Procedure 1.

Genomic Mating

1:  for Each breeding cycle i ∈ (0, 1, 2, 3, …) do

2:       Let Pi denote the ith population of parents, Mi, Gi be corresponding markers matrix, the matrix of coancestories.

3:       if i is even then

4:            obtain the vector of estimated genetic values ${\widehat{g}}_i$ for Pi based on a phenotypic experiment,

5:            based on a regression of the estimated genetic values $\widehat{g}$ on the additive coding of the markers estimate the vector of additive effects for the markers; ${\widehat{b}}_i.$

6:       else

7:            ${\widehat{b}}_i={\widehat{b}}_{i-1}.$

8:       Given Nc, λ1 and λ2 find the optimizer of Equation (5) using the GA described in Procedure 2, denote this by $P_{32}^i.$

9:       Make the crosses indicated by to $P_{32}^i$ using parents Pi to obtain Pi+1.