A note on the hierarchical nature of n-parent variation operators in evolutionary algorithms

Abstract Variation operators can be characterized by the probability mass that they associate with potential solutions from the state space of all possible solutions. Analysis is undertaken to show that the space of reachable probability mass functions is fundamentally hierarchical. The class of n -parent operators can generate a more diverse set of possible probabilistic searches of the state space than can be obtained by ( n −1)-parent operators, or even a succession of ( n −1)-parent operators. The result suggests that greater attention might be usefully applied in the exploration of multiparent variation operators.