Theoretical parameter value for appropriate population variance of the distribution of children in real-coded GA

The purposes of this paper are to discuss theoretical parameter value for crossover operators in real-coded GAs (RCGAs) and to bridge the gap between earlier related studies. Crossover operator in RCGAs has at least one parameter that forms its probability distribution function. The appropriateness of the value for this parameter affects optimization performance of RCGA. To obtain suitable parameter value, some manners have been reported. However, they have confused us by their several differences, such as the reference point often used as the first choice to be tuned. This paper has theoretically introduced a constraint that explains that these manners are essentially identical. Parameter values determined under this constraint have been empirically confirmed that they satisfy requirements of the manners. Experiments on several test functions have supported that such parameter values are suitable for the reference point.