For real-coded genetic algorithms, there have been proposed many crossover operators so far. While they have been evaluated by some benchmark problems, theoretically clear guidelines or design principles for them have not been established yet. This paper, first, discusses the importance of the distribution and statistics of the offspring yielded by a crossover operator for its evaluation. Then, from this viewpoint, the unimodal normal distribution crossover (UNDX) developed by Ono et al. (1997) is analyzed. The results of analysis provide us with a clear understanding of the characteristics of the UNDX. It is also shown that the values of the adjustable parameters of the UNDX tuned empirically is desirable in the sense that the offspring population inherits the statistics such as the mean value and the covariance matrix from the parent population.
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