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The two-generation competitive genetic algorithm changes the selection method of simple genetic algorithms, and improves the search efficiency. However, this algorithm is easy to become premature, and the local best search ability cannot be improved. The improved genetic algorithm on these problems has been improved in this paper, thought an adaptive adjustment of the mutation probability, and the position of crossover and mutation in chromosomes. The searching speed and the ability of the local area search, the convergence stability and the global optimum accuracy are improved. It is shown in optimizing functions experiment that the improved algorithms can efficiently overcome the premature problem and increase the ability of the local best search.