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This paper provides theoretical aspects and some numerical results for design optimization of geodesic dome structure. In particular, the genetic algorithm is adopted to investigate its possibility on the design optimization for spatial structures. It is well known that the genetic algorithm mimics the principles of the nature and so design optimization process with the genetic algorithm can gradually improve the structural design through the operations such as fitness, selection, crossover and mutation. In this study, new aspect of the genetic algorithm such as re-birthing technique is also consistently introduced to the three dimensional design optimization problems. As numerical tests, the optimum member sizes of typical three dimensional truss and geodesic dome against several external loads is evaluated by the ISADO-GAα' in-house code. From two numerical examples, we found that the genetic algorithm is very effective to calculate the optimum member sizes of three dimensional discrete structures and give a useful information on the existing structural system and it also has a huge potential to produce new structural system for large spatial structures.