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The first supplement for the international document Guide to Expression of Uncertainty in Measurement suggests to apply principle of maximum entropy in assigning a probability to a measurable quantity based on various types of information. This paper discusses the optimization algorithms in the maximum entropy distribution estimation. By an analysis to the characters of non-linear programming problem in this paper, it adopts the Genetic Algorithms to optimize the estimation of maximum entropy distribution. As for illustrations, two simulative cases with numerical results are represents to demonstrate the efficiency of entropy distribution estimation based on Genetic Algorithms and also the measurement uncertainty evaluated according to the estimated maximum entropy distribution.