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Starting with principles of neural network and genetic algorithm, new approach, combining genetic algorithm and neural network, of structure optimization were given. Structure optimum target function and design variables set were defined, and with learning algorithm of neural network, non-linear global mapping relationship, between design parameters such as weight, stress, displacement and etc., was built. Then structure optimum target function needed by genetic algorithm could be acquired. Through searching calculating, the optimum solution could be found. One of significant advantage of above method is that only a small amount samples were needed to build the global mapping relationship of input to output, and consequently a large amount of values of target function needed by genetic algorithm for optimum solution could be gained, reducing greatly the calculating times of finite element. To demonstrate application of above method, an optimum example of column cross-section of shelf structure is given. Derived by neural network and genetic algorithm on basis of sufficient training samples determined by orthogonal design method, the optimum result is quite reliable.