The Optimal design of planetary gears is a problem with high dimensional multi-objective and with complicated calculations & constraints et al. A general method for high dimensional multi-objective optimal design is presented based on degree of grey incidence with hybrid discrete variables. Using grey degree of improved absolute incidence, multi-objective optimization design can be convened to single objective optimization. The method could reasonably deal with value adopting problems of hybrid discrete variables in optimization design. A chaos emigration operator is introduced for carrying out improvement on the fundamental genetic algorithm, and the grey compound genetic algorithmic program GSCHGA for the multiobjective optimization of hybrid discrete variables is developed. The high dimensional multi-objective optimal design example of planetary gears type AA design shows that this algorithm has no special requirements on the characteristics of optimal designing problems, it has a fairly good universal adaptability and a reliable operation of program with a strong ability of overall convergence.