Fig. 1

Illustrative example. The high-dimensional state space \(\Theta\) is symbolized by the horizontal plane. The state \({\varvec\uptheta}_n\in \Theta\) of the population changes from one generation to the next in accordance with the breeding policy \({\varvec\uppi}\) until the desired final state \(\breve{\varvec\uptheta}\) is reached. The breed’s profit \(\phi (\varvec\upxi ({\varvec\uptheta}_n))\) in each generation is shown on the vertical axis. While the state \({\varvec\uptheta}_1\) in the first generation is determined by the vector \(\bf{c}_{\varvec\uppi}\) with genetic contributions of the selection candidates, the change in state from one generation to the next in the following generations is given by a mapping \(\Gamma _{\varvec\uppi}:\Theta \rightarrow \Theta\)