported by the OSS against the telescope elevation change simultaneously. The program successfully generated an ultra light-weight OSS design whose weight is only 8 tons including the optical elements and actuators (4 tons) with an eigen frequency of 9.5 Hz. The deviations of the 54 nodes from their original configuration of the designed OSS are less than 100 μm in the range of elevation angle 20 - 90 degrees. A real model of the OSS is under test construction. We also report the results of static test and deformation performance of this OSS model.