This short paper describes the authors’ contention that analysis can be undertaken to show that the space of reachable probability mass functions is basically hierarchical. This leads to the suggestion that more study should be made of the exploration of multiparent variation operators.

In the introduction, the authors discuss the results, which come from increasing the number of parents involved in generating offspring. The analysis involves the probability of a new structure through selection according to a random variable through the use of the probability mass function. A second theorem is then developed for the case N > 2. The discussion involves possibilities for comparing operators and their arity. In the conclusion, the authors suggest the need for more research involving multiparent operators with the goal of developing algorithms for practical real-world applications.