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In this paper, how to use DNA genetic algorithm to solve stochastic integer programming expected value models is discussed. Since DNA genetic algorithm has the merits of plentiful coding, and decoding, conveying complex knowledge flexibly. These merits and the technique of stochastic simulation are combined, which for estimating the random variables of stochastic integer programming expected value models problem. Base on them, a best solution of this problem can be found. The classical newspaper-selling boy problem is calculated for testifying the feasibility and effectiveness of this method.